* Added initial builtin-support for a subset of Cuba
This has not been tested too much (so it might be better not to build the BMWlibs at the moment) In case shared library support will become available from T. Hahn, this support will be dropped again. * Added a few " " to musrgui (calls to musrview, musrt0 and msr<->mlog) These are needed in the simple system commands to support paths with spaces and other strange things... :-(
This commit is contained in:
Bastian M. Wojek
parent
6f49067095
commit
39f00e58a2
2
COPYING
2
COPYING
@ -278,7 +278,7 @@ PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
|
|||||||
POSSIBILITY OF SUCH DAMAGES.
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POSSIBILITY OF SUCH DAMAGES.
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||||||
|
|
||||||
END OF TERMS AND CONDITIONS
|
END OF TERMS AND CONDITIONS
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||||||
|
|
||||||
How to Apply These Terms to Your New Programs
|
How to Apply These Terms to Your New Programs
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||||||
|
|
||||||
If you develop a new program, and you want it to be of the greatest
|
If you develop a new program, and you want it to be of the greatest
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||||||
|
|||||||
89
configure.ac
89
configure.ac
@ -50,6 +50,11 @@ PLUGIN_MAJOR_VERSION=1
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PLUGIN_MINOR_VERSION=0
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PLUGIN_MINOR_VERSION=0
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PLUGIN_MICRO_VERSION=0
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PLUGIN_MICRO_VERSION=0
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#release versioning
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CUBA_MAJOR_VERSION=1
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CUBA_MINOR_VERSION=6
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CUBA_MICRO_VERSION=0
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#API version
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#API version
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MUSR_API_VERSION=MUSR_MAJOR_VERSION.MUSR_MINOR_VERSION
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MUSR_API_VERSION=MUSR_MAJOR_VERSION.MUSR_MINOR_VERSION
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AC_SUBST(MUSR_API_VERSION)
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AC_SUBST(MUSR_API_VERSION)
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@ -66,7 +71,11 @@ AC_SUBST(MUD_API_VERSION)
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PLUGIN_API_VERSION=PLUGIN_MAJOR_VERSION.PLUGIN_MINOR_VERSION
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PLUGIN_API_VERSION=PLUGIN_MAJOR_VERSION.PLUGIN_MINOR_VERSION
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AC_SUBST(PLUGIN_API_VERSION)
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AC_SUBST(PLUGIN_API_VERSION)
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CUBA_API_VERSION=CUBA_MAJOR_VERSION.CUBA_MINOR_VERSION
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AC_SUBST(CUBA_API_VERSION)
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#shared library versioning
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#shared library versioning
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CUBA_LIBRARY_VERSION=1:6:0
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PLUGIN_LIBRARY_VERSION=1:0:0
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PLUGIN_LIBRARY_VERSION=1:0:0
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LEM_LIBRARY_VERSION=1:5:0
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LEM_LIBRARY_VERSION=1:5:0
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PSIBIN_LIBRARY_VERSION=0:0:0
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PSIBIN_LIBRARY_VERSION=0:0:0
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@ -89,6 +98,7 @@ AC_SUBST(LEM_LIBRARY_VERSION)
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AC_SUBST(PSIBIN_LIBRARY_VERSION)
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AC_SUBST(PSIBIN_LIBRARY_VERSION)
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AC_SUBST(MUD_LIBRARY_VERSION)
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AC_SUBST(MUD_LIBRARY_VERSION)
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AC_SUBST(PLUGIN_LIBRARY_VERSION)
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AC_SUBST(PLUGIN_LIBRARY_VERSION)
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AC_SUBST(CUBA_LIBRARY_VERSION)
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PACKAGE=$MUSR_PROGRAM_NAME
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PACKAGE=$MUSR_PROGRAM_NAME
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AC_SUBST(MUSR_LIBRARY_NAME)
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AC_SUBST(MUSR_LIBRARY_NAME)
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@ -121,8 +131,15 @@ PLUGIN_RELEASE=$PLUGIN_MAJOR_VERSION.$PLUGIN_MINOR_VERSION
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AC_SUBST(PLUGIN_RELEASE)
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AC_SUBST(PLUGIN_RELEASE)
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AC_SUBST(PLUGIN_VERSION)
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AC_SUBST(PLUGIN_VERSION)
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CUBA_VERSION=$CUBA_MAJOR_VERSION.$CUBA_MINOR_VERSION.$CUBA_MICRO_VERSION
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CUBA_RELEASE=$CUBA_MAJOR_VERSION.$CUBA_MINOR_VERSION
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AC_SUBST(CUBA_RELEASE)
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AC_SUBST(CUBA_VERSION)
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VERSION=$MUSR_VERSION
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VERSION=$MUSR_VERSION
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USER_CFLAGS="$CFLAGS"
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dnl -----------------------------------------------
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dnl -----------------------------------------------
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dnl Automake initialization and program checks
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dnl Automake initialization and program checks
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dnl -----------------------------------------------
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dnl -----------------------------------------------
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@ -328,6 +345,7 @@ dnl -----------------------------------------------
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AC_ARG_ENABLE([BMWlibs], [AC_HELP_STRING([--enable-BMWlibs],[build optional BMW plug-ins [default=no]])],
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AC_ARG_ENABLE([BMWlibs], [AC_HELP_STRING([--enable-BMWlibs],[build optional BMW plug-ins [default=no]])],
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[CUBA_FOUND=0
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[CUBA_FOUND=0
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BUILD_CUBA=0
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AC_ARG_WITH([cuba],
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AC_ARG_WITH([cuba],
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[AC_HELP_STRING([--with-cuba],[prefix of CUBA installation, e.g. /usr/local or /usr])],
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[AC_HELP_STRING([--with-cuba],[prefix of CUBA installation, e.g. /usr/local or /usr])],
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[CUBA_PREFIX=$with_cuba
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[CUBA_PREFIX=$with_cuba
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@ -352,22 +370,66 @@ AC_ARG_ENABLE([BMWlibs], [AC_HELP_STRING([--enable-BMWlibs],[build optional BMW
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CUBA_PREFIX="/opt/local"
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CUBA_PREFIX="/opt/local"
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AC_MSG_RESULT([${CUBA_PREFIX}])
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AC_MSG_RESULT([${CUBA_PREFIX}])
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else
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else
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AC_MSG_RESULT([no])
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BUILD_CUBA=1
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||||||
AC_MSG_ERROR(
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AC_MSG_RESULT([builtin-cuba])
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||||||
[CUBA not found. Please call configure with the --with-cuba option.
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||||||
This tells configure where to find the CUBA C library and header,
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||||||
e.g. --with-cuba=/usr/local or --with-cuba=/usr]
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|
||||||
)
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||||||
fi
|
fi
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||||||
]
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]
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||||||
)
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)
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]
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]
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)
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)
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AC_SUBST(CUBA_PREFIX)
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if test "${CUBA_FOUND}" != "1"; then
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if test "${BUILD_CUBA}" -eq 1; then
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CUBA_LIBS="-L${CUBA_PREFIX}/lib -lcuba -lm"
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if test "x$GCC" = "xyes" ; then
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CUBA_CFLAGS="-I${CUBA_PREFIX}/include"
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CUBA_BUILD_CFLAGS=${USER_CFLAGS:--O3 -fomit-frame-pointer -ffast-math}
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||||||
|
else
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||||||
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CUBA_BUILD_CFLAGS=${USER_CFLAGS:--O}
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||||||
|
fi
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||||||
|
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||||||
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AC_C_CONST
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||||||
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AC_C_INLINE
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||||||
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AC_C_LONG_DOUBLE
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||||||
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||||||
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AC_CHECK_FUNCS([powl])
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||||||
|
AC_CHECK_FUNCS([erf])
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||||||
|
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MAXDIM=${MAXDIM:-16}
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AC_ARG_WITH(maxdim,
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[AS_HELP_STRING([--with-maxdim=N],
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|
[[Cuba option] the maximum dimension for integration,
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|
if variable-size array are not supported])],
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[MAXDIM=$withval])
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MAXCOMP=${MAXCOMP:-4}
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AC_ARG_WITH(maxcomp,
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||||||
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[AS_HELP_STRING([--with-maxcomp=N],
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||||||
|
[[Cuba option] the maximum number of components of the integrand,
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||||||
|
if variable-size array are not supported])],
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||||||
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[MAXCOMP=$withval])
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||||||
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||||||
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AC_MSG_CHECKING([for variable-size arrays])
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||||||
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AC_COMPILE_IFELSE([AC_LANG_SOURCE(,[[
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||||||
|
void test(int n)
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|
{
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char s[n];
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}
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||||||
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]])],
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[AC_MSG_RESULT([yes])],
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||||||
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[AC_MSG_RESULT([no, using MAXDIM=$MAXDIM and MAXCOMP=$MAXCOMP])
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||||||
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AC_DEFINE_UNQUOTED([NDIM], [$MAXDIM], [Maximum number of components])
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||||||
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AC_DEFINE_UNQUOTED([NCOMP], [$MAXCOMP], [Maximum number of dimensions])]
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)
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||||||
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||||||
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CUBA_SRCDIR="$(pwd)/src/external/libCuba/src"
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||||||
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CUBA_LIBS="${CUBA_SRCDIR}/libcuba.la"
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||||||
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CUBA_CFLAGS="-I${CUBA_SRCDIR}"
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||||||
|
else
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||||||
|
if test "${CUBA_FOUND}" != "1"; then
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||||||
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CUBA_LIBS="-L${CUBA_PREFIX}/lib -lcuba -lm"
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||||||
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CUBA_CFLAGS="-I${CUBA_PREFIX}/include"
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||||||
|
fi
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||||||
fi
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fi
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||||||
|
|
||||||
|
AC_SUBST(CUBA_PREFIX)
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||||||
AC_SUBST(CUBA_LIBS)
|
AC_SUBST(CUBA_LIBS)
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||||||
AC_SUBST(CUBA_CFLAGS)
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AC_SUBST(CUBA_CFLAGS)
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||||||
|
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||||||
@ -427,6 +489,7 @@ LOCAL_BIN_CXXFLAGS="-Wall -Wno-trigraphs"
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|||||||
LOCAL_LIB_CXXFLAGS="${LOCAL_BIN_CXXFLAGS}"
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LOCAL_LIB_CXXFLAGS="${LOCAL_BIN_CXXFLAGS}"
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||||||
LOCAL_PSIBIN_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
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LOCAL_PSIBIN_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
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||||||
LOCAL_MUD_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
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LOCAL_MUD_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
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||||||
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LOCAL_CUBA_LIB_CFLAGS="${LOCAL_LIB_CXXFLAGS} ${CUBA_BUILD_CFLAGS}"
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||||||
LOCAL_BIN_LDFLAGS=
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LOCAL_BIN_LDFLAGS=
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||||||
LOCAL_LIB_LDFLAGS=
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LOCAL_LIB_LDFLAGS=
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||||||
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||||||
@ -436,6 +499,7 @@ case "$host" in
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LOCAL_LIB_CXXFLAGS="${LOCAL_BIN_CXXFLAGS} -D_DLL"
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LOCAL_LIB_CXXFLAGS="${LOCAL_BIN_CXXFLAGS} -D_DLL"
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||||||
LOCAL_PSIBIN_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS} -D_WIN32GCC"
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LOCAL_PSIBIN_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS} -D_WIN32GCC"
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||||||
LOCAL_MUD_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
|
LOCAL_MUD_LIB_CXXFLAGS="${LOCAL_LIB_CXXFLAGS}"
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||||||
|
LOCAL_CUBA_LIB_CFLAGS="${LOCAL_LIB_CXXFLAGS} ${CUBA_BUILD_CFLAGS}"
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||||||
LOCAL_BIN_LDFLAGS="${LOCAL_BIN_LDFLAGS} -Wl,--enable-auto-import -Wl,--enable-runtime-pseudo-reloc"
|
LOCAL_BIN_LDFLAGS="${LOCAL_BIN_LDFLAGS} -Wl,--enable-auto-import -Wl,--enable-runtime-pseudo-reloc"
|
||||||
LOCAL_LIB_LDFLAGS="-no-undefined ${LOCAL_BIN_LDFLAGS} -Wl,--export-all-symbols"
|
LOCAL_LIB_LDFLAGS="-no-undefined ${LOCAL_BIN_LDFLAGS} -Wl,--export-all-symbols"
|
||||||
;;
|
;;
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||||||
@ -448,6 +512,7 @@ AC_SUBST(LOCAL_BIN_CXXFLAGS)
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|||||||
AC_SUBST(LOCAL_LIB_CXXFLAGS)
|
AC_SUBST(LOCAL_LIB_CXXFLAGS)
|
||||||
AC_SUBST(LOCAL_PSIBIN_LIB_CXXFLAGS)
|
AC_SUBST(LOCAL_PSIBIN_LIB_CXXFLAGS)
|
||||||
AC_SUBST(LOCAL_MUD_LIB_CXXFLAGS)
|
AC_SUBST(LOCAL_MUD_LIB_CXXFLAGS)
|
||||||
|
AC_SUBST(LOCAL_CUBA_LIB_CFLAGS)
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||||||
AC_SUBST(LOCAL_BIN_LDFLAGS)
|
AC_SUBST(LOCAL_BIN_LDFLAGS)
|
||||||
AC_SUBST(LOCAL_LIB_LDFLAGS)
|
AC_SUBST(LOCAL_LIB_LDFLAGS)
|
||||||
|
|
||||||
@ -478,6 +543,7 @@ dnl -----------------------------------------------
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|||||||
dnl Specify the files that are going to be created by configure
|
dnl Specify the files that are going to be created by configure
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||||||
dnl -----------------------------------------------
|
dnl -----------------------------------------------
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||||||
|
|
||||||
|
AM_CONDITIONAL([BUILD_CUBALIB], [test "${BUILD_CUBA}" -eq 1])
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||||||
AM_CONDITIONAL([BUILD_BMWLIBS], [test "${BUILD_BMW_LIBS}" -eq 1])
|
AM_CONDITIONAL([BUILD_BMWLIBS], [test "${BUILD_BMW_LIBS}" -eq 1])
|
||||||
AM_CONDITIONAL([BUILD_ASLIBS], [test "${BUILD_AS_LIBS}" -eq 1])
|
AM_CONDITIONAL([BUILD_ASLIBS], [test "${BUILD_AS_LIBS}" -eq 1])
|
||||||
|
|
||||||
@ -494,6 +560,9 @@ AC_CONFIG_FILES([Makefile \
|
|||||||
src/external/mud/Makefile \
|
src/external/mud/Makefile \
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||||||
src/external/mud/src/Makefile \
|
src/external/mud/src/Makefile \
|
||||||
src/external/mud/src/mud.pc \
|
src/external/mud/src/mud.pc \
|
||||||
|
src/external/libCuba/Makefile \
|
||||||
|
src/external/libCuba/src/Makefile \
|
||||||
|
src/external/libCuba/src/cuba.pc \
|
||||||
src/external/TFitPofB-lib/Makefile \
|
src/external/TFitPofB-lib/Makefile \
|
||||||
src/external/TFitPofB-lib/classes/Makefile \
|
src/external/TFitPofB-lib/classes/Makefile \
|
||||||
src/external/libLFRelaxation/Makefile \
|
src/external/libLFRelaxation/Makefile \
|
||||||
|
|||||||
6
src/external/Makefile.am
vendored
6
src/external/Makefile.am
vendored
@ -2,6 +2,10 @@ if BUILD_ASLIBS
|
|||||||
ASDIRS = Nonlocal
|
ASDIRS = Nonlocal
|
||||||
endif
|
endif
|
||||||
|
|
||||||
|
if BUILD_CUBALIB
|
||||||
|
CUBADIRS = libCuba
|
||||||
|
endif
|
||||||
|
|
||||||
if BUILD_BMWLIBS
|
if BUILD_BMWLIBS
|
||||||
BMWDIRS = TFitPofB-lib \
|
BMWDIRS = TFitPofB-lib \
|
||||||
libLFRelaxation \
|
libLFRelaxation \
|
||||||
@ -9,4 +13,4 @@ if BUILD_BMWLIBS
|
|||||||
libCalcMeanFieldsLEM
|
libCalcMeanFieldsLEM
|
||||||
endif
|
endif
|
||||||
|
|
||||||
SUBDIRS = $(ASDIRS) $(BMWDIRS)
|
SUBDIRS = $(ASDIRS) $(CUBADIRS) $(BMWDIRS)
|
||||||
|
|||||||
481
src/external/libCuba/COPYING
vendored
Normal file
481
src/external/libCuba/COPYING
vendored
Normal file
@ -0,0 +1,481 @@
|
|||||||
|
GNU LIBRARY GENERAL PUBLIC LICENSE
|
||||||
|
Version 2, June 1991
|
||||||
|
|
||||||
|
Copyright (C) 1991 Free Software Foundation, Inc.
|
||||||
|
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||||
|
Everyone is permitted to copy and distribute verbatim copies
|
||||||
|
of this license document, but changing it is not allowed.
|
||||||
|
|
||||||
|
[This is the first released version of the library GPL. It is
|
||||||
|
numbered 2 because it goes with version 2 of the ordinary GPL.]
|
||||||
|
|
||||||
|
Preamble
|
||||||
|
|
||||||
|
The licenses for most software are designed to take away your
|
||||||
|
freedom to share and change it. By contrast, the GNU General Public
|
||||||
|
Licenses are intended to guarantee your freedom to share and change
|
||||||
|
free software--to make sure the software is free for all its users.
|
||||||
|
|
||||||
|
This license, the Library General Public License, applies to some
|
||||||
|
specially designated Free Software Foundation software, and to any
|
||||||
|
other libraries whose authors decide to use it. You can use it for
|
||||||
|
your libraries, too.
|
||||||
|
|
||||||
|
When we speak of free software, we are referring to freedom, not
|
||||||
|
price. Our General Public Licenses are designed to make sure that you
|
||||||
|
have the freedom to distribute copies of free software (and charge for
|
||||||
|
this service if you wish), that you receive source code or can get it
|
||||||
|
if you want it, that you can change the software or use pieces of it
|
||||||
|
in new free programs; and that you know you can do these things.
|
||||||
|
|
||||||
|
To protect your rights, we need to make restrictions that forbid
|
||||||
|
anyone to deny you these rights or to ask you to surrender the rights.
|
||||||
|
These restrictions translate to certain responsibilities for you if
|
||||||
|
you distribute copies of the library, or if you modify it.
|
||||||
|
|
||||||
|
For example, if you distribute copies of the library, whether gratis
|
||||||
|
or for a fee, you must give the recipients all the rights that we gave
|
||||||
|
you. You must make sure that they, too, receive or can get the source
|
||||||
|
code. If you link a program with the library, you must provide
|
||||||
|
complete object files to the recipients so that they can relink them
|
||||||
|
with the library, after making changes to the library and recompiling
|
||||||
|
it. And you must show them these terms so they know their rights.
|
||||||
|
|
||||||
|
Our method of protecting your rights has two steps: (1) copyright
|
||||||
|
the library, and (2) offer you this license which gives you legal
|
||||||
|
permission to copy, distribute and/or modify the library.
|
||||||
|
|
||||||
|
Also, for each distributor's protection, we want to make certain
|
||||||
|
that everyone understands that there is no warranty for this free
|
||||||
|
library. If the library is modified by someone else and passed on, we
|
||||||
|
want its recipients to know that what they have is not the original
|
||||||
|
version, so that any problems introduced by others will not reflect on
|
||||||
|
the original authors' reputations.
|
||||||
|
|
||||||
|
Finally, any free program is threatened constantly by software
|
||||||
|
patents. We wish to avoid the danger that companies distributing free
|
||||||
|
software will individually obtain patent licenses, thus in effect
|
||||||
|
transforming the program into proprietary software. To prevent this,
|
||||||
|
we have made it clear that any patent must be licensed for everyone's
|
||||||
|
free use or not licensed at all.
|
||||||
|
|
||||||
|
Most GNU software, including some libraries, is covered by the ordinary
|
||||||
|
GNU General Public License, which was designed for utility programs. This
|
||||||
|
license, the GNU Library General Public License, applies to certain
|
||||||
|
designated libraries. This license is quite different from the ordinary
|
||||||
|
one; be sure to read it in full, and don't assume that anything in it is
|
||||||
|
the same as in the ordinary license.
|
||||||
|
|
||||||
|
The reason we have a separate public license for some libraries is that
|
||||||
|
they blur the distinction we usually make between modifying or adding to a
|
||||||
|
program and simply using it. Linking a program with a library, without
|
||||||
|
changing the library, is in some sense simply using the library, and is
|
||||||
|
analogous to running a utility program or application program. However, in
|
||||||
|
a textual and legal sense, the linked executable is a combined work, a
|
||||||
|
derivative of the original library, and the ordinary General Public License
|
||||||
|
treats it as such.
|
||||||
|
|
||||||
|
Because of this blurred distinction, using the ordinary General
|
||||||
|
Public License for libraries did not effectively promote software
|
||||||
|
sharing, because most developers did not use the libraries. We
|
||||||
|
concluded that weaker conditions might promote sharing better.
|
||||||
|
|
||||||
|
However, unrestricted linking of non-free programs would deprive the
|
||||||
|
users of those programs of all benefit from the free status of the
|
||||||
|
libraries themselves. This Library General Public License is intended to
|
||||||
|
permit developers of non-free programs to use free libraries, while
|
||||||
|
preserving your freedom as a user of such programs to change the free
|
||||||
|
libraries that are incorporated in them. (We have not seen how to achieve
|
||||||
|
this as regards changes in header files, but we have achieved it as regards
|
||||||
|
changes in the actual functions of the Library.) The hope is that this
|
||||||
|
will lead to faster development of free libraries.
|
||||||
|
|
||||||
|
The precise terms and conditions for copying, distribution and
|
||||||
|
modification follow. Pay close attention to the difference between a
|
||||||
|
"work based on the library" and a "work that uses the library". The
|
||||||
|
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||||||
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|
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|
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END OF TERMS AND CONDITIONS
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||||||
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How to Apply These Terms to Your New Libraries
|
||||||
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|
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|
If you develop a new library, and you want it to be of the greatest
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||||||
|
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||||||
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|
||||||
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|
||||||
|
To apply these terms, attach the following notices to the library. It is
|
||||||
|
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|
||||||
|
convey the exclusion of warranty; and each file should have at least the
|
||||||
|
"copyright" line and a pointer to where the full notice is found.
|
||||||
|
|
||||||
|
<one line to give the library's name and a brief idea of what it does.>
|
||||||
|
Copyright (C) <year> <name of author>
|
||||||
|
|
||||||
|
This library is free software; you can redistribute it and/or
|
||||||
|
modify it under the terms of the GNU Library General Public
|
||||||
|
License as published by the Free Software Foundation; either
|
||||||
|
version 2 of the License, or (at your option) any later version.
|
||||||
|
|
||||||
|
This library is distributed in the hope that it will be useful,
|
||||||
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||||
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
||||||
|
Library General Public License for more details.
|
||||||
|
|
||||||
|
You should have received a copy of the GNU Library General Public
|
||||||
|
License along with this library; if not, write to the Free
|
||||||
|
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
||||||
|
|
||||||
|
Also add information on how to contact you by electronic and paper mail.
|
||||||
|
|
||||||
|
You should also get your employer (if you work as a programmer) or your
|
||||||
|
school, if any, to sign a "copyright disclaimer" for the library, if
|
||||||
|
necessary. Here is a sample; alter the names:
|
||||||
|
|
||||||
|
Yoyodyne, Inc., hereby disclaims all copyright interest in the
|
||||||
|
library `Frob' (a library for tweaking knobs) written by James Random Hacker.
|
||||||
|
|
||||||
|
<signature of Ty Coon>, 1 April 1990
|
||||||
|
Ty Coon, President of Vice
|
||||||
|
|
||||||
|
That's all there is to it!
|
||||||
1
src/external/libCuba/Makefile.am
vendored
Normal file
1
src/external/libCuba/Makefile.am
vendored
Normal file
@ -0,0 +1 @@
|
|||||||
|
SUBDIRS = src
|
||||||
22
src/external/libCuba/README
vendored
Normal file
22
src/external/libCuba/README
vendored
Normal file
@ -0,0 +1,22 @@
|
|||||||
|
#---------------------------------------------------------------------
|
||||||
|
# README
|
||||||
|
# Bastian M. Wojek, 2010/01/05
|
||||||
|
# $Id:
|
||||||
|
#---------------------------------------------------------------------
|
||||||
|
|
||||||
|
This directory contains a subset of the code
|
||||||
|
- namely the C-routines (of which only a subset is automatically built) -
|
||||||
|
included in the Cuba library for multidimensional numerical integration
|
||||||
|
written by Thomas Hahn.
|
||||||
|
Cuba is an open-source package and free of charge.
|
||||||
|
If you want to use Cuba in a commercial application,
|
||||||
|
make sure you understand the GNU Lesser General Public License
|
||||||
|
under which Cuba is distributed.
|
||||||
|
Cuba is being developed at the Max-Planck-Institute for Physics in Munich.
|
||||||
|
|
||||||
|
For further information as well as the full package please refer to
|
||||||
|
http://www.feynarts.de/cuba
|
||||||
|
|
||||||
|
#---------------------------------------------------------------------
|
||||||
|
# this is the end ...
|
||||||
|
#---------------------------------------------------------------------
|
||||||
26
src/external/libCuba/src/Makefile.am
vendored
Normal file
26
src/external/libCuba/src/Makefile.am
vendored
Normal file
@ -0,0 +1,26 @@
|
|||||||
|
## Process this file with automake to create Makefile.in
|
||||||
|
|
||||||
|
h_sources = cuba.h
|
||||||
|
|
||||||
|
c_sources = cuhre/Cuhre.c \
|
||||||
|
divonne/Divonne.c \
|
||||||
|
suave/Suave.c \
|
||||||
|
vegas/Vegas.c
|
||||||
|
|
||||||
|
include_HEADERS = cuba.h
|
||||||
|
|
||||||
|
INCLUDES = -I. -Icommon
|
||||||
|
AM_CFLAGS = $(LOCAL_CUBA_LIB_CFLAGS)
|
||||||
|
|
||||||
|
AM_LDFLAGS = $(LOCAL_LIB_LDFLAGS)
|
||||||
|
CLEANFILES = *~ core
|
||||||
|
|
||||||
|
lib_LTLIBRARIES = libcuba.la
|
||||||
|
|
||||||
|
libcuba_la_SOURCES = $(h_sources) $(c_sources)
|
||||||
|
libcuba_la_LIBADD = -lm
|
||||||
|
libcuba_la_LDFLAGS = -version-info $(CUBA_LIBRARY_VERSION) -release $(CUBA_RELEASE) $(AM_LDFLAGS)
|
||||||
|
|
||||||
|
pkgconfigdir = $(libdir)/pkgconfig
|
||||||
|
pkgconfig_DATA = cuba.pc
|
||||||
|
|
||||||
87
src/external/libCuba/src/common/ChiSquare.c
vendored
Normal file
87
src/external/libCuba/src/common/ChiSquare.c
vendored
Normal file
@ -0,0 +1,87 @@
|
|||||||
|
/*
|
||||||
|
ChiSquare.c
|
||||||
|
the chi-square cdf
|
||||||
|
after W.J. Kennedy and J.E. Gentle,
|
||||||
|
Statistical computing, p. 116
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#ifdef HAVE_ERF
|
||||||
|
#define Erf erf
|
||||||
|
#else
|
||||||
|
#include "Erf.c"
|
||||||
|
#endif
|
||||||
|
|
||||||
|
static inline real Normal(creal x)
|
||||||
|
{
|
||||||
|
return .5*Erf(x/1.414213562373095048801689) + .5;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real ChiSquare(creal x, cint df)
|
||||||
|
{
|
||||||
|
real y;
|
||||||
|
|
||||||
|
if( df <= 0 ) return -999;
|
||||||
|
|
||||||
|
if( x <= 0 ) return 0;
|
||||||
|
if( x > 1000*df ) return 1;
|
||||||
|
|
||||||
|
if( df > 1000 ) {
|
||||||
|
if( x < 2 ) return 0;
|
||||||
|
y = 2./(9*df);
|
||||||
|
y = (pow(x/df, 1/3.) - (1 - y))/sqrt(y);
|
||||||
|
if( y > 5 ) return 1;
|
||||||
|
if( y < -18.8055 ) return 0;
|
||||||
|
return Normal(y);
|
||||||
|
}
|
||||||
|
|
||||||
|
y = .5*x;
|
||||||
|
|
||||||
|
if( df & 1 ) {
|
||||||
|
creal sqrty = sqrt(y);
|
||||||
|
real h = Erf(sqrty);
|
||||||
|
count i;
|
||||||
|
|
||||||
|
if( df == 1 ) return h;
|
||||||
|
|
||||||
|
y = sqrty*exp(-y)/.8862269254527579825931;
|
||||||
|
for( i = 3; i < df; i += 2 ) {
|
||||||
|
h -= y;
|
||||||
|
y *= x/i;
|
||||||
|
}
|
||||||
|
y = h - y;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
real term = exp(-y), sum = term;
|
||||||
|
count i;
|
||||||
|
|
||||||
|
for( i = 1; i < df/2; ++i )
|
||||||
|
sum += term *= y/i;
|
||||||
|
y = 1 - sum;
|
||||||
|
}
|
||||||
|
|
||||||
|
return Max(0., y);
|
||||||
|
}
|
||||||
|
|
||||||
70
src/external/libCuba/src/common/Erf.c
vendored
Normal file
70
src/external/libCuba/src/common/Erf.c
vendored
Normal file
@ -0,0 +1,70 @@
|
|||||||
|
/*
|
||||||
|
Erf.c
|
||||||
|
Gaussian error function
|
||||||
|
= 2/Sqrt[Pi] Integrate[Exp[-t^2], {t, 0, x}]
|
||||||
|
Code from Takuya Ooura's gamerf2a.f
|
||||||
|
http://www.kurims.kyoto-u.ac.jp/~ooura/gamerf.html
|
||||||
|
last modified 8 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
static real Erfc(creal x)
|
||||||
|
{
|
||||||
|
static creal c[] = {
|
||||||
|
2.96316885199227378e-01, 6.12158644495538758e-02,
|
||||||
|
1.81581125134637070e-01, 5.50942780056002085e-01,
|
||||||
|
6.81866451424939493e-02, 1.53039662058770397e+00,
|
||||||
|
1.56907543161966709e-02, 2.99957952311300634e+00,
|
||||||
|
2.21290116681517573e-03, 4.95867777128246701e+00,
|
||||||
|
1.91395813098742864e-04, 7.41471251099335407e+00,
|
||||||
|
9.71013284010551623e-06, 1.04765104356545238e+01,
|
||||||
|
1.66642447174307753e-07, 1.48455557345597957e+01,
|
||||||
|
6.10399733098688199e+00, 1.26974899965115684e+01 };
|
||||||
|
real y = x*x;
|
||||||
|
y = exp(-y)*x*(
|
||||||
|
c[0]/(y + c[1]) + c[2]/(y + c[3]) +
|
||||||
|
c[4]/(y + c[5]) + c[6]/(y + c[7]) +
|
||||||
|
c[8]/(y + c[9]) + c[10]/(y + c[11]) +
|
||||||
|
c[12]/(y + c[13]) + c[14]/(y + c[15]) );
|
||||||
|
if( x < c[16] ) y += 2/(exp(c[17]*x) + 1);
|
||||||
|
return y;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static real Erf(creal x)
|
||||||
|
{
|
||||||
|
static creal c[] = {
|
||||||
|
1.12837916709551257e+00,
|
||||||
|
-3.76126389031833602e-01,
|
||||||
|
1.12837916706621301e-01,
|
||||||
|
-2.68661698447642378e-02,
|
||||||
|
5.22387877685618101e-03,
|
||||||
|
-8.49202435186918470e-04 };
|
||||||
|
real y = fabs(x);
|
||||||
|
if( y > .125 ) {
|
||||||
|
y = 1 - Erfc(y);
|
||||||
|
return (x > 0) ? y : -y;
|
||||||
|
}
|
||||||
|
y *= y;
|
||||||
|
return x*(c[0] + y*(c[1] + y*(c[2] +
|
||||||
|
y*(c[3] + y*(c[4] + y*c[5])))));
|
||||||
|
}
|
||||||
303
src/external/libCuba/src/common/Random.c
vendored
Normal file
303
src/external/libCuba/src/common/Random.c
vendored
Normal file
@ -0,0 +1,303 @@
|
|||||||
|
/*
|
||||||
|
Random.c
|
||||||
|
quasi- and pseudo-random-number generation
|
||||||
|
last modified 2 Apr 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
/*
|
||||||
|
PART 1: Sobol quasi-random-number generator
|
||||||
|
adapted from ACM TOMS algorithm 659
|
||||||
|
*/
|
||||||
|
|
||||||
|
#define SOBOL_MINDIM 1
|
||||||
|
#define SOBOL_MAXDIM 40
|
||||||
|
|
||||||
|
static struct {
|
||||||
|
real norm;
|
||||||
|
number v[SOBOL_MAXDIM][30], prev[SOBOL_MAXDIM];
|
||||||
|
number seq;
|
||||||
|
} sobol_;
|
||||||
|
|
||||||
|
|
||||||
|
static inline void SobolIni(cnumber n)
|
||||||
|
{
|
||||||
|
static number ini[9*40] = {
|
||||||
|
3, 1, 0, 0, 0, 0, 0, 0, 0,
|
||||||
|
7, 1, 1, 0, 0, 0, 0, 0, 0,
|
||||||
|
11, 1, 3, 7, 0, 0, 0, 0, 0,
|
||||||
|
13, 1, 1, 5, 0, 0, 0, 0, 0,
|
||||||
|
19, 1, 3, 1, 1, 0, 0, 0, 0,
|
||||||
|
25, 1, 1, 3, 7, 0, 0, 0, 0,
|
||||||
|
37, 1, 3, 3, 9, 9, 0, 0, 0,
|
||||||
|
59, 1, 3, 7, 13, 3, 0, 0, 0,
|
||||||
|
47, 1, 1, 5, 11, 27, 0, 0, 0,
|
||||||
|
61, 1, 3, 5, 1, 15, 0, 0, 0,
|
||||||
|
55, 1, 1, 7, 3, 29, 0, 0, 0,
|
||||||
|
41, 1, 3, 7, 7, 21, 0, 0, 0,
|
||||||
|
67, 1, 1, 1, 9, 23, 37, 0, 0,
|
||||||
|
97, 1, 3, 3, 5, 19, 33, 0, 0,
|
||||||
|
91, 1, 1, 3, 13, 11, 7, 0, 0,
|
||||||
|
109, 1, 1, 7, 13, 25, 5, 0, 0,
|
||||||
|
103, 1, 3, 5, 11, 7, 11, 0, 0,
|
||||||
|
115, 1, 1, 1, 3, 13, 39, 0, 0,
|
||||||
|
131, 1, 3, 1, 15, 17, 63, 13, 0,
|
||||||
|
193, 1, 1, 5, 5, 1, 27, 33, 0,
|
||||||
|
137, 1, 3, 3, 3, 25, 17, 115, 0,
|
||||||
|
145, 1, 1, 3, 15, 29, 15, 41, 0,
|
||||||
|
143, 1, 3, 1, 7, 3, 23, 79, 0,
|
||||||
|
241, 1, 3, 7, 9, 31, 29, 17, 0,
|
||||||
|
157, 1, 1, 5, 13, 11, 3, 29, 0,
|
||||||
|
185, 1, 3, 1, 9, 5, 21, 119, 0,
|
||||||
|
167, 1, 1, 3, 1, 23, 13, 75, 0,
|
||||||
|
229, 1, 3, 3, 11, 27, 31, 73, 0,
|
||||||
|
171, 1, 1, 7, 7, 19, 25, 105, 0,
|
||||||
|
213, 1, 3, 5, 5, 21, 9, 7, 0,
|
||||||
|
191, 1, 1, 1, 15, 5, 49, 59, 0,
|
||||||
|
253, 1, 1, 1, 1, 1, 33, 65, 0,
|
||||||
|
203, 1, 3, 5, 15, 17, 19, 21, 0,
|
||||||
|
211, 1, 1, 7, 11, 13, 29, 3, 0,
|
||||||
|
239, 1, 3, 7, 5, 7, 11, 113, 0,
|
||||||
|
247, 1, 1, 5, 3, 15, 19, 61, 0,
|
||||||
|
285, 1, 3, 1, 1, 9, 27, 89, 7,
|
||||||
|
369, 1, 1, 3, 7, 31, 15, 45, 23,
|
||||||
|
299, 1, 3, 3, 9, 9, 25, 107, 39 };
|
||||||
|
|
||||||
|
count dim, bit, nbits;
|
||||||
|
number max, *pini = ini;
|
||||||
|
|
||||||
|
for( nbits = 0, max = 1; max <= n; max <<= 1 ) ++nbits;
|
||||||
|
sobol_.norm = 1./max;
|
||||||
|
|
||||||
|
for( bit = 0; bit < nbits; ++bit )
|
||||||
|
sobol_.v[0][bit] = (max >>= 1);
|
||||||
|
|
||||||
|
for( dim = 1; dim < ndim_; ++dim ) {
|
||||||
|
number *pv = sobol_.v[dim], *pvv = pv;
|
||||||
|
number powers = *pini++, j;
|
||||||
|
int inibits = -1, bit;
|
||||||
|
for( j = powers; j; j >>= 1 ) ++inibits;
|
||||||
|
|
||||||
|
memcpy(pv, pini, inibits*sizeof(*pini));
|
||||||
|
pini += 8;
|
||||||
|
|
||||||
|
for( bit = inibits; bit < nbits; ++bit ) {
|
||||||
|
number newv = *pvv, j = powers;
|
||||||
|
int b;
|
||||||
|
for( b = 0; b < inibits; ++b ) {
|
||||||
|
if( j & 1 ) newv ^= pvv[b] << (inibits - b);
|
||||||
|
j >>= 1;
|
||||||
|
}
|
||||||
|
pvv[inibits] = newv;
|
||||||
|
++pvv;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( bit = 0; bit < nbits - 1; ++bit )
|
||||||
|
pv[bit] <<= nbits - bit - 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
sobol_.seq = 0;
|
||||||
|
VecClear(sobol_.prev);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void SobolGet(real *x)
|
||||||
|
{
|
||||||
|
number seq = sobol_.seq++;
|
||||||
|
count zerobit = 0, dim;
|
||||||
|
|
||||||
|
while( seq & 1 ) {
|
||||||
|
++zerobit;
|
||||||
|
seq >>= 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
sobol_.prev[dim] ^= sobol_.v[dim][zerobit];
|
||||||
|
x[dim] = sobol_.prev[dim]*sobol_.norm;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void SobolSkip(number n)
|
||||||
|
{
|
||||||
|
while( n-- ) {
|
||||||
|
number seq = sobol_.seq++;
|
||||||
|
count zerobit = 0, dim;
|
||||||
|
|
||||||
|
while( seq & 1 ) {
|
||||||
|
++zerobit;
|
||||||
|
seq >>= 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
sobol_.prev[dim] ^= sobol_.v[dim][zerobit];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/*
|
||||||
|
PART 2: Mersenne Twister pseudo-random-number generator
|
||||||
|
adapted from T. Nishimura's and M. Matsumoto's C code at
|
||||||
|
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* length of state vector */
|
||||||
|
#define MERSENNE_N 624
|
||||||
|
|
||||||
|
/* period parameter */
|
||||||
|
#define MERSENNE_M 397
|
||||||
|
|
||||||
|
/* 32 or 53 random bits */
|
||||||
|
#define RANDOM_BITS 32
|
||||||
|
|
||||||
|
typedef unsigned int state_t;
|
||||||
|
|
||||||
|
static struct {
|
||||||
|
state_t state[MERSENNE_N];
|
||||||
|
count next;
|
||||||
|
} mersenne_;
|
||||||
|
|
||||||
|
unsigned int SUFFIX(mersenneseed);
|
||||||
|
|
||||||
|
|
||||||
|
static inline state_t Twist(state_t a, state_t b)
|
||||||
|
{
|
||||||
|
state_t mixbits = (a & 0x80000000) | (b & 0x7fffffff);
|
||||||
|
state_t matrixA = (-(b & 1)) & 0x9908b0df;
|
||||||
|
return (mixbits >> 1) ^ matrixA;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void MersenneReload()
|
||||||
|
{
|
||||||
|
state_t *s = mersenne_.state;
|
||||||
|
int j;
|
||||||
|
|
||||||
|
for( j = MERSENNE_N - MERSENNE_M + 1; --j; ++s )
|
||||||
|
*s = s[MERSENNE_M] ^ Twist(s[0], s[1]);
|
||||||
|
for( j = MERSENNE_M; --j; ++s )
|
||||||
|
*s = s[MERSENNE_M - MERSENNE_N] ^ Twist(s[0], s[1]);
|
||||||
|
*s = s[MERSENNE_M - MERSENNE_N] ^ Twist(s[0], mersenne_.state[0]);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void MersenneIni()
|
||||||
|
{
|
||||||
|
state_t seed = SUFFIX(mersenneseed);
|
||||||
|
state_t *next = mersenne_.state;
|
||||||
|
int j;
|
||||||
|
|
||||||
|
if( seed == 0 ) seed = 5489;
|
||||||
|
|
||||||
|
for( j = 1; j <= MERSENNE_N; ++j ) {
|
||||||
|
*next++ = seed;
|
||||||
|
seed = 0x6c078965*(seed ^ (seed >> 30)) + j;
|
||||||
|
/* see Knuth TAOCP Vol 2, 3rd Ed, p. 106 for multiplier */
|
||||||
|
}
|
||||||
|
|
||||||
|
MersenneReload();
|
||||||
|
mersenne_.next = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline state_t MersenneInt(count next)
|
||||||
|
{
|
||||||
|
state_t s = mersenne_.state[next];
|
||||||
|
s ^= s >> 11;
|
||||||
|
s ^= (s << 7) & 0x9d2c5680;
|
||||||
|
s ^= (s << 15) & 0xefc60000;
|
||||||
|
return s ^ (s >> 18);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void MersenneGet(real *x)
|
||||||
|
{
|
||||||
|
count next = mersenne_.next, dim;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
#if RANDOM_BITS == 53
|
||||||
|
state_t a, b;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
if( next >= MERSENNE_N ) {
|
||||||
|
MersenneReload();
|
||||||
|
next = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
#if RANDOM_BITS == 53
|
||||||
|
a = MersenneInt(next++) >> 5;
|
||||||
|
b = MersenneInt(next++) >> 6;
|
||||||
|
x[dim] = (67108864.*a + b)/9007199254740992.;
|
||||||
|
#else
|
||||||
|
x[dim] = MersenneInt(next++)/4294967296.;
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
mersenne_.next = next;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline void MersenneSkip(number n)
|
||||||
|
{
|
||||||
|
#if RANDOM_BITS == 53
|
||||||
|
n = 2*n*ndim_ + mersenne_.next;
|
||||||
|
#else
|
||||||
|
n = n*ndim_ + mersenne_.next;
|
||||||
|
#endif
|
||||||
|
mersenne_.next = n % MERSENNE_N;
|
||||||
|
n /= MERSENNE_N;
|
||||||
|
while( n-- ) MersenneReload();
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/*
|
||||||
|
PART 3: User routines:
|
||||||
|
|
||||||
|
- IniRandom sets up the random-number generator to produce a
|
||||||
|
sequence of at least n ndim_-dimensional random vectors.
|
||||||
|
|
||||||
|
- GetRandom retrieves one random vector.
|
||||||
|
|
||||||
|
- SkipRandom skips over n random vectors.
|
||||||
|
*/
|
||||||
|
|
||||||
|
static void IniRandom(cnumber n, cint flags)
|
||||||
|
{
|
||||||
|
if( PSEUDORNG ) {
|
||||||
|
sobol_.seq = -1;
|
||||||
|
MersenneIni();
|
||||||
|
}
|
||||||
|
else SobolIni(n);
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline void GetRandom(real *x)
|
||||||
|
{
|
||||||
|
if( sobol_.seq == -1 ) MersenneGet(x);
|
||||||
|
else SobolGet(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline void SkipRandom(cnumber n)
|
||||||
|
{
|
||||||
|
if( sobol_.seq == -1 ) MersenneSkip(n);
|
||||||
|
else SobolSkip(n);
|
||||||
|
}
|
||||||
|
|
||||||
105
src/external/libCuba/src/common/debug.c
vendored
Normal file
105
src/external/libCuba/src/common/debug.c
vendored
Normal file
@ -0,0 +1,105 @@
|
|||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#define DEBFile stdout
|
||||||
|
|
||||||
|
#define DEBF "%9.5f"
|
||||||
|
//#define DEBF "%21.17f"
|
||||||
|
//#define DEBF "%a"
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef DEBFile
|
||||||
|
|
||||||
|
#define DEBOpen()
|
||||||
|
#define DEBClose()
|
||||||
|
|
||||||
|
#else
|
||||||
|
|
||||||
|
FILE *DEBFile;
|
||||||
|
|
||||||
|
static inline void DEBOpen()
|
||||||
|
{
|
||||||
|
#ifdef MLVERSION
|
||||||
|
DEBFile = fopen("log-mma", "w");
|
||||||
|
#else
|
||||||
|
DEBFile = fopen("log-c", "w");
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline void DEBClose()
|
||||||
|
{
|
||||||
|
fclose(DEBFile);
|
||||||
|
}
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
||||||
|
|
||||||
|
#define DEB(...) fprintf(DEBFile, __VA_ARGS__); fflush(DEBFile)
|
||||||
|
|
||||||
|
|
||||||
|
static inline void DEBVec(const char *s, creal *d)
|
||||||
|
{
|
||||||
|
char space[strlen(s) + 2];
|
||||||
|
count dim;
|
||||||
|
|
||||||
|
memset(space, ' ', sizeof(space));
|
||||||
|
space[sizeof(space) - 1] = 0;
|
||||||
|
|
||||||
|
DEB("%s=" DEBF "\n", s, d[0]);
|
||||||
|
for( dim = 1; dim < ndim_; ++dim )
|
||||||
|
DEB("%s" DEBF "\n", space, d[dim]);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/*
|
||||||
|
static inline void DEBRegion(const char *s, cBounds *b)
|
||||||
|
{
|
||||||
|
char space[strlen(s) + 3];
|
||||||
|
count dim;
|
||||||
|
|
||||||
|
memset(space, ' ', sizeof(space));
|
||||||
|
space[sizeof(space) - 1] = 0;
|
||||||
|
|
||||||
|
DEB("%s: " DEBF " - " DEBF "\n", s, b[0].lower, b[0].upper);
|
||||||
|
for( dim = 1; dim < ndim_; ++dim )
|
||||||
|
DEB("%s" DEBF " - " DEBF "\n", space, b[dim].lower, b[dim].upper);
|
||||||
|
}
|
||||||
|
*/
|
||||||
|
|
||||||
|
|
||||||
|
static inline void DEBMem(const char *s)
|
||||||
|
{
|
||||||
|
int kbytes = -1;
|
||||||
|
FILE *f;
|
||||||
|
char procfile[128];
|
||||||
|
|
||||||
|
sprintf(procfile, "/proc/%d/status", getpid());
|
||||||
|
f = fopen(procfile, "r");
|
||||||
|
while( !feof(f) ) {
|
||||||
|
char s[128];
|
||||||
|
*s = 0;
|
||||||
|
fgets(s, sizeof(s), f);
|
||||||
|
if( sscanf(s, "VmSize: %d", &kbytes) == 1 ) break;
|
||||||
|
}
|
||||||
|
fclose(f);
|
||||||
|
|
||||||
|
DEB("MEM %s: %d kbytes\n", s, kbytes);
|
||||||
|
}
|
||||||
|
|
||||||
198
src/external/libCuba/src/common/stddecl.h
vendored
Normal file
198
src/external/libCuba/src/common/stddecl.h
vendored
Normal file
@ -0,0 +1,198 @@
|
|||||||
|
/*
|
||||||
|
stddecl.h
|
||||||
|
Type declarations common to all Cuba routines
|
||||||
|
last modified 29 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#ifndef __stddecl_h__
|
||||||
|
#define __stddecl_h__
|
||||||
|
|
||||||
|
#ifdef HAVE_CONFIG_H
|
||||||
|
#include "config.h"
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#include <stdio.h>
|
||||||
|
#include <stdlib.h>
|
||||||
|
#include <string.h>
|
||||||
|
#include <math.h>
|
||||||
|
#include <float.h>
|
||||||
|
#include <limits.h>
|
||||||
|
#include <unistd.h>
|
||||||
|
#include <fcntl.h>
|
||||||
|
#include <sys/stat.h>
|
||||||
|
|
||||||
|
|
||||||
|
#ifndef NDIM
|
||||||
|
#define NDIM ndim_
|
||||||
|
#endif
|
||||||
|
#ifndef NCOMP
|
||||||
|
#define NCOMP ncomp_
|
||||||
|
#endif
|
||||||
|
|
||||||
|
|
||||||
|
#define VERBOSE (flags & 3)
|
||||||
|
#define LAST (flags & 4)
|
||||||
|
#define PSEUDORNG (flags & 8)
|
||||||
|
#define SHARPEDGES (flags & 16)
|
||||||
|
#define REGIONS (flags & 256)
|
||||||
|
|
||||||
|
#define INFTY DBL_MAX
|
||||||
|
|
||||||
|
#define NOTZERO 0x1p-104
|
||||||
|
|
||||||
|
|
||||||
|
#define Elements(x) (sizeof(x)/sizeof(*x))
|
||||||
|
|
||||||
|
#define Copy(d, s, n) memcpy(d, s, (n)*sizeof(*(d)))
|
||||||
|
|
||||||
|
#define VecCopy(d, s) Copy(d, s, ndim_)
|
||||||
|
|
||||||
|
#define ResCopy(d, s) Copy(d, s, ncomp_)
|
||||||
|
|
||||||
|
#define Clear(d, n) memset(d, 0, (n)*sizeof(*(d)))
|
||||||
|
|
||||||
|
#define VecClear(d) Clear(d, ndim_)
|
||||||
|
|
||||||
|
#define ResClear(d) Clear(d, ncomp_)
|
||||||
|
|
||||||
|
#define Zap(d) memset(d, 0, sizeof(d))
|
||||||
|
|
||||||
|
#define MaxErr(avg) Max(epsrel*fabs(avg), epsabs)
|
||||||
|
|
||||||
|
#ifdef __cplusplus
|
||||||
|
#define mallocset(p, n) (*(void **)&p = malloc(n))
|
||||||
|
#define reallocset(p, n) (*(void **)&p = realloc(p, n))
|
||||||
|
#else
|
||||||
|
#define mallocset(p, n) (p = malloc(n))
|
||||||
|
#define reallocset(p, n) (p = realloc(p, n))
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#define ChkAlloc(r) if( r == NULL ) { \
|
||||||
|
fprintf(stderr, "Out of memory in " __FILE__ " line %d.\n", __LINE__); \
|
||||||
|
exit(1); \
|
||||||
|
}
|
||||||
|
|
||||||
|
#define Alloc(p, n) MemAlloc(p, (n)*sizeof(*p))
|
||||||
|
#define MemAlloc(p, n) ChkAlloc(mallocset(p, n))
|
||||||
|
#define ReAlloc(p, n) ChkAlloc(reallocset(p, n))
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef __cplusplus
|
||||||
|
#define Extern extern "C"
|
||||||
|
#else
|
||||||
|
#define Extern extern
|
||||||
|
typedef enum { false, true } bool;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
typedef const bool cbool;
|
||||||
|
|
||||||
|
typedef const int cint;
|
||||||
|
|
||||||
|
typedef const long clong;
|
||||||
|
|
||||||
|
#define COUNT "%d"
|
||||||
|
typedef /*unsigned*/ int count;
|
||||||
|
typedef const count ccount;
|
||||||
|
|
||||||
|
#ifdef LONGLONGINT
|
||||||
|
#define PREFIX(s) ll##s
|
||||||
|
#define NUMBER "%lld"
|
||||||
|
#define NUMBER7 "%7lld"
|
||||||
|
typedef long long int number;
|
||||||
|
#else
|
||||||
|
#define PREFIX(s) s
|
||||||
|
#define NUMBER "%d"
|
||||||
|
#define NUMBER7 "%7d"
|
||||||
|
typedef int number;
|
||||||
|
#endif
|
||||||
|
typedef const number cnumber;
|
||||||
|
|
||||||
|
#define REAL "%g"
|
||||||
|
#define REALF "%f"
|
||||||
|
typedef /*long*/ double real;
|
||||||
|
/* Switching to long double is not as trivial as it
|
||||||
|
might seem here. sqrt, erf, exp, pow need to be
|
||||||
|
replaced by their long double versions (sqrtl, ...),
|
||||||
|
printf formats need to be updated similarly, and
|
||||||
|
ferrying long doubles to Mathematica is of course
|
||||||
|
quite another matter, too. */
|
||||||
|
|
||||||
|
typedef const real creal;
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef UNDERSCORE
|
||||||
|
#define SUFFIX(s) s##_
|
||||||
|
#else
|
||||||
|
#define SUFFIX(s) s
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#define EXPORT(s) EXPORT_(PREFIX(s))
|
||||||
|
#define EXPORT_(s) SUFFIX(s)
|
||||||
|
|
||||||
|
|
||||||
|
static inline real Sq(creal x)
|
||||||
|
{
|
||||||
|
return x*x;
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline real Min(creal a, creal b)
|
||||||
|
{
|
||||||
|
return (a < b) ? a : b;
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline real Max(creal a, creal b)
|
||||||
|
{
|
||||||
|
return (a > b) ? a : b;
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline real Weight(creal sum, creal sqsum, cnumber n)
|
||||||
|
{
|
||||||
|
creal w = sqrt(sqsum*n);
|
||||||
|
return (n - 1)/Max((w + sum)*(w - sum), NOTZERO);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
/* (a < 0) ? -1 : 0 */
|
||||||
|
#define NegQ(a) ((a) >> (sizeof(a)*8 - 1))
|
||||||
|
|
||||||
|
/* (a < 0) ? 0 : a */
|
||||||
|
#define IDim(a) ((a) & NegQ(-(a)))
|
||||||
|
|
||||||
|
/* (a < b) ? a : b */
|
||||||
|
#define IMin(a, b) ((a) - IDim((a) - (b)))
|
||||||
|
|
||||||
|
/* (a > b) ? a : b */
|
||||||
|
#define IMax(a, b) ((b) + IDim((a) - (b)))
|
||||||
|
|
||||||
|
/* (a == 0) ? 0 : -1 */
|
||||||
|
#define TrueQ(a) NegQ((a) | (-a))
|
||||||
|
|
||||||
|
/* a + (a == 0) */
|
||||||
|
#define Min1(a) ((a) + 1 + TrueQ(a))
|
||||||
|
|
||||||
|
/* abs(a) + (a == 0) */
|
||||||
|
#define Abs1(a) (((a) ^ NegQ(a)) - NegQ((a) - 1))
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
||||||
120
src/external/libCuba/src/cuba.h
vendored
Normal file
120
src/external/libCuba/src/cuba.h
vendored
Normal file
@ -0,0 +1,120 @@
|
|||||||
|
/*
|
||||||
|
cuba.h
|
||||||
|
Prototypes for the Cuba library
|
||||||
|
this file is part of Cuba
|
||||||
|
last modified 5 Dec 08 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#ifdef __cplusplus
|
||||||
|
extern "C" {
|
||||||
|
#endif
|
||||||
|
|
||||||
|
typedef void (*integrand_t)(const int *, const double [],
|
||||||
|
const int *, double []);
|
||||||
|
|
||||||
|
/* Note: Divonne actually passes a fifth argument, a const int *
|
||||||
|
which points to the integration phase. This is used only rarely
|
||||||
|
and most users are confused by the warnings the compiler emits
|
||||||
|
if the `correct' prototype is used. Thus, if you need to access
|
||||||
|
this argument, use an explicit cast to integrand_t when invoking
|
||||||
|
Divonne. */
|
||||||
|
|
||||||
|
|
||||||
|
void Vegas(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const int mineval, const int maxeval,
|
||||||
|
const int nstart, const int nincrease,
|
||||||
|
int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void llVegas(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const long long int mineval, const long long int maxeval,
|
||||||
|
const long long int nstart, const long long int nincrease,
|
||||||
|
long long int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void Suave(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const int mineval, const int maxeval,
|
||||||
|
const int nnew, const double flatness,
|
||||||
|
int *nregions, int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void llSuave(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const long long int mineval, const long long int maxeval,
|
||||||
|
const long long int nnew, const double flatness,
|
||||||
|
int *nregions, long long int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void Divonne(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const int mineval, const int maxeval,
|
||||||
|
const int key1, const int key2, const int key3, const int maxpass,
|
||||||
|
const double border, const double maxchisq, const double mindeviation,
|
||||||
|
const int ngiven, const int ldxgiven, double xgiven[],
|
||||||
|
const int nextra,
|
||||||
|
void (*peakfinder)(const int *, const double [], int *, double []),
|
||||||
|
int *nregions, int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void llDivonne(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const long long int mineval, const long long int maxeval,
|
||||||
|
const int key1, const int key2, const int key3, const int maxpass,
|
||||||
|
const double border, const double maxchisq, const double mindeviation,
|
||||||
|
const long long int ngiven, const int ldxgiven, double xgiven[],
|
||||||
|
const long long int nextra,
|
||||||
|
void (*peakfinder)(const int *, const double [], int *, double []),
|
||||||
|
int *nregions, long long int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void Cuhre(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const int mineval, const int maxeval,
|
||||||
|
const int key,
|
||||||
|
int *nregions, int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
void llCuhre(const int ndim, const int ncomp, integrand_t integrand,
|
||||||
|
const double epsrel, const double epsabs,
|
||||||
|
const int flags, const long long int mineval, const long long int maxeval,
|
||||||
|
const int key,
|
||||||
|
int *nregions, long long int *neval, int *fail,
|
||||||
|
double integral[], double error[], double prob[]);
|
||||||
|
|
||||||
|
extern int vegasnbatch;
|
||||||
|
extern int vegasgridno;
|
||||||
|
extern char vegasstate[128];
|
||||||
|
|
||||||
|
extern int llvegasnbatch;
|
||||||
|
extern int llvegasgridno;
|
||||||
|
extern char llvegasstate[128];
|
||||||
|
|
||||||
|
extern unsigned int mersenneseed;
|
||||||
|
|
||||||
|
#ifdef __cplusplus
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
10
src/external/libCuba/src/cuba.pc.in
vendored
Normal file
10
src/external/libCuba/src/cuba.pc.in
vendored
Normal file
@ -0,0 +1,10 @@
|
|||||||
|
prefix=@prefix@
|
||||||
|
exec_prefix=@exec_prefix@
|
||||||
|
libdir=@libdir@
|
||||||
|
includedir=@includedir@
|
||||||
|
|
||||||
|
Name: mud
|
||||||
|
Description: C shared library providing the cuba numerical integration routines
|
||||||
|
Version: @CUBA_VERSION@
|
||||||
|
Libs: -L${libdir} -l@CUBA_LIBRARY_NAME@
|
||||||
|
Cflags: -I${includedir}
|
||||||
92
src/external/libCuba/src/cuhre/Cuhre.c
vendored
Normal file
92
src/external/libCuba/src/cuhre/Cuhre.c
vendored
Normal file
@ -0,0 +1,92 @@
|
|||||||
|
/*
|
||||||
|
Cuhre.c
|
||||||
|
Adaptive integration using cubature rules
|
||||||
|
by Thomas Hahn
|
||||||
|
last modified 2 Mar 06 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "util.c"
|
||||||
|
|
||||||
|
#define Print(s) puts(s); fflush(stdout)
|
||||||
|
|
||||||
|
static Integrand integrand_;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void DoSample(count n, creal *x, real *f)
|
||||||
|
{
|
||||||
|
neval_ += n;
|
||||||
|
while( n-- ) {
|
||||||
|
integrand_(&ndim_, x, &ncomp_, f);
|
||||||
|
x += ndim_;
|
||||||
|
f += ncomp_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
#include "common.c"
|
||||||
|
|
||||||
|
Extern void EXPORT(Cuhre)(ccount ndim, ccount ncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
ccount key,
|
||||||
|
count *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
ndim_ = ndim;
|
||||||
|
ncomp_ = ncomp;
|
||||||
|
|
||||||
|
if( BadComponent(ncomp) || BadDimension(ndim) ) *pfail = -1;
|
||||||
|
else {
|
||||||
|
neval_ = 0;
|
||||||
|
integrand_ = integrand;
|
||||||
|
|
||||||
|
*pfail = Integrate(epsrel, Max(epsabs, NOTZERO),
|
||||||
|
flags, mineval, maxeval, key,
|
||||||
|
integral, error, prob);
|
||||||
|
*pnregions = nregions_;
|
||||||
|
*pneval = neval_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
Extern void EXPORT(cuhre)(ccount *pndim, ccount *pncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal *pepsrel, creal *pepsabs,
|
||||||
|
cint *pflags, cnumber *pmineval, cnumber *pmaxeval,
|
||||||
|
ccount *pkey,
|
||||||
|
count *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
EXPORT(Cuhre)(*pndim, *pncomp, integrand,
|
||||||
|
*pepsrel, *pepsabs,
|
||||||
|
*pflags, *pmineval, *pmaxeval,
|
||||||
|
*pkey,
|
||||||
|
pnregions, pneval, pfail,
|
||||||
|
integral, error, prob);
|
||||||
|
}
|
||||||
|
|
||||||
272
src/external/libCuba/src/cuhre/Integrate.c
vendored
Normal file
272
src/external/libCuba/src/cuhre/Integrate.c
vendored
Normal file
@ -0,0 +1,272 @@
|
|||||||
|
/*
|
||||||
|
Integrate.c
|
||||||
|
integrate over the unit hypercube
|
||||||
|
this file is part of Cuhre
|
||||||
|
last modified 8 Apr 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#define POOLSIZE 1024
|
||||||
|
|
||||||
|
static int Integrate(creal epsrel, creal epsabs,
|
||||||
|
cint flags, number mineval, cnumber maxeval, ccount key,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
typedef struct pool {
|
||||||
|
struct pool *next;
|
||||||
|
Region region[POOLSIZE];
|
||||||
|
} Pool;
|
||||||
|
|
||||||
|
count dim, comp, ncur, nregions, ipool, npool;
|
||||||
|
int fail = 1;
|
||||||
|
Rule rule;
|
||||||
|
Totals totals[NCOMP];
|
||||||
|
Pool *cur = NULL, *pool;
|
||||||
|
Region *region;
|
||||||
|
|
||||||
|
if( VERBOSE > 1 ) {
|
||||||
|
char s[256];
|
||||||
|
sprintf(s, "Cuhre input parameters:\n"
|
||||||
|
" ndim " COUNT "\n ncomp " COUNT "\n"
|
||||||
|
" epsrel " REAL "\n epsabs " REAL "\n"
|
||||||
|
" flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n"
|
||||||
|
" key " COUNT,
|
||||||
|
ndim_, ncomp_,
|
||||||
|
epsrel, epsabs,
|
||||||
|
flags, mineval, maxeval,
|
||||||
|
key);
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( setjmp(abort_) ) goto abort;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
if( key == 13 && ndim_ == 2 ) Rule13Alloc(&rule);
|
||||||
|
else if( key == 11 && ndim_ == 3 ) Rule11Alloc(&rule);
|
||||||
|
else if( key == 9 ) Rule9Alloc(&rule);
|
||||||
|
else if( key == 7 ) Rule7Alloc(&rule);
|
||||||
|
else {
|
||||||
|
if( ndim_ == 2 ) Rule13Alloc(&rule);
|
||||||
|
else if( ndim_ == 3 ) Rule11Alloc(&rule);
|
||||||
|
else Rule9Alloc(&rule);
|
||||||
|
}
|
||||||
|
|
||||||
|
Alloc(rule.x, rule.n*(ndim_ + ncomp_));
|
||||||
|
rule.f = rule.x + rule.n*ndim_;
|
||||||
|
|
||||||
|
mineval = IMax(mineval, rule.n + 1);
|
||||||
|
|
||||||
|
Alloc(cur, 1);
|
||||||
|
cur->next = NULL;
|
||||||
|
ncur = 1;
|
||||||
|
|
||||||
|
region = cur->region;
|
||||||
|
region->div = 0;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
Bounds *b = ®ion->bounds[dim];
|
||||||
|
b->lower = 0;
|
||||||
|
b->upper = 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
Sample(&rule, region, flags);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
Result *r = ®ion->result[comp];
|
||||||
|
tot->avg = tot->lastavg = tot->guess = r->avg;
|
||||||
|
tot->err = tot->lasterr = r->err;
|
||||||
|
tot->weightsum = 1/Max(Sq(r->err), NOTZERO);
|
||||||
|
tot->avgsum = tot->weightsum*r->avg;
|
||||||
|
tot->chisq = tot->chisqsum = tot->chisum = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( nregions = 1; ; ++nregions ) {
|
||||||
|
count maxcomp, bisectdim;
|
||||||
|
real maxratio, maxerr;
|
||||||
|
Result result[NCOMP];
|
||||||
|
Region *regionL, *regionR;
|
||||||
|
Bounds *bL, *bR;
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[128 + 128*NCOMP], *p = s;
|
||||||
|
|
||||||
|
p += sprintf(p, "\n"
|
||||||
|
"Iteration " COUNT ": " NUMBER " integrand evaluations so far",
|
||||||
|
nregions, neval_);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cTotals *tot = &totals[comp];
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)",
|
||||||
|
comp + 1, tot->avg, tot->err, tot->chisq, nregions - 1);
|
||||||
|
}
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
maxratio = -INFTY;
|
||||||
|
maxcomp = 0;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
creal ratio = totals[comp].err/MaxErr(totals[comp].avg);
|
||||||
|
if( ratio > maxratio ) {
|
||||||
|
maxratio = ratio;
|
||||||
|
maxcomp = comp;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( maxratio <= 1 && neval_ >= mineval ) {
|
||||||
|
fail = 0;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( neval_ >= maxeval ) break;
|
||||||
|
|
||||||
|
maxerr = -INFTY;
|
||||||
|
regionL = cur->region;
|
||||||
|
npool = ncur;
|
||||||
|
for( pool = cur; pool; npool = POOLSIZE, pool = pool->next )
|
||||||
|
for( ipool = 0; ipool < npool; ++ipool ) {
|
||||||
|
Region *region = &pool->region[ipool];
|
||||||
|
creal err = region->result[maxcomp].err;
|
||||||
|
if( err > maxerr ) {
|
||||||
|
maxerr = err;
|
||||||
|
regionL = region;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( ncur == POOLSIZE ) {
|
||||||
|
Pool *prev = cur;
|
||||||
|
Alloc(cur, 1);
|
||||||
|
cur->next = prev;
|
||||||
|
ncur = 0;
|
||||||
|
}
|
||||||
|
regionR = &cur->region[ncur++];
|
||||||
|
|
||||||
|
regionR->div = ++regionL->div;
|
||||||
|
ResCopy(result, regionL->result);
|
||||||
|
VecCopy(regionR->bounds, regionL->bounds);
|
||||||
|
|
||||||
|
bisectdim = result[maxcomp].bisectdim;
|
||||||
|
bL = ®ionL->bounds[bisectdim];
|
||||||
|
bR = ®ionR->bounds[bisectdim];
|
||||||
|
bL->upper = bR->lower = .5*(bL->upper + bL->lower);
|
||||||
|
|
||||||
|
Sample(&rule, regionL, flags);
|
||||||
|
Sample(&rule, regionR, flags);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = &result[comp];
|
||||||
|
Result *rL = ®ionL->result[comp];
|
||||||
|
Result *rR = ®ionR->result[comp];
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
real diff, err, w, avg, sigsq;
|
||||||
|
|
||||||
|
tot->lastavg += diff = rL->avg + rR->avg - r->avg;
|
||||||
|
|
||||||
|
diff = fabs(.25*diff);
|
||||||
|
err = rL->err + rR->err;
|
||||||
|
if( err > 0 ) {
|
||||||
|
creal c = 1 + 2*diff/err;
|
||||||
|
rL->err *= c;
|
||||||
|
rR->err *= c;
|
||||||
|
}
|
||||||
|
rL->err += diff;
|
||||||
|
rR->err += diff;
|
||||||
|
tot->lasterr += rL->err + rR->err - r->err;
|
||||||
|
|
||||||
|
tot->weightsum += w = 1/Max(Sq(tot->lasterr), NOTZERO);
|
||||||
|
sigsq = 1/tot->weightsum;
|
||||||
|
tot->avgsum += w*tot->lastavg;
|
||||||
|
avg = sigsq*tot->avgsum;
|
||||||
|
tot->chisum += w *= tot->lastavg - tot->guess;
|
||||||
|
tot->chisqsum += w*tot->lastavg;
|
||||||
|
tot->chisq = tot->chisqsum - avg*tot->chisum;
|
||||||
|
|
||||||
|
if( LAST ) {
|
||||||
|
tot->avg = tot->lastavg;
|
||||||
|
tot->err = tot->lasterr;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
tot->avg = avg;
|
||||||
|
tot->err = sqrt(sigsq);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cTotals *tot = &totals[comp];
|
||||||
|
integral[comp] = tot->avg;
|
||||||
|
error[comp] = tot->err;
|
||||||
|
prob[comp] = ChiSquare(tot->chisq, nregions - 1);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( REGIONS ) {
|
||||||
|
MLPutFunction(stdlink, "List", 2);
|
||||||
|
MLPutFunction(stdlink, "List", nregions);
|
||||||
|
|
||||||
|
npool = ncur;
|
||||||
|
for( pool = cur; pool; npool = POOLSIZE, pool = pool->next )
|
||||||
|
for( ipool = 0; ipool < npool; ++ipool ) {
|
||||||
|
Region const *region = &pool->region[ipool];
|
||||||
|
real lower[NDIM], upper[NDIM];
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
lower[dim] = b->lower;
|
||||||
|
upper[dim] = b->upper;
|
||||||
|
}
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "Cuba`Cuhre`region", 3);
|
||||||
|
MLPutRealList(stdlink, lower, ndim_);
|
||||||
|
MLPutRealList(stdlink, upper, ndim_);
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "List", ncomp_);
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
real res[] = {r->avg, r->err};
|
||||||
|
MLPutRealList(stdlink, res, Elements(res));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
abort:
|
||||||
|
#endif
|
||||||
|
|
||||||
|
while( (pool = cur) ) {
|
||||||
|
cur = cur->next;
|
||||||
|
free(pool);
|
||||||
|
}
|
||||||
|
|
||||||
|
free(rule.x);
|
||||||
|
RuleFree(&rule);
|
||||||
|
|
||||||
|
nregions_ = nregions;
|
||||||
|
|
||||||
|
return fail;
|
||||||
|
}
|
||||||
|
|
||||||
744
src/external/libCuba/src/cuhre/Rule.c
vendored
Normal file
744
src/external/libCuba/src/cuhre/Rule.c
vendored
Normal file
@ -0,0 +1,744 @@
|
|||||||
|
/*
|
||||||
|
Rule.c
|
||||||
|
integration with cubature rules
|
||||||
|
code lifted with minor modifications from DCUHRE
|
||||||
|
by J. Berntsen, T. Espelid, and A. Genz
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
enum { nrules = 5 };
|
||||||
|
|
||||||
|
#define TYPEDEFSET \
|
||||||
|
typedef struct { \
|
||||||
|
count n; \
|
||||||
|
real weight[nrules], scale[nrules], norm[nrules]; \
|
||||||
|
real gen[NDIM]; \
|
||||||
|
} Set
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void RuleFree(Rule *rule)
|
||||||
|
{
|
||||||
|
free(rule->first);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule13Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[][nrules] = {
|
||||||
|
{ .00844923090033615, .3213775489050763, .3372900883288987,
|
||||||
|
-.8264123822525677, .6539094339575232 },
|
||||||
|
{ .023771474018994404, -.1767341636743844, -.1644903060344491,
|
||||||
|
.306583861409436, -.2041614154424632},
|
||||||
|
{ .02940016170142405, .07347600537466073, .07707849911634623,
|
||||||
|
.002389292538329435, -.174698151579499 },
|
||||||
|
{ .006644436465817374, -.03638022004364754, -.03804478358506311,
|
||||||
|
-.1343024157997222, .03937939671417803 },
|
||||||
|
{ .0042536044255016, .021252979220987123, .02223559940380806,
|
||||||
|
.08833366840533902, .006974520545933992 },
|
||||||
|
{ 0, .1460984204026913, .1480693879765931,
|
||||||
|
0, 0 },
|
||||||
|
{ .0040664827465935255, .017476132861520992, 4.467143702185815e-6,
|
||||||
|
.0009786283074168292, .0066677021717782585 },
|
||||||
|
{ .03362231646315497, .1444954045641582, .150894476707413,
|
||||||
|
-.1319227889147519, .05512960621544304 },
|
||||||
|
{ .033200804136503725, .0001307687976001325, 3.6472001075162155e-5,
|
||||||
|
.00799001220015063, .05443846381278608 },
|
||||||
|
{ .014093686924979677, .0005380992313941161, .000577719899901388,
|
||||||
|
.0033917470797606257, .02310903863953934 },
|
||||||
|
{ .000977069770327625, .0001042259576889814, .0001041757313688177,
|
||||||
|
.0022949157182832643, .01506937747477189 },
|
||||||
|
{ .007531996943580376, -.001401152865045733, -.001452822267047819,
|
||||||
|
-.01358584986119197, -.060570216489018905 },
|
||||||
|
{ .02577183086722915, .008041788181514763, .008338339968783704,
|
||||||
|
.04025866859057809, .04225737654686337},
|
||||||
|
{ .015625, -.1420416552759383, -.147279632923196,
|
||||||
|
.003760268580063992, .02561989142123099 }
|
||||||
|
};
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.12585646717265545, .3506966822267133,
|
||||||
|
.4795480315809981, .4978005239276064,
|
||||||
|
.25, .07972723291487795,
|
||||||
|
.1904495567970094, .3291384627633596,
|
||||||
|
.43807365825146577, .499121592026599,
|
||||||
|
.4895111329084231, .32461421628226944,
|
||||||
|
.43637106005656195, .1791307322940614,
|
||||||
|
.2833333333333333, .1038888888888889 };
|
||||||
|
|
||||||
|
enum { nsets = 14, ndim = 2 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
count n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
Copy(last->weight, w[0], nrules);
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[1], nrules);
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[2], nrules);
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[3], nrules);
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[4], nrules);
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[5], nrules);
|
||||||
|
last->gen[0] = g[4];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[6], nrules);
|
||||||
|
last->gen[0] = g[5];
|
||||||
|
last->gen[1] = g[5];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[7], nrules);
|
||||||
|
last->gen[0] = g[6];
|
||||||
|
last->gen[1] = g[6];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[8], nrules);
|
||||||
|
last->gen[0] = g[7];
|
||||||
|
last->gen[1] = g[7];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[9], nrules);
|
||||||
|
last->gen[0] = g[8];
|
||||||
|
last->gen[1] = g[8];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[10], nrules);
|
||||||
|
last->gen[0] = g[9];
|
||||||
|
last->gen[1] = g[9];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[11], nrules);
|
||||||
|
last->gen[0] = g[10];
|
||||||
|
last->gen[1] = g[11];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[12], nrules);
|
||||||
|
last->gen[0] = g[12];
|
||||||
|
last->gen[1] = g[13];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[13], nrules);
|
||||||
|
last->gen[0] = g[14];
|
||||||
|
last->gen[1] = g[15];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 10;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule11Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[][nrules] = {
|
||||||
|
{ .0009903847688882167, 1.715006248224684, 1.936014978949526,
|
||||||
|
.517082819560576, 2.05440450381852 },
|
||||||
|
{ .0084964717409851, -.3755893815889209, -.3673449403754268,
|
||||||
|
.01445269144914044, .013777599884901202 },
|
||||||
|
{ .00013587331735072814, .1488632145140549, .02929778657898176,
|
||||||
|
-.3601489663995932, -.576806291790441 },
|
||||||
|
{ .022982920777660364, -.2497046640620823, -.1151883520260315,
|
||||||
|
.3628307003418485, .03726835047700328 },
|
||||||
|
{ .004202649722286289, .1792501419135204, .05086658220872218,
|
||||||
|
.007148802650872729, .0068148789397772195 },
|
||||||
|
{ .0012671889041675774, .0034461267589738897, .04453911087786469,
|
||||||
|
-.09222852896022966, .057231697338518496 },
|
||||||
|
{ .0002109560854981544, -.005140483185555825, -.022878282571259,
|
||||||
|
.01719339732471725, -.044930187438112855 },
|
||||||
|
{ .016830857056410086, .006536017839876424, .02908926216345833,
|
||||||
|
-.102141653746035, .027292365738663484 },
|
||||||
|
{ .00021876823557504823, -.00065134549392297, -.002898884350669207,
|
||||||
|
-.007504397861080493, .000354747395055699 },
|
||||||
|
{ .009690420479796819, -.006304672433547204, -.028059634133074954,
|
||||||
|
.01648362537726711, .01571366799739551 },
|
||||||
|
{ .030773311284628138, .01266959399788263, .05638741361145884,
|
||||||
|
.05234610158469334, .049900992192785674 },
|
||||||
|
{ .0084974310856038, -.005454241018647931, -.02427469611942451,
|
||||||
|
.014454323316130661, .0137791555266677 },
|
||||||
|
{ .0017749535291258914, .004826995274768427, .021483070341828822,
|
||||||
|
.003019236275367777, .0028782064230998723 }
|
||||||
|
};
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.095, .25,
|
||||||
|
.375, .4,
|
||||||
|
.4975, .49936724991757,
|
||||||
|
.38968518428362114, .49998494965443835,
|
||||||
|
.3951318612385894, .22016983438253684,
|
||||||
|
.4774686911397297, .2189239229503431,
|
||||||
|
.4830546566815374, .2288552938881567 };
|
||||||
|
|
||||||
|
enum { nsets = 13, ndim = 3 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
count n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
Copy(last->weight, w[0], nrules);
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[1], nrules);
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[2], nrules);
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[3], nrules);
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[4], nrules);
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[5], nrules);
|
||||||
|
last->gen[0] = g[4];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[6], nrules);
|
||||||
|
last->gen[0] = g[5];
|
||||||
|
last->gen[1] = g[5];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[7], nrules);
|
||||||
|
last->gen[0] = g[6];
|
||||||
|
last->gen[1] = g[6];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[8], nrules);
|
||||||
|
last->gen[0] = g[7];
|
||||||
|
last->gen[1] = g[7];
|
||||||
|
last->gen[2] = g[7];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[9], nrules);
|
||||||
|
last->gen[0] = g[8];
|
||||||
|
last->gen[1] = g[8];
|
||||||
|
last->gen[2] = g[8];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[10], nrules);
|
||||||
|
last->gen[0] = g[9];
|
||||||
|
last->gen[1] = g[9];
|
||||||
|
last->gen[2] = g[9];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
|
||||||
|
Copy(last->weight, w[11], nrules);
|
||||||
|
last->gen[0] = g[10];
|
||||||
|
last->gen[1] = g[11];
|
||||||
|
last->gen[2] = g[11];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
|
||||||
|
Copy(last->weight, w[12], nrules);
|
||||||
|
last->gen[0] = g[12];
|
||||||
|
last->gen[1] = g[12];
|
||||||
|
last->gen[2] = g[13];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 4;
|
||||||
|
rule->errcoeff[1] = .5;
|
||||||
|
rule->errcoeff[2] = 3;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule9Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[] = {
|
||||||
|
-.0023611709677855117884, .11415390023857325268,
|
||||||
|
-.63833920076702389094, .74849988504685208004,
|
||||||
|
-.0014324017033399125142, .057471507864489725949,
|
||||||
|
-.14225104571434243234, -.062875028738286979989,
|
||||||
|
.254591133248959089, -1.207328566678236261,
|
||||||
|
.89567365764160676508, -.36479356986049146661,
|
||||||
|
.0035417564516782676826, -.072609367395893679605,
|
||||||
|
.10557491625218991012, .0021486025550098687713,
|
||||||
|
-.032268563892953949998, .010636783990231217481,
|
||||||
|
.014689102496143490175, .51134708346467591431,
|
||||||
|
.45976448120806344646, .18239678493024573331,
|
||||||
|
-.04508628929435784076, .21415883524352793401,
|
||||||
|
-.027351546526545644722, .054941067048711234101,
|
||||||
|
.11937596202570775297, .65089519391920250593,
|
||||||
|
.14744939829434460168, .057693384490973483573,
|
||||||
|
.034999626602143583822, -1.3868627719278281436,
|
||||||
|
-.2386668732575008879, .015532417276607053264,
|
||||||
|
.0035328099607090870236, .09231719987444221619,
|
||||||
|
.02254314464717892038, .013675773263272822361,
|
||||||
|
-.32544759695960125297, .0017708782258391338413,
|
||||||
|
.0010743012775049343856, .25150011495314791996 };
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.47795365790226950619, .20302858736911986780,
|
||||||
|
.44762735462617812882, .125,
|
||||||
|
.34303789878087814570 };
|
||||||
|
|
||||||
|
enum { nsets = 9 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
ccount ndim = ndim_;
|
||||||
|
ccount twondim = 1 << ndim;
|
||||||
|
count dim, n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
last->weight[0] = ndim*(ndim*(ndim*w[0] + w[1]) + w[2]) + w[3];
|
||||||
|
last->weight[1] = ndim*(ndim*(ndim*w[4] + w[5]) + w[6]) - w[7];
|
||||||
|
last->weight[2] = ndim*w[8] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*(ndim*w[9] + w[10]) - 1 + last->weight[0];
|
||||||
|
last->weight[4] = ndim*w[11] + 1 - last->weight[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = ndim*(ndim*w[12] + w[13]) + w[14];
|
||||||
|
last->weight[1] = ndim*(ndim*w[15] + w[16]) + w[17];
|
||||||
|
last->weight[2] = w[18] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*w[19] + w[20] + last->weight[0];
|
||||||
|
last->weight[4] = w[21] - last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = ndim*w[22] + w[23];
|
||||||
|
last->weight[1] = ndim*w[24] + w[25];
|
||||||
|
last->weight[2] = w[26] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*w[27] + w[28];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[29];
|
||||||
|
last->weight[1] = w[30];
|
||||||
|
last->weight[2] = -w[29];
|
||||||
|
last->weight[3] = w[31];
|
||||||
|
last->weight[4] = -w[29];
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[2] = w[32];
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = w[33] - ndim*w[12];
|
||||||
|
last->weight[1] = w[34] - ndim*w[15];
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = w[35] + last->weight[0];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = w[36];
|
||||||
|
last->weight[1] = w[37];
|
||||||
|
last->weight[2] = -w[37];
|
||||||
|
last->weight[3] = w[38];
|
||||||
|
last->weight[4] = -w[36];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
last->weight[0] = w[39];
|
||||||
|
last->weight[1] = w[40];
|
||||||
|
last->weight[2] = -w[40];
|
||||||
|
last->weight[3] = w[39];
|
||||||
|
last->weight[4] = -w[39];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
last->gen[2] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = twondim;
|
||||||
|
last->weight[0] = w[41]/twondim;
|
||||||
|
last->weight[1] = w[7]/twondim;
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = last->weight[0];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
last->gen[dim] = g[4];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 5;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule7Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[] = {
|
||||||
|
.019417866674748388428, -.40385257701150182546,
|
||||||
|
.64485668767465982223, .01177982690775806141,
|
||||||
|
-.18041318740733609012, -.088785828081335044443,
|
||||||
|
.056328645808285941374, -.0097089333373741942142,
|
||||||
|
-.99129176779582358138, -.17757165616267008889,
|
||||||
|
.12359398032043233572, .074978148702033690681,
|
||||||
|
.55489147051423559776, .088041241522692771226,
|
||||||
|
.021118358455513385083, -.0099302203239653333087,
|
||||||
|
-.064100053285010904179, .030381729038221007659,
|
||||||
|
.0058899134538790307051, -.0048544666686870971071,
|
||||||
|
.35514331232534017777 };
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.47795365790226950619, .20302858736911986780,
|
||||||
|
.375, .34303789878087814570 };
|
||||||
|
|
||||||
|
enum { nsets = 6 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
ccount ndim = ndim_;
|
||||||
|
ccount twondim = 1 << ndim;
|
||||||
|
count dim, n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
last->weight[0] = ndim*(ndim*w[0] + w[1]) + w[2];
|
||||||
|
last->weight[1] = ndim*(ndim*w[3] + w[4]) - w[5];
|
||||||
|
last->weight[2] = ndim*w[6] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*(ndim*w[7] + w[8]) - w[9];
|
||||||
|
last->weight[4] = 1 - last->weight[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[10];
|
||||||
|
last->weight[1] = w[11];
|
||||||
|
last->weight[2] = -w[10];
|
||||||
|
last->weight[3] = w[12];
|
||||||
|
last->weight[4] = -w[10];
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[13] - ndim*w[0];
|
||||||
|
last->weight[1] = w[14] - ndim*w[3];
|
||||||
|
last->weight[2] = w[15] - last->weight[1];
|
||||||
|
last->weight[3] = w[16] - ndim*w[7];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[2] = w[17];
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = -w[7];
|
||||||
|
last->weight[1] = w[18];
|
||||||
|
last->weight[2] = -w[18];
|
||||||
|
last->weight[3] = w[19];
|
||||||
|
last->weight[4] = w[7];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = twondim;
|
||||||
|
last->weight[0] = w[20]/twondim;
|
||||||
|
last->weight[1] = w[5]/twondim;
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = w[9]/twondim;
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
last->gen[dim] = g[3];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 5;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real *ExpandFS(cBounds *b, real *g, real *x)
|
||||||
|
{
|
||||||
|
count dim, ndim = ndim_;
|
||||||
|
|
||||||
|
next:
|
||||||
|
/* Compute centrally symmetric sum for permutation of G */
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
*x++ = (.5 + g[dim])*b[dim].lower + (.5 - g[dim])*b[dim].upper;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim; ) {
|
||||||
|
g[dim] = -g[dim];
|
||||||
|
if( g[dim++] < 0 ) goto next;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Find next distinct permutation of G and loop back for next sum.
|
||||||
|
Permutations are generated in reverse lexicographic order. */
|
||||||
|
|
||||||
|
for( dim = 1; dim < ndim; ++dim ) {
|
||||||
|
creal gd = g[dim];
|
||||||
|
if( g[dim - 1] > gd ) {
|
||||||
|
count i, ix, j = dim, dx = dim - 1;
|
||||||
|
for( i = 0; i < --j; ++i ) {
|
||||||
|
creal tmp = g[i];
|
||||||
|
g[i] = g[j];
|
||||||
|
g[j] = tmp;
|
||||||
|
if( tmp <= gd ) --dx;
|
||||||
|
if( g[i] > gd ) ix = i;
|
||||||
|
}
|
||||||
|
if( g[dx] <= gd ) dx = ix;
|
||||||
|
g[dim] = g[dx];
|
||||||
|
g[dx] = gd;
|
||||||
|
goto next;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Restore original order to generators */
|
||||||
|
|
||||||
|
for( dim = 0; dim < --ndim; ++dim ) {
|
||||||
|
creal tmp = g[dim];
|
||||||
|
g[dim] = g[ndim];
|
||||||
|
g[ndim] = tmp;
|
||||||
|
}
|
||||||
|
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Sample(cRule *rule, void *voidregion, cint flags)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
Region *const region = (Region *)voidregion;
|
||||||
|
creal vol = ldexp(1., -region->div);
|
||||||
|
|
||||||
|
real *x = rule->x, *f = rule->f;
|
||||||
|
Set *first = (Set *)rule->first, *last = (Set *)rule->last, *s;
|
||||||
|
creal *errcoeff = rule->errcoeff;
|
||||||
|
creal ratio = Sq(first[2].gen[0]/first[1].gen[0]);
|
||||||
|
|
||||||
|
ccount offset = 2*ndim_*ncomp_;
|
||||||
|
count dim, comp, rul, n, maxdim = 0;
|
||||||
|
real maxrange = 0;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
creal range = b->upper - b->lower;
|
||||||
|
if( range > maxrange ) {
|
||||||
|
maxrange = range;
|
||||||
|
maxdim = dim;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
if( s->n ) x = ExpandFS(region->bounds, s->gen, x);
|
||||||
|
|
||||||
|
DoSample(rule->n, rule->x, f);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Result *r = ®ion->result[comp];
|
||||||
|
real sum[nrules];
|
||||||
|
creal *f1 = f;
|
||||||
|
creal base = *f1*2*(1 - ratio);
|
||||||
|
real maxdiff = 0;
|
||||||
|
count bisectdim = maxdim;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
creal *fp = f1 + ncomp_;
|
||||||
|
creal *fm = fp + ncomp_;
|
||||||
|
creal fourthdiff = fabs(base +
|
||||||
|
ratio*(fp[0] + fm[0]) - (fp[offset] + fm[offset]));
|
||||||
|
f1 = fm;
|
||||||
|
if( fourthdiff > maxdiff ) {
|
||||||
|
maxdiff = fourthdiff;
|
||||||
|
bisectdim = dim;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
r->bisectdim = bisectdim;
|
||||||
|
|
||||||
|
f1 = f++;
|
||||||
|
Zap(sum);
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( n = s->n; n; --n ) {
|
||||||
|
creal fun = *f1;
|
||||||
|
f1 += ncomp_;
|
||||||
|
for( rul = 0; rul < nrules; ++rul )
|
||||||
|
sum[rul] += fun*s->weight[rul];
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Search for the null rule, in the linear space spanned by two
|
||||||
|
successive null rules in our sequence, which gives the greatest
|
||||||
|
error estimate among all normalized (1-norm) null rules in this
|
||||||
|
space. */
|
||||||
|
|
||||||
|
for( rul = 1; rul < nrules - 1; ++rul ) {
|
||||||
|
real maxerr = 0;
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
maxerr = Max(maxerr,
|
||||||
|
fabs(sum[rul + 1] + s->scale[rul]*sum[rul])*s->norm[rul]);
|
||||||
|
sum[rul] = maxerr;
|
||||||
|
}
|
||||||
|
|
||||||
|
r->avg = vol*sum[0];
|
||||||
|
r->err = vol*(
|
||||||
|
(errcoeff[0]*sum[1] <= sum[2] && errcoeff[0]*sum[2] <= sum[3]) ?
|
||||||
|
errcoeff[1]*sum[1] :
|
||||||
|
errcoeff[2]*Max(Max(sum[1], sum[2]), sum[3]) );
|
||||||
|
}
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
char s[64*NDIM + 128*NCOMP], *p = s;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
p += sprintf(p,
|
||||||
|
(dim == 0) ? "\nRegion (" REALF ") - (" REALF ")" :
|
||||||
|
"\n (" REALF ") - (" REALF ")",
|
||||||
|
b->lower, b->upper);
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL, comp + 1, r->avg, r->err);
|
||||||
|
}
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
50
src/external/libCuba/src/cuhre/common.c
vendored
Normal file
50
src/external/libCuba/src/cuhre/common.c
vendored
Normal file
@ -0,0 +1,50 @@
|
|||||||
|
/*
|
||||||
|
common.c
|
||||||
|
includes most of the modules
|
||||||
|
this file is part of Cuhre
|
||||||
|
last modified 14 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "ChiSquare.c"
|
||||||
|
#include "Rule.c"
|
||||||
|
#include "Integrate.c"
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadDimension(ccount ndim)
|
||||||
|
{
|
||||||
|
#if NDIM > 0
|
||||||
|
if( ndim > NDIM ) return true;
|
||||||
|
#endif
|
||||||
|
return ndim < 2;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadComponent(cint ncomp)
|
||||||
|
{
|
||||||
|
#if NCOMP > 0
|
||||||
|
if( ncomp > NCOMP ) return true;
|
||||||
|
#endif
|
||||||
|
return ncomp < 1;
|
||||||
|
}
|
||||||
|
|
||||||
75
src/external/libCuba/src/cuhre/decl.h
vendored
Normal file
75
src/external/libCuba/src/cuhre/decl.h
vendored
Normal file
@ -0,0 +1,75 @@
|
|||||||
|
/*
|
||||||
|
decl.h
|
||||||
|
Type declarations
|
||||||
|
this file is part of Cuhre
|
||||||
|
last modified 8 Apr 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "stddecl.h"
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real avg, err;
|
||||||
|
count bisectdim;
|
||||||
|
} Result;
|
||||||
|
|
||||||
|
typedef const Result cResult;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real avg, err, lastavg, lasterr;
|
||||||
|
real weightsum, avgsum;
|
||||||
|
real guess, chisum, chisqsum, chisq;
|
||||||
|
} Totals;
|
||||||
|
|
||||||
|
typedef const Totals cTotals;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real lower, upper;
|
||||||
|
} Bounds;
|
||||||
|
|
||||||
|
typedef const Bounds cBounds;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real *x, *f;
|
||||||
|
void *first, *last;
|
||||||
|
real errcoeff[3];
|
||||||
|
count n;
|
||||||
|
} Rule;
|
||||||
|
|
||||||
|
typedef const Rule cRule;
|
||||||
|
|
||||||
|
|
||||||
|
#define TYPEDEFREGION \
|
||||||
|
typedef struct region { \
|
||||||
|
count div; \
|
||||||
|
Result result[NCOMP]; \
|
||||||
|
Bounds bounds[NDIM]; \
|
||||||
|
} Region
|
||||||
|
|
||||||
|
|
||||||
|
typedef void (*Integrand)(ccount *, creal *, ccount *, real *);
|
||||||
|
|
||||||
38
src/external/libCuba/src/cuhre/util.c
vendored
Normal file
38
src/external/libCuba/src/cuhre/util.c
vendored
Normal file
@ -0,0 +1,38 @@
|
|||||||
|
/*
|
||||||
|
util.c
|
||||||
|
Utility functions
|
||||||
|
this file is part of Cuhre
|
||||||
|
last modified 9 Jan 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "decl.h"
|
||||||
|
|
||||||
|
static count ndim_, ncomp_, nregions_;
|
||||||
|
static number neval_;
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
#include "debug.c"
|
||||||
|
#endif
|
||||||
|
|
||||||
145
src/external/libCuba/src/divonne/Divonne.c
vendored
Normal file
145
src/external/libCuba/src/divonne/Divonne.c
vendored
Normal file
@ -0,0 +1,145 @@
|
|||||||
|
/*
|
||||||
|
Divonne.c
|
||||||
|
Multidimensional integration by partitioning
|
||||||
|
originally by J.H. Friedman and M.H. Wright
|
||||||
|
(CERNLIB subroutine D151)
|
||||||
|
this version by Thomas Hahn
|
||||||
|
last modified 2 Mar 06 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "util.c"
|
||||||
|
|
||||||
|
#define Print(s) puts(s); fflush(stdout)
|
||||||
|
|
||||||
|
static Integrand integrand_;
|
||||||
|
static PeakFinder peakfinder_;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void DoSample(number n, ccount ldx, creal *x, real *f)
|
||||||
|
{
|
||||||
|
neval_ += n;
|
||||||
|
while( n-- ) {
|
||||||
|
integrand_(&ndim_, x, &ncomp_, f, &phase_);
|
||||||
|
x += ldx;
|
||||||
|
f += ncomp_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline count SampleExtra(cBounds *b)
|
||||||
|
{
|
||||||
|
number n = nextra_;
|
||||||
|
peakfinder_(&ndim_, b, &n, xextra_);
|
||||||
|
DoSample(n, ldxgiven_, xextra_, fextra_);
|
||||||
|
return n;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
#include "common.c"
|
||||||
|
|
||||||
|
Extern void EXPORT(Divonne)(ccount ndim, ccount ncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
cint key1, cint key2, cint key3, ccount maxpass,
|
||||||
|
creal border, creal maxchisq, creal mindeviation,
|
||||||
|
cnumber ngiven, ccount ldxgiven, real *xgiven,
|
||||||
|
cnumber nextra, PeakFinder peakfinder,
|
||||||
|
int *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
ndim_ = ndim;
|
||||||
|
ncomp_ = ncomp;
|
||||||
|
|
||||||
|
if( BadComponent(ncomp) ||
|
||||||
|
BadDimension(ndim, flags, key1) ||
|
||||||
|
BadDimension(ndim, flags, key2) ||
|
||||||
|
((key3 & -2) && BadDimension(ndim, flags, key3)) ) *pfail = -1;
|
||||||
|
else {
|
||||||
|
neval_ = neval_opt_ = neval_cut_ = 0;
|
||||||
|
integrand_ = integrand;
|
||||||
|
peakfinder_ = peakfinder;
|
||||||
|
border_.lower = border;
|
||||||
|
border_.upper = 1 - border_.lower;
|
||||||
|
ngiven_ = ngiven;
|
||||||
|
xgiven_ = NULL;
|
||||||
|
ldxgiven_ = IMax(ldxgiven, ndim_);
|
||||||
|
nextra_ = nextra;
|
||||||
|
|
||||||
|
if( ngiven + nextra ) {
|
||||||
|
cnumber nxgiven = ngiven*ldxgiven;
|
||||||
|
cnumber nxextra = nextra*ldxgiven;
|
||||||
|
cnumber nfgiven = ngiven*ncomp;
|
||||||
|
cnumber nfextra = nextra*ncomp;
|
||||||
|
|
||||||
|
Alloc(xgiven_, nxgiven + nxextra + nfgiven + nfextra);
|
||||||
|
xextra_ = xgiven_ + nxgiven;
|
||||||
|
fgiven_ = xextra_ + nxextra;
|
||||||
|
fextra_ = fgiven_ + nfgiven;
|
||||||
|
|
||||||
|
if( nxgiven ) {
|
||||||
|
phase_ = 0;
|
||||||
|
Copy(xgiven_, xgiven, nxgiven);
|
||||||
|
DoSample(ngiven_, ldxgiven_, xgiven_, fgiven_);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
*pfail = Integrate(epsrel, Max(epsabs, NOTZERO),
|
||||||
|
flags, mineval, maxeval, key1, key2, key3, maxpass,
|
||||||
|
maxchisq, mindeviation,
|
||||||
|
integral, error, prob);
|
||||||
|
*pnregions = nregions_;
|
||||||
|
*pneval = neval_;
|
||||||
|
|
||||||
|
if( xgiven_ ) free(xgiven_);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
Extern void EXPORT(divonne)(ccount *pndim, ccount *pncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal *pepsrel, creal *pepsabs,
|
||||||
|
cint *pflags, cnumber *pmineval, cnumber *pmaxeval,
|
||||||
|
cint *pkey1, cint *pkey2, cint *pkey3, ccount *pmaxpass,
|
||||||
|
creal *pborder, creal *pmaxchisq, creal *pmindeviation,
|
||||||
|
cnumber *pngiven, ccount *pldxgiven, real *xgiven,
|
||||||
|
cnumber *pnextra, PeakFinder peakfinder,
|
||||||
|
int *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
EXPORT(Divonne)(*pndim, *pncomp,
|
||||||
|
integrand,
|
||||||
|
*pepsrel, *pepsabs,
|
||||||
|
*pflags, *pmineval, *pmaxeval,
|
||||||
|
*pkey1, *pkey2, *pkey3, *pmaxpass,
|
||||||
|
*pborder, *pmaxchisq, *pmindeviation,
|
||||||
|
*pngiven, *pldxgiven, xgiven,
|
||||||
|
*pnextra, peakfinder,
|
||||||
|
pnregions, pneval, pfail,
|
||||||
|
integral, error, prob);
|
||||||
|
}
|
||||||
|
|
||||||
199
src/external/libCuba/src/divonne/Explore.c
vendored
Normal file
199
src/external/libCuba/src/divonne/Explore.c
vendored
Normal file
@ -0,0 +1,199 @@
|
|||||||
|
/*
|
||||||
|
Explore.c
|
||||||
|
sample region, determine min and max, split if necessary
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 25 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real fmin, fmax;
|
||||||
|
real *xmin, *xmax;
|
||||||
|
} Extrema;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static bool Explore(count iregion, cSamples *samples, cint depth, cint flags)
|
||||||
|
{
|
||||||
|
#define SPLICE (flags & 1)
|
||||||
|
#define HAVESAMPLES (flags & 2)
|
||||||
|
|
||||||
|
TYPEDEFREGION;
|
||||||
|
|
||||||
|
count n, dim, comp, maxcomp;
|
||||||
|
Extrema extrema[NCOMP];
|
||||||
|
Result *r;
|
||||||
|
real *x, *f;
|
||||||
|
real halfvol, maxerr;
|
||||||
|
Region *region;
|
||||||
|
Bounds *bounds;
|
||||||
|
Result *result;
|
||||||
|
|
||||||
|
/* needed as of gcc 3.3 to make gcc correctly address region #@$&! */
|
||||||
|
sizeof(*region);
|
||||||
|
|
||||||
|
if( SPLICE ) {
|
||||||
|
if( nregions_ == size_ ) {
|
||||||
|
size_ += CHUNKSIZE;
|
||||||
|
ReAlloc(voidregion_, size_*sizeof(Region));
|
||||||
|
}
|
||||||
|
VecCopy(region_[nregions_].bounds, region_[iregion].bounds);
|
||||||
|
iregion = nregions_++;
|
||||||
|
}
|
||||||
|
region = ®ion_[iregion];
|
||||||
|
bounds = region->bounds;
|
||||||
|
result = region->result;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Extrema *e = &extrema[comp];
|
||||||
|
e->fmin = INFTY;
|
||||||
|
e->fmax = -INFTY;
|
||||||
|
e->xmin = e->xmax = NULL;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( !HAVESAMPLES ) {
|
||||||
|
real vol = 1;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = &bounds[dim];
|
||||||
|
vol *= b->upper - b->lower;
|
||||||
|
}
|
||||||
|
region->vol = vol;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Result *r = &result[comp];
|
||||||
|
r->fmin = INFTY;
|
||||||
|
r->fmax = -INFTY;
|
||||||
|
}
|
||||||
|
|
||||||
|
x = xgiven_;
|
||||||
|
f = fgiven_;
|
||||||
|
n = ngiven_;
|
||||||
|
if( nextra_ ) n += SampleExtra(bounds);
|
||||||
|
|
||||||
|
for( ; n; --n ) {
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = &bounds[dim];
|
||||||
|
if( x[dim] < b->lower || x[dim] > b->upper ) goto skip;
|
||||||
|
}
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Extrema *e = &extrema[comp];
|
||||||
|
creal y = f[comp];
|
||||||
|
if( y < e->fmin ) e->fmin = y, e->xmin = x;
|
||||||
|
if( y > e->fmax ) e->fmax = y, e->xmax = x;
|
||||||
|
}
|
||||||
|
skip:
|
||||||
|
x += ldxgiven_;
|
||||||
|
f += ncomp_;
|
||||||
|
}
|
||||||
|
|
||||||
|
samples->sampler(samples, bounds, vol);
|
||||||
|
}
|
||||||
|
|
||||||
|
x = samples->x;
|
||||||
|
f = samples->f;
|
||||||
|
for( n = samples->n; n; --n ) {
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Extrema *e = &extrema[comp];
|
||||||
|
creal y = *f++;
|
||||||
|
if( y < e->fmin ) e->fmin = y, e->xmin = x;
|
||||||
|
if( y > e->fmax ) e->fmax = y, e->xmax = x;
|
||||||
|
}
|
||||||
|
x += ndim_;
|
||||||
|
}
|
||||||
|
neval_opt_ -= neval_;
|
||||||
|
|
||||||
|
halfvol = .5*region->vol;
|
||||||
|
maxerr = -INFTY;
|
||||||
|
maxcomp = -1;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Extrema *e = &extrema[comp];
|
||||||
|
Result *r = &result[comp];
|
||||||
|
real xtmp[NDIM], ftmp, err;
|
||||||
|
|
||||||
|
if( e->xmin ) { /* not all NaNs */
|
||||||
|
selectedcomp_ = comp;
|
||||||
|
|
||||||
|
sign_ = 1;
|
||||||
|
VecCopy(xtmp, e->xmin);
|
||||||
|
ftmp = FindMinimum(bounds, xtmp, e->fmin);
|
||||||
|
if( ftmp < r->fmin ) {
|
||||||
|
r->fmin = ftmp;
|
||||||
|
VecCopy(r->xmin, xtmp);
|
||||||
|
}
|
||||||
|
|
||||||
|
sign_ = -1;
|
||||||
|
VecCopy(xtmp, e->xmax);
|
||||||
|
ftmp = -FindMinimum(bounds, xtmp, -e->fmax);
|
||||||
|
if( ftmp > r->fmax ) {
|
||||||
|
r->fmax = ftmp;
|
||||||
|
VecCopy(r->xmax, xtmp);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
r->avg = samples->avg[comp];
|
||||||
|
r->err = samples->err[comp];
|
||||||
|
r->spread = halfvol*(r->fmax - r->fmin);
|
||||||
|
|
||||||
|
err = r->spread/Max(fabs(r->avg), NOTZERO);
|
||||||
|
if( err > maxerr ) {
|
||||||
|
maxerr = err;
|
||||||
|
maxcomp = comp;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
neval_opt_ += neval_;
|
||||||
|
|
||||||
|
if( maxcomp == -1 ) { /* all NaNs */
|
||||||
|
region->depth = 0;
|
||||||
|
return false;
|
||||||
|
}
|
||||||
|
|
||||||
|
region->cutcomp = maxcomp;
|
||||||
|
r = ®ion->result[maxcomp];
|
||||||
|
if( halfvol*(r->fmin + r->fmax) > r->avg ) {
|
||||||
|
region->fminor = r->fmin;
|
||||||
|
region->fmajor = r->fmax;
|
||||||
|
region->xmajor = r->xmax - (real *)region->result;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
region->fminor = r->fmax;
|
||||||
|
region->fmajor = r->fmin;
|
||||||
|
region->xmajor = r->xmin - (real *)region->result;
|
||||||
|
}
|
||||||
|
|
||||||
|
region->depth = IDim(depth);
|
||||||
|
|
||||||
|
if( !HAVESAMPLES ) {
|
||||||
|
if( samples->weight*r->spread < r->err ||
|
||||||
|
r->spread < totals_[maxcomp].secondspread ) region->depth = 0;
|
||||||
|
if( region->depth == 0 )
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
totals_[comp].secondspread =
|
||||||
|
Max(totals_[comp].secondspread, result[comp].spread);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( region->depth ) Split(iregion, region->depth);
|
||||||
|
return true;
|
||||||
|
}
|
||||||
|
|
||||||
720
src/external/libCuba/src/divonne/FindMinimum.c
vendored
Normal file
720
src/external/libCuba/src/divonne/FindMinimum.c
vendored
Normal file
@ -0,0 +1,720 @@
|
|||||||
|
/*
|
||||||
|
FindMinimum.c
|
||||||
|
find minimum (maximum) of hyperrectangular region
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 7 Mar 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#define EPS 0x1p-52
|
||||||
|
#define RTEPS 0x1p-26
|
||||||
|
#define QEPS 0x1p-13
|
||||||
|
|
||||||
|
#define DELTA 0x1p-16
|
||||||
|
#define RTDELTA 0x1p-8
|
||||||
|
#define QDELTA 0x1p-4
|
||||||
|
|
||||||
|
/*
|
||||||
|
#define DELTA 1e-5
|
||||||
|
#define RTDELTA 3.1622776601683791e-3
|
||||||
|
#define QDELTA 5.6234132519034912e-2
|
||||||
|
*/
|
||||||
|
|
||||||
|
#define SUFTOL 8*QEPS*QDELTA
|
||||||
|
#define FTOL 5e-2
|
||||||
|
#define GTOL 1e-2
|
||||||
|
|
||||||
|
#define Hessian(i, j) hessian[(i)*ndim_ + j]
|
||||||
|
|
||||||
|
#define Tag(x) ((x) | 0x8000)
|
||||||
|
#define Untag(x) ((x) & 0x7fff)
|
||||||
|
#define TaggedQ(x) ((x) & 0x8000)
|
||||||
|
|
||||||
|
typedef struct { real dx, f; } Point;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real SignSample(real *x)
|
||||||
|
{
|
||||||
|
return sign_*Sample(x);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real Dot(ccount n, creal *a, creal *b)
|
||||||
|
{
|
||||||
|
real sum = 0;
|
||||||
|
count i;
|
||||||
|
for( i = 0; i < n; ++i ) sum += a[i]*b[i];
|
||||||
|
return sum;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real Length(ccount n, creal *vec)
|
||||||
|
{
|
||||||
|
return sqrt(Dot(n, vec, vec));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void LinearSolve(ccount n, creal *hessian,
|
||||||
|
creal *grad, real *p)
|
||||||
|
{
|
||||||
|
int i, j;
|
||||||
|
real dir;
|
||||||
|
|
||||||
|
for( i = 0; i < n; ++i ) {
|
||||||
|
dir = -grad[i];
|
||||||
|
for( j = 0; j < i; ++j )
|
||||||
|
dir -= Hessian(i, j)*p[j];
|
||||||
|
p[i] = dir;
|
||||||
|
}
|
||||||
|
|
||||||
|
while( --i >= 0 ) {
|
||||||
|
if( Hessian(i, i) <= 0 ) return;
|
||||||
|
dir = p[i]/Hessian(i, i);
|
||||||
|
for( j = i + 1; j < n; ++j )
|
||||||
|
dir -= Hessian(j, i)*p[j];
|
||||||
|
p[i] = dir;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void RenormalizeCholesky(ccount n, real *hessian,
|
||||||
|
real *z, real alpha)
|
||||||
|
{
|
||||||
|
count i, j;
|
||||||
|
|
||||||
|
for( i = 0; i < n; ++i ) {
|
||||||
|
creal dir = z[i];
|
||||||
|
real beta = alpha*dir;
|
||||||
|
real gamma = Hessian(i, i);
|
||||||
|
real gammanew = Hessian(i, i) += beta*dir;
|
||||||
|
|
||||||
|
if( i + 1 >= n || gammanew < 0 ||
|
||||||
|
(gammanew < 1 && gamma > DBL_MAX*gammanew) ) return;
|
||||||
|
|
||||||
|
gamma /= gammanew;
|
||||||
|
beta /= gammanew;
|
||||||
|
alpha *= gamma;
|
||||||
|
|
||||||
|
if( gamma < .25 ) {
|
||||||
|
for( j = i + 1; j < n; ++j ) {
|
||||||
|
real delta = beta*z[j];
|
||||||
|
z[j] -= dir*Hessian(j, i);
|
||||||
|
Hessian(j, i) = Hessian(j, i)*gamma + delta;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
for( j = i + 1; j < n; ++j ) {
|
||||||
|
z[j] -= dir*Hessian(j, i);
|
||||||
|
Hessian(j, i) += beta*z[j];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void UpdateCholesky(ccount n, real *hessian,
|
||||||
|
real *z, real *p)
|
||||||
|
{
|
||||||
|
int i, j;
|
||||||
|
real gamma = 0;
|
||||||
|
|
||||||
|
for( i = 0; i < n; ++i ) {
|
||||||
|
real dir = z[i];
|
||||||
|
for( j = 0; j < i; ++j )
|
||||||
|
dir -= Hessian(i, j)*p[j];
|
||||||
|
p[i] = dir;
|
||||||
|
gamma += Sq(dir)/Hessian(i, i);
|
||||||
|
}
|
||||||
|
gamma = Max(fabs(1 - gamma), EPS);
|
||||||
|
|
||||||
|
while( --i >= 0 ) {
|
||||||
|
creal dir = z[i] = p[i];
|
||||||
|
real beta = dir/Hessian(i, i);
|
||||||
|
creal gammanew = gamma + dir*beta;
|
||||||
|
Hessian(i, i) *= gamma/gammanew;
|
||||||
|
beta /= gamma;
|
||||||
|
gamma = gammanew;
|
||||||
|
for( j = i + 1; j < n; ++j ) {
|
||||||
|
creal delta = beta*z[j];
|
||||||
|
z[j] += dir*Hessian(j, i);
|
||||||
|
Hessian(j, i) -= delta;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void BFGS(ccount n, real *hessian,
|
||||||
|
creal *gnew, creal *g, real *p, creal dx)
|
||||||
|
{
|
||||||
|
real y[NDIM], c;
|
||||||
|
count i, j;
|
||||||
|
|
||||||
|
for( i = 0; i < n; ++i )
|
||||||
|
y[i] = gnew[i] - g[i];
|
||||||
|
c = dx*Dot(n, y, p);
|
||||||
|
if( c < 1e-10 ) return;
|
||||||
|
RenormalizeCholesky(n, hessian, y, 1/c);
|
||||||
|
|
||||||
|
c = Dot(n, g, p);
|
||||||
|
if( c >= 0 ) return;
|
||||||
|
c = 1/sqrt(-c);
|
||||||
|
for( i = 0; i < n; ++i )
|
||||||
|
y[i] = c*g[i];
|
||||||
|
UpdateCholesky(n, hessian, y, p);
|
||||||
|
|
||||||
|
for( i = 0; i < n - 1; ++i )
|
||||||
|
for( j = i + 1; j < n; ++j )
|
||||||
|
Hessian(i, j) = Hessian(j, i);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Gradient(ccount nfree, ccount *ifree,
|
||||||
|
cBounds *b, real *x, creal y, real *grad)
|
||||||
|
{
|
||||||
|
count i;
|
||||||
|
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = Untag(ifree[i]);
|
||||||
|
creal xd = x[dim];
|
||||||
|
creal delta = (b[dim].upper - xd < DELTA) ? -DELTA : DELTA;
|
||||||
|
x[dim] += delta;
|
||||||
|
grad[i] = (SignSample(x) - y)/delta;
|
||||||
|
x[dim] = xd;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static Point LineSearch(ccount nfree, ccount *ifree,
|
||||||
|
creal *p, creal *xini, real fini, real *x,
|
||||||
|
real step, creal range, creal grad,
|
||||||
|
creal ftol, creal xtol, creal gtol)
|
||||||
|
{
|
||||||
|
real tol = ftol, tol2 = tol + tol;
|
||||||
|
Point cur = {0, fini};
|
||||||
|
|
||||||
|
VecCopy(x, xini);
|
||||||
|
|
||||||
|
/* don't even try if
|
||||||
|
a) we'd walk backwards,
|
||||||
|
b) the range to explore is too small,
|
||||||
|
c) the gradient is positive, i.e. we'd move uphill */
|
||||||
|
|
||||||
|
if( step > 0 && range > tol2 && grad <= 0 ) {
|
||||||
|
creal eps = RTEPS*fabs(range) + ftol;
|
||||||
|
creal mingrad = -1e-4*grad, maxgrad = -gtol*grad;
|
||||||
|
|
||||||
|
real end = range + eps;
|
||||||
|
real maxstep = range - eps/(1 + RTEPS);
|
||||||
|
|
||||||
|
Point min = cur, v = cur, w = cur;
|
||||||
|
Point a = cur, b = {end, 0};
|
||||||
|
real a1, b1 = end;
|
||||||
|
|
||||||
|
/* distmin: distance along p from xini to the minimum,
|
||||||
|
u: second-lowest point,
|
||||||
|
v: third-lowest point,
|
||||||
|
a, b: interval in which the minimum is sought. */
|
||||||
|
|
||||||
|
real distmin = 0, dist, mid, q, r, s;
|
||||||
|
count i;
|
||||||
|
int shift;
|
||||||
|
bool first;
|
||||||
|
|
||||||
|
for( first = true; ; first = false ) {
|
||||||
|
if( step >= maxstep ) {
|
||||||
|
step = maxstep;
|
||||||
|
maxstep = maxstep*(1 + .75*RTEPS) + .75*tol;
|
||||||
|
}
|
||||||
|
|
||||||
|
cur.dx = (fabs(step) >= tol) ? step : (step > 0) ? tol : -tol;
|
||||||
|
dist = distmin + cur.dx;
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
x[dim] = xini[dim] + dist*p[i];
|
||||||
|
}
|
||||||
|
cur.f = SignSample(x);
|
||||||
|
|
||||||
|
if( cur.f <= min.f ) {
|
||||||
|
v = w;
|
||||||
|
w = min;
|
||||||
|
min.f = cur.f;
|
||||||
|
distmin = dist;
|
||||||
|
|
||||||
|
/* shift everything to the new minimum position */
|
||||||
|
maxstep -= cur.dx;
|
||||||
|
v.dx -= cur.dx;
|
||||||
|
w.dx -= cur.dx;
|
||||||
|
a.dx -= cur.dx;
|
||||||
|
b.dx -= cur.dx;
|
||||||
|
if( cur.dx < 0 ) b = w;
|
||||||
|
else a = w;
|
||||||
|
|
||||||
|
tol = RTEPS*fabs(distmin) + ftol;
|
||||||
|
tol2 = tol + tol;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
if( cur.dx < 0 ) a = cur;
|
||||||
|
else b = cur;
|
||||||
|
if( cur.f <= w.f || w.dx == 0 ) v = w, w = cur;
|
||||||
|
else if( cur.f <= v.f || v.dx == 0 || v.dx == w.dx ) v = cur;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( distmin + b.dx <= xtol ) break;
|
||||||
|
if( min.f < fini &&
|
||||||
|
a.f - min.f <= fabs(a.dx)*maxgrad &&
|
||||||
|
(fabs(distmin - range) > tol || maxstep < b.dx) ) break;
|
||||||
|
|
||||||
|
mid = .5*(a.dx + b.dx);
|
||||||
|
if( fabs(mid) <= tol2 - .5*(b.dx - a.dx) ) break;
|
||||||
|
|
||||||
|
r = q = s = 0;
|
||||||
|
if( fabs(end) > tol ) {
|
||||||
|
if( first ) {
|
||||||
|
creal s1 = w.dx*grad;
|
||||||
|
creal s2 = w.f - min.f;
|
||||||
|
s = (s1 - ((distmin == 0) ? 0 : 2*s2))*w.dx;
|
||||||
|
q = 2*(s2 - s1);
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
creal s1 = w.dx*(v.f - min.f);
|
||||||
|
creal s2 = v.dx*(w.f - min.f);
|
||||||
|
s = s1*w.dx - s2*v.dx;
|
||||||
|
q = 2*(s2 - s1);
|
||||||
|
}
|
||||||
|
if( q > 0 ) s = -s;
|
||||||
|
q = fabs(q);
|
||||||
|
r = end;
|
||||||
|
if( step != b1 || b.dx <= maxstep ) end = step;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( distmin == a.dx ) step = mid;
|
||||||
|
else if( b.dx > maxstep ) step = (step < b.dx) ? -4*a.dx : maxstep;
|
||||||
|
else {
|
||||||
|
real num = a.dx, den = b.dx;
|
||||||
|
if( fabs(b.dx) <= tol || (w.dx > 0 && fabs(a.dx) > tol) )
|
||||||
|
num = b.dx, den = a.dx;
|
||||||
|
num /= -den;
|
||||||
|
step = (num < 1) ? .5*den*sqrt(num) : 5/11.*den*(.1 + 1/num);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( step > 0 ) a1 = a.dx, b1 = step;
|
||||||
|
else a1 = step, b1 = b.dx;
|
||||||
|
if( fabs(s) < fabs(.5*q*r) && s > q*a1 && s < q*b1 ) {
|
||||||
|
step = s/q;
|
||||||
|
if( step - a.dx < tol2 || b.dx - step < tol2 )
|
||||||
|
step = (mid > 0) ? tol : -tol;
|
||||||
|
}
|
||||||
|
else end = (mid > 0) ? b.dx : a.dx;
|
||||||
|
}
|
||||||
|
|
||||||
|
first = true;
|
||||||
|
if( fabs(distmin - range) < tol ) {
|
||||||
|
distmin = range;
|
||||||
|
if( maxstep > b.dx ) first = false;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( cur.dx = distmin, cur.f = min.f, shift = -1; ;
|
||||||
|
cur.dx = Max(ldexp(distmin, shift), ftol), shift <<= 1 ) {
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
x[dim] = xini[dim] + cur.dx*p[i];
|
||||||
|
}
|
||||||
|
if( !first ) cur.f = SignSample(x);
|
||||||
|
|
||||||
|
if( cur.dx + b.dx <= xtol ) {
|
||||||
|
cur.dx = 0;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
if( fini - cur.f > cur.dx*mingrad ) break;
|
||||||
|
if( cur.dx <= ftol ) {
|
||||||
|
cur.dx = 0;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
first = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return cur;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real LocalSearch(ccount nfree, ccount *ifree, cBounds *b,
|
||||||
|
creal *x, creal fx, real *z)
|
||||||
|
{
|
||||||
|
real delta, smax, sopp, spmax, snmax;
|
||||||
|
real y[NDIM], fy, fz, ftest;
|
||||||
|
real p[NDIM];
|
||||||
|
int sign;
|
||||||
|
count i;
|
||||||
|
|
||||||
|
/* Choose a direction p along which to move away from the
|
||||||
|
present x. We choose the direction which leads farthest
|
||||||
|
away from all borders. */
|
||||||
|
|
||||||
|
smax = INFTY;
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
creal sp = b[dim].upper - x[dim];
|
||||||
|
creal sn = x[dim] - b[dim].lower;
|
||||||
|
if( sp < sn ) {
|
||||||
|
smax = Min(smax, sn);
|
||||||
|
p[i] = -1;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
smax = Min(smax, sp);
|
||||||
|
p[i] = 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
smax *= .9;
|
||||||
|
|
||||||
|
/* Move along p until the integrand changes appreciably
|
||||||
|
or we come close to a border. */
|
||||||
|
|
||||||
|
VecCopy(y, x);
|
||||||
|
ftest = SUFTOL*(1 + fabs(fx));
|
||||||
|
delta = RTDELTA/5;
|
||||||
|
do {
|
||||||
|
delta = Min(5*delta, smax);
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
y[dim] = x[dim] + delta*p[i];
|
||||||
|
}
|
||||||
|
fy = SignSample(y);
|
||||||
|
if( fabs(fy - fx) > ftest ) break;
|
||||||
|
} while( delta != smax );
|
||||||
|
|
||||||
|
/* Construct a second direction p' orthogonal to p, i.e. p.p' = 0.
|
||||||
|
We let pairs of coordinates cancel in the dot product,
|
||||||
|
i.e. we choose p'[0] = p[0], p'[1] = -p[1], etc.
|
||||||
|
(It should really be 1/p and -1/p, but p consists of 1's and -1's.)
|
||||||
|
For odd nfree, we let the last three components cancel by
|
||||||
|
choosing p'[nfree - 3] = p[nfree - 3],
|
||||||
|
p'[nfree - 2] = -1/2 p[nfree - 2], and
|
||||||
|
p'[nfree - 1] = -1/2 p[nfree - 1]. */
|
||||||
|
|
||||||
|
sign = (nfree <= 1 && fy > fx) ? 1 : -1;
|
||||||
|
spmax = snmax = INFTY;
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
real sp, sn;
|
||||||
|
p[i] *= (nfree & 1 && nfree - i <= 2) ? -.5*sign : (sign = -sign);
|
||||||
|
sp = (b[dim].upper - y[dim])/p[i];
|
||||||
|
sn = (y[dim] - b[dim].lower)/p[i];
|
||||||
|
if( p[i] > 0 ) {
|
||||||
|
spmax = Min(spmax, sp);
|
||||||
|
snmax = Min(snmax, sn);
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
spmax = Min(spmax, -sn);
|
||||||
|
snmax = Min(snmax, -sp);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
smax = .9*spmax;
|
||||||
|
sopp = .9*snmax;
|
||||||
|
|
||||||
|
if( nfree > 1 && smax < snmax ) {
|
||||||
|
real tmp = smax;
|
||||||
|
smax = sopp;
|
||||||
|
sopp = tmp;
|
||||||
|
for( i = 0; i < nfree; ++i )
|
||||||
|
p[i] = -p[i];
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Move along p' until the integrand changes appreciably
|
||||||
|
or we come close to a border. */
|
||||||
|
|
||||||
|
VecCopy(z, y);
|
||||||
|
ftest = SUFTOL*(1 + fabs(fy));
|
||||||
|
delta = RTDELTA/5;
|
||||||
|
do {
|
||||||
|
delta = Min(5*delta, smax);
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
z[dim] = y[dim] + delta*p[i];
|
||||||
|
}
|
||||||
|
fz = SignSample(z);
|
||||||
|
if( fabs(fz - fy) > ftest ) break;
|
||||||
|
} while( delta != smax );
|
||||||
|
|
||||||
|
if( fy != fz ) {
|
||||||
|
real pleneps, grad, range, step;
|
||||||
|
Point low;
|
||||||
|
|
||||||
|
if( fy > fz ) {
|
||||||
|
grad = (fz - fy)/delta;
|
||||||
|
range = smax/.9;
|
||||||
|
step = Min(delta + delta, smax);
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
grad = (fy - fz)/delta;
|
||||||
|
range = sopp/.9 + delta;
|
||||||
|
step = Min(delta + delta, sopp);
|
||||||
|
VecCopy(y, z);
|
||||||
|
fy = fz;
|
||||||
|
for( i = 0; i < nfree; ++i )
|
||||||
|
p[i] = -p[i];
|
||||||
|
}
|
||||||
|
|
||||||
|
pleneps = Length(nfree, p) + RTEPS;
|
||||||
|
low = LineSearch(nfree, ifree, p, y, fy, z, step, range, grad,
|
||||||
|
RTEPS/pleneps, 0., RTEPS);
|
||||||
|
fz = low.f;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( fz != fx ) {
|
||||||
|
real pleneps, grad, range, step;
|
||||||
|
Point low;
|
||||||
|
|
||||||
|
spmax = snmax = INFTY;
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
p[i] = z[dim] - x[dim];
|
||||||
|
if( p[i] != 0 ) {
|
||||||
|
creal sp = (b[dim].upper - x[dim])/p[i];
|
||||||
|
creal sn = (x[dim] - b[dim].lower)/p[i];
|
||||||
|
if( p[i] > 0 ) {
|
||||||
|
spmax = Min(spmax, sp);
|
||||||
|
snmax = Min(snmax, sn);
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
spmax = Min(spmax, -sn);
|
||||||
|
snmax = Min(snmax, -sp);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
grad = fz - fx;
|
||||||
|
range = spmax;
|
||||||
|
step = Min(.9*spmax, 2.);
|
||||||
|
pleneps = Length(nfree, p) + RTEPS;
|
||||||
|
if( fz > fx ) {
|
||||||
|
delta = Min(.9*snmax, RTDELTA/pleneps);
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
ccount dim = ifree[i];
|
||||||
|
z[dim] = x[dim] - delta*p[i];
|
||||||
|
}
|
||||||
|
fz = SignSample(z);
|
||||||
|
if( fz < fx ) {
|
||||||
|
grad = (fz - fx)/delta;
|
||||||
|
range = snmax;
|
||||||
|
step = Min(.9*snmax, delta + delta);
|
||||||
|
for( i = 0; i < nfree; ++i )
|
||||||
|
p[i] = -p[i];
|
||||||
|
}
|
||||||
|
else if( delta < 1 ) grad = (fx - fz)/delta;
|
||||||
|
}
|
||||||
|
|
||||||
|
low = LineSearch(nfree, ifree, p, x, fx, z, step, range, grad,
|
||||||
|
RTEPS/pleneps, 0., RTEPS);
|
||||||
|
fz = low.f;
|
||||||
|
}
|
||||||
|
|
||||||
|
return fz;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real FindMinimum(cBounds *b, real *xmin, real fmin)
|
||||||
|
{
|
||||||
|
real hessian[NDIM*NDIM];
|
||||||
|
real gfree[NDIM], p[NDIM];
|
||||||
|
real tmp[NDIM], ftmp, fini = fmin;
|
||||||
|
ccount maxeval = neval_ + 50*ndim_;
|
||||||
|
count nfree, nfix;
|
||||||
|
count ifree[NDIM], ifix[NDIM];
|
||||||
|
count dim, local;
|
||||||
|
|
||||||
|
Zap(hessian);
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
Hessian(dim, dim) = 1;
|
||||||
|
|
||||||
|
/* Step 1: - classify the variables as "fixed" (sufficiently close
|
||||||
|
to a border) and "free",
|
||||||
|
- if the integrand is flat in the direction of the gradient
|
||||||
|
w.r.t. the free dimensions, perform a local search. */
|
||||||
|
|
||||||
|
for( local = 0; local < 2; ++local ) {
|
||||||
|
bool resample = false;
|
||||||
|
nfree = nfix = 0;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
if( xmin[dim] < b[dim].lower + (1 + fabs(b[dim].lower))*QEPS ) {
|
||||||
|
xmin[dim] = b[dim].lower;
|
||||||
|
ifix[nfix++] = dim;
|
||||||
|
resample = true;
|
||||||
|
}
|
||||||
|
else if( xmin[dim] > b[dim].upper - (1 + fabs(b[dim].upper))*QEPS ) {
|
||||||
|
xmin[dim] = b[dim].upper;
|
||||||
|
ifix[nfix++] = Tag(dim);
|
||||||
|
resample = true;
|
||||||
|
}
|
||||||
|
else ifree[nfree++] = dim;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( resample ) fini = fmin = SignSample(xmin);
|
||||||
|
|
||||||
|
if( nfree == 0 ) goto releasebounds;
|
||||||
|
|
||||||
|
Gradient(nfree, ifree, b, xmin, fmin, gfree);
|
||||||
|
if( local || Length(nfree, gfree) > GTOL ) break;
|
||||||
|
|
||||||
|
ftmp = LocalSearch(nfree, ifree, b, xmin, fmin, tmp);
|
||||||
|
if( ftmp > fmin - (1 + fabs(fmin))*RTEPS )
|
||||||
|
goto releasebounds;
|
||||||
|
fmin = ftmp;
|
||||||
|
VecCopy(xmin, tmp);
|
||||||
|
}
|
||||||
|
|
||||||
|
while( neval_ <= maxeval ) {
|
||||||
|
|
||||||
|
/* Step 2a: perform a quasi-Newton iteration on the free
|
||||||
|
variables only. */
|
||||||
|
|
||||||
|
if( nfree > 0 ) {
|
||||||
|
real plen, pleneps;
|
||||||
|
real minstep;
|
||||||
|
count i, mini, minfix;
|
||||||
|
Point low;
|
||||||
|
|
||||||
|
LinearSolve(nfree, hessian, gfree, p);
|
||||||
|
plen = Length(nfree, p);
|
||||||
|
pleneps = plen + RTEPS;
|
||||||
|
|
||||||
|
minstep = INFTY;
|
||||||
|
for( i = 0; i < nfree; ++i ) {
|
||||||
|
count dim = Untag(ifree[i]);
|
||||||
|
if( fabs(p[i]) > EPS ) {
|
||||||
|
real step;
|
||||||
|
count fix;
|
||||||
|
if( p[i] < 0 ) {
|
||||||
|
step = (b[dim].lower - xmin[dim])/p[i];
|
||||||
|
fix = dim;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
step = (b[dim].upper - xmin[dim])/p[i];
|
||||||
|
fix = Tag(dim);
|
||||||
|
}
|
||||||
|
if( step < minstep ) {
|
||||||
|
minstep = step;
|
||||||
|
mini = i;
|
||||||
|
minfix = fix;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( minstep*pleneps <= DELTA ) {
|
||||||
|
fixbound:
|
||||||
|
ifix[nfix++] = minfix;
|
||||||
|
|
||||||
|
if( mini < --nfree ) {
|
||||||
|
creal diag = Hessian(mini, mini);
|
||||||
|
|
||||||
|
Clear(tmp, mini);
|
||||||
|
for( i = mini; i < nfree; ++i )
|
||||||
|
tmp[i] = Hessian(i + 1, mini);
|
||||||
|
|
||||||
|
for( i = mini; i < nfree; ++i ) {
|
||||||
|
Copy(&Hessian(i, 0), &Hessian(i + 1, 0), i);
|
||||||
|
Hessian(i, i) = Hessian(i + 1, i + 1);
|
||||||
|
}
|
||||||
|
RenormalizeCholesky(nfree, hessian, tmp, diag);
|
||||||
|
|
||||||
|
Copy(&ifree[mini], &ifree[mini + 1], nfree - mini);
|
||||||
|
Copy(&gfree[mini], &gfree[mini + 1], nfree - mini);
|
||||||
|
}
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
|
||||||
|
low = LineSearch(nfree, ifree, p, xmin, fmin, tmp,
|
||||||
|
Min(minstep, 1.), Min(minstep, 100.), Dot(nfree, gfree, p),
|
||||||
|
RTEPS/pleneps, DELTA/pleneps, .2);
|
||||||
|
|
||||||
|
if( low.dx > 0 ) {
|
||||||
|
real fdiff;
|
||||||
|
|
||||||
|
fmin = low.f;
|
||||||
|
VecCopy(xmin, tmp);
|
||||||
|
|
||||||
|
Gradient(nfree, ifree, b, xmin, fmin, tmp);
|
||||||
|
BFGS(nfree, hessian, tmp, gfree, p, low.dx);
|
||||||
|
VecCopy(gfree, tmp);
|
||||||
|
|
||||||
|
if( fabs(low.dx - minstep) < QEPS*minstep ) goto fixbound;
|
||||||
|
|
||||||
|
fdiff = fini - fmin;
|
||||||
|
fini = fmin;
|
||||||
|
if( fdiff > (1 + fabs(fmin))*FTOL ||
|
||||||
|
low.dx*plen > (1 + Length(ndim_, xmin))*FTOL ) continue;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Step 2b: check whether freeing any fixed variable will lead
|
||||||
|
to a reduction in f. */
|
||||||
|
|
||||||
|
releasebounds:
|
||||||
|
if( nfix > 0 ) {
|
||||||
|
real mingrad = INFTY;
|
||||||
|
count i, mini = 0;
|
||||||
|
bool repeat = false;
|
||||||
|
|
||||||
|
Gradient(nfix, ifix, b, xmin, fmin, tmp);
|
||||||
|
|
||||||
|
for( i = 0; i < nfix; ++i ) {
|
||||||
|
creal grad = TaggedQ(ifix[i]) ? -tmp[i] : tmp[i];
|
||||||
|
if( grad < -RTEPS ) {
|
||||||
|
repeat = true;
|
||||||
|
if( grad < mingrad ) {
|
||||||
|
mingrad = grad;
|
||||||
|
mini = i;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( repeat ) {
|
||||||
|
gfree[nfree] = tmp[mini];
|
||||||
|
ifree[nfree] = Untag(ifix[mini]);
|
||||||
|
Clear(&Hessian(nfree, 0), nfree);
|
||||||
|
Hessian(nfree, nfree) = 1;
|
||||||
|
++nfree;
|
||||||
|
|
||||||
|
--nfix;
|
||||||
|
Copy(&ifix[mini], &ifix[mini + 1], nfix - mini);
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
return fmin;
|
||||||
|
}
|
||||||
|
|
||||||
475
src/external/libCuba/src/divonne/Integrate.c
vendored
Normal file
475
src/external/libCuba/src/divonne/Integrate.c
vendored
Normal file
@ -0,0 +1,475 @@
|
|||||||
|
/*
|
||||||
|
Integrate.c
|
||||||
|
partition the integration region until each region
|
||||||
|
has approximately equal spread = 1/2 vol (max - min),
|
||||||
|
then do a main integration over all regions
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 8 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#define INIDEPTH 3
|
||||||
|
#define DEPTH 5
|
||||||
|
#define POSTDEPTH 15
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static int Integrate(creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
int key1, int key2, int key3, ccount maxpass,
|
||||||
|
creal maxchisq, creal mindeviation,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
|
||||||
|
Totals totals[NCOMP];
|
||||||
|
real nneed, weight;
|
||||||
|
count dim, comp, iter, pass = 0, err, iregion;
|
||||||
|
number nwant, nmin = INT_MAX;
|
||||||
|
int fail = -1;
|
||||||
|
|
||||||
|
if( VERBOSE > 1 ) {
|
||||||
|
char s[512];
|
||||||
|
sprintf(s, "Divonne input parameters:\n"
|
||||||
|
" ndim " COUNT "\n ncomp " COUNT "\n"
|
||||||
|
" epsrel " REAL "\n epsabs " REAL "\n"
|
||||||
|
" flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n"
|
||||||
|
" key1 %d\n key2 %d\n key3 %d\n maxpass " COUNT "\n"
|
||||||
|
" border " REAL "\n maxchisq " REAL "\n mindeviation " REAL "\n"
|
||||||
|
" ngiven " NUMBER "\n nextra " NUMBER "\n",
|
||||||
|
ndim_, ncomp_,
|
||||||
|
epsrel, epsabs,
|
||||||
|
flags, mineval, maxeval,
|
||||||
|
key1, key2, key3, maxpass,
|
||||||
|
border_.lower, maxchisq, mindeviation,
|
||||||
|
ngiven_, nextra_);
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
size_ = CHUNKSIZE;
|
||||||
|
MemAlloc(voidregion_, size_*sizeof(Region));
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
Bounds *b = ®ion_->bounds[dim];
|
||||||
|
b->lower = 0;
|
||||||
|
b->upper = 1;
|
||||||
|
}
|
||||||
|
nregions_ = 0;
|
||||||
|
|
||||||
|
RuleIni(&rule7_);
|
||||||
|
RuleIni(&rule9_);
|
||||||
|
RuleIni(&rule11_);
|
||||||
|
RuleIni(&rule13_);
|
||||||
|
SamplesIni(&samples_[0]);
|
||||||
|
SamplesIni(&samples_[1]);
|
||||||
|
SamplesIni(&samples_[2]);
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( setjmp(abort_) ) goto abort;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/* Step 1: partition the integration region */
|
||||||
|
|
||||||
|
if( VERBOSE ) Print("Partitioning phase:");
|
||||||
|
|
||||||
|
if( IsSobol(key1) || IsSobol(key2) || IsSobol(key3) )
|
||||||
|
IniRandom(2*maxeval, flags);
|
||||||
|
|
||||||
|
SamplesLookup(&samples_[0], key1,
|
||||||
|
(number)47, (number)INT_MAX, (number)0);
|
||||||
|
SamplesAlloc(&samples_[0]);
|
||||||
|
|
||||||
|
totals_ = totals;
|
||||||
|
Zap(totals);
|
||||||
|
phase_ = 1;
|
||||||
|
|
||||||
|
Explore(0, &samples_[0], INIDEPTH, 1);
|
||||||
|
|
||||||
|
for( iter = 1; ; ++iter ) {
|
||||||
|
Totals *maxtot;
|
||||||
|
count valid;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
tot->avg = tot->spreadsq = 0;
|
||||||
|
tot->spread = tot->secondspread = -INFTY;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( iregion = 0; iregion < nregions_; ++iregion ) {
|
||||||
|
Region *region = ®ion_[iregion];
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
tot->avg += r->avg;
|
||||||
|
tot->spreadsq += Sq(r->spread);
|
||||||
|
if( r->spread > tot->spread ) {
|
||||||
|
tot->secondspread = tot->spread;
|
||||||
|
tot->spread = r->spread;
|
||||||
|
tot->iregion = iregion;
|
||||||
|
}
|
||||||
|
else if( r->spread > tot->secondspread )
|
||||||
|
tot->secondspread = r->spread;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
maxtot = totals;
|
||||||
|
valid = 0;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
integral[comp] = tot->avg;
|
||||||
|
valid += tot->avg == tot->avg;
|
||||||
|
if( tot->spreadsq > maxtot->spreadsq ) maxtot = tot;
|
||||||
|
tot->spread = sqrt(tot->spreadsq);
|
||||||
|
error[comp] = tot->spread*samples_[0].weight;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[128 + 64*NCOMP], *p = s;
|
||||||
|
|
||||||
|
p += sprintf(p, "\n"
|
||||||
|
"Iteration " COUNT " (pass " COUNT "): " COUNT " regions\n"
|
||||||
|
NUMBER7 " integrand evaluations so far,\n"
|
||||||
|
NUMBER7 " in optimizing regions,\n"
|
||||||
|
NUMBER7 " in finding cuts",
|
||||||
|
iter, pass, nregions_, neval_, neval_opt_, neval_cut_);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL,
|
||||||
|
comp + 1, integral[comp], error[comp]);
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( valid == 0 ) goto abort; /* all NaNs */
|
||||||
|
|
||||||
|
if( neval_ > maxeval ) break;
|
||||||
|
|
||||||
|
nneed = maxtot->spread/MaxErr(maxtot->avg);
|
||||||
|
if( nneed < MAXPRIME ) {
|
||||||
|
cnumber n = neval_ + nregions_*(number)ceil(nneed);
|
||||||
|
if( n < nmin ) {
|
||||||
|
nmin = n;
|
||||||
|
pass = 0;
|
||||||
|
}
|
||||||
|
else if( ++pass > maxpass && n >= mineval ) break;
|
||||||
|
}
|
||||||
|
|
||||||
|
Split(maxtot->iregion, DEPTH);
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Step 2: do a "full" integration on each region */
|
||||||
|
|
||||||
|
/* nneed = samples_[0].neff + 1; */
|
||||||
|
nneed = 2*samples_[0].neff;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
creal maxerr = MaxErr(tot->avg);
|
||||||
|
tot->nneed = tot->spread/maxerr;
|
||||||
|
nneed = Max(nneed, tot->nneed);
|
||||||
|
tot->maxerrsq = Sq(maxerr);
|
||||||
|
tot->mindevsq = tot->maxerrsq*Sq(mindeviation);
|
||||||
|
}
|
||||||
|
nwant = (number)Min(ceil(nneed), MARKMASK/40.);
|
||||||
|
|
||||||
|
err = SamplesLookup(&samples_[1], key2, nwant,
|
||||||
|
(maxeval - neval_)/nregions_ + 1, samples_[0].n + 1);
|
||||||
|
|
||||||
|
/* the number of points needed to reach the desired accuracy */
|
||||||
|
fail = Unmark(err)*nregions_;
|
||||||
|
|
||||||
|
if( Marked(err) ) {
|
||||||
|
if( VERBOSE ) Print("\nNot enough samples left for main integration.");
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
prob[comp] = -999;
|
||||||
|
weight = samples_[0].weight;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
bool can_adjust = (key3 == 1 && samples_[1].sampler != SampleRule &&
|
||||||
|
(key2 < 0 || samples_[1].neff < MAXPRIME));
|
||||||
|
count df, nlimit;
|
||||||
|
|
||||||
|
SamplesAlloc(&samples_[1]);
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[128];
|
||||||
|
sprintf(s, "\nMain integration on " COUNT
|
||||||
|
" regions with " NUMBER " samples per region.",
|
||||||
|
nregions_, samples_[1].neff);
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
ResClear(integral);
|
||||||
|
ResClear(error);
|
||||||
|
ResClear(prob);
|
||||||
|
|
||||||
|
nlimit = maxeval - nregions_*samples_[1].n;
|
||||||
|
df = 0;
|
||||||
|
|
||||||
|
for( iregion = 0; iregion < nregions_; ++iregion ) {
|
||||||
|
Region *region = ®ion_[iregion];
|
||||||
|
char s[64*NDIM + 256*NCOMP], *p = s;
|
||||||
|
int todo;
|
||||||
|
|
||||||
|
refine:
|
||||||
|
phase_ = 2;
|
||||||
|
samples_[1].sampler(&samples_[1], region->bounds, region->vol);
|
||||||
|
|
||||||
|
if( can_adjust )
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
totals[comp].spreadsq -= Sq(region->result[comp].spread);
|
||||||
|
|
||||||
|
nlimit += samples_[1].n;
|
||||||
|
todo = 0;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
Totals *tot = &totals[comp];
|
||||||
|
|
||||||
|
samples_[0].avg[comp] = r->avg;
|
||||||
|
samples_[0].err[comp] = r->err;
|
||||||
|
|
||||||
|
if( neval_ < nlimit ) {
|
||||||
|
creal avg2 = samples_[1].avg[comp];
|
||||||
|
creal err2 = samples_[1].err[comp];
|
||||||
|
creal diffsq = Sq(avg2 - r->avg);
|
||||||
|
|
||||||
|
#define Var(s) Sq((s.err[comp] == 0) ? r->spread*s.weight : s.err[comp])
|
||||||
|
|
||||||
|
if( err2*tot->nneed > r->spread ||
|
||||||
|
diffsq > Max(maxchisq*(Var(samples_[0]) + Var(samples_[1])),
|
||||||
|
EPS*Sq(avg2)) ) {
|
||||||
|
if( key3 && diffsq > tot->mindevsq ) {
|
||||||
|
if( key3 == 1 ) {
|
||||||
|
ccount xregion = nregions_;
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) Print("\nSplit");
|
||||||
|
|
||||||
|
phase_ = 1;
|
||||||
|
Explore(iregion, &samples_[1], POSTDEPTH, 2);
|
||||||
|
|
||||||
|
if( can_adjust ) {
|
||||||
|
number nnew;
|
||||||
|
count ireg, xreg;
|
||||||
|
|
||||||
|
for( ireg = iregion, xreg = xregion;
|
||||||
|
ireg < nregions_; ireg = xreg++ ) {
|
||||||
|
cResult *result = region_[ireg].result;
|
||||||
|
count c;
|
||||||
|
for( c = 0; c < ncomp_; ++c )
|
||||||
|
totals[c].spreadsq += Sq(result[c].spread);
|
||||||
|
}
|
||||||
|
|
||||||
|
nnew = (tot->spreadsq/Sq(MARKMASK) > tot->maxerrsq) ?
|
||||||
|
MARKMASK :
|
||||||
|
(number)ceil(sqrt(tot->spreadsq/tot->maxerrsq));
|
||||||
|
if( nnew > nwant + nwant/64 ) {
|
||||||
|
ccount err = SamplesLookup(&samples_[1], key2, nnew,
|
||||||
|
(maxeval - neval_)/nregions_ + 1, samples_[1].n);
|
||||||
|
fail += Unmark(err)*nregions_;
|
||||||
|
nwant = nnew;
|
||||||
|
SamplesFree(&samples_[1]);
|
||||||
|
SamplesAlloc(&samples_[1]);
|
||||||
|
|
||||||
|
if( key2 > 0 && samples_[1].neff >= MAXPRIME )
|
||||||
|
can_adjust = false;
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
char s[128];
|
||||||
|
sprintf(s, "Sampling remaining " COUNT
|
||||||
|
" regions with " NUMBER " points per region.",
|
||||||
|
nregions_, samples_[1].neff);
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
goto refine;
|
||||||
|
}
|
||||||
|
todo |= 3;
|
||||||
|
}
|
||||||
|
todo |= 1;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( can_adjust ) {
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
totals[comp].maxerrsq -=
|
||||||
|
Sq(region->result[comp].spread*samples_[1].weight);
|
||||||
|
}
|
||||||
|
|
||||||
|
switch( todo ) {
|
||||||
|
case 1: /* get spread right */
|
||||||
|
Explore(iregion, &samples_[1], 0, 2);
|
||||||
|
break;
|
||||||
|
|
||||||
|
case 3: /* sample region again with more points */
|
||||||
|
if( MEM(&samples_[2]) == NULL ) {
|
||||||
|
SamplesLookup(&samples_[2], key3,
|
||||||
|
nwant, (number)INT_MAX, (number)0);
|
||||||
|
SamplesAlloc(&samples_[2]);
|
||||||
|
}
|
||||||
|
phase_ = 3;
|
||||||
|
samples_[2].sampler(&samples_[2], region->bounds, region->vol);
|
||||||
|
Explore(iregion, &samples_[2], 0, 2);
|
||||||
|
++region->depth; /* misused for df here */
|
||||||
|
++df;
|
||||||
|
}
|
||||||
|
|
||||||
|
++region->depth; /* misused for df here */
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
p += sprintf(p,
|
||||||
|
(dim == 0) ? "\nRegion (" REALF ") - (" REALF ")" :
|
||||||
|
"\n (" REALF ") - (" REALF ")",
|
||||||
|
b->lower, b->upper);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Result *r = ®ion->result[comp];
|
||||||
|
|
||||||
|
creal x1 = samples_[0].avg[comp];
|
||||||
|
creal s1 = Var(samples_[0]);
|
||||||
|
creal x2 = samples_[1].avg[comp];
|
||||||
|
creal s2 = Var(samples_[1]);
|
||||||
|
creal r2 = (s1 == 0) ? Sq(samples_[1].neff*samples_[0].weight) : s2/s1;
|
||||||
|
|
||||||
|
real norm = 1 + r2;
|
||||||
|
real avg = x2 + r2*x1;
|
||||||
|
real sigsq = s2;
|
||||||
|
real chisq = Sq(x2 - x1);
|
||||||
|
real chiden = s1 + s2;
|
||||||
|
|
||||||
|
if( todo == 3 ) {
|
||||||
|
creal x3 = samples_[2].avg[comp];
|
||||||
|
creal s3 = Var(samples_[2]);
|
||||||
|
creal r3 = (s2 == 0) ? Sq(samples_[2].neff*samples_[1].weight) : s3/s2;
|
||||||
|
|
||||||
|
norm = 1 + r3*norm;
|
||||||
|
avg = x3 + r3*avg;
|
||||||
|
sigsq = s3;
|
||||||
|
chisq = s1*Sq(x3 - x2) + s2*Sq(x3 - x1) + s3*chisq;
|
||||||
|
chiden = s1*s2 + s3*chiden;
|
||||||
|
}
|
||||||
|
|
||||||
|
avg = LAST ? r->avg : (sigsq *= norm = 1/norm, avg*norm);
|
||||||
|
if( chisq > EPS ) chisq /= Max(chiden, NOTZERO);
|
||||||
|
|
||||||
|
#define Out(s) s.avg[comp], r->spread*s.weight, s.err[comp]
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL "(" REAL ")\n "
|
||||||
|
REAL " +- " REAL "(" REAL ")",
|
||||||
|
comp + 1, Out(samples_[0]), Out(samples_[1]));
|
||||||
|
if( todo == 3 ) p += sprintf(p, "\n "
|
||||||
|
REAL " +- " REAL "(" REAL ")",
|
||||||
|
Out(samples_[2]));
|
||||||
|
p += sprintf(p, " \tchisq " REAL, chisq);
|
||||||
|
}
|
||||||
|
|
||||||
|
integral[comp] += avg;
|
||||||
|
error[comp] += sigsq;
|
||||||
|
prob[comp] += chisq;
|
||||||
|
|
||||||
|
r->avg = avg;
|
||||||
|
r->spread = sqrt(sigsq);
|
||||||
|
r->chisq = chisq;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
error[comp] = sqrt(error[comp]);
|
||||||
|
|
||||||
|
df += nregions_;
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
char s[16 + 128*NCOMP], *p = s;
|
||||||
|
|
||||||
|
p += sprintf(p, "\nTotals:");
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)",
|
||||||
|
comp + 1, integral[comp], error[comp], prob[comp], df);
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
prob[comp] = ChiSquare(prob[comp], df);
|
||||||
|
|
||||||
|
weight = 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( REGIONS ) {
|
||||||
|
MLPutFunction(stdlink, "List", 2);
|
||||||
|
MLPutFunction(stdlink, "List", nregions_);
|
||||||
|
for( iregion = 0; iregion < nregions_; ++iregion ) {
|
||||||
|
Region *region = ®ion_[iregion];
|
||||||
|
cBounds *b = region->bounds;
|
||||||
|
real lower[NDIM], upper[NDIM];
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
lower[dim] = b[dim].lower;
|
||||||
|
upper[dim] = b[dim].upper;
|
||||||
|
}
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "Cuba`Divonne`region", 4);
|
||||||
|
|
||||||
|
MLPutRealList(stdlink, lower, ndim_);
|
||||||
|
MLPutRealList(stdlink, upper, ndim_);
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "List", ncomp_);
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
real res[] = {r->avg, r->spread*weight, r->chisq};
|
||||||
|
MLPutRealList(stdlink, res, Elements(res));
|
||||||
|
}
|
||||||
|
|
||||||
|
MLPutInteger(stdlink, region->depth); /* misused for df */
|
||||||
|
}
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
|
abort:
|
||||||
|
|
||||||
|
SamplesFree(&samples_[2]);
|
||||||
|
SamplesFree(&samples_[1]);
|
||||||
|
SamplesFree(&samples_[0]);
|
||||||
|
RuleFree(&rule13_);
|
||||||
|
RuleFree(&rule11_);
|
||||||
|
RuleFree(&rule9_);
|
||||||
|
RuleFree(&rule7_);
|
||||||
|
|
||||||
|
free(region_);
|
||||||
|
|
||||||
|
return fail;
|
||||||
|
}
|
||||||
|
|
||||||
901
src/external/libCuba/src/divonne/KorobovCoeff.c
vendored
Normal file
901
src/external/libCuba/src/divonne/KorobovCoeff.c
vendored
Normal file
@ -0,0 +1,901 @@
|
|||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#define KOROBOV_MINDIM 2
|
||||||
|
#define KOROBOV_MAXDIM 33
|
||||||
|
#define MAXPRIME 9689
|
||||||
|
|
||||||
|
#define Hash(x) ((19945 - x)*(-47 + x))/121634
|
||||||
|
|
||||||
|
static int prime[] = {
|
||||||
|
FIRST,47,53,59,67,71,79,83,89,97,103,109,113,127,131,137,139,149,151,
|
||||||
|
157,163,173,179,181,191,193,199,211,223,227,229,233,239,241,251,257,263,
|
||||||
|
269,277,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,
|
||||||
|
389,397,401,409,419,421,431,433,439,443,449,457,461,467,479,487,491,499,
|
||||||
|
503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,
|
||||||
|
619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,
|
||||||
|
743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,
|
||||||
|
863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,
|
||||||
|
997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,
|
||||||
|
1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,
|
||||||
|
1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,
|
||||||
|
1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,
|
||||||
|
1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,
|
||||||
|
1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,
|
||||||
|
1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,
|
||||||
|
1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,
|
||||||
|
1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,
|
||||||
|
1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,
|
||||||
|
2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,
|
||||||
|
2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,
|
||||||
|
2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,
|
||||||
|
2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,
|
||||||
|
2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,
|
||||||
|
2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,
|
||||||
|
2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,
|
||||||
|
2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,
|
||||||
|
2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,
|
||||||
|
3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,
|
||||||
|
3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,
|
||||||
|
3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,
|
||||||
|
3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,
|
||||||
|
3511,3517,3527,3529,3533,3539,3547,3557,3571,3581,3583,3593,3607,3613,
|
||||||
|
3623,3631,3643,3659,3671,3673,3677,3691,3701,3709,3719,3733,3739,3761,
|
||||||
|
3767,3769,3779,3793,3797,3803,3821,3833,3847,3851,3853,3863,3877,3889,
|
||||||
|
3907,3911,3917,3929,3943,3947,3967,3989,4001,4003,4007,4013,4019,4027,
|
||||||
|
4049,4051,4057,4073,4079,4091,4099,4111,4127,4133,4139,4153,4159,4177,
|
||||||
|
4201,4211,4217,4219,4229,4231,4243,4259,4271,4283,4289,4297,4327,4337,
|
||||||
|
4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4451,4463,4481,
|
||||||
|
4483,4493,4507,4517,4523,4547,4549,4561,4567,4583,4597,4603,4621,4637,
|
||||||
|
4639,4651,4663,4673,4691,4703,4721,4723,4733,4751,4759,4783,4787,4789,
|
||||||
|
4801,4813,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4943,4957,
|
||||||
|
4969,4987,4993,5003,5021,5023,5039,5051,5059,5077,5087,5101,5119,5147,
|
||||||
|
5153,5167,5171,5179,5189,5209,5227,5231,5237,5261,5273,5281,5297,5309,
|
||||||
|
5323,5333,5347,5351,5381,5387,5399,5413,5431,5437,5449,5471,5479,5501,
|
||||||
|
5507,5519,5531,5557,5563,5573,5591,5623,5639,5641,5647,5657,5669,5683,
|
||||||
|
5701,5711,5737,5743,5749,5779,5783,5801,5813,5827,5843,5857,5869,5881,
|
||||||
|
5903,5923,5927,5953,5981,5987,6007,6011,6029,6037,6053,6067,6089,6101,
|
||||||
|
6113,6131,6151,6163,6173,6197,6211,6229,6247,6257,6277,6287,6311,6323,
|
||||||
|
6343,6359,6373,6389,6421,6427,6449,6469,6481,6491,6521,6529,6547,6563,
|
||||||
|
6581,6599,6619,6637,6653,6673,6691,6709,6733,6737,6763,6781,6803,6823,
|
||||||
|
6841,6863,6883,6899,6917,6947,6961,6983,7001,7019,7043,7057,7079,7103,
|
||||||
|
7127,7151,7159,7187,7211,7229,7253,7283,7297,7321,7349,7369,7393,7417,
|
||||||
|
7433,7459,7487,7507,7537,7561,7583,7607,7639,7669,7687,7717,7741,7759,
|
||||||
|
7793,7823,7853,7883,7907,7937,7963,7993,8039,8059,8093,8123,8161,8191,
|
||||||
|
8221,8263,8297,8329,8369,8419,8447,8501,8527,8563,8609,8663,8699,8747,
|
||||||
|
8803,8849,8893,8963,9029,9091,9157,9239,9319,9413,9533,MarkLast(9689)
|
||||||
|
};
|
||||||
|
|
||||||
|
static short coeff[][32] = {
|
||||||
|
{13,11,10,3,9,2,2,2,2,9,2,2,7,2,2,2,2,2,2,6,2,2,2,13,11,10,3,9,2,2,2,2},
|
||||||
|
{23,17,12,11,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,12,12,12,14,14,14},
|
||||||
|
{18,14,5,14,2,2,19,19,25,25,18,18,18,2,2,2,2,2,2,2,2,2,2,2,25,6,2,2,2,18,14,5},
|
||||||
|
{18,13,23,5,2,12,6,12,12,12,10,10,16,2,16,16,2,2,2,2,2,2,2,10,2,2,2,2,10,2,2,2},
|
||||||
|
{21,22,7,21,2,20,20,2,2,2,2,22,2,2,2,2,2,2,2,6,6,21,2,2,2,2,2,2,2,2,6,6},
|
||||||
|
{29,19,27,32,6,8,2,2,2,2,2,8,8,2,2,2,2,9,9,9,9,2,2,2,2,2,2,2,9,9,2,2},
|
||||||
|
{30,19,24,16,22,8,2,2,22,5,9,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{34,28,13,28,27,27,2,4,2,2,2,16,16,4,20,20,36,20,36,5,5,5,36,36,5,5,5,7,5,7,7,2},
|
||||||
|
{35,19,33,8,21,30,8,2,4,2,4,4,2,2,2,2,2,2,2,2,2,17,2,2,11,25,11,17,17,17,17,17},
|
||||||
|
{37,21,35,29,27,19,19,2,2,2,5,15,2,2,15,15,19,19,19,19,19,2,2,2,2,2,19,2,2,2,2,2},
|
||||||
|
{45,44,13,25,17,47,30,2,30,2,2,2,2,2,2,2,2,2,19,19,19,17,17,2,2,2,2,2,2,2,2,2},
|
||||||
|
{35,22,37,9,35,12,35,8,2,2,50,50,2,2,32,32,32,31,13,8,8,8,2,22,50,9,9,9,22,22,22,10},
|
||||||
|
{29,24,43,36,49,2,2,8,4,25,49,25,2,2,8,10,10,10,5,5,5,40,10,33,40,40,2,27,10,25,25,25},
|
||||||
|
{50,18,32,39,21,2,2,2,4,4,36,36,14,14,14,14,2,2,2,17,17,17,16,16,2,14,14,14,14,2,2,2},
|
||||||
|
{31,28,45,20,18,43,43,13,28,2,2,2,31,31,31,31,31,2,2,2,43,43,2,2,2,2,2,2,2,2,30,2},
|
||||||
|
{39,15,41,7,24,2,2,30,40,2,2,25,25,25,25,2,2,2,2,2,2,6,6,2,25,2,5,2,2,25,2,2},
|
||||||
|
{44,20,29,39,7,21,21,21,2,2,45,2,2,2,49,49,49,49,49,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{56,20,22,13,18,35,35,6,2,4,2,4,2,2,2,23,16,16,4,23,2,34,52,2,34,2,4,2,2,2,23,16},
|
||||||
|
{46,32,17,18,29,27,31,31,31,2,2,4,15,2,2,2,2,2,2,2,2,2,2,2,2,2,23,32,32,32,15,15},
|
||||||
|
{62,42,43,17,23,13,13,2,2,13,2,2,2,2,2,2,2,10,2,2,2,2,9,10,2,2,2,19,9,9,9,9},
|
||||||
|
{64,34,16,28,16,51,47,2,2,2,6,18,39,39,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,12,12,2},
|
||||||
|
{74,26,44,25,50,24,54,39,58,42,2,42,42,2,2,2,2,2,2,2,2,33,33,2,2,39,11,2,2,58,39,58},
|
||||||
|
{70,22,50,22,16,9,25,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{74,21,17,25,35,33,10,2,10,20,20,57,57,57,2,2,57,2,2,2,2,2,2,2,13,2,2,2,2,2,2,2},
|
||||||
|
{81,18,10,11,47,38,71,37,2,37,2,2,2,2,2,26,26,26,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{55,30,85,42,16,36,45,67,2,2,68,2,2,2,2,2,2,2,68,10,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{64,17,24,26,49,12,10,39,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,59,2,2},
|
||||||
|
{68,57,23,38,61,38,13,13,8,2,2,2,2,2,2,2,2,2,2,2,2,2,2,68,15,2,44,44,44,2,2,2},
|
||||||
|
{94,28,58,29,13,5,15,8,66,2,2,2,39,39,15,66,2,2,6,6,2,2,66,66,66,66,2,2,2,2,2,66},
|
||||||
|
{94,85,9,41,41,37,29,29,17,2,2,2,7,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,8,8},
|
||||||
|
{89,32,75,77,77,13,2,30,30,2,2,2,2,2,2,2,2,2,2,67,67,2,2,2,2,2,2,2,2,8,19,32},
|
||||||
|
{70,45,58,63,67,10,72,72,70,6,2,36,2,70,70,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{101,33,76,13,45,63,2,2,6,19,2,2,32,32,32,32,32,65,2,63,63,11,11,11,19,19,19,19,9,63,63,63},
|
||||||
|
{70,89,44,37,19,45,2,2,2,8,10,8,54,54,80,80,80,80,80,2,116,2,116,2,2,80,40,51,100,100,8,2},
|
||||||
|
{71,54,83,51,42,98,2,2,8,8,14,30,93,22,15,15,30,30,30,44,44,44,2,2,22,22,22,117,44,11,11,11},
|
||||||
|
{109,37,51,113,17,10,2,2,17,17,55,2,55,55,55,55,55,55,2,2,2,57,48,48,55,55,2,2,55,2,2,55},
|
||||||
|
{75,38,68,89,11,52,2,2,81,39,2,38,2,2,2,2,2,2,2,2,2,2,2,19,2,2,2,2,2,2,2,2},
|
||||||
|
{81,84,35,34,20,93,2,12,12,12,2,96,2,96,96,2,96,2,2,2,2,2,2,2,2,2,2,2,2,56,56,56},
|
||||||
|
{104,32,56,46,77,11,35,35,24,56,19,2,2,2,78,2,2,75,2,2,2,2,78,2,2,2,2,2,2,2,2,2},
|
||||||
|
{81,103,25,35,28,15,20,20,20,2,2,2,2,20,20,20,107,107,2,2,2,2,2,2,2,2,2,2,2,2,13,13},
|
||||||
|
{119,75,42,29,74,23,54,36,39,2,2,4,4,19,19,2,2,2,2,2,2,2,2,54,2,2,2,2,2,2,2,54},
|
||||||
|
{115,73,22,102,75,138,16,73,50,16,2,50,2,2,2,133,2,2,2,2,2,2,2,2,2,2,2,2,2,33,33,33},
|
||||||
|
{119,48,66,51,14,22,20,20,2,2,2,2,2,60,2,2,2,2,2,2,2,2,60,2,2,2,2,2,2,60,2,65},
|
||||||
|
{121,94,80,29,51,69,42,36,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,17,2,2},
|
||||||
|
{129,123,41,79,43,34,24,11,2,2,4,2,2,2,2,75,16,16,16,75,75,75,16,16,16,25,2,99,2,2,75,16},
|
||||||
|
{128,33,35,68,22,8,62,94,2,2,2,62,62,2,98,2,2,4,98,2,2,32,81,32,32,32,98,98,98,98,98,98},
|
||||||
|
{101,109,154,15,57,6,27,36,2,2,37,37,2,2,2,2,2,2,2,107,2,2,2,107,107,2,2,2,2,2,2,2},
|
||||||
|
{106,40,24,38,61,118,106,106,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{149,111,58,79,127,13,41,33,27,16,30,2,61,2,72,2,2,2,2,2,2,2,2,2,2,2,2,75,75,2,2,2},
|
||||||
|
{105,92,43,156,25,53,57,115,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{99,40,62,67,66,29,99,99,99,78,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,79},
|
||||||
|
{109,42,96,95,66,41,103,84,13,103,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{111,72,16,89,25,86,117,29,14,14,2,2,2,2,2,60,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{106,72,49,94,140,44,97,157,75,2,2,4,123,123,2,2,123,123,123,123,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{115,67,74,32,43,50,21,36,135,36,85,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{151,71,157,42,41,37,80,27,18,2,2,2,2,2,2,2,2,2,2,2,2,2,115,128,128,128,128,128,32,2,128,80},
|
||||||
|
{119,91,38,30,92,44,32,76,22,2,34,2,2,2,2,2,2,2,2,2,2,2,2,2,2,129,2,2,129,2,2,2},
|
||||||
|
{121,126,31,52,120,37,57,10,171,2,2,2,2,35,35,35,2,2,97,97,97,97,97,97,97,35,35,35,97,97,97,2},
|
||||||
|
{155,86,49,104,87,94,64,45,61,91,91,91,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{164,121,44,166,47,33,7,15,13,2,2,122,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{128,120,133,17,71,52,25,107,42,21,21,2,2,2,2,4,4,96,2,9,9,2,9,94,94,94,94,94,94,94,94,96},
|
||||||
|
{179,82,157,76,61,35,13,90,197,2,69,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,39,39},
|
||||||
|
{136,136,148,63,66,10,169,95,95,163,30,28,28,2,41,130,2,2,2,21,2,2,2,2,2,2,2,2,2,2,2,36},
|
||||||
|
{131,40,112,63,55,30,53,79,79,79,2,79,2,2,2,2,2,79,2,2,2,2,14,36,2,21,21,21,21,2,2,91},
|
||||||
|
{165,81,92,48,9,110,12,40,40,34,2,2,2,107,107,107,2,107,2,2,2,2,2,2,2,2,2,2,2,15,41,41},
|
||||||
|
{169,66,170,97,35,56,55,86,32,32,2,2,2,2,14,2,40,2,37,2,2,37,40,40,40,2,2,2,37,37,37,37},
|
||||||
|
{135,63,126,156,70,18,49,143,6,117,2,109,109,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{193,59,51,68,68,15,170,170,170,143,143,12,2,2,2,63,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{145,101,56,65,23,76,110,2,4,4,4,146,146,146,2,146,2,2,2,2,2,2,2,2,2,2,2,2,2,2,146,146},
|
||||||
|
{144,129,26,98,36,46,47,52,52,52,82,2,2,2,2,2,17,2,2,2,2,2,2,2,2,2,2,2,2,91,2,2},
|
||||||
|
{145,78,166,171,56,20,63,2,2,33,33,33,33,2,78,47,47,47,47,47,2,2,2,2,2,78,78,78,2,2,2,2},
|
||||||
|
{191,69,176,54,47,75,167,2,2,2,188,188,188,30,30,2,67,67,117,2,117,117,117,2,2,36,2,2,2,2,2,2},
|
||||||
|
{186,96,29,122,47,96,170,157,157,157,157,108,159,2,195,195,26,26,26,26,26,2,2,2,2,132,132,132,2,2,2,2},
|
||||||
|
{151,118,226,91,54,49,33,2,2,2,2,4,4,4,143,143,2,2,143,25,25,25,2,143,143,143,143,143,143,143,143,143},
|
||||||
|
{144,91,237,82,81,75,138,163,163,163,117,117,44,2,44,136,136,136,136,2,2,2,2,2,122,122,122,122,2,2,2,136},
|
||||||
|
{189,78,178,64,118,27,189,2,2,67,67,110,110,110,110,2,28,28,2,2,2,2,2,2,2,102,2,2,2,2,2,2},
|
||||||
|
{165,202,83,76,125,65,42,2,44,44,23,2,23,23,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{209,204,92,75,85,146,104,2,7,18,8,2,2,2,204,95,95,95,2,2,2,95,95,95,95,95,95,95,2,2,2,95},
|
||||||
|
{169,68,89,16,193,82,33,262,262,175,148,148,148,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{171,162,78,43,61,17,112,10,171,182,118,33,2,2,2,2,118,2,2,2,2,2,2,151,2,2,2,2,2,2,2,2},
|
||||||
|
{211,121,119,55,90,211,96,89,225,25,178,36,36,36,2,2,108,2,2,2,2,2,2,2,2,2,2,2,2,184,2,2},
|
||||||
|
{154,101,83,17,16,210,41,79,70,158,2,27,27,2,2,2,2,2,2,2,2,2,2,2,2,153,2,2,2,2,2,2},
|
||||||
|
{169,179,130,79,148,180,136,17,47,119,2,119,119,169,169,2,169,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{241,171,148,31,172,34,66,60,156,140,2,2,2,75,75,2,2,2,2,2,2,2,190,190,2,2,2,30,2,2,2,2},
|
||||||
|
{229,189,183,106,118,138,82,149,265,39,2,2,265,2,2,2,2,2,2,130,2,2,2,71,71,2,2,2,71,2,2,71},
|
||||||
|
{165,157,127,21,64,15,80,130,130,130,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,74,2},
|
||||||
|
{221,130,203,84,83,83,29,121,54,54,2,141,2,2,94,94,94,4,4,4,2,4,2,2,2,54,54,108,16,16,94,52},
|
||||||
|
{230,166,20,160,121,102,153,94,16,67,2,2,2,2,2,2,97,97,97,2,2,97,97,2,97,97,97,97,97,97,97,97},
|
||||||
|
{181,79,137,119,139,24,77,17,50,25,25,25,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{239,242,192,40,41,62,124,193,193,31,193,2,2,2,2,2,2,2,2,2,2,2,2,148,2,2,2,2,2,2,2,2},
|
||||||
|
{239,178,73,122,239,51,95,48,78,88,78,2,2,2,2,2,2,2,2,2,2,2,144,144,2,2,144,144,144,2,144,144},
|
||||||
|
{234,117,198,34,143,21,74,6,252,252,98,2,2,2,2,197,38,2,2,2,2,2,47,2,47,47,47,47,2,2,2,47},
|
||||||
|
{179,110,38,28,58,39,16,29,42,125,202,8,8,129,4,4,2,2,2,67,67,2,2,2,2,2,2,8,67,67,2,2},
|
||||||
|
{246,53,189,50,18,59,179,179,7,137,137,2,2,103,103,103,103,40,40,40,2,2,2,2,73,73,73,2,103,103,103,103},
|
||||||
|
{239,133,87,92,193,12,206,238,238,238,31,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{191,244,60,193,18,32,193,104,74,125,125,66,2,2,2,2,2,2,2,2,2,2,125,125,2,125,125,125,2,2,2,2},
|
||||||
|
{177,74,90,91,172,219,63,84,32,2,2,196,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{253,143,54,39,122,32,75,107,234,2,6,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{282,89,71,88,30,23,81,105,105,2,2,105,105,131,107,2,2,2,2,2,195,195,2,2,29,29,21,21,128,195,195,195},
|
||||||
|
{259,115,171,40,156,71,67,24,24,2,2,2,24,4,4,4,2,234,2,2,2,2,2,2,2,2,2,74,74,2,2,2},
|
||||||
|
{264,237,49,203,247,108,75,75,75,2,2,32,16,8,16,16,16,164,14,164,2,2,32,16,8,16,16,32,42,42,42,2},
|
||||||
|
{264,106,89,51,29,226,23,286,286,151,151,151,151,151,2,2,2,2,2,2,31,31,31,2,2,2,2,2,2,2,2,284},
|
||||||
|
{194,215,82,23,213,23,108,127,74,2,201,32,178,2,285,2,2,2,2,285,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{196,267,251,111,231,14,30,52,95,2,154,53,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{266,67,22,101,102,157,53,95,130,2,42,76,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{281,205,107,178,236,122,122,316,76,215,215,2,60,2,2,2,2,2,2,227,2,2,2,2,2,2,2,2,27,2,2,2},
|
||||||
|
{271,89,65,195,132,162,102,45,56,174,104,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{200,169,170,121,155,68,131,167,78,113,113,2,2,64,2,2,2,2,2,2,2,2,2,2,2,2,2,173,2,2,2,2},
|
||||||
|
{288,143,265,264,71,19,231,169,27,27,27,2,2,2,2,2,2,2,2,2,2,2,2,2,51,2,2,2,2,2,2,2},
|
||||||
|
{311,141,96,173,90,119,134,151,35,252,39,2,39,39,2,2,2,2,2,2,2,2,2,113,113,2,2,2,2,2,2,113},
|
||||||
|
{311,230,52,138,225,346,162,216,216,91,160,182,91,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{275,167,128,244,184,184,44,210,237,139,139,139,139,2,2,2,2,2,2,2,2,2,2,73,2,2,2,2,2,2,2,2},
|
||||||
|
{176,156,83,135,46,197,108,63,33,33,33,2,133,2,213,213,213,213,133,133,2,133,2,2,133,133,2,2,2,2,2,2},
|
||||||
|
{283,125,141,192,89,181,106,208,124,124,2,112,112,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{289,191,171,152,191,173,54,13,21,56,56,56,2,2,2,2,2,2,2,2,2,220,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{334,305,132,132,99,126,54,116,164,105,2,105,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,287,2,2,2,2},
|
||||||
|
{240,166,44,193,153,333,15,99,246,99,2,2,99,99,2,2,2,2,195,195,195,2,195,195,2,263,263,2,195,195,195,263},
|
||||||
|
{246,194,265,79,225,65,24,62,46,181,2,2,2,314,2,2,2,2,2,2,2,215,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{229,334,285,302,21,26,24,97,64,40,2,2,2,231,231,231,231,65,2,148,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{251,295,55,249,135,173,164,78,261,261,2,2,2,2,114,2,2,2,2,2,256,142,142,2,2,2,2,2,2,2,2,185},
|
||||||
|
{232,153,55,60,181,79,107,70,29,35,2,2,58,58,2,58,2,2,2,2,61,61,2,61,61,2,2,61,61,90,2,90},
|
||||||
|
{246,116,45,146,109,90,32,103,133,119,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{246,113,146,232,162,262,204,47,45,331,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{360,150,84,275,13,26,368,49,244,244,63,63,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{239,295,174,87,30,87,85,36,103,36,2,278,2,2,2,2,2,2,163,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{356,300,75,310,123,301,200,107,183,37,218,37,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{358,207,168,150,150,21,156,50,195,275,275,275,2,2,2,2,2,251,2,2,2,251,251,251,251,251,251,251,251,251,2,2},
|
||||||
|
{322,194,234,62,236,147,239,400,255,255,80,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{326,276,134,100,143,113,115,221,13,339,194,194,194,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{337,132,27,45,14,81,110,84,238,224,211,2,29,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{192,213,113,174,403,117,342,342,311,35,35,2,2,2,2,2,2,2,2,101,2,2,2,2,2,2,2,2,2,101,101,101},
|
||||||
|
{264,273,316,53,40,330,51,285,115,219,147,2,2,2,335,2,2,2,2,2,173,2,173,2,2,173,173,173,173,173,173,83},
|
||||||
|
{254,293,407,118,54,296,160,231,4,4,93,2,2,2,2,2,60,61,2,2,120,127,127,127,88,88,88,88,88,88,88,88},
|
||||||
|
{341,78,336,263,281,164,99,334,296,114,109,2,163,163,163,163,2,2,2,2,2,2,2,125,125,292,292,292,292,125,125,125},
|
||||||
|
{355,87,212,100,89,210,133,344,120,45,45,138,138,138,138,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{274,141,46,219,158,284,38,79,73,185,35,6,81,2,2,2,2,53,2,2,81,81,2,81,2,2,2,53,53,53,53,53},
|
||||||
|
{349,303,439,19,95,240,174,191,2,162,162,2,2,2,76,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{360,91,201,205,67,181,59,77,2,44,103,103,103,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,125},
|
||||||
|
{283,154,261,91,77,147,227,105,116,311,256,256,2,116,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,32,2},
|
||||||
|
{287,288,111,89,249,370,55,16,248,67,67,115,2,2,134,134,2,2,2,2,2,2,2,2,2,2,2,2,2,22,22,22},
|
||||||
|
{284,270,282,37,29,181,160,49,285,285,374,250,2,374,374,2,2,2,179,179,35,2,179,179,2,179,179,2,2,285,285,285},
|
||||||
|
{359,305,52,36,243,231,7,92,2,68,68,307,62,45,2,2,112,311,311,311,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{288,119,218,137,364,38,27,380,2,2,211,23,33,2,2,2,2,2,225,225,225,2,2,225,225,225,2,2,2,2,2,2},
|
||||||
|
{277,155,232,309,370,365,348,75,214,214,214,4,4,2,2,2,210,210,210,210,210,210,210,2,2,2,2,2,2,2,2,2},
|
||||||
|
{292,204,91,41,124,190,107,322,125,125,125,125,125,25,25,62,2,2,146,146,2,2,62,146,2,146,114,146,114,2,2,2},
|
||||||
|
{282,195,192,409,68,99,253,106,2,2,2,231,55,55,2,323,323,55,55,285,285,285,285,2,2,2,2,2,2,285,285,323},
|
||||||
|
{299,122,174,403,113,77,63,275,2,2,2,138,276,227,38,227,2,237,2,2,2,2,2,2,2,2,2,2,352,352,352,2},
|
||||||
|
{282,222,268,86,21,109,353,408,2,2,2,2,135,12,12,216,241,241,241,241,241,241,241,241,241,303,303,303,135,135,135,2},
|
||||||
|
{374,94,89,257,137,246,186,196,2,2,2,2,2,454,122,122,122,122,2,2,2,28,28,94,94,94,94,94,122,122,122,122},
|
||||||
|
{288,92,62,428,122,153,481,66,2,2,2,250,250,177,177,177,177,279,279,279,279,279,279,279,2,2,279,177,177,177,177,177},
|
||||||
|
{288,370,141,284,207,192,450,67,2,2,2,183,217,217,217,183,183,167,202,202,202,202,167,167,2,2,2,164,164,80,167,167},
|
||||||
|
{286,293,199,39,158,332,242,103,2,2,2,408,266,315,2,2,365,253,315,315,315,315,315,2,2,315,2,2,2,2,2,2},
|
||||||
|
{407,83,435,187,40,16,52,65,2,2,244,39,77,119,119,2,2,2,119,342,342,2,2,2,2,2,342,2,2,58,58,119},
|
||||||
|
{398,88,78,57,260,203,203,43,131,131,131,204,204,322,204,2,102,2,325,325,325,325,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{390,174,70,155,163,67,225,49,2,34,34,151,151,2,2,111,2,2,111,111,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{393,129,393,169,23,192,168,47,2,2,312,150,71,2,150,2,2,2,61,2,2,61,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{408,136,71,63,63,159,222,68,181,181,124,227,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{294,169,79,242,160,123,178,290,186,186,56,399,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{415,228,69,68,193,122,21,362,33,22,362,57,2,2,2,2,46,46,196,196,196,2,196,196,196,2,196,2,2,2,2,2},
|
||||||
|
{415,130,241,185,312,175,309,199,94,281,47,47,2,2,2,2,206,307,221,2,2,2,2,2,239,239,239,239,239,206,206,206},
|
||||||
|
{417,238,147,165,346,19,92,164,266,291,291,43,2,2,2,345,2,2,2,345,345,2,2,2,2,2,345,2,2,2,2,2},
|
||||||
|
{456,192,86,182,35,174,342,102,210,210,210,393,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,256,256,158},
|
||||||
|
{307,255,92,38,325,61,103,246,176,319,80,89,2,241,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{432,168,63,154,166,46,479,145,144,288,288,288,288,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{341,256,113,85,188,233,161,29,110,167,91,91,253,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{311,360,312,158,73,16,106,209,472,48,24,203,203,2,2,2,2,234,234,234,2,234,234,203,2,2,2,234,234,234,234,234},
|
||||||
|
{437,196,161,100,132,246,395,187,35,35,35,2,2,35,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{438,174,338,145,155,276,422,374,4,463,463,99,224,70,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{426,225,211,130,325,283,353,96,282,23,299,2,2,2,63,63,2,276,276,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{430,101,288,38,200,332,325,193,123,123,88,2,2,2,2,2,231,231,139,139,139,139,139,139,139,139,139,139,139,139,139,139},
|
||||||
|
{434,143,308,389,365,363,174,63,121,125,260,2,2,260,260,2,2,2,2,2,2,2,2,2,2,258,2,2,2,258,2,2},
|
||||||
|
{453,123,201,141,229,223,234,494,102,102,102,2,2,102,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,252},
|
||||||
|
{438,168,65,264,304,74,168,88,114,132,187,2,127,127,2,2,2,2,2,81,81,56,2,2,2,307,2,2,2,2,81,81},
|
||||||
|
{324,181,141,129,33,171,173,291,227,373,52,301,301,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{448,119,431,111,135,50,242,95,148,49,49,49,68,2,2,2,2,2,2,2,2,49,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{335,114,55,47,33,173,287,345,198,198,136,238,238,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{468,377,243,237,332,512,27,167,22,169,14,14,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{456,162,188,223,408,209,28,164,299,299,258,186,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{445,391,115,226,96,456,239,214,556,158,158,282,2,2,2,2,2,2,2,2,2,2,2,2,2,331,2,2,2,2,2,2},
|
||||||
|
{360,397,130,172,407,479,295,13,38,199,199,346,2,2,2,2,2,2,145,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{512,136,129,361,180,61,274,128,422,27,292,165,2,2,2,2,2,2,363,117,117,117,117,2,2,2,2,363,2,2,2,2},
|
||||||
|
{478,433,483,302,200,227,273,27,171,171,371,102,2,2,2,2,2,20,2,2,2,2,2,2,2,2,403,403,2,2,2,2},
|
||||||
|
{485,158,454,86,212,60,93,40,209,188,188,106,2,231,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{390,448,111,145,47,555,367,317,315,52,429,435,429,429,2,2,2,2,2,2,2,2,229,2,2,229,2,2,2,229,2,2},
|
||||||
|
{490,331,187,398,407,373,497,219,423,423,378,378,2,419,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{378,406,112,198,539,550,516,59,240,240,23,316,2,122,2,2,2,2,2,2,2,2,2,2,111,111,2,2,2,95,2,2},
|
||||||
|
{474,373,248,330,40,113,105,273,103,407,2,165,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{495,406,306,239,172,323,236,50,37,435,2,310,56,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{498,447,112,241,552,119,227,189,140,140,140,140,140,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{505,132,169,418,342,28,319,301,172,530,317,317,335,2,2,2,2,2,2,376,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{397,393,191,269,462,151,264,134,307,307,2,163,163,2,2,2,2,2,2,2,2,2,2,2,2,2,159,2,2,2,2,2},
|
||||||
|
{485,491,325,149,122,145,228,100,311,64,2,62,137,2,137,2,2,2,2,2,2,2,392,2,2,2,2,2,2,2,2,2},
|
||||||
|
{364,462,360,383,182,187,123,69,129,146,2,156,149,2,149,2,2,2,2,2,2,2,303,303,303,2,2,2,2,2,149,266},
|
||||||
|
{507,195,130,401,363,171,483,20,86,464,2,89,89,2,26,2,2,2,2,2,425,425,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{380,220,87,122,242,78,207,371,95,305,2,2,2,2,440,440,445,358,358,331,331,358,445,445,445,445,445,445,445,445,445,445},
|
||||||
|
{507,221,247,137,182,90,28,207,325,438,2,2,2,2,2,187,232,438,2,2,68,37,37,37,37,37,37,37,37,37,161,2},
|
||||||
|
{509,265,101,126,203,86,152,416,352,85,2,2,2,284,391,368,2,2,152,2,2,2,325,2,2,2,2,2,2,2,2,2},
|
||||||
|
{572,359,332,480,68,535,59,504,365,21,2,2,246,54,246,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{415,178,178,372,415,400,73,82,348,99,2,23,325,44,2,2,2,2,2,2,2,2,325,2,2,2,2,2,2,2,2,2},
|
||||||
|
{430,275,236,361,42,552,368,236,653,74,65,458,288,307,307,2,2,2,2,2,2,2,65,65,2,2,2,2,2,2,2,2},
|
||||||
|
{434,139,58,437,130,441,188,15,63,145,145,145,300,2,2,2,2,300,2,2,2,2,2,2,2,2,401,401,401,401,401,401},
|
||||||
|
{542,138,266,514,552,202,103,197,574,48,2,96,96,2,2,96,96,217,2,2,2,2,2,2,2,2,2,2,2,2,2,217},
|
||||||
|
{546,494,72,272,550,219,213,209,169,404,69,464,86,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{602,466,332,458,99,244,255,183,446,670,2,186,323,2,2,2,2,2,2,2,2,2,2,2,2,2,2,292,165,165,165,165},
|
||||||
|
{422,413,561,110,242,62,436,478,18,150,606,88,643,2,249,2,2,2,2,456,2,2,2,2,2,2,2,2,2,2,2,456},
|
||||||
|
{522,141,154,253,264,53,120,93,274,52,44,203,556,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{600,249,375,555,421,322,317,84,517,517,268,106,353,2,2,2,2,2,2,2,2,2,268,2,2,2,2,2,2,302,2,2},
|
||||||
|
{555,516,310,438,290,559,52,265,248,193,285,441,285,285,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{555,300,232,386,470,300,355,177,57,407,450,279,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{544,177,79,306,256,402,205,496,398,115,115,43,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{534,274,194,220,575,81,206,544,341,85,137,429,429,429,429,344,2,2,2,2,2,315,315,315,315,315,315,72,72,72,2,2},
|
||||||
|
{400,136,112,136,273,277,205,578,122,122,230,230,2,2,2,2,2,2,2,2,2,2,2,2,2,2,302,2,2,2,2,2},
|
||||||
|
{576,421,115,52,253,373,17,657,43,178,178,58,485,485,485,485,485,485,2,2,2,159,159,159,159,2,619,2,2,2,2,2},
|
||||||
|
{576,301,142,329,96,41,302,528,126,112,206,206,2,2,2,2,2,2,206,206,2,206,206,2,191,206,206,191,191,191,191,206},
|
||||||
|
{548,538,508,250,539,102,73,285,119,433,480,480,2,2,2,480,480,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{622,526,294,56,498,176,237,351,25,26,474,55,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{446,163,469,481,240,278,51,373,491,13,22,419,2,2,2,2,2,2,2,2,2,176,176,2,2,2,2,2,2,2,2,2},
|
||||||
|
{445,223,102,108,120,166,68,214,737,504,96,96,206,377,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,39,39,528},
|
||||||
|
{453,121,489,84,434,505,78,575,468,372,468,468,83,468,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{425,355,128,58,194,82,438,117,10,34,34,35,112,107,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{432,479,328,443,253,634,271,429,406,543,406,543,543,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{433,294,192,205,152,70,99,68,392,169,309,390,390,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,199,2,2,2},
|
||||||
|
{456,383,487,311,57,579,673,264,582,187,184,43,43,2,2,2,2,501,501,501,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{437,561,384,619,363,420,614,117,217,247,405,142,142,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{434,372,239,508,478,26,375,255,151,151,650,112,251,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{437,133,516,423,305,90,135,25,266,487,6,286,286,2,2,2,2,2,2,2,2,2,2,2,2,510,510,2,2,2,2,2},
|
||||||
|
{463,341,170,401,178,79,305,98,162,166,32,392,335,335,335,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{610,477,478,516,318,184,267,423,190,494,494,2,336,336,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{611,211,491,224,47,54,124,268,271,271,223,2,2,2,2,2,2,2,2,2,2,2,2,359,2,2,2,2,2,2,2,2},
|
||||||
|
{590,463,461,162,162,622,167,254,29,377,377,75,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{478,388,612,404,491,561,180,80,262,58,94,2,2,275,2,2,2,2,2,151,2,2,2,2,2,312,312,312,2,2,2,275},
|
||||||
|
{629,225,67,623,298,588,354,49,41,185,176,63,63,63,2,2,2,2,2,2,2,2,2,2,2,2,8,435,32,32,435,435},
|
||||||
|
{671,275,392,298,612,328,337,215,58,58,124,2,2,490,392,2,2,2,125,457,457,2,2,2,2,2,2,2,2,2,2,457},
|
||||||
|
{448,126,129,168,209,340,40,96,509,509,509,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{667,246,160,68,737,203,168,628,46,128,358,2,2,2,121,121,2,2,2,2,2,2,560,121,2,2,2,2,2,2,2,121},
|
||||||
|
{635,212,284,356,187,591,275,361,194,317,488,2,2,2,2,2,2,97,6,2,6,247,2,2,2,2,2,2,2,2,2,6},
|
||||||
|
{612,395,104,86,264,321,521,325,252,53,178,100,100,100,16,343,343,343,343,343,2,2,2,2,2,2,2,2,2,343,343,343},
|
||||||
|
{486,428,287,472,292,141,504,178,585,98,282,2,2,2,2,2,2,2,2,2,2,2,2,284,284,284,78,284,2,2,2,2},
|
||||||
|
{612,327,212,565,450,385,201,649,423,491,106,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{462,579,236,447,60,162,427,258,73,742,742,2,742,742,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{495,440,89,439,65,207,459,407,139,131,624,2,380,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{469,507,276,227,66,237,260,386,27,666,31,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{646,393,273,238,24,13,253,127,368,316,316,316,150,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{626,196,111,465,386,431,181,414,614,391,349,318,389,2,389,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{667,257,290,122,109,523,95,26,282,49,374,236,236,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,88,2,2},
|
||||||
|
{653,169,261,533,488,282,213,443,337,480,503,174,534,2,2,2,2,2,534,2,2,2,2,534,2,2,2,2,534,2,2,2},
|
||||||
|
{670,555,160,90,604,604,50,459,376,545,316,180,526,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{639,253,95,380,108,448,223,254,381,30,6,644,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{642,160,702,90,157,254,278,521,650,277,74,554,122,2,2,2,2,2,2,517,174,174,174,2,2,2,2,2,2,2,2,2},
|
||||||
|
{678,254,190,197,637,49,130,25,374,357,357,411,643,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,537,2,2},
|
||||||
|
{512,347,65,546,434,87,18,123,672,412,316,6,699,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{657,233,108,38,147,53,136,168,408,477,477,279,268,289,2,2,2,2,2,2,289,2,2,2,2,2,2,2,2,289,289,2},
|
||||||
|
{498,431,217,101,78,143,111,113,181,825,458,140,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{660,624,376,472,165,66,158,308,492,779,305,305,2,576,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{521,249,388,155,467,245,134,311,72,312,312,623,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{408,348,216,299,302,668,347,63,172,141,272,168,678,2,2,2,512,2,2,2,2,4,2,2,2,494,64,64,64,128,16,512},
|
||||||
|
{669,421,230,70,212,845,237,347,148,76,823,472,2,2,2,132,2,2,2,2,2,2,2,383,132,383,2,2,383,383,383,383},
|
||||||
|
{693,530,139,82,780,416,270,278,330,484,484,200,2,2,2,2,137,94,2,2,2,2,2,2,2,2,484,2,2,2,2,2},
|
||||||
|
{672,150,164,622,196,75,302,119,42,314,314,132,60,60,60,298,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{705,302,411,705,691,160,809,40,32,867,826,826,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{684,229,138,46,407,399,82,254,267,31,31,45,2,209,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{707,323,409,27,31,157,492,463,886,412,251,251,304,190,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{715,521,636,304,402,459,435,571,611,214,214,43,43,358,2,2,2,2,358,2,2,2,2,2,2,358,358,358,2,2,358,358},
|
||||||
|
{768,224,219,425,467,147,151,643,316,263,263,263,263,263,2,2,2,2,2,272,139,2,2,2,2,2,2,2,2,2,272,53},
|
||||||
|
{555,543,434,78,850,174,277,194,4,100,471,69,69,424,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{690,206,572,877,600,129,288,52,19,147,222,222,147,147,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{793,279,264,566,252,495,872,492,482,107,294,503,350,350,2,2,2,2,2,2,2,285,285,273,273,273,273,2,2,2,2,2},
|
||||||
|
{703,427,225,320,136,47,103,547,239,217,73,68,68,204,204,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{791,275,60,137,352,839,67,476,356,216,216,563,563,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{703,312,472,588,228,512,386,668,477,617,389,389,389,2,296,2,2,2,2,343,343,2,2,343,343,2,2,617,617,617,617,2},
|
||||||
|
{709,509,697,145,252,194,304,192,192,623,623,4,423,2,2,2,199,423,2,2,2,222,222,2,2,623,623,623,623,623,2,222},
|
||||||
|
{587,453,117,107,672,86,248,568,568,294,294,513,78,2,2,164,82,2,2,2,2,22,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{741,466,378,135,737,131,159,469,59,2,59,59,187,2,204,2,2,2,2,2,2,2,2,2,798,2,2,798,798,798,798,798},
|
||||||
|
{539,310,463,103,553,45,609,326,197,2,62,113,272,2,62,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{750,703,182,242,92,335,272,466,594,2,701,569,474,129,140,140,2,507,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{547,210,113,361,584,121,65,307,98,2,2,552,514,514,2,514,207,514,514,514,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{555,229,328,91,272,815,483,749,468,2,92,92,4,92,2,2,2,258,258,258,2,258,258,2,2,2,2,258,2,2,258,258},
|
||||||
|
{580,145,358,434,630,73,604,366,366,2,2,398,398,207,2,207,487,2,2,487,207,2,2,207,207,207,2,2,2,2,207,207},
|
||||||
|
{457,520,93,460,275,525,300,184,354,147,147,147,147,179,82,82,82,82,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{872,630,513,218,719,174,197,104,86,281,281,281,541,642,281,94,2,45,94,2,335,335,2,2,2,2,2,2,2,2,2,84},
|
||||||
|
{765,421,129,298,867,365,222,476,401,142,90,22,22,88,226,657,2,2,477,2,2,2,2,2,226,226,2,226,2,2,2,226},
|
||||||
|
{833,634,228,520,113,329,279,420,581,2,2,385,385,110,450,2,733,2,2,2,561,561,2,561,2,2,2,2,2,2,2,2},
|
||||||
|
{587,553,360,539,227,800,312,143,536,2,2,2,64,64,64,2,2,2,179,179,493,2,2,184,184,184,58,2,2,2,493,493},
|
||||||
|
{744,466,389,280,229,134,363,177,389,2,2,2,536,273,536,536,536,536,168,45,45,45,45,2,2,2,2,2,2,2,2,2},
|
||||||
|
{841,222,158,469,253,91,347,241,766,2,2,2,88,88,88,439,439,439,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{462,653,478,67,269,150,474,711,220,669,669,669,669,669,390,352,325,2,229,545,545,545,545,545,545,545,545,2,545,352,309,352},
|
||||||
|
{468,430,849,689,202,427,45,34,105,2,2,2,2,4,4,4,4,4,4,4,2,2,2,4,4,4,4,4,2,2,2,2},
|
||||||
|
{610,289,503,744,775,512,605,454,484,2,2,2,444,466,145,631,2,631,631,631,631,631,631,631,631,631,2,2,631,631,631,858},
|
||||||
|
{792,169,306,843,246,123,293,229,483,2,2,2,165,163,163,163,163,440,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{563,325,717,766,440,705,290,123,228,2,2,2,32,64,146,2,2,2,116,79,79,2,146,146,79,79,79,2,2,146,146,79},
|
||||||
|
{795,185,350,211,82,537,106,680,62,2,2,537,423,423,423,2,2,501,501,2,501,2,501,2,2,2,2,2,2,2,2,2},
|
||||||
|
{633,425,295,548,497,163,381,461,89,2,2,831,583,896,38,2,625,2,2,2,276,276,2,2,276,2,2,2,2,2,2,2},
|
||||||
|
{767,318,84,97,208,387,423,196,417,2,396,396,396,396,396,128,128,2,2,2,328,328,4,4,4,4,101,2,2,328,82,16},
|
||||||
|
{802,533,869,638,67,192,805,223,219,2,2,191,178,178,77,77,2,2,2,2,431,431,2,2,2,431,431,2,2,431,2,2},
|
||||||
|
{781,638,410,399,336,465,856,426,28,2,4,4,6,6,2,2,2,449,372,372,449,449,449,2,2,449,449,449,449,449,449,2},
|
||||||
|
{807,377,237,443,388,286,158,349,491,32,32,260,260,260,2,2,260,615,615,615,2,2,260,260,260,260,260,615,615,615,615,615},
|
||||||
|
{780,359,766,618,41,596,86,636,287,707,707,96,49,373,613,373,2,2,2,2,2,2,2,613,613,613,2,2,2,2,2,2},
|
||||||
|
{788,497,334,93,319,169,273,540,904,2,903,569,569,569,272,272,2,2,2,2,571,571,571,571,571,571,571,571,571,571,571,571},
|
||||||
|
{622,309,913,550,994,90,257,588,29,526,526,526,496,496,576,2,2,2,2,2,182,182,182,2,2,447,447,447,447,447,447,182},
|
||||||
|
{814,652,456,774,624,870,27,739,464,2,108,578,578,561,295,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{818,280,99,873,165,426,341,74,479,342,727,684,684,662,662,2,2,2,2,2,2,662,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{593,411,953,203,89,57,785,354,349,424,424,707,707,707,829,2,2,2,2,2,670,670,670,2,2,424,424,424,2,2,670,424},
|
||||||
|
{629,560,621,245,683,633,495,551,472,2,31,74,489,684,555,684,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{901,490,693,410,666,119,703,593,201,61,70,70,774,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,418,418},
|
||||||
|
{669,321,391,548,189,157,337,42,796,871,276,622,30,2,2,2,2,2,2,2,580,580,107,2,2,2,2,2,434,434,434,434},
|
||||||
|
{610,236,633,300,681,358,72,281,148,466,466,283,275,2,386,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{929,360,102,893,329,136,515,33,170,581,268,35,777,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{859,584,475,745,506,900,40,869,143,612,175,275,209,12,12,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{822,581,76,382,72,347,964,324,137,61,61,28,623,351,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{655,330,324,151,166,431,58,174,142,115,1003,66,724,778,2,2,2,503,503,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{867,820,301,252,61,331,105,309,562,218,365,326,768,672,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{623,330,182,489,212,223,741,490,40,412,801,681,681,801,2,2,71,2,2,2,2,2,2,427,2,2,2,2,2,2,2,2},
|
||||||
|
{859,844,510,859,118,190,550,29,159,622,622,382,258,382,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{612,237,272,53,534,682,372,935,494,536,536,599,599,599,2,536,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{843,730,235,233,816,495,598,134,131,604,227,378,378,553,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{667,397,121,526,321,660,848,729,357,137,268,711,521,521,2,2,2,2,2,2,2,2,2,2,2,2,2,194,2,2,2,521},
|
||||||
|
{939,783,796,676,259,643,103,289,15,471,80,80,2,239,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,888},
|
||||||
|
{670,595,333,257,907,413,548,341,327,350,612,700,700,700,700,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{678,274,695,790,169,701,707,1084,470,123,846,846,217,121,317,2,2,2,83,83,83,83,83,83,83,83,83,2,2,2,2,2},
|
||||||
|
{877,181,375,79,199,256,223,295,135,371,395,354,2,307,944,2,813,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{882,417,475,424,311,646,346,207,74,157,590,356,2,2,324,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{708,442,186,698,345,103,687,463,163,416,416,107,2,2,2,375,375,416,6,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{865,675,786,568,112,197,225,348,372,497,215,215,2,2,2,2,159,159,150,224,224,141,2,2,2,2,141,141,141,141,141,141},
|
||||||
|
{844,244,672,489,839,263,14,233,422,392,8,392,2,2,2,2,2,2,815,815,815,815,257,257,105,105,2,2,2,815,815,815},
|
||||||
|
{693,726,117,167,535,725,224,78,716,100,460,299,2,2,2,2,921,744,2,2,2,2,2,378,2,2,178,178,178,2,178,178},
|
||||||
|
{898,559,396,742,51,143,411,221,116,756,756,756,2,2,2,701,701,2,2,2,2,240,225,256,322,322,240,240,240,240,240,322},
|
||||||
|
{697,540,358,391,932,309,103,73,35,353,353,503,2,2,353,134,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{982,579,548,413,416,103,71,101,1039,526,684,684,2,2,656,2,2,2,2,2,2,2,2,2,2,2,656,656,656,2,656,656},
|
||||||
|
{695,881,335,126,429,476,772,667,974,98,433,49,129,129,2,2,2,2,2,2,2,2,2,2,544,2,544,2,2,2,2,544},
|
||||||
|
{859,361,215,569,255,378,543,436,220,34,105,105,816,816,816,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{705,770,134,178,940,944,654,600,46,797,797,591,2,145,616,2,2,2,2,2,2,389,389,2,122,2,2,2,389,389,909,389},
|
||||||
|
{642,757,247,513,372,54,546,971,271,61,61,1018,2,143,332,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{988,271,675,163,379,108,48,472,870,485,485,18,2,485,528,528,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{865,827,614,74,725,685,724,190,178,272,835,722,2,35,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{923,397,722,186,203,575,24,144,36,526,206,787,12,100,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{718,359,103,558,684,560,67,35,120,342,680,265,265,265,2,2,265,2,2,2,2,2,2,2,2,2,430,2,2,2,2,2},
|
||||||
|
{927,493,988,194,97,1006,377,578,105,248,707,784,98,784,2,2,2,2,2,2,2,2,2,370,370,2,370,2,2,2,2,2},
|
||||||
|
{900,455,485,601,353,69,67,965,25,226,314,314,883,923,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{903,259,153,106,289,916,861,41,441,368,131,131,262,671,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{945,358,160,196,82,403,362,195,376,877,521,336,521,77,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{912,516,108,555,306,274,55,197,565,174,659,208,441,441,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{753,242,194,619,345,94,463,485,163,85,412,575,270,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{940,226,320,666,269,54,542,174,109,290,754,524,649,2,202,2,2,2,2,2,2,2,776,202,776,776,776,2,2,202,202,202},
|
||||||
|
{915,210,456,377,303,237,225,521,621,175,569,20,124,2,601,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{672,652,792,253,796,404,171,90,406,433,43,159,72,2,2,372,2,540,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{733,439,537,37,149,650,916,443,743,621,921,664,664,2,2,2,2,2,682,523,523,523,2,2,523,523,523,523,523,523,523,523},
|
||||||
|
{982,344,812,567,243,52,246,369,439,205,600,739,730,2,2,2,61,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{982,604,126,65,633,657,22,776,161,45,725,44,4,2,2,2,2,2,2,2,2,2,269,269,2,2,2,2,2,2,2,2},
|
||||||
|
{745,600,284,1117,459,1135,300,52,845,331,334,334,334,2,334,334,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{936,409,217,57,574,395,481,245,548,268,447,598,375,2,192,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{986,241,233,45,721,325,350,222,35,1065,1065,1065,1065,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{755,796,877,981,259,194,1180,215,90,658,662,662,662,2,36,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{981,626,987,827,466,458,578,346,475,223,223,223,342,1058,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,728},
|
||||||
|
{949,422,941,491,66,786,592,429,307,123,40,478,478,478,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{992,723,625,251,431,544,309,466,700,644,484,837,904,320,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1077,496,819,340,974,122,39,1209,819,18,461,648,648,394,2,2,2,2,2,2,61,2,2,2,2,2,394,2,2,2,2,394},
|
||||||
|
{999,674,212,673,279,579,462,754,89,866,345,110,110,887,2,2,2,2,2,707,707,2,2,2,2,2,2,2,2,2,2,707},
|
||||||
|
{1083,356,367,357,559,213,606,477,71,103,790,103,299,299,2,2,2,2,2,2,406,406,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1005,260,389,960,501,714,118,73,334,1019,704,204,504,205,822,822,2,2,2,2,2,2,2,2,2,2,684,2,2,2,2,2},
|
||||||
|
{738,749,769,610,306,326,328,578,479,840,840,840,68,192,2,150,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1010,937,449,474,154,456,766,318,275,444,709,2,778,778,778,806,779,779,2,2,2,2,2,2,2,2,806,2,2,2,287,287},
|
||||||
|
{1011,780,134,945,183,42,741,25,252,164,205,222,222,222,147,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1118,427,294,404,268,217,922,515,19,1045,1045,2,833,291,448,2,2,2,2,2,2,2,2,2,175,2,2,2,2,2,2,2},
|
||||||
|
{1094,640,912,223,67,472,623,623,1244,65,1009,1209,1209,812,387,2,2,2,513,2,2,2,2,2,2,2,2,2,2,2,1209,234},
|
||||||
|
{722,375,264,390,515,498,1161,391,884,551,238,2,2,825,549,2,2,2,551,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{792,250,299,210,496,682,94,207,220,227,227,2,2,227,73,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1022,409,93,359,983,345,280,280,104,940,940,2,2,382,1039,2,2,2,2,831,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1027,925,413,335,327,826,250,122,293,773,564,541,420,420,420,774,763,2,2,2,2,2,2,900,110,110,2,763,2,2,2,2},
|
||||||
|
{1028,730,807,119,209,146,230,498,164,309,309,2,2,2,693,912,430,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{997,525,680,120,466,728,288,110,1082,544,572,2,2,663,290,290,2,2,754,2,2,2,2,2,582,582,582,582,582,2,2,2},
|
||||||
|
{1055,395,795,561,222,85,294,433,377,89,89,2,2,2,456,821,2,2,821,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{997,614,240,638,755,575,874,321,600,235,665,2,2,2,154,154,767,767,2,767,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{802,298,672,424,104,623,152,159,476,760,66,2,2,2,215,215,490,490,490,2,2,2,2,2,490,490,490,490,490,490,490,490},
|
||||||
|
{1128,788,124,501,561,1015,419,787,48,620,705,2,2,2,2,88,18,2,215,215,215,2,2,215,215,2,2,2,215,2,2,2},
|
||||||
|
{807,433,721,434,449,242,170,842,21,4,642,2,2,2,2,2,4,4,4,4,2,856,856,856,885,885,856,856,856,856,856,885},
|
||||||
|
{755,612,235,265,369,855,414,362,478,518,518,2,2,64,16,8,32,4,16,8,8,1041,501,1041,2,2,64,16,8,8,16,270},
|
||||||
|
{1004,719,1041,460,551,516,135,417,130,698,698,2,2,2,655,655,655,655,655,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1017,568,930,1113,556,1299,114,881,690,475,641,2,2,2,779,779,103,2,528,2,2,2,2,2,2,528,528,2,2,910,910,2},
|
||||||
|
{814,473,286,752,476,779,420,569,742,164,490,2,2,2,793,812,812,812,2,812,812,2,2,526,526,812,526,2,2,2,526,526},
|
||||||
|
{818,301,273,664,206,971,895,590,912,523,523,2,2,452,384,255,2,130,130,130,130,865,2,2,2,255,2,2,2,2,2,2},
|
||||||
|
{820,249,292,1017,1017,143,403,37,433,456,515,2,2,69,640,2,2,2,2,2,2,2,2,2,2,2,2,824,824,824,2,2},
|
||||||
|
{1078,527,589,244,170,892,827,606,1165,773,189,2,2,240,22,2,2,2,2,2,2,759,621,621,621,621,621,621,621,621,621,621},
|
||||||
|
{865,1132,428,582,254,408,536,376,825,116,116,1266,1266,1266,705,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1062,268,389,1325,598,276,1270,48,572,439,302,2,544,609,544,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1065,517,247,1142,247,674,385,120,592,177,98,2,956,364,275,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{635,503,594,203,456,1246,221,396,1151,178,66,2,781,587,86,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1157,395,446,280,1130,695,668,271,111,882,477,615,615,615,2,2,2,2,2,2,2,2,615,615,615,615,615,615,615,2,305,2},
|
||||||
|
{830,397,932,519,818,113,367,694,88,535,535,414,343,175,2,2,2,2,2,2,2,2,2,2,414,864,2,2,864,864,864,864},
|
||||||
|
{793,463,329,730,390,551,968,92,511,470,424,563,672,563,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1050,749,809,479,87,757,288,172,597,722,4,418,418,390,2,2,2,2,2,390,390,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1084,402,130,1077,276,154,1068,779,511,853,83,757,757,38,2,2,2,2,2,202,2,2,2,2,2,2,2,2,2,2,757,2},
|
||||||
|
{1090,255,271,110,159,235,158,236,271,815,1300,416,416,416,2,2,416,416,2,2,2,399,791,791,2,791,2,2,2,2,791,791},
|
||||||
|
{1058,417,271,172,312,363,184,191,28,183,759,214,759,39,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1057,385,263,395,901,274,727,340,1117,263,813,870,858,429,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1102,846,985,1085,764,124,764,51,874,612,478,801,478,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1120,665,311,695,319,1033,511,297,602,1030,1030,714,240,240,2,2,2,2,2,2,2,2,2,2,2,2,2,953,2,2,2,2},
|
||||||
|
{814,293,763,661,575,631,524,636,112,691,595,1103,405,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1106,662,258,190,1315,214,530,263,318,904,877,1317,318,2,510,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1206,469,299,1052,655,114,189,213,321,188,64,475,475,2,2,662,662,662,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1120,1159,358,347,838,207,357,167,476,52,672,38,822,2,2,2,2,2,2,213,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1076,596,553,545,79,727,881,121,298,169,639,368,695,115,115,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1130,177,84,673,350,543,543,95,128,954,430,884,884,2,884,884,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1222,412,430,707,691,746,131,607,311,607,112,217,912,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{820,461,681,382,273,273,358,274,274,91,887,676,386,2,676,676,2,2,2,2,2,2,2,200,2,2,2,2,200,2,2,2},
|
||||||
|
{1096,1166,209,407,1127,400,974,322,428,906,631,134,171,2,2,2,2,664,664,664,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1091,946,437,51,527,802,597,639,587,645,510,586,586,2,2,2,2,2,2,2,2,2,2,2,2,2,2,168,168,168,168,168},
|
||||||
|
{1148,585,868,1282,666,417,733,1231,515,332,1213,337,337,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1103,276,174,408,233,170,955,108,530,354,585,38,677,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,476},
|
||||||
|
{1167,478,1169,1053,563,371,108,772,413,497,1338,991,660,2,2,2,2,2,2,2,2,2,2,2,2,27,2,2,2,2,2,2},
|
||||||
|
{1108,437,1160,324,868,686,361,399,786,1161,1161,707,731,731,655,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1116,331,280,422,1109,341,570,243,849,241,566,61,608,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{898,782,478,1208,196,983,608,537,196,1141,141,296,715,715,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1099,1187,300,240,268,413,1366,634,184,768,773,365,783,224,783,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1158,945,300,1115,205,495,435,302,187,774,774,843,843,284,284,2,2,2,2,909,933,933,933,2,2,909,909,2,2,2,2,909},
|
||||||
|
{904,660,1283,46,33,124,416,218,152,970,1241,305,307,307,307,260,894,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1127,553,287,58,739,99,514,739,766,42,580,241,598,598,936,936,936,629,629,629,629,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1142,370,287,925,307,1232,129,11,1284,1056,33,33,536,521,2,1286,2,2,2,2,2,2,2,2,2,2,2,2,847,847,847,847},
|
||||||
|
{1140,814,528,677,84,1192,305,637,335,451,103,325,77,969,2,651,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1297,600,419,985,846,493,186,109,147,239,197,762,762,327,327,1004,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1181,615,482,653,238,130,313,506,98,1314,730,730,730,730,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{921,613,628,1288,111,150,191,233,633,83,387,602,105,394,2,2,2,2,2,2,2,351,2,2,351,351,351,2,2,2,351,351},
|
||||||
|
{1192,555,586,516,1288,733,64,653,364,273,421,215,75,75,2,2,2,2,2,2,953,953,953,953,8,383,383,2,161,383,953,953},
|
||||||
|
{1160,617,505,1205,374,906,23,408,194,91,91,91,585,984,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1203,1101,497,352,254,309,464,123,607,1080,265,1145,1145,1145,284,284,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1210,656,1026,782,802,442,1319,734,794,165,165,796,93,796,2,829,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{963,646,721,1161,219,667,1088,485,692,692,663,535,553,662,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,686,686,2},
|
||||||
|
{966,590,140,297,189,844,633,12,847,742,742,244,281,34,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{941,231,1038,309,173,770,413,560,855,660,721,1103,721,721,721,2,2,2,2,2,2,2,2,2,2,2,2,174,2,2,2,2},
|
||||||
|
{1213,305,656,983,1399,1196,692,986,9,339,754,308,2,308,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{972,768,1109,523,642,546,1452,29,1296,13,813,813,2,1496,2,2,2,2,2,2,2,165,165,165,165,165,165,2,2,2,2,544},
|
||||||
|
{1330,671,528,831,1426,735,33,425,364,119,363,978,2,761,483,476,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1188,217,838,237,379,202,785,949,479,169,348,872,2,872,872,2,2,2,2,2,2,1028,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1190,286,513,881,390,215,387,130,749,554,1110,519,160,160,160,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1247,353,973,217,1044,1318,1115,319,203,390,1244,225,2,2,508,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{893,560,132,1420,721,191,568,799,412,22,322,93,2,4,4,4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{987,774,678,175,145,264,588,97,1308,6,828,1129,2,2,2,45,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{955,980,753,96,574,259,1327,556,342,1415,1036,1036,478,478,478,478,507,2,2,2,2,151,2,2,317,2,2,2,2,2,595,595},
|
||||||
|
{882,1038,211,110,942,337,1305,1225,661,183,381,381,2,2,2,2,347,2,2,2,2,2,2,2,600,431,431,431,431,431,431,431},
|
||||||
|
{1208,486,343,725,677,1204,135,139,924,170,1111,317,2,2,2,2,202,706,202,107,107,107,2,2,706,706,107,107,2,2,2,706},
|
||||||
|
{1259,1017,456,298,443,838,137,744,551,334,36,951,2,2,2,699,718,2,2,984,2,2,2,2,2,2,984,984,2,2,2,2},
|
||||||
|
{1212,1186,641,284,565,636,895,82,690,117,184,184,2,2,2,397,902,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1263,370,132,635,381,47,537,179,1192,301,1282,33,2,2,2,1553,2,2,2,2,2,2,2,2,2,2,2,307,307,2,2,2},
|
||||||
|
{1223,433,252,572,424,82,221,107,382,430,203,461,2,915,362,964,2,2,964,2,2,2,2,2,964,964,964,964,964,485,485,485},
|
||||||
|
{1015,593,112,1408,51,104,199,221,931,1010,928,928,2,2,878,878,2,2,2,2,731,731,2,731,731,2,731,2,731,731,731,2},
|
||||||
|
{1220,410,1193,352,260,434,469,41,1090,961,961,728,2,2,330,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{898,1043,391,1289,29,830,184,321,1136,85,1133,1082,864,864,2,2,2,2,2,2,2,2,789,789,2,789,789,2,2,789,789,2},
|
||||||
|
{1223,434,851,152,140,1495,190,397,925,37,1080,430,2,2,204,2,759,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{989,1043,184,232,64,403,284,745,171,171,995,223,380,380,1400,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{939,1070,1288,254,973,901,321,109,568,713,336,988,2,946,262,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1276,636,569,258,325,675,342,85,88,579,833,833,833,833,520,2,2,2,2,520,520,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{982,508,815,214,206,602,448,685,446,572,1549,8,1047,1047,1047,2,2,2,2,2,2,2,363,502,2,2,71,363,2,2,363,363},
|
||||||
|
{1288,1398,789,514,151,600,1618,1194,1419,441,234,204,1191,438,828,2,857,857,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1002,342,1045,757,1008,979,322,240,1211,171,552,123,2,129,129,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1401,402,525,293,97,223,452,808,61,169,1023,1023,886,886,1023,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1001,644,263,164,136,939,624,95,489,1023,1107,331,331,10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1011,475,845,532,567,951,663,295,877,1275,227,39,618,683,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1401,741,509,797,47,157,1256,482,1513,899,736,780,780,210,2,2,2,2,783,783,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1047,880,369,402,641,446,639,586,277,396,419,275,825,820,2,2,2,238,238,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1273,701,831,1294,1580,137,162,415,563,11,92,116,116,116,2,2,2,2,2,2,1029,1029,1029,504,504,877,877,877,877,877,1029,1029},
|
||||||
|
{1335,400,315,412,172,125,568,1024,58,601,398,985,640,577,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1453,947,486,485,453,415,1164,684,504,605,422,998,727,727,2,2,2,1136,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1057,1198,146,529,284,1286,160,135,75,686,648,1425,821,586,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1052,442,936,64,132,1378,1323,161,161,161,230,131,12,12,2,2,2,2,2,2,2,2,2,2,2,998,998,998,998,2,2,2},
|
||||||
|
{1422,838,234,554,736,243,344,526,1108,33,1303,699,249,305,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1279,681,423,813,806,269,412,420,985,485,761,1013,649,796,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{938,614,523,557,898,624,178,461,287,985,371,371,260,613,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1335,834,652,528,536,523,497,60,173,777,238,59,4,59,4,8,2,2,2,559,559,559,559,559,559,559,2,2,559,559,559,2},
|
||||||
|
{1040,998,324,93,887,497,1326,443,152,1193,595,80,80,80,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1302,1116,283,1006,891,838,768,373,468,968,1178,1178,1269,1269,876,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1027,1128,114,395,357,417,848,22,389,1257,734,838,838,301,900,2,90,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1072,724,717,877,873,369,1031,698,917,1641,1641,1641,53,549,549,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{987,1243,424,240,53,1150,558,292,1107,574,814,1474,1474,1068,1186,2,2,2,2,2,2,2,2,2,2,2,2,2,2,859,2,2},
|
||||||
|
{1040,420,960,882,64,661,292,146,976,427,689,248,248,248,638,2,2,2,2,2,2,2,2,2,2,2,2,861,861,861,2,861},
|
||||||
|
{1040,522,666,398,78,208,293,818,134,867,147,147,482,2,4,629,629,629,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{987,1280,1245,1300,926,676,56,546,541,690,84,42,1000,1383,1383,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1324,588,1378,592,1445,1029,759,1296,739,931,363,704,312,704,704,704,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1058,454,1557,191,129,297,695,1390,1274,460,923,923,923,2,4,1059,2,2,2,2,2,2,2,2,2,2,2,2,2,1059,2,2},
|
||||||
|
{1327,572,282,1022,907,1276,409,643,1050,633,187,187,187,2,228,45,2,2,2,2,2,2,320,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1395,958,237,101,559,891,560,47,524,747,197,589,589,917,887,887,887,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1395,529,461,402,194,392,122,781,111,162,780,593,593,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1378,541,848,848,347,856,102,104,183,156,395,130,1377,2,2,2,159,159,159,2,2,2,772,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1062,212,784,63,252,873,1302,1108,1380,84,1375,1375,1375,2,2,2,375,374,2,980,2,2,2,980,980,980,2,2,2,2,2,2},
|
||||||
|
{1384,549,430,781,946,879,901,924,741,114,14,451,36,2,2,2,2,287,287,287,803,803,803,803,2,2,2,803,803,803,803,803},
|
||||||
|
{1413,627,1329,1092,526,197,31,417,1149,981,964,1003,685,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,717,717,2,2},
|
||||||
|
{1084,1174,1601,949,910,960,500,461,1290,23,1042,636,212,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1420,531,626,738,376,537,814,206,990,235,847,812,201,201,201,201,726,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1420,624,363,537,1436,278,292,377,263,820,376,382,382,2,654,655,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1091,793,1353,208,506,599,846,503,1011,247,289,61,1050,61,61,61,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1533,978,284,156,914,162,685,1184,252,1375,189,256,640,2,640,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1531,692,414,277,541,1371,1447,682,536,109,432,1240,1240,2,1022,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1128,398,791,1170,76,661,408,259,756,495,79,553,10,10,1532,1532,1532,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1040,704,618,854,374,1470,274,383,941,519,351,351,351,351,351,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1427,988,498,1529,99,678,1323,149,33,426,543,543,335,1507,772,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1102,349,490,266,144,220,599,437,743,764,647,1128,605,265,324,324,324,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1118,496,645,592,354,1133,935,428,72,532,182,182,1370,660,123,2,294,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1102,1042,315,745,1006,771,630,68,587,1187,295,295,295,408,408,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1118,724,1322,405,199,614,1087,885,1313,317,769,660,660,1158,535,2,2,2,373,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1120,772,743,488,346,126,784,584,943,153,311,133,133,969,605,605,2,2,2,2,2,2,2,605,2,2,2,2,2,2,2,2},
|
||||||
|
{1404,284,176,590,1128,1371,322,543,1136,546,1315,174,174,777,777,891,2,2,2,2,2,2,2,579,579,579,579,2,2,2,2,2},
|
||||||
|
{1441,791,233,141,141,316,89,296,462,1263,758,482,599,599,578,341,2,2,2,2,2,2,2,2,2,2,2,525,525,525,2,2},
|
||||||
|
{1413,406,700,547,1166,250,518,543,104,331,205,205,691,691,2,2,118,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1485,400,1497,168,82,680,1103,554,249,702,493,101,296,236,2,236,236,944,944,2,2,394,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1127,869,558,533,1215,194,1762,784,593,777,1153,1079,1079,1079,2,2,2,330,1045,2,1045,1045,2,2,2,2,2,2,2,2,2,787},
|
||||||
|
{1459,1243,467,533,266,1364,1031,890,1402,486,1678,1678,93,978,2,2,2,978,947,947,2,978,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1139,809,117,522,955,1096,1120,1470,116,184,1565,1565,557,557,2,2,2,2,2,829,1326,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1142,984,1044,590,340,241,662,357,366,1305,2,125,631,474,2,2,2,980,2,2,2,2,2,2,2,2,2,2,2,2,2,1273},
|
||||||
|
{1469,1247,1277,616,209,486,106,552,219,217,471,272,272,1201,2,2,503,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1148,542,1478,496,950,464,1011,235,136,180,2,416,758,453,2,909,2,2,2,2,2,2,2,2,2,2,1019,1019,2,2,2,2},
|
||||||
|
{1495,1178,874,415,1100,368,1057,1228,562,215,31,31,680,680,680,1208,2,2,2,2,2,2,2,2,1208,2,2,2,2,1208,1208,2},
|
||||||
|
{1497,1166,1613,1403,107,803,993,539,1436,1289,2,240,334,634,532,1147,2,2,2,2,2,2,2,117,2,2,2,2,2,2,2,117},
|
||||||
|
{1617,289,1033,169,355,260,30,45,721,906,88,44,44,418,417,218,2,2,846,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1628,721,400,239,728,1336,984,425,65,120,1232,463,463,640,349,616,616,2,2,2,2,2,2,2,2,147,147,2,2,2,2,2},
|
||||||
|
{1628,286,541,530,1610,201,1220,1592,272,181,2,38,263,1586,1157,1157,1157,2,2,2,1157,1157,2,2,2,1157,2,2,2,2,1157,1157},
|
||||||
|
{1531,621,210,755,482,82,1308,317,427,168,2,232,116,190,701,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,701},
|
||||||
|
{1532,575,1245,360,249,630,133,1406,920,1539,63,63,76,82,82,2,2,2,770,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1102,785,118,93,1491,988,275,53,1328,26,2,2,240,647,240,761,761,761,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1478,722,113,1534,1751,115,1728,1234,777,282,508,508,1184,63,1184,855,855,2,2,2,738,738,578,578,2,2,2,2,2,2,2,2},
|
||||||
|
{1480,536,1421,164,429,84,970,1673,548,497,2,2,530,156,156,128,245,2,2,2,2,260,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1533,1302,1286,538,619,526,1669,145,1034,125,2,1038,1038,388,388,387,729,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1482,961,1093,556,1746,628,427,689,510,751,684,37,37,1229,1256,882,1507,1507,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1472,852,533,433,924,57,53,1036,410,675,1212,1212,1212,600,600,1212,1259,1245,1245,1245,1245,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1228,425,1030,699,407,171,568,925,1104,97,2,2,1286,1286,1286,502,2,1219,1219,1219,1290,2,1219,1219,1219,1219,2,2,2,59,2,2},
|
||||||
|
{1547,657,777,695,1254,224,933,367,212,385,2,2,2,1422,749,245,885,710,2,2,710,710,710,45,710,710,710,710,2,336,710,2},
|
||||||
|
{1678,466,549,145,351,816,1041,334,192,192,2,2,348,1017,130,4,4,180,180,180,180,512,2,2,2,512,512,512,512,512,128,8},
|
||||||
|
{1550,569,481,1041,1680,1114,1265,160,386,194,2,2,2,533,929,531,422,531,1355,1355,1355,1355,531,216,216,2,2,2,2,2,2,2},
|
||||||
|
{1559,462,850,289,1570,71,512,858,810,835,2,2,2,2,1028,1205,1205,546,546,546,1205,1205,1205,1205,1205,2,1205,1205,1205,1205,1205,1205},
|
||||||
|
{1192,888,701,164,131,613,282,237,525,366,2,2,2,2,1737,845,845,750,2,1062,1062,1062,1062,1062,1062,1062,1062,1062,1062,2,1261,1261},
|
||||||
|
{1208,426,412,1072,274,248,1544,627,9,458,2,2,2,2,2,2,270,270,270,150,715,282,150,150,150,150,150,150,150,150,150,150},
|
||||||
|
{1128,393,1522,96,160,581,540,120,441,176,2,2,2,2,2,2,1427,551,1102,1102,328,328,592,592,592,592,592,592,592,592,592,592},
|
||||||
|
{1202,538,171,1177,1090,690,1566,746,1012,1012,2,2,2,2,313,781,808,313,1125,1117,930,1117,1117,1117,1117,1117,1117,1117,1117,2,2,2},
|
||||||
|
{1567,1265,372,1633,613,484,243,1523,21,275,2,2,2,431,431,431,431,2,2,978,489,889,889,889,889,889,889,889,2,2,2,2},
|
||||||
|
{1566,982,815,133,891,412,1179,831,651,268,2,2,2,367,366,367,367,63,63,767,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1522,1422,1017,124,499,451,731,1112,1355,1355,2,2,2,854,854,336,854,336,1297,2,2,2,193,193,193,193,193,2,2,2,2,2},
|
||||||
|
{1160,1331,917,1696,401,547,122,592,863,863,2,2,703,703,703,703,495,495,495,2,2,495,495,495,495,495,269,2,2,2,269,269},
|
||||||
|
{1538,814,1027,677,524,226,756,202,242,102,2,2,912,564,1289,682,2,1125,1125,1125,1125,2,1289,1289,1289,1125,1125,1125,2,1289,1289,1289},
|
||||||
|
{1598,397,1471,1471,1162,866,236,948,1557,737,2,2,153,737,1408,765,765,608,2,2,2,171,608,608,608,608,2,608,608,2,2,2},
|
||||||
|
{1598,434,107,270,148,1317,835,123,642,1236,2,2,67,633,771,878,771,878,878,2,2,2,771,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1628,1502,1042,822,80,403,1335,684,464,426,671,671,336,336,336,2,425,896,2,2,2,2,1337,1337,1337,1337,1337,1337,2,2,2,2},
|
||||||
|
{1630,715,1368,1273,993,293,385,545,1267,896,1038,1038,270,1325,1325,2,2,961,961,961,961,961,961,2,2,961,961,2,2,961,2,961},
|
||||||
|
{1612,723,409,641,796,1087,1228,1398,623,262,740,740,870,870,397,2,2,893,893,2,2,1367,328,2,328,2,2,2,2,2,2,2},
|
||||||
|
{1614,588,652,105,441,844,734,912,532,878,1073,1073,62,1415,693,1431,1431,1431,1431,925,925,925,925,925,925,925,2,2,2,2,2,2},
|
||||||
|
{1607,1503,1072,471,221,277,854,1236,263,752,2,694,1657,934,553,2,2,2,498,498,2,802,2,46,2,2,2,2,2,2,2,2},
|
||||||
|
{1172,987,140,1964,584,600,852,1725,456,1199,718,718,791,981,791,2,2,2,2,2,1260,2,2,2,2,2,718,2,2,718,2,718},
|
||||||
|
{1746,771,620,415,1057,437,613,1034,1662,837,2,1149,1466,1149,1149,1149,1466,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1263,835,1533,789,1259,174,1497,557,644,203,2,289,604,434,434,434,2,844,844,2,2,2,1111,1111,1111,2,2,2,2,2,2,2},
|
||||||
|
{1272,884,388,1889,956,159,1172,595,219,645,2,629,107,107,1279,75,2,2,2,211,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1797,904,172,659,349,177,692,448,1141,990,640,99,1073,806,640,640,2,640,640,911,911,911,640,640,640,640,2,2,2,2,2,2},
|
||||||
|
{1276,442,1008,1352,243,162,711,301,552,1002,668,668,384,71,384,384,2,2,2,2,2,727,727,727,777,777,777,777,777,777,2,777},
|
||||||
|
{1600,1130,171,1113,813,722,117,990,37,24,969,94,825,1398,1398,1398,1398,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1198,496,714,609,644,1159,873,249,186,1539,136,239,379,1994,2,68,68,68,68,68,2,2,192,2,969,2,2,969,2,2,969,969},
|
||||||
|
{1678,1316,460,1133,1003,150,1236,1316,1417,218,1763,1763,77,77,2,1491,771,771,771,771,771,2,771,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1682,449,1067,393,136,854,36,492,637,1053,247,1111,1111,1111,2,247,247,247,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1288,1690,702,760,420,333,1213,1911,805,351,67,67,1568,1568,2,2,604,142,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1288,1858,152,894,346,104,997,203,249,1006,1278,1489,1489,555,2,2,2,1074,1074,518,2,2,518,2,2,518,2,2,2,2,2,2},
|
||||||
|
{1601,697,532,408,697,1140,1568,47,1499,780,1171,318,318,318,2,2,2,2,318,318,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1283,1078,791,873,655,412,389,835,292,958,1245,678,1611,1519,2,2,185,2,2,2,2,2,2,1245,1245,2,2,2,2,2,2,1245},
|
||||||
|
{1685,1610,1447,1093,1255,937,703,431,522,1384,988,988,253,988,2,1892,1892,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1822,589,236,205,797,39,241,1048,181,386,102,102,102,111,1361,1361,1361,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1233,843,813,157,396,669,1531,439,640,733,996,996,996,1566,951,608,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1342,705,302,595,1200,52,83,647,519,139,103,103,103,513,2,513,2,2,2,2,2,513,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1630,1244,142,767,1299,719,629,1716,419,837,1145,1136,1148,1405,1405,1405,2,2,2,2,2,309,309,309,309,309,2,2,2,2,2,2},
|
||||||
|
{1636,974,279,419,893,1608,1491,156,1486,115,730,730,863,509,924,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1318,1234,213,1089,1567,602,1330,404,467,718,249,215,354,177,59,332,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1732,1771,584,533,297,1056,669,293,146,311,1176,311,590,590,277,2,2,2,2,2,2,2,2,2,539,539,2,2,2,2,2,2},
|
||||||
|
{1026,512,1196,394,1259,1313,762,549,311,1576,1576,465,465,140,465,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1360,383,1470,502,1010,153,1588,619,1246,396,1107,1107,112,423,423,2,2,2,2,2,202,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1320,1636,858,1210,509,194,1575,154,1424,455,1860,832,1075,581,262,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1670,1350,689,1074,437,956,587,642,1154,439,196,1108,1108,1108,990,2,2,2,2,2,1112,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1873,890,920,874,591,651,768,478,331,76,760,760,760,760,67,2,2,2,2,1241,1241,1241,1241,2,2,2,2,2,2,2,1241,1241},
|
||||||
|
{1682,867,333,102,628,891,654,506,995,684,961,563,1313,1313,1313,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1672,1248,429,813,262,92,809,1248,560,1365,1392,753,753,1259,1261,2,2,2,2,2,2,2,2,177,177,2,2,2,2,2,2,2},
|
||||||
|
{1391,1598,1112,590,797,584,1354,47,1473,1291,1874,48,491,463,990,463,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1875,1576,924,677,461,134,1525,1619,44,701,299,743,728,791,791,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,791,791},
|
||||||
|
{1267,904,1187,1595,765,1451,494,1573,950,909,87,1265,757,1371,1005,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1360,1091,1478,1237,97,578,1616,494,1422,223,865,1092,359,2,1080,4,2,2,2,688,1965,2,1965,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1750,386,393,840,723,791,1707,1319,1525,83,1302,571,280,2,280,73,2,2,2,1207,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1763,1018,1859,432,717,723,874,1294,1050,1800,1237,619,1074,2,10,1237,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1376,652,461,225,361,936,1073,1279,149,619,983,511,1994,2,2,1076,1076,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1947,393,495,946,1375,391,2128,582,1143,695,1872,760,760,2,2,1456,974,974,435,974,974,435,974,2,974,974,2,2,2,2,2,2},
|
||||||
|
{1768,1463,531,1008,95,1677,362,1105,985,177,1682,1682,244,2,2,1234,1041,1041,1041,2,2,2,1041,1041,2,2,2,2,2,2,1894,2},
|
||||||
|
{1780,1739,1357,1684,1586,736,208,966,1691,339,339,128,128,2,2,128,128,128,2,2,128,2,2,2,2,1929,2,2,338,2,2,338},
|
||||||
|
{1387,1459,358,1409,1919,917,777,223,313,1847,1012,1024,1024,2,2,2,2,1420,1420,1428,1420,2,1420,1420,2,2,2,1420,1117,1117,1117,1117},
|
||||||
|
{1289,907,228,665,1695,1735,489,214,762,1777,321,1674,932,2,2,2,2,1358,709,2,1959,1959,372,2,2,372,372,2,2,372,372,372},
|
||||||
|
{1378,680,1117,1367,759,62,319,563,505,1138,1093,345,693,2,2,2,780,780,2,2,2,729,729,729,2,2,2,2,2,2,729,729},
|
||||||
|
{1802,1645,453,1079,604,618,334,855,541,167,37,88,849,2,2,518,518,2,2,530,2,2,2,2,2,2,2,119,119,2,2,2},
|
||||||
|
{1275,1612,143,1586,502,987,555,436,2236,1826,494,494,358,2,2,213,2,2,2,2,2,2,1585,1585,1585,1585,1585,1585,1585,1585,1585,1585},
|
||||||
|
{1322,512,560,432,365,87,1835,1137,515,1271,1739,309,309,1229,1229,1229,2,2,2,2,2,2,2,2,416,416,416,416,2,2,2,2},
|
||||||
|
{1758,835,287,888,391,875,1834,516,1432,1171,98,408,302,976,976,1963,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1444,394,1613,796,645,1406,186,158,402,1364,314,588,606,2,577,117,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1337,1391,137,371,165,87,1026,20,419,99,572,572,918,854,918,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1323,589,526,1555,1636,1172,86,42,1545,57,627,1769,1769,2,867,343,2,2,2,2,2,2,2,724,2,2,2,2,724,724,2,2},
|
||||||
|
{1323,1647,384,301,270,549,1098,1144,1066,55,88,1805,683,2,945,120,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1327,1075,539,1017,926,350,1102,236,494,1268,286,286,1293,267,227,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1472,661,1538,487,94,2209,563,138,881,1735,718,203,1382,1473,1473,1473,1473,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1413,766,349,1471,45,625,733,1082,170,58,1268,207,1081,1081,1081,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1861,1487,419,97,799,1791,458,1029,370,627,57,414,414,1540,247,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1881,716,268,387,2138,1212,999,408,1363,434,1429,1429,1648,1648,1007,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1480,1131,1089,1688,340,962,505,1816,139,44,1350,403,1385,1996,173,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1868,650,1146,1690,948,43,497,692,1628,1302,1302,108,462,731,731,2,2,2,2,2,2,2,185,185,185,2,2,2,2,2,2,2},
|
||||||
|
{2023,1204,531,733,1054,618,668,363,783,218,1302,2055,559,2055,2055,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1328,601,601,617,554,467,391,1545,162,1361,807,1565,1565,243,1344,2,725,510,510,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1808,1525,1129,652,1195,329,1410,558,1322,911,161,536,737,94,306,2,2,2,2,2,2,2,2,2,541,541,541,2,2,2,2,2},
|
||||||
|
{1911,1338,639,1106,854,128,19,1353,847,253,618,517,2054,2054,93,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1825,850,180,1483,864,953,50,81,106,432,1372,1372,1212,10,10,10,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1892,441,977,228,1252,604,735,136,889,878,1319,1319,2127,2127,1963,367,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1820,1553,536,1351,425,1268,227,1742,429,348,1397,552,1151,1151,2,180,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1453,1044,556,833,305,1493,989,1158,726,1790,532,1229,1229,1229,2,2,2,2,2,2,2,2,2,2,259,2,2,2,2,2,420,2},
|
||||||
|
{2059,592,492,973,137,1331,392,334,635,1480,2254,1796,1796,284,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1460,986,709,268,755,824,83,893,115,656,2071,1323,1001,144,2,2,2,2,2,2,2,2,1527,1527,1527,1527,1527,1527,1527,2,801,801},
|
||||||
|
{1850,1476,792,840,2037,229,1578,526,431,1485,1450,1001,1001,1001,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1922,1383,813,346,1247,666,1931,1111,2042,79,682,501,1349,1930,2,2,681,681,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1922,542,1739,625,88,1376,259,49,338,318,505,788,1314,657,2,2,2,1314,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1948,1530,576,582,1069,119,2131,41,1178,1677,1677,1677,325,346,2,2,2,2,2,2,1401,2,33,2,2,2,2,2,2,71,71,71},
|
||||||
|
{1928,1111,168,1252,1467,1083,1927,603,1278,714,1027,50,751,1970,2,2,2,2,621,2,100,2,2,10,10,2,2,2,2,793,793,793},
|
||||||
|
{1394,896,674,2350,1375,1599,1858,135,762,722,628,685,705,28,2,2,2,2,2,2,2,2,2,2,2,855,2,2,2,2,2,2},
|
||||||
|
{1540,791,518,419,1130,1068,299,1386,1378,134,859,859,71,162,2,71,71,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2107,709,828,154,542,184,1094,1665,307,1549,177,2007,85,773,2,2,2,2,2,2,2,2,2,2,2,697,2,2,2,2,697,2},
|
||||||
|
{1977,1218,244,365,576,666,761,238,629,913,1907,986,1351,986,704,1257,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1496,1912,1291,1053,510,2322,1048,1530,2223,673,894,594,628,332,2,2,2,2,2,295,295,295,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1520,1107,1082,687,484,1732,676,1595,467,653,1091,428,2113,332,332,332,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1905,612,920,848,562,2032,230,1305,1073,851,731,798,798,357,516,2,2,2,2,2,2,2,2,1465,1465,373,2,2,2,2,2,2},
|
||||||
|
{1428,1062,1016,75,297,1130,533,768,464,753,48,1510,1510,418,375,1626,2,221,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1396,729,1710,337,371,489,1341,2117,132,1870,853,853,408,1079,328,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1978,1051,977,588,1423,1001,508,409,825,497,659,1063,384,463,463,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1534,854,2007,1207,947,1773,1571,1505,909,1471,1655,1655,2334,1327,409,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2157,2106,679,238,378,49,1101,588,811,1313,1556,2301,475,812,812,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2187,1515,549,1416,1073,1613,47,1046,390,252,1214,1404,1404,933,1013,2,2,2,1025,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2145,1069,662,709,737,1141,1737,827,1384,1628,107,107,1032,277,277,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2173,1379,155,393,1578,610,1911,899,697,58,185,597,597,1249,1369,2,2,2,2,1369,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1413,1589,1603,2268,520,333,1416,859,1619,867,1154,512,1291,413,413,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1600,1823,1698,1268,623,583,1932,1674,522,529,1862,1281,246,989,246,2,246,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1559,992,174,1313,612,1487,1487,461,702,37,1660,839,2,95,1628,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2066,1719,710,1294,2041,377,1005,690,132,756,1618,187,187,726,187,615,615,2,2,2,2,851,2,2,2,2,2,2,2,2,2,744},
|
||||||
|
{2192,1029,310,1609,592,1542,265,117,2006,82,162,205,2,2009,2009,1201,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1570,1504,1414,1143,1999,1932,1015,1015,556,514,626,79,2,79,1795,1461,1461,2,2,2,2,2,2,2,1461,1461,1461,1461,1461,2,2,2},
|
||||||
|
{1562,937,1964,934,1349,378,459,109,1676,1655,1339,1809,2,768,768,188,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1965,949,1057,1043,2256,1571,970,348,69,1324,1174,485,105,105,105,2172,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2044,1869,838,1424,1097,155,1142,230,1335,420,235,1510,2,431,425,622,2,2,2,2,2,625,2,2,2,625,625,2,2,2,2,2},
|
||||||
|
{1976,1433,820,504,421,1007,388,1083,635,82,1524,750,2,2,870,106,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1990,1948,1138,1787,253,115,312,1912,341,1624,260,1783,1315,1315,790,790,790,790,790,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1993,585,327,1393,1013,1671,1758,1436,1989,1217,1109,1476,2,2,1042,756,1042,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2056,1062,1605,1943,680,445,113,857,650,1388,2016,1231,2,2,1292,1292,1292,2,1039,1039,1039,1039,1039,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2008,1773,416,1954,1314,742,1694,505,202,1747,785,375,2,2,2,477,1538,477,2,2,2,2,2,1309,1309,1309,1309,2,2,2,1309,2},
|
||||||
|
{1658,1008,258,749,427,1071,2052,263,1047,2152,1602,1602,2,2,2,1311,669,669,2,1897,1897,1897,669,669,669,669,669,669,669,669,669,669},
|
||||||
|
{2258,1887,1875,1021,863,604,543,1115,509,1243,312,213,2,2,2,2,335,770,770,2,1143,567,2,2,567,567,567,411,2,2,2,411},
|
||||||
|
{2266,1872,991,1468,1168,939,907,833,624,701,386,1713,2,2,2,2,2,931,861,381,1299,2,861,2,2,2,861,861,861,861,861,2},
|
||||||
|
{2273,1510,803,2278,842,1245,1389,230,822,1564,113,1276,2,2,2,2,1350,273,273,2,2,2,2,2,1281,1281,1281,2,2,1281,1281,1281},
|
||||||
|
{2278,1028,548,373,190,1443,614,2386,1940,930,557,2069,2,2,2,558,112,103,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2108,776,1568,342,2215,1882,681,1292,1601,586,1481,618,1930,1930,1930,1930,2146,89,89,2,2,2,2,2,2,2,1171,2,2,2,2,2},
|
||||||
|
{2139,2177,1652,392,715,605,778,632,472,1619,64,64,2,2,2,1747,859,2,2,2,2,2,216,216,216,216,1747,1747,1747,1747,1747,1747},
|
||||||
|
{1492,448,271,135,1288,417,130,83,235,2313,482,746,2,2,746,609,611,611,611,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1628,846,1504,138,464,401,501,506,967,1027,1540,1035,2,1921,1539,1539,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1630,1677,1624,301,1038,909,887,374,411,143,1021,174,2,1393,19,634,2,2,2,2,2,2,2,873,2,2,873,873,2,2,2,2},
|
||||||
|
{1654,1131,2054,994,2170,548,801,252,87,219,488,2239,2,1232,1839,1822,2,2,2,968,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2065,1520,1423,1797,899,1425,1801,776,2365,58,646,695,2,998,998,1342,2,2,2,2,2,2,2,2,2,2,2,2,1150,1150,2,2},
|
||||||
|
{2304,1948,316,1063,237,607,1143,2575,1388,1022,127,251,2,438,1570,1570,1570,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2177,710,1912,617,809,1078,199,905,673,519,457,52,2,1348,1348,410,2,2,2,2,2,340,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2073,1543,1586,1296,2466,753,455,46,119,1694,2035,1592,206,206,206,2,2,2,2,2,2,2,2,1172,2,2,2,2,2,2,2,2},
|
||||||
|
{2075,1056,874,2101,566,1790,1333,386,538,1560,2254,331,717,717,717,454,454,2,2,2,2,2,2,2,2,2,2,2,454,454,2,2},
|
||||||
|
{1670,977,1540,553,855,1729,239,757,191,62,732,549,1092,1092,199,199,199,199,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2096,1155,2257,125,1986,245,1208,2146,2287,680,1413,73,467,1410,1410,2,2,2,2,2,133,133,133,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1538,1026,2157,1457,1784,2559,184,29,614,273,697,697,1922,697,697,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2106,856,1025,382,389,272,425,672,1021,216,601,292,510,510,876,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1662,608,2478,266,1330,505,40,2058,964,724,596,1221,1221,310,42,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1600,1338,196,1510,1371,1138,957,169,545,1176,1131,2460,1708,541,541,2,363,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1682,1008,737,444,822,999,2066,283,646,1860,1008,778,1178,1178,458,1743,2,2,2,2,2,2,2,2,2,2,2,2,2,1743,1743,1743},
|
||||||
|
{2132,756,1097,166,202,411,640,717,514,1389,633,633,633,633,633,633,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2386,748,620,478,647,898,320,53,1115,190,60,1860,1860,802,802,2,2,2,2,1264,1346,1346,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2125,996,1081,124,1140,628,1668,1913,151,2495,523,430,260,708,2190,2190,2190,2,2,2,2,2,1660,2,2,497,497,497,497,497,497,2},
|
||||||
|
{1602,1489,895,383,56,698,2081,1728,794,789,16,16,797,302,52,2,2,2,2,2,2,2,2,2,2,797,797,797,797,797,797,1808},
|
||||||
|
{2210,606,901,547,131,1924,1852,1271,194,766,390,390,520,795,1429,1429,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1731,599,817,724,718,1038,1082,2503,1341,936,421,1802,1304,1304,1491,186,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1614,1058,847,689,749,1028,1047,1474,117,1369,1442,1442,1540,700,104,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1733,679,2041,2420,326,934,1172,1431,193,370,1073,1073,1073,260,2,2,2,2,2,2,2,2,2,2,2,2,1193,2,2,2,2,2},
|
||||||
|
{2168,1532,769,2570,1303,357,1793,1633,1226,1025,205,1218,1984,764,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2234,1706,356,581,532,933,1704,387,1345,1345,34,135,350,307,614,614,307,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1656,2093,354,310,306,1553,106,459,175,55,1482,958,254,254,2,356,356,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1654,1035,330,533,1446,953,499,142,1527,1748,265,1437,265,510,2,2,2,2,2,2,2,1835,1835,1835,1835,2,2,2,2,2,2,2},
|
||||||
|
{1600,479,1457,246,2025,618,1612,2139,169,1492,1097,1327,2007,2007,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1744,447,845,2145,748,1555,1193,1312,916,1770,1294,546,794,323,2,2,2,2,2,1733,1733,2,2,1730,2,1733,1733,2,2,1733,551,551},
|
||||||
|
{1766,1558,1901,1393,987,1859,815,1165,50,2065,88,88,1453,1453,2,2,2,995,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1615,1267,1242,1494,399,663,68,1209,1573,528,640,1200,248,640,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1678,592,1351,509,312,721,163,1597,1262,199,2643,1330,1661,992,2,2,719,2,2,2,2,2,2,2,2,2,2,2,2,2,1704,2},
|
||||||
|
{2207,970,838,2043,1016,561,267,329,584,608,679,303,832,1613,959,959,959,1409,1409,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2217,352,447,914,1200,561,614,1616,509,2292,1114,1114,1229,52,1053,1053,1053,2,2,2,2,2,2,2,2,2,2,2,2,2,795,795},
|
||||||
|
{2313,595,1593,1951,133,282,372,2396,1117,226,2104,267,374,267,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2312,1231,1604,997,652,1096,1070,320,481,662,911,1610,342,2527,606,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2245,1541,1828,783,615,428,1282,1892,848,1219,2465,314,314,314,2,2,2,2,2,2,2,2,2,2,2,2,1323,2,2,2,2,1323},
|
||||||
|
{2522,1030,324,1264,628,1339,480,234,2351,1085,1979,2333,1339,1356,1356,2286,2,2,2,2,2,2,2,2,2,2,2,2,2530,2,2,2},
|
||||||
|
{2519,1136,612,209,994,1179,1060,2621,130,485,661,1444,2122,124,258,1114,2,2,806,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2524,1894,253,2072,1242,355,888,1362,28,480,452,1216,595,545,354,1145,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2569,1356,1053,410,437,58,1508,831,2272,383,1725,615,1191,1191,1191,2493,186,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2386,1106,709,251,784,929,1551,2481,304,2148,1546,955,2453,866,866,2,2,2264,2264,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2228,1163,1995,649,1000,680,325,1591,774,767,711,711,1418,524,711,401,976,2,2,2,2,2005,2005,2,2,2,2,2,2,1390,1390,2},
|
||||||
|
{2362,1706,564,1088,1296,1267,70,1015,496,1298,758,154,240,240,154,154,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1715,2260,357,557,783,1195,2288,1997,1120,144,247,175,1277,203,203,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2294,2360,1353,748,1439,226,940,2316,1112,1527,214,1406,1429,712,1124,2,595,595,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2303,1018,316,280,1616,909,97,1126,1295,736,216,54,2045,726,1673,2,2,2,2,2,779,779,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2390,491,1217,1148,2314,2250,2180,308,613,662,1346,1346,1346,1280,778,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1732,527,1303,664,71,294,404,917,1074,180,2618,2412,441,1987,1750,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1695,1287,1346,1181,1412,1653,830,2025,957,1720,1614,887,964,964,964,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1756,2308,1986,101,957,633,1940,1002,390,1237,95,1441,95,95,705,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2461,1412,540,1183,229,300,47,585,518,402,1863,1863,560,1326,1326,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1707,717,366,287,1883,50,599,1371,474,1551,947,2142,1885,947,2008,1004,1004,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2632,567,1149,1227,1156,2052,643,1585,1197,581,63,718,699,149,149,1940,2,2,2,2,2,2,2,2,2,2,2,2146,2,2,2,2},
|
||||||
|
{1773,2024,377,340,1938,103,1180,600,199,848,2449,2449,506,506,762,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2435,1920,394,1482,266,1637,911,1697,1689,1249,1085,1085,397,2292,1355,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2345,662,270,324,1061,1080,1952,593,1480,2111,2667,2093,2059,2120,955,1447,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1777,455,1487,1190,455,1542,977,2308,437,1129,410,856,1420,412,412,766,2,2034,2034,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2662,2224,1142,656,59,598,730,458,226,1151,741,1286,1015,2,688,2017,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2666,768,529,990,2329,130,1678,2466,318,1083,387,1524,511,2,731,731,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2501,1216,246,1278,718,704,2019,88,273,1203,67,1488,1828,2,2,1489,1489,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2474,2292,1818,2061,2833,751,2172,1708,1210,1675,370,131,163,2,2,163,163,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1751,1575,889,828,82,1956,712,499,1420,1686,339,2326,2035,2,2,558,558,2,1234,2,2,2,2,2,2,2,2,2,2,2,1239,1239},
|
||||||
|
{2522,1148,1943,168,218,252,543,1535,2004,130,353,353,42,2,2,2,1173,1173,2,1547,2,2,2,2,2,2,2,1547,1173,1547,1547,2},
|
||||||
|
{2695,432,1213,579,865,1637,1857,84,447,155,2492,347,1980,2,2,2,1155,1155,1155,2,1933,1933,1933,2,2,2,2,2,2,2,1901,1901},
|
||||||
|
{1808,1683,474,1761,106,602,1416,217,1351,1602,366,393,1966,2,2,2,2,2,378,378,606,606,606,2,2,2,2,2,919,919,919,919},
|
||||||
|
{2428,1576,1692,449,2012,240,1167,418,272,1557,2197,645,645,2,2,2,2,2,2150,2150,2,2,562,715,2,2,2,81,81,2,2,2},
|
||||||
|
{2727,781,1689,1709,997,2563,1032,468,44,992,1214,725,75,2,2,2,2,360,360,380,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1948,1085,1344,2090,1435,2389,3193,1007,1003,244,667,1838,2062,2,2,2,1802,299,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2433,932,689,818,2014,1498,749,1645,867,1627,47,1766,2193,2,2,2030,2030,2,430,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2463,712,1525,2092,2942,352,761,242,2178,2339,483,1905,1347,2,2,65,529,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2547,920,386,925,74,579,323,2319,520,2332,1535,751,1591,2,770,770,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2452,2588,2055,665,818,2622,413,1260,965,211,989,1219,166,2,1251,1251,2,1256,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1957,2311,993,276,293,2826,1087,880,927,1811,1122,2974,2974,2,2,590,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2552,998,533,827,1619,831,1861,918,750,1955,241,1899,448,2151,2151,449,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1860,579,1000,1575,898,170,185,1032,293,2754,438,459,459,2,1199,1199,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2602,2417,1888,2528,1410,669,1543,233,814,2478,225,1449,1449,224,1671,1671,2,2,931,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1889,2527,1366,1371,387,925,1751,162,250,1064,292,467,467,546,1244,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2492,1186,1350,1616,2749,1962,33,708,279,813,1390,489,1203,268,173,2410,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2500,1575,423,541,561,380,262,1564,1923,1242,2084,1758,1283,2213,924,924,2,2,2,2,2,2,2,2,2,2,2,1827,1827,2,2,2},
|
||||||
|
{1842,1736,489,743,1539,1681,683,1412,1418,312,2778,2778,1975,1975,803,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2824,1183,2201,278,241,2230,1591,1648,1036,818,1321,1312,754,813,813,813,813,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1900,2506,952,1059,163,870,681,1235,1271,1188,2071,1705,1183,648,404,2,2,2,2,2,2,2,2,2236,2236,2,2,2,2,2,2,2},
|
||||||
|
{2662,1443,2327,132,490,1149,1572,744,429,621,1763,2383,1903,1246,964,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2673,2182,1307,1776,1233,1828,1828,340,249,216,503,160,160,582,926,2129,2129,2129,2129,2129,2129,2129,2129,2129,2129,2129,2129,2,1018,1018,1103,1103},
|
||||||
|
{2042,620,1074,2057,2758,859,815,1127,766,1693,252,808,981,416,416,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2102,881,2170,1673,705,101,58,1712,1568,214,758,488,1007,269,243,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2692,2665,961,1478,324,429,1311,376,1648,130,2083,1047,409,343,343,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2122,1087,563,1669,647,2996,151,2458,250,310,71,1348,355,965,2815,1333,1333,2,2,2,2,2218,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1952,1968,2260,2945,2464,1055,2626,570,1316,1828,1828,970,970,221,220,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2072,1947,1779,254,2822,1552,855,804,3452,202,695,82,684,208,1270,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1947,1699,1341,486,1765,1960,264,899,1082,1674,987,1878,930,1008,930,930,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1953,1527,1643,591,1517,2427,1232,1555,2542,495,675,2534,2534,3106,83,3106,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2744,1728,2213,792,761,1667,1908,31,447,442,815,2865,762,762,762,762,2,2,2,2,2,2,2,2,2,2,2,2,649,649,649,2},
|
||||||
|
{2722,1406,1257,807,2191,3017,1330,1023,602,2124,794,530,733,733,1083,2528,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{1963,1525,437,398,609,393,2420,3059,435,1251,1977,1672,450,1960,1954,1960,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2626,2468,2838,845,2060,218,1080,912,911,1973,1365,920,1316,1316,2,1316,1316,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2734,1727,1743,1026,809,1154,779,244,1238,1616,812,784,825,1810,1810,1810,1810,1559,1559,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2180,2262,1651,204,3193,2121,2725,1016,629,1834,603,2848,26,26,728,728,728,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2648,1328,2578,133,1377,105,2485,2139,323,1045,145,761,1201,1848,2,814,814,814,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2999,358,250,1379,102,2349,1491,2074,42,376,2811,1220,296,296,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2810,1274,499,742,1724,425,190,1561,1302,2603,2255,917,661,661,2,2,2,495,2,2,2,2,2,2,2,2,2,2575,2,2,2,2},
|
||||||
|
{2150,589,876,1616,2655,432,902,1028,433,1375,574,1400,1400,1400,2,2,2,2,2,1529,1529,1529,1529,1529,1529,1529,1529,1529,1529,1529,1529,1529},
|
||||||
|
{1665,1856,201,824,796,249,1217,590,1375,1175,1599,824,824,3319,2,2,2,601,1961,1961,2,2,2,1961,2,2,2,2,2,2,1961,2},
|
||||||
|
{2704,2239,1260,140,2161,2781,1840,574,2353,343,3218,61,2108,2038,1873,2,1833,1408,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2173,876,802,2197,3338,176,1783,224,1763,1160,1264,1264,2864,554,2,552,552,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2708,1663,2279,824,836,1598,2101,1620,1202,1606,1368,1079,1167,1999,2848,2848,2848,1101,1101,1101,2,2,2,662,2,2,2,2272,2,2,2,2},
|
||||||
|
{1987,1463,2328,1890,1443,2086,283,2895,522,1577,1514,1657,2605,891,2,1181,1181,2,2,2121,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2173,1637,1139,905,1802,1378,296,439,1507,1017,1427,209,708,462,1508,1508,1508,2,2,2,2,2,2,2,2,2,2,2240,2240,1459,1459,1459},
|
||||||
|
{2206,1526,628,2877,802,2587,1253,1258,1044,2195,3246,40,2898,2898,1704,598,2,2145,2,2,2,2145,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2182,618,1022,1433,1138,1580,2590,149,796,2090,743,294,294,1117,720,3003,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2025,1805,1466,1213,2006,1903,568,1700,1355,865,1783,1006,1006,1070,1070,268,2,2,2,2,2388,2388,845,845,845,2,2,2,2,2,2,2},
|
||||||
|
{2185,1038,3050,1461,2270,2159,958,1637,233,2483,525,987,437,437,437,3065,2,2,2160,2160,2,2,2,2,2,2,2,2,2,2,2160,2160},
|
||||||
|
{2083,1465,847,1450,502,447,2168,794,1761,1324,162,188,2853,2853,636,973,2,563,2,2,2,2,2,2,2,2089,2089,2089,2089,2089,2,2},
|
||||||
|
{2923,2303,203,508,472,648,3169,269,515,3147,2415,1700,1700,1700,1461,1461,1461,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2300,1116,1555,2794,1095,998,1999,894,963,753,324,2130,2675,2675,554,2045,2,2,2,2,2,2,2,2130,2130,2130,2,2,2,2,2,2},
|
||||||
|
{2103,768,702,1548,1486,2228,2846,861,665,1497,1046,1046,2252,394,394,1901,1155,2,2,2,2,2,2,2,2,2,2,2,192,192,192,192},
|
||||||
|
{2923,640,661,2179,1207,182,872,171,738,269,1372,222,908,2069,2069,2,1550,516,2,2,2,2,2,2,2,2,2,2,1109,2,2,2},
|
||||||
|
{2833,2005,387,733,562,468,317,224,94,478,1606,2522,1606,2001,1087,2,2,1087,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2125,2479,1749,1226,1169,1681,459,652,1087,2211,1613,686,2213,1689,2446,2,2,2925,2925,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2953,1059,205,3093,138,132,2148,1345,1499,216,151,1296,2446,1610,1632,2,2,2,2,4,4,2,2,2,987,987,2,2,2,2,2,2},
|
||||||
|
{3199,1431,593,2050,2785,507,1540,1103,1740,459,62,1766,1781,1121,1600,2,1600,1600,125,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2258,1714,415,373,1919,2605,693,827,1918,496,1479,1903,86,1083,415,2,2,38,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3289,2032,329,2169,2323,1599,517,1704,1847,804,632,40,40,40,40,40,40,40,40,2,2,1600,2,2,1600,2,2,2,2,2,2,2},
|
||||||
|
{2165,2725,2293,368,705,3063,494,103,12,1332,175,2331,3144,2165,1709,1709,2090,2,2,2,2,1363,1363,2,566,2,2,2,2,2,2,2},
|
||||||
|
{2300,1070,2169,2540,734,1002,912,1386,2215,224,1285,880,2052,2052,1301,959,563,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3267,1852,1037,648,611,1250,432,853,1467,179,715,2,2033,841,2607,2607,2607,2607,2,2,2,2,1874,1874,2,1874,899,2,2,2,2,2},
|
||||||
|
{2348,2565,794,859,1740,1596,532,462,457,1014,1227,2,2761,954,249,249,2,458,458,2,2,2,2,2,909,909,2,2,2,2,2,2},
|
||||||
|
{3038,2399,1450,1276,1222,727,552,646,1055,2351,686,63,252,504,3166,1802,2,2,1165,1165,1165,2,2,2,2,1165,1165,1165,2,2,1165,2},
|
||||||
|
{3038,2519,1494,107,2597,802,535,1669,1695,1928,1940,1580,1580,85,2274,1551,2,2,2431,560,560,560,2,2,1098,2,2,2,2,2,2,2},
|
||||||
|
{3040,1044,1927,1952,1479,3124,1373,1990,588,2550,1277,2,629,2671,1842,2712,840,1702,2,1669,2,1347,2,2,2,2,1669,1669,1669,1669,2,1669},
|
||||||
|
{3056,1567,691,1243,653,751,248,842,1954,480,458,2,2,2451,934,3172,3556,2259,2312,2,2562,2562,2,2,2562,2562,2562,2562,2562,2,2,2},
|
||||||
|
{2959,2553,1333,877,2492,3169,2498,686,2030,2820,3233,1313,1313,1471,1471,1471,1471,2,2,1471,1471,2,2,1481,2,1887,2,2,2,2,2,2},
|
||||||
|
{3398,964,862,301,1705,2002,310,644,144,1091,1507,2,2,2460,496,496,2517,2517,1842,2,2,1964,2,2,2,2,2,1676,2,2,2,2},
|
||||||
|
{2379,3034,166,302,2108,1078,2976,68,158,134,1567,2,2,1514,1514,1514,1883,1883,2,2,1883,1883,1883,1883,1883,1883,1883,1883,1883,2,2,2},
|
||||||
|
{2386,1270,1204,1032,1474,224,496,2296,1536,1219,311,2,2,2,2,1238,2108,2108,2108,2108,2108,2108,2108,2108,1444,1444,1444,1444,1444,1444,1444,2},
|
||||||
|
{2431,739,2488,1386,1632,2107,2602,2139,1751,349,3147,2,2,64,16,8,32,4,4,32,728,728,728,728,2,2,64,16,8,180,180,180},
|
||||||
|
{3405,2142,1621,110,2112,2097,807,740,747,282,372,2,2,2,2,2493,2493,2493,1299,2,132,1872,2,1843,2,2,2,2,2,2,2,2},
|
||||||
|
{3157,1230,685,1513,663,1335,2100,1441,1826,1670,1539,2,2,2,2899,2899,1378,54,2,46,46,2,2,1362,1362,2,2,2,2,2,2,2},
|
||||||
|
{2415,822,3658,449,1980,891,129,823,1787,621,514,2668,2668,2668,2668,2668,666,269,2830,2,2,2,2,241,370,370,370,370,2,2,2,2},
|
||||||
|
{2463,2664,2825,1208,882,629,428,428,356,343,1730,2,769,769,769,1714,769,2,2,955,769,2,2,955,955,955,2,2,2,955,955,955},
|
||||||
|
{2447,1588,1077,831,1413,2362,1499,1812,1112,815,129,1034,1034,1867,194,518,1454,723,723,1251,2,160,2,2,1251,1251,2,2,2,2,2,2},
|
||||||
|
{3094,1638,1514,843,1503,1884,1481,727,723,1319,226,2,676,2401,1699,562,639,639,1176,2,2,2,2,824,2,2,2,2,2,2,2,2},
|
||||||
|
{3125,2004,547,2986,2919,471,948,1747,201,1862,802,2,1238,1277,1277,1277,2,2,1245,1245,1245,2,2,2743,1245,1245,2,2,2,2,2,2},
|
||||||
|
{2582,2469,533,1726,1575,1505,2448,2031,1257,427,588,1633,202,3553,1938,672,195,195,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2378,636,1958,1628,1255,2285,2208,1626,719,2944,1086,1436,1436,1719,2111,655,2637,2637,2,2,2,2637,2637,2,2637,2637,2637,2637,2637,2,2637,2637},
|
||||||
|
{2372,3079,2161,515,368,847,955,1257,1937,315,2666,1938,1723,1252,1252,362,362,2,2205,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2518,2060,1055,362,1455,1899,1105,1560,2237,2451,2080,181,2346,181,1829,1829,1829,2,2,1509,1509,1509,2,1509,2,2,2,2,2,2,2,2},
|
||||||
|
{3580,1671,674,1838,814,1409,323,3021,1047,2579,2579,2968,2968,102,2656,2638,2638,4006,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3194,1576,1084,859,2879,1600,953,1429,471,867,1105,1490,293,293,293,2,2,198,2619,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3215,2004,3333,2271,3283,1660,2135,1696,1413,1362,834,253,253,253,3802,2,2,2,1881,690,690,2,2,2,1881,1881,1881,1881,1881,2,1881,1881},
|
||||||
|
{3719,2441,2094,1665,1707,1827,1310,230,1635,143,386,1029,1070,1062,1062,2,1062,1062,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3249,1309,1232,472,711,2557,1479,1027,145,489,1377,2928,2928,3522,3522,3522,968,415,415,2,2,2,2,1332,1332,1332,2,1332,2891,2,1332,2891},
|
||||||
|
{2462,1962,257,2244,1966,1905,204,262,799,319,752,1696,971,971,3781,1426,1426,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3434,3131,1399,3413,1533,281,3288,1242,810,135,2506,2506,1742,946,1015,1044,1044,1044,2,2,2,2,1044,1837,1837,1837,1837,1837,2,2,2,2},
|
||||||
|
{2518,1200,631,596,1946,365,2960,413,592,3878,242,2714,2364,1402,1402,2322,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3362,2012,1759,2002,1365,150,3120,471,1590,3246,1296,196,196,196,2984,2323,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{3382,899,3140,2860,1155,1840,2822,355,1753,1856,1018,822,52,52,52,1102,1102,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2728,1334,274,1330,2674,2614,931,2250,883,1506,2193,1345,1089,500,2,219,390,2,2,2,2,2,2,2,390,2,2,2,2,2,2,2},
|
||||||
|
{3911,3343,202,675,1733,71,166,176,1323,2864,899,2155,1108,2172,2,2,1829,2172,1107,2,2,2,2,1107,1107,1107,2,2,2,1107,2,2},
|
||||||
|
{2757,3466,1411,1168,340,2760,1053,524,53,2090,1227,26,260,830,2,2,2,1139,2,2,2,2,2,2,2,2,2,2,2,2,2,2},
|
||||||
|
{2662,902,2371,1920,1097,1476,1008,1012,3556,468,3374,2560,591,1446,2,298,298,149,149,149,149,149,3135,3135,3135,3135,3135,2,2,2,2,2},
|
||||||
|
{2861,1407,1848,245,2186,1209,164,2577,625,132,657,2333,2333,2213,2213,2213,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2}
|
||||||
|
};
|
||||||
699
src/external/libCuba/src/divonne/Rule.c
vendored
Normal file
699
src/external/libCuba/src/divonne/Rule.c
vendored
Normal file
@ -0,0 +1,699 @@
|
|||||||
|
/*
|
||||||
|
Rule.c
|
||||||
|
integration with cubature rules
|
||||||
|
code lifted with minor modifications from DCUHRE
|
||||||
|
by J. Berntsen, T. Espelid, and A. Genz
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
enum { nrules = 5 };
|
||||||
|
|
||||||
|
#define TYPEDEFSET \
|
||||||
|
typedef struct { \
|
||||||
|
count n; \
|
||||||
|
real weight[nrules], scale[nrules], norm[nrules]; \
|
||||||
|
real gen[NDIM]; \
|
||||||
|
} Set
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void RuleIni(Rule *rule)
|
||||||
|
{
|
||||||
|
rule->first = NULL;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void RuleFree(Rule *rule)
|
||||||
|
{
|
||||||
|
if( rule->first ) free(rule->first);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule13Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[][nrules] = {
|
||||||
|
{ .00844923090033615, .3213775489050763, .3372900883288987,
|
||||||
|
-.8264123822525677, .6539094339575232 },
|
||||||
|
{ .023771474018994404, -.1767341636743844, -.1644903060344491,
|
||||||
|
.306583861409436, -.2041614154424632},
|
||||||
|
{ .02940016170142405, .07347600537466073, .07707849911634623,
|
||||||
|
.002389292538329435, -.174698151579499 },
|
||||||
|
{ .006644436465817374, -.03638022004364754, -.03804478358506311,
|
||||||
|
-.1343024157997222, .03937939671417803 },
|
||||||
|
{ .0042536044255016, .021252979220987123, .02223559940380806,
|
||||||
|
.08833366840533902, .006974520545933992 },
|
||||||
|
{ 0, .1460984204026913, .1480693879765931,
|
||||||
|
0, 0 },
|
||||||
|
{ .0040664827465935255, .017476132861520992, 4.467143702185815e-6,
|
||||||
|
.0009786283074168292, .0066677021717782585 },
|
||||||
|
{ .03362231646315497, .1444954045641582, .150894476707413,
|
||||||
|
-.1319227889147519, .05512960621544304 },
|
||||||
|
{ .033200804136503725, .0001307687976001325, 3.6472001075162155e-5,
|
||||||
|
.00799001220015063, .05443846381278608 },
|
||||||
|
{ .014093686924979677, .0005380992313941161, .000577719899901388,
|
||||||
|
.0033917470797606257, .02310903863953934 },
|
||||||
|
{ .000977069770327625, .0001042259576889814, .0001041757313688177,
|
||||||
|
.0022949157182832643, .01506937747477189 },
|
||||||
|
{ .007531996943580376, -.001401152865045733, -.001452822267047819,
|
||||||
|
-.01358584986119197, -.060570216489018905 },
|
||||||
|
{ .02577183086722915, .008041788181514763, .008338339968783704,
|
||||||
|
.04025866859057809, .04225737654686337},
|
||||||
|
{ .015625, -.1420416552759383, -.147279632923196,
|
||||||
|
.003760268580063992, .02561989142123099 }
|
||||||
|
};
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.12585646717265545, .3506966822267133,
|
||||||
|
.4795480315809981, .4978005239276064,
|
||||||
|
.25, .07972723291487795,
|
||||||
|
.1904495567970094, .3291384627633596,
|
||||||
|
.43807365825146577, .499121592026599,
|
||||||
|
.4895111329084231, .32461421628226944,
|
||||||
|
.43637106005656195, .1791307322940614,
|
||||||
|
.2833333333333333, .1038888888888889 };
|
||||||
|
|
||||||
|
enum { nsets = 14, ndim = 2 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
count n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
Copy(last->weight, w[0], nrules);
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[1], nrules);
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[2], nrules);
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[3], nrules);
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[4], nrules);
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[5], nrules);
|
||||||
|
last->gen[0] = g[4];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[6], nrules);
|
||||||
|
last->gen[0] = g[5];
|
||||||
|
last->gen[1] = g[5];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[7], nrules);
|
||||||
|
last->gen[0] = g[6];
|
||||||
|
last->gen[1] = g[6];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[8], nrules);
|
||||||
|
last->gen[0] = g[7];
|
||||||
|
last->gen[1] = g[7];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[9], nrules);
|
||||||
|
last->gen[0] = g[8];
|
||||||
|
last->gen[1] = g[8];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[10], nrules);
|
||||||
|
last->gen[0] = g[9];
|
||||||
|
last->gen[1] = g[9];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[11], nrules);
|
||||||
|
last->gen[0] = g[10];
|
||||||
|
last->gen[1] = g[11];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[12], nrules);
|
||||||
|
last->gen[0] = g[12];
|
||||||
|
last->gen[1] = g[13];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[13], nrules);
|
||||||
|
last->gen[0] = g[14];
|
||||||
|
last->gen[1] = g[15];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 10;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule11Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[][nrules] = {
|
||||||
|
{ .0009903847688882167, 1.715006248224684, 1.936014978949526,
|
||||||
|
.517082819560576, 2.05440450381852 },
|
||||||
|
{ .0084964717409851, -.3755893815889209, -.3673449403754268,
|
||||||
|
.01445269144914044, .013777599884901202 },
|
||||||
|
{ .00013587331735072814, .1488632145140549, .02929778657898176,
|
||||||
|
-.3601489663995932, -.576806291790441 },
|
||||||
|
{ .022982920777660364, -.2497046640620823, -.1151883520260315,
|
||||||
|
.3628307003418485, .03726835047700328 },
|
||||||
|
{ .004202649722286289, .1792501419135204, .05086658220872218,
|
||||||
|
.007148802650872729, .0068148789397772195 },
|
||||||
|
{ .0012671889041675774, .0034461267589738897, .04453911087786469,
|
||||||
|
-.09222852896022966, .057231697338518496 },
|
||||||
|
{ .0002109560854981544, -.005140483185555825, -.022878282571259,
|
||||||
|
.01719339732471725, -.044930187438112855 },
|
||||||
|
{ .016830857056410086, .006536017839876424, .02908926216345833,
|
||||||
|
-.102141653746035, .027292365738663484 },
|
||||||
|
{ .00021876823557504823, -.00065134549392297, -.002898884350669207,
|
||||||
|
-.007504397861080493, .000354747395055699 },
|
||||||
|
{ .009690420479796819, -.006304672433547204, -.028059634133074954,
|
||||||
|
.01648362537726711, .01571366799739551 },
|
||||||
|
{ .030773311284628138, .01266959399788263, .05638741361145884,
|
||||||
|
.05234610158469334, .049900992192785674 },
|
||||||
|
{ .0084974310856038, -.005454241018647931, -.02427469611942451,
|
||||||
|
.014454323316130661, .0137791555266677 },
|
||||||
|
{ .0017749535291258914, .004826995274768427, .021483070341828822,
|
||||||
|
.003019236275367777, .0028782064230998723 }
|
||||||
|
};
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.095, .25,
|
||||||
|
.375, .4,
|
||||||
|
.4975, .49936724991757,
|
||||||
|
.38968518428362114, .49998494965443835,
|
||||||
|
.3951318612385894, .22016983438253684,
|
||||||
|
.4774686911397297, .2189239229503431,
|
||||||
|
.4830546566815374, .2288552938881567 };
|
||||||
|
|
||||||
|
enum { nsets = 13, ndim = 3 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
count n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
Copy(last->weight, w[0], nrules);
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[1], nrules);
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[2], nrules);
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[3], nrules);
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[4], nrules);
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
Copy(last->weight, w[5], nrules);
|
||||||
|
last->gen[0] = g[4];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[6], nrules);
|
||||||
|
last->gen[0] = g[5];
|
||||||
|
last->gen[1] = g[5];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
Copy(last->weight, w[7], nrules);
|
||||||
|
last->gen[0] = g[6];
|
||||||
|
last->gen[1] = g[6];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[8], nrules);
|
||||||
|
last->gen[0] = g[7];
|
||||||
|
last->gen[1] = g[7];
|
||||||
|
last->gen[2] = g[7];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[9], nrules);
|
||||||
|
last->gen[0] = g[8];
|
||||||
|
last->gen[1] = g[8];
|
||||||
|
last->gen[2] = g[8];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
Copy(last->weight, w[10], nrules);
|
||||||
|
last->gen[0] = g[9];
|
||||||
|
last->gen[1] = g[9];
|
||||||
|
last->gen[2] = g[9];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
|
||||||
|
Copy(last->weight, w[11], nrules);
|
||||||
|
last->gen[0] = g[10];
|
||||||
|
last->gen[1] = g[11];
|
||||||
|
last->gen[2] = g[11];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2);
|
||||||
|
Copy(last->weight, w[12], nrules);
|
||||||
|
last->gen[0] = g[12];
|
||||||
|
last->gen[1] = g[12];
|
||||||
|
last->gen[2] = g[13];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 4;
|
||||||
|
rule->errcoeff[1] = .5;
|
||||||
|
rule->errcoeff[2] = 3;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule9Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[] = {
|
||||||
|
-.0023611709677855117884, .11415390023857325268,
|
||||||
|
-.63833920076702389094, .74849988504685208004,
|
||||||
|
-.0014324017033399125142, .057471507864489725949,
|
||||||
|
-.14225104571434243234, -.062875028738286979989,
|
||||||
|
.254591133248959089, -1.207328566678236261,
|
||||||
|
.89567365764160676508, -.36479356986049146661,
|
||||||
|
.0035417564516782676826, -.072609367395893679605,
|
||||||
|
.10557491625218991012, .0021486025550098687713,
|
||||||
|
-.032268563892953949998, .010636783990231217481,
|
||||||
|
.014689102496143490175, .51134708346467591431,
|
||||||
|
.45976448120806344646, .18239678493024573331,
|
||||||
|
-.04508628929435784076, .21415883524352793401,
|
||||||
|
-.027351546526545644722, .054941067048711234101,
|
||||||
|
.11937596202570775297, .65089519391920250593,
|
||||||
|
.14744939829434460168, .057693384490973483573,
|
||||||
|
.034999626602143583822, -1.3868627719278281436,
|
||||||
|
-.2386668732575008879, .015532417276607053264,
|
||||||
|
.0035328099607090870236, .09231719987444221619,
|
||||||
|
.02254314464717892038, .013675773263272822361,
|
||||||
|
-.32544759695960125297, .0017708782258391338413,
|
||||||
|
.0010743012775049343856, .25150011495314791996 };
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.47795365790226950619, .20302858736911986780,
|
||||||
|
.44762735462617812882, .125,
|
||||||
|
.34303789878087814570 };
|
||||||
|
|
||||||
|
enum { nsets = 9 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
ccount ndim = ndim_;
|
||||||
|
ccount twondim = 1 << ndim;
|
||||||
|
count dim, n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
last->weight[0] = ndim*(ndim*(ndim*w[0] + w[1]) + w[2]) + w[3];
|
||||||
|
last->weight[1] = ndim*(ndim*(ndim*w[4] + w[5]) + w[6]) - w[7];
|
||||||
|
last->weight[2] = ndim*w[8] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*(ndim*w[9] + w[10]) - 1 + last->weight[0];
|
||||||
|
last->weight[4] = ndim*w[11] + 1 - last->weight[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = ndim*(ndim*w[12] + w[13]) + w[14];
|
||||||
|
last->weight[1] = ndim*(ndim*w[15] + w[16]) + w[17];
|
||||||
|
last->weight[2] = w[18] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*w[19] + w[20] + last->weight[0];
|
||||||
|
last->weight[4] = w[21] - last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = ndim*w[22] + w[23];
|
||||||
|
last->weight[1] = ndim*w[24] + w[25];
|
||||||
|
last->weight[2] = w[26] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*w[27] + w[28];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[29];
|
||||||
|
last->weight[1] = w[30];
|
||||||
|
last->weight[2] = -w[29];
|
||||||
|
last->weight[3] = w[31];
|
||||||
|
last->weight[4] = -w[29];
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[2] = w[32];
|
||||||
|
last->gen[0] = g[3];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = w[33] - ndim*w[12];
|
||||||
|
last->weight[1] = w[34] - ndim*w[15];
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = w[35] + last->weight[0];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = w[36];
|
||||||
|
last->weight[1] = w[37];
|
||||||
|
last->weight[2] = -w[37];
|
||||||
|
last->weight[3] = w[38];
|
||||||
|
last->weight[4] = -w[36];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 4*ndim*(ndim - 1)*(ndim - 2)/3;
|
||||||
|
last->weight[0] = w[39];
|
||||||
|
last->weight[1] = w[40];
|
||||||
|
last->weight[2] = -w[40];
|
||||||
|
last->weight[3] = w[39];
|
||||||
|
last->weight[4] = -w[39];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
last->gen[2] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = twondim;
|
||||||
|
last->weight[0] = w[41]/twondim;
|
||||||
|
last->weight[1] = w[7]/twondim;
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = last->weight[0];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
last->gen[dim] = g[4];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 5;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Rule7Alloc(Rule *rule)
|
||||||
|
{
|
||||||
|
static creal w[] = {
|
||||||
|
.019417866674748388428, -.40385257701150182546,
|
||||||
|
.64485668767465982223, .01177982690775806141,
|
||||||
|
-.18041318740733609012, -.088785828081335044443,
|
||||||
|
.056328645808285941374, -.0097089333373741942142,
|
||||||
|
-.99129176779582358138, -.17757165616267008889,
|
||||||
|
.12359398032043233572, .074978148702033690681,
|
||||||
|
.55489147051423559776, .088041241522692771226,
|
||||||
|
.021118358455513385083, -.0099302203239653333087,
|
||||||
|
-.064100053285010904179, .030381729038221007659,
|
||||||
|
.0058899134538790307051, -.0048544666686870971071,
|
||||||
|
.35514331232534017777 };
|
||||||
|
|
||||||
|
static creal g[] = {
|
||||||
|
.47795365790226950619, .20302858736911986780,
|
||||||
|
.375, .34303789878087814570 };
|
||||||
|
|
||||||
|
enum { nsets = 6 };
|
||||||
|
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
ccount ndim = ndim_;
|
||||||
|
ccount twondim = 1 << ndim;
|
||||||
|
count dim, n, r;
|
||||||
|
Set *first, *last, *s, *t;
|
||||||
|
|
||||||
|
Alloc(first, nsets);
|
||||||
|
Clear(first, nsets);
|
||||||
|
|
||||||
|
last = first;
|
||||||
|
n = last->n = 1;
|
||||||
|
last->weight[0] = ndim*(ndim*w[0] + w[1]) + w[2];
|
||||||
|
last->weight[1] = ndim*(ndim*w[3] + w[4]) - w[5];
|
||||||
|
last->weight[2] = ndim*w[6] - last->weight[1];
|
||||||
|
last->weight[3] = ndim*(ndim*w[7] + w[8]) - w[9];
|
||||||
|
last->weight[4] = 1 - last->weight[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[10];
|
||||||
|
last->weight[1] = w[11];
|
||||||
|
last->weight[2] = -w[10];
|
||||||
|
last->weight[3] = w[12];
|
||||||
|
last->weight[4] = -w[10];
|
||||||
|
last->gen[0] = g[1];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[0] = w[13] - ndim*w[0];
|
||||||
|
last->weight[1] = w[14] - ndim*w[3];
|
||||||
|
last->weight[2] = w[15] - last->weight[1];
|
||||||
|
last->weight[3] = w[16] - ndim*w[7];
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim;
|
||||||
|
last->weight[2] = w[17];
|
||||||
|
last->gen[0] = g[2];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = 2*ndim*(ndim - 1);
|
||||||
|
last->weight[0] = -w[7];
|
||||||
|
last->weight[1] = w[18];
|
||||||
|
last->weight[2] = -w[18];
|
||||||
|
last->weight[3] = w[19];
|
||||||
|
last->weight[4] = w[7];
|
||||||
|
last->gen[0] = g[0];
|
||||||
|
last->gen[1] = g[0];
|
||||||
|
|
||||||
|
++last;
|
||||||
|
n += last->n = twondim;
|
||||||
|
last->weight[0] = w[20]/twondim;
|
||||||
|
last->weight[1] = w[5]/twondim;
|
||||||
|
last->weight[2] = -last->weight[1];
|
||||||
|
last->weight[3] = w[9]/twondim;
|
||||||
|
last->weight[4] = -last->weight[0];
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
last->gen[dim] = g[3];
|
||||||
|
|
||||||
|
rule->first = first;
|
||||||
|
rule->last = last;
|
||||||
|
rule->errcoeff[0] = 5;
|
||||||
|
rule->errcoeff[1] = 1;
|
||||||
|
rule->errcoeff[2] = 5;
|
||||||
|
rule->n = n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( r = 1; r < nrules - 1; ++r ) {
|
||||||
|
creal scale = (s->weight[r] == 0) ? 100 :
|
||||||
|
-s->weight[r + 1]/s->weight[r];
|
||||||
|
real sum = 0;
|
||||||
|
for( t = first; t <= last; ++t )
|
||||||
|
sum += t->n*fabs(t->weight[r + 1] + scale*t->weight[r]);
|
||||||
|
s->scale[r] = scale;
|
||||||
|
s->norm[r] = 1/sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real *ExpandFS(cBounds *b, real *g, real *x)
|
||||||
|
{
|
||||||
|
count dim, ndim = ndim_;
|
||||||
|
|
||||||
|
next:
|
||||||
|
/* Compute centrally symmetric sum for permutation of G */
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim; ++dim )
|
||||||
|
*x++ = (.5 + g[dim])*b[dim].lower + (.5 - g[dim])*b[dim].upper;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim; ) {
|
||||||
|
g[dim] = -g[dim];
|
||||||
|
if( g[dim++] < 0 ) goto next;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Find next distinct permutation of G and loop back for next sum.
|
||||||
|
Permutations are generated in reverse lexicographic order. */
|
||||||
|
|
||||||
|
for( dim = 1; dim < ndim; ++dim ) {
|
||||||
|
creal gd = g[dim];
|
||||||
|
count big = dim - 1;
|
||||||
|
if( g[big] > gd ) {
|
||||||
|
count i, j = dim, lastbig = big;
|
||||||
|
for( i = 0; i < --j; ++i ) {
|
||||||
|
creal tmp = g[i];
|
||||||
|
g[i] = g[j];
|
||||||
|
g[j] = tmp;
|
||||||
|
if( tmp <= gd ) --big;
|
||||||
|
if( g[i] > gd ) lastbig = i;
|
||||||
|
}
|
||||||
|
if( g[big] <= gd ) big = lastbig;
|
||||||
|
g[dim] = g[big];
|
||||||
|
g[big] = gd;
|
||||||
|
goto next;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Restore original order to generators */
|
||||||
|
|
||||||
|
for( dim = 0; dim < --ndim; ++dim ) {
|
||||||
|
creal tmp = g[dim];
|
||||||
|
g[dim] = g[ndim];
|
||||||
|
g[ndim] = tmp;
|
||||||
|
}
|
||||||
|
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void SampleRule(cSamples *samples, cBounds *b, creal vol)
|
||||||
|
{
|
||||||
|
TYPEDEFSET;
|
||||||
|
|
||||||
|
real *x = samples->x, *f = samples->f;
|
||||||
|
Set *first = (Set *)samples->rule->first;
|
||||||
|
Set *last = (Set *)samples->rule->last;
|
||||||
|
Set *s;
|
||||||
|
creal *errcoeff = samples->rule->errcoeff;
|
||||||
|
count comp, rul, n;
|
||||||
|
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
if( s->n ) x = ExpandFS(b, s->gen, x);
|
||||||
|
|
||||||
|
DoSample(samples->n, ndim_, samples->x, f);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
real sum[nrules];
|
||||||
|
creal *f1 = f++;
|
||||||
|
|
||||||
|
Zap(sum);
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
for( n = s->n; n; --n ) {
|
||||||
|
creal fun = *f1;
|
||||||
|
f1 += ncomp_;
|
||||||
|
for( rul = 0; rul < nrules; ++rul )
|
||||||
|
sum[rul] += fun*s->weight[rul];
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Search for the null rule, in the linear space spanned by two
|
||||||
|
successive null rules in our sequence, which gives the greatest
|
||||||
|
error estimate among all normalized (1-norm) null rules in this
|
||||||
|
space. */
|
||||||
|
|
||||||
|
for( rul = 1; rul < nrules - 1; ++rul ) {
|
||||||
|
real maxerr = 0;
|
||||||
|
for( s = first; s <= last; ++s )
|
||||||
|
maxerr = Max(maxerr,
|
||||||
|
fabs(sum[rul + 1] + s->scale[rul]*sum[rul])*s->norm[rul]);
|
||||||
|
sum[rul] = maxerr;
|
||||||
|
}
|
||||||
|
|
||||||
|
samples->avg[comp] = vol*sum[0];
|
||||||
|
samples->err[comp] = vol*(
|
||||||
|
(errcoeff[0]*sum[1] <= sum[2] && errcoeff[0]*sum[2] <= sum[3]) ?
|
||||||
|
errcoeff[1]*sum[1] :
|
||||||
|
errcoeff[2]*Max(Max(sum[1], sum[2]), sum[3]));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
273
src/external/libCuba/src/divonne/Sample.c
vendored
Normal file
273
src/external/libCuba/src/divonne/Sample.c
vendored
Normal file
@ -0,0 +1,273 @@
|
|||||||
|
/*
|
||||||
|
Sample.c
|
||||||
|
most of what is related to sampling
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 4 Mar 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#define MARKMASK 0xfffffff
|
||||||
|
#define Marked(x) ((x) & ~MARKMASK)
|
||||||
|
#define Unmark(x) ((x) & MARKMASK)
|
||||||
|
|
||||||
|
#define MEM(samples) (samples)->x
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void SamplesIni(Samples *samples)
|
||||||
|
{
|
||||||
|
MEM(samples) = NULL;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void SamplesFree(cSamples *samples)
|
||||||
|
{
|
||||||
|
if( MEM(samples) ) free(MEM(samples));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void SampleSobol(cSamples *samples, cBounds *b, creal vol)
|
||||||
|
{
|
||||||
|
creal norm = vol*samples->weight;
|
||||||
|
real *x = samples->x, *f = samples->f, *avg = samples->avg;
|
||||||
|
cnumber n = samples->n;
|
||||||
|
number i;
|
||||||
|
count dim, comp;
|
||||||
|
|
||||||
|
for( i = 0; i < n; ++i ) {
|
||||||
|
GetRandom(x);
|
||||||
|
for( dim = 0; dim < ndim_; ++x, ++dim )
|
||||||
|
*x = b[dim].lower + *x*(b[dim].upper - b[dim].lower);
|
||||||
|
}
|
||||||
|
|
||||||
|
DoSample(n, ndim_, samples->x, f);
|
||||||
|
|
||||||
|
ResCopy(avg, f);
|
||||||
|
f += ncomp_;
|
||||||
|
for( i = 1; i < n; ++i )
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
avg[comp] += *f++;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
avg[comp] *= norm;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void SampleKorobov(cSamples *samples, cBounds *b, creal vol)
|
||||||
|
{
|
||||||
|
creal norm = vol*samples->weight;
|
||||||
|
real *x = samples->x, *xlast = x + ndim_;
|
||||||
|
real *f = samples->f, *flast = f + ncomp_;
|
||||||
|
real *avg = samples->avg;
|
||||||
|
cnumber n = samples->n, neff = samples->neff;
|
||||||
|
number nextra = n, i;
|
||||||
|
real dist = 0;
|
||||||
|
count dim, comp;
|
||||||
|
|
||||||
|
for( i = 1; i < n; ++i ) {
|
||||||
|
number c = i;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
creal dx = abs(2*c - neff)*samples->weight;
|
||||||
|
*xlast++ = b[dim].lower + dx*(b[dim].upper - b[dim].lower);
|
||||||
|
c = c*samples->coeff % neff;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
creal dx = (x[dim] = b[dim].upper) - border_.upper;
|
||||||
|
if( dx > 0 ) dist += Sq(dx);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( dist > 0 ) {
|
||||||
|
dist = sqrt(dist)/EXTRAPOLATE_EPS;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
real x2 = x[dim], dx = x2 - border_.upper;
|
||||||
|
if( dx > 0 ) {
|
||||||
|
x[dim] = border_.upper;
|
||||||
|
x2 = border_.upper - dx/dist;
|
||||||
|
}
|
||||||
|
xlast[dim] = x2;
|
||||||
|
}
|
||||||
|
++nextra;
|
||||||
|
}
|
||||||
|
|
||||||
|
DoSample(nextra, ndim_, x, f);
|
||||||
|
|
||||||
|
ResCopy(avg, flast);
|
||||||
|
flast += ncomp_;
|
||||||
|
for( i = 2; i < n; ++i )
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
avg[comp] += *flast++;
|
||||||
|
|
||||||
|
if( nextra > n ) {
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
f[comp] += dist*(f[comp] - flast[comp]);
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
x[dim] = b[dim].upper;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
avg[comp] = (avg[comp] + avg[comp] + f[comp])*norm;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
#define IsSobol(k) NegQ(k)
|
||||||
|
#define IsRule(k, d) (k == 9 || k == 7 || (k == 11 && d == 3) || (k == 13 && d == 2))
|
||||||
|
|
||||||
|
/* The following coding is used for key1, key2, key3:
|
||||||
|
0 = for key1, key2: use default,
|
||||||
|
for key3: do nothing,
|
||||||
|
1 = for key3: split region again,
|
||||||
|
7 = degree-7 cubature rule,
|
||||||
|
9 = degree-9 cubature rule,
|
||||||
|
11 = degree-11 cubature rule (only in 3 dims),
|
||||||
|
13 = degree-13 cubature rule (only in 2 dims),
|
||||||
|
-inf..-40 = absolute # of points, Sobol numbers,
|
||||||
|
-39..-1 = multiplicator, Sobol numbers,
|
||||||
|
1..39 = multiplicator, Korobov numbers,
|
||||||
|
40..inf = absolute # of points, Korobov numbers. */
|
||||||
|
|
||||||
|
static count SamplesLookup(Samples *samples, cint key,
|
||||||
|
cnumber nwant, cnumber nmax, number nmin)
|
||||||
|
{
|
||||||
|
number n;
|
||||||
|
|
||||||
|
if( key == 13 && ndim_ == 2 ) {
|
||||||
|
if( rule13_.first == NULL ) Rule13Alloc(&rule13_);
|
||||||
|
samples->rule = &rule13_;
|
||||||
|
samples->n = n = nmin = rule13_.n;
|
||||||
|
samples->sampler = SampleRule;
|
||||||
|
}
|
||||||
|
else if( key == 11 && ndim_ == 3 ) {
|
||||||
|
if( rule11_.first == NULL ) Rule11Alloc(&rule11_);
|
||||||
|
samples->rule = &rule11_;
|
||||||
|
samples->n = n = nmin = rule11_.n;
|
||||||
|
samples->sampler = SampleRule;
|
||||||
|
}
|
||||||
|
else if( key == 9 ) {
|
||||||
|
if( rule9_.first == NULL ) Rule9Alloc(&rule9_);
|
||||||
|
samples->rule = &rule9_;
|
||||||
|
samples->n = n = nmin = rule9_.n;
|
||||||
|
samples->sampler = SampleRule;
|
||||||
|
}
|
||||||
|
else if( key == 7 ) {
|
||||||
|
if( rule7_.first == NULL ) Rule7Alloc(&rule7_);
|
||||||
|
samples->rule = &rule7_;
|
||||||
|
samples->n = n = nmin = rule7_.n;
|
||||||
|
samples->sampler = SampleRule;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
n = Abs1(key);
|
||||||
|
if( n < 40 ) n *= nwant;
|
||||||
|
samples->sampler = (key < 0) ? SampleSobol :
|
||||||
|
(n = n/2 + 1, SampleKorobov);
|
||||||
|
samples->n = IMin(n, nmax);
|
||||||
|
}
|
||||||
|
|
||||||
|
samples->neff = samples->n;
|
||||||
|
|
||||||
|
return IDim(n - nmax) | Marked(nmax - nmin);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void SamplesAlloc(Samples *samples)
|
||||||
|
{
|
||||||
|
#define FIRST -INT_MAX
|
||||||
|
#define MarkLast(x) (x | Marked(INT_MAX))
|
||||||
|
|
||||||
|
#include "KorobovCoeff.c"
|
||||||
|
|
||||||
|
number nx, nf;
|
||||||
|
|
||||||
|
if( samples->sampler == SampleKorobov ) {
|
||||||
|
enum { max = Elements(prime) - 2 };
|
||||||
|
cint n = IMin(2*samples->n - 1, MAXPRIME);
|
||||||
|
int i = Hash(n), p;
|
||||||
|
count shift = 2 + NegQ(n - 1000);
|
||||||
|
|
||||||
|
while( i = IMin(IDim(i), max),
|
||||||
|
n > (p = prime[i + 1]) || n <= prime[i] ) {
|
||||||
|
cint d = (n - Unmark(p)) >> ++shift;
|
||||||
|
i += Min1(d);
|
||||||
|
}
|
||||||
|
|
||||||
|
samples->coeff = coeff[i][ndim_ - KOROBOV_MINDIM];
|
||||||
|
samples->neff = p = Unmark(p);
|
||||||
|
samples->n = p/2 + 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
nx = ndim_*(samples->n + 1); /* need 1 for extrapolation */
|
||||||
|
nf = ncomp_*(samples->n + 1);
|
||||||
|
|
||||||
|
Alloc(samples->x, nx + nf + ncomp_ + ncomp_);
|
||||||
|
samples->f = samples->x + nx;
|
||||||
|
samples->avg = samples->f + nf;
|
||||||
|
samples->err = samples->avg + ncomp_;
|
||||||
|
ResClear(samples->err);
|
||||||
|
|
||||||
|
samples->weight = 1./samples->neff;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static real Sample(creal *x0)
|
||||||
|
{
|
||||||
|
real xtmp[2*NDIM], ftmp[2*NCOMP], *xlast = xtmp, f;
|
||||||
|
real dist = 0;
|
||||||
|
count dim;
|
||||||
|
number nextra = 1;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
creal x1 = *xlast++ = Min(Max(*x0++, 0.), 1.);
|
||||||
|
real dx;
|
||||||
|
if( (dx = x1 - border_.lower) < 0 ||
|
||||||
|
(dx = x1 - border_.upper) > 0 ) dist += Sq(dx);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( dist > 0 ) {
|
||||||
|
dist = sqrt(dist)/EXTRAPOLATE_EPS;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
real x2 = xtmp[dim], dx, b;
|
||||||
|
if( (dx = x2 - (b = border_.lower)) < 0 ||
|
||||||
|
(dx = x2 - (b = border_.upper)) > 0 ) {
|
||||||
|
xtmp[dim] = b;
|
||||||
|
x2 = b - dx/dist;
|
||||||
|
}
|
||||||
|
*xlast++ = x2;
|
||||||
|
}
|
||||||
|
nextra = 2;
|
||||||
|
}
|
||||||
|
|
||||||
|
DoSample(nextra, ndim_, xtmp, ftmp);
|
||||||
|
|
||||||
|
f = ftmp[selectedcomp_];
|
||||||
|
if( nextra > 1 ) f += dist*(f - ftmp[selectedcomp_ + ncomp_]);
|
||||||
|
|
||||||
|
return f;
|
||||||
|
}
|
||||||
|
|
||||||
368
src/external/libCuba/src/divonne/Split.c
vendored
Normal file
368
src/external/libCuba/src/divonne/Split.c
vendored
Normal file
@ -0,0 +1,368 @@
|
|||||||
|
/*
|
||||||
|
Split.c
|
||||||
|
determine optimal cuts for splitting a region
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 22 Jul 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#define BNDTOL .05
|
||||||
|
#define FRACT .5
|
||||||
|
#define BIG 1e10
|
||||||
|
#define SINGTOL 1e-4
|
||||||
|
|
||||||
|
#define LHSTOL .1
|
||||||
|
#define GAMMATOL .1
|
||||||
|
|
||||||
|
/* the next four macros must be in sync with the typedef of Bounds! */
|
||||||
|
#define Lower(d) (2*d)
|
||||||
|
#define Upper(d) (2*d + 1)
|
||||||
|
#define Dim(i) ((i) >> 1)
|
||||||
|
#define SignedDelta(i) ((i & 1) ? delta[i] : -delta[i])
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
count i;
|
||||||
|
real save, delta;
|
||||||
|
real f, df, fold;
|
||||||
|
real lhs, row, sol;
|
||||||
|
} Cut;
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real diff, err, spread;
|
||||||
|
} Errors;
|
||||||
|
|
||||||
|
typedef const Errors cErrors;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real Div(creal a, creal b)
|
||||||
|
{
|
||||||
|
return (b != 0 && fabs(b) < BIG*fabs(a)) ? a/b : a;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void SomeCut(Cut *cut, Bounds *b)
|
||||||
|
{
|
||||||
|
count dim, maxdim;
|
||||||
|
static count nextdim = 0;
|
||||||
|
real xmid[NDIM], ymid, maxdev;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
xmid[dim] = .5*(b[dim].upper + b[dim].lower);
|
||||||
|
ymid = Sample(xmid);
|
||||||
|
|
||||||
|
maxdev = 0;
|
||||||
|
maxdim = 0;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
real ylower, yupper, dev;
|
||||||
|
creal x = xmid[dim];
|
||||||
|
xmid[dim] = b[dim].lower;
|
||||||
|
ylower = Sample(xmid);
|
||||||
|
xmid[dim] = b[dim].upper;
|
||||||
|
yupper = Sample(xmid);
|
||||||
|
xmid[dim] = x;
|
||||||
|
|
||||||
|
dev = fabs(ymid - .5*(ylower + yupper));
|
||||||
|
if( dev >= maxdev ) {
|
||||||
|
maxdev = dev;
|
||||||
|
maxdim = dim;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( maxdev > 0 ) nextdim = 0;
|
||||||
|
else maxdim = nextdim++ % ndim_;
|
||||||
|
|
||||||
|
cut->i = Upper(maxdim);
|
||||||
|
cut->save = b[maxdim].upper;
|
||||||
|
b[maxdim].upper = xmid[maxdim];
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real Volume(creal *delta)
|
||||||
|
{
|
||||||
|
real vol = 1;
|
||||||
|
count dim;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
vol *= delta[Lower(dim)] + delta[Upper(dim)];
|
||||||
|
return vol;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline real SetupEqs(Cut *cut, ccount ncut, real f)
|
||||||
|
{
|
||||||
|
real sqsum = 0;
|
||||||
|
Cut *c = &cut[ncut];
|
||||||
|
while( --c >= cut ) {
|
||||||
|
sqsum += Sq(c->lhs = f - c->f);
|
||||||
|
f = c->f;
|
||||||
|
}
|
||||||
|
return sqsum;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void SolveEqs(Cut *cut, count ncut,
|
||||||
|
creal *delta, creal diff)
|
||||||
|
{
|
||||||
|
real last = 0;
|
||||||
|
real r = 1;
|
||||||
|
Cut *c;
|
||||||
|
|
||||||
|
for( c = cut; ; ++c ) {
|
||||||
|
ccount dim = Dim(c->i);
|
||||||
|
c->row = r -=
|
||||||
|
Div(diff, (delta[Lower(dim)] + delta[Upper(dim)])*c->df);
|
||||||
|
if( --ncut == 0 ) break;
|
||||||
|
last += r*c->lhs;
|
||||||
|
}
|
||||||
|
|
||||||
|
last = Div(c->lhs - last, r);
|
||||||
|
|
||||||
|
for( ; c >= cut; last += (--c)->lhs ) {
|
||||||
|
creal delmin = -(c->delta = delta[c->i]);
|
||||||
|
creal delmax = FRACT*(delmin + c->save);
|
||||||
|
c->sol = Div(last, c->df);
|
||||||
|
if( c->sol > delmax ) c->sol = .75*delmax;
|
||||||
|
if( c->sol < delmin ) c->sol = .75*delmin;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static count FindCuts(Cut *cut, Bounds *bounds, creal vol,
|
||||||
|
real *xmajor, creal fmajor, creal fdiff)
|
||||||
|
{
|
||||||
|
cint sign = (fdiff < 0) ? -1 : 1;
|
||||||
|
|
||||||
|
count ncut = 0, icut;
|
||||||
|
real delta[2*NDIM];
|
||||||
|
real gamma, fgamma, lhssq;
|
||||||
|
count dim, div;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
// cBounds *b = &bounds[dim];
|
||||||
|
// creal xsave = xmajor[dim];
|
||||||
|
cBounds *b;
|
||||||
|
real xsave;
|
||||||
|
b = &bounds[dim];
|
||||||
|
xsave = xmajor[dim];
|
||||||
|
real dist = b->upper - xsave;
|
||||||
|
if( dist >= BNDTOL*(b->upper - b->lower) ) {
|
||||||
|
Cut *c = &cut[ncut++];
|
||||||
|
c->i = Upper(dim);
|
||||||
|
c->save = dist;
|
||||||
|
xmajor[dim] += dist *= FRACT;
|
||||||
|
c->f = Sample(xmajor);
|
||||||
|
xmajor[dim] = xsave;
|
||||||
|
}
|
||||||
|
delta[Upper(dim)] = dist;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = &bounds[dim];
|
||||||
|
creal xsave = xmajor[dim];
|
||||||
|
real dist = xsave - b->lower;
|
||||||
|
if( dist >= BNDTOL*(b->upper - b->lower) ) {
|
||||||
|
Cut *c = &cut[ncut++];
|
||||||
|
c->i = Lower(dim);
|
||||||
|
c->save = dist;
|
||||||
|
xmajor[dim] -= dist *= FRACT;
|
||||||
|
c->f = Sample(xmajor);
|
||||||
|
xmajor[dim] = xsave;
|
||||||
|
}
|
||||||
|
delta[Lower(dim)] = dist;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( ncut == 0 ) {
|
||||||
|
SomeCut(cut, bounds);
|
||||||
|
return 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( ; ; ) {
|
||||||
|
real mindiff = INFTY;
|
||||||
|
Cut *mincut = cut;
|
||||||
|
|
||||||
|
for( icut = 0; icut < ncut; ++icut ) {
|
||||||
|
Cut *c = &cut[icut];
|
||||||
|
creal diff = fabs(fmajor - c->f);
|
||||||
|
if( diff <= mindiff ) {
|
||||||
|
mindiff = diff;
|
||||||
|
mincut = c;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
gamma = Volume(delta)/vol;
|
||||||
|
fgamma = fmajor + (gamma - 1)*fdiff;
|
||||||
|
|
||||||
|
if( sign*(mincut->f - fgamma) < 0 ) break;
|
||||||
|
|
||||||
|
if( --ncut == 0 ) {
|
||||||
|
SomeCut(cut, bounds);
|
||||||
|
return 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
delta[mincut->i] = mincut->save;
|
||||||
|
memcpy(mincut, mincut + 1, (char *)&cut[ncut] - (char *)mincut);
|
||||||
|
}
|
||||||
|
|
||||||
|
for( icut = 0; icut < ncut; ++icut ) {
|
||||||
|
Cut *c = &cut[icut];
|
||||||
|
c->fold = c->f;
|
||||||
|
c->df = (c->f - fmajor)/delta[c->i];
|
||||||
|
}
|
||||||
|
|
||||||
|
lhssq = SetupEqs(cut, ncut, fgamma);
|
||||||
|
|
||||||
|
repeat:
|
||||||
|
SolveEqs(cut, ncut, delta, gamma*fdiff);
|
||||||
|
|
||||||
|
for( div = 1; div <= 16; div *= 4 ) {
|
||||||
|
real gammanew, lhssqnew;
|
||||||
|
|
||||||
|
for( icut = 0; icut < ncut; ++icut ) {
|
||||||
|
Cut *c = &cut[icut];
|
||||||
|
real *x = &xmajor[Dim(c->i)];
|
||||||
|
creal xsave = *x;
|
||||||
|
delta[c->i] = c->delta + c->sol/div;
|
||||||
|
*x += SignedDelta(c->i);
|
||||||
|
c->f = Sample(xmajor);
|
||||||
|
*x = xsave;
|
||||||
|
}
|
||||||
|
|
||||||
|
gammanew = Volume(delta)/vol;
|
||||||
|
fgamma = fmajor + (gammanew - 1)*fdiff;
|
||||||
|
lhssqnew = SetupEqs(cut, ncut, fgamma);
|
||||||
|
|
||||||
|
if( lhssqnew <= lhssq ) {
|
||||||
|
real fmax;
|
||||||
|
|
||||||
|
if( fabs(gammanew - gamma) < GAMMATOL*gamma ) break;
|
||||||
|
gamma = gammanew;
|
||||||
|
|
||||||
|
fmax = fabs(fgamma);
|
||||||
|
for( icut = 0; icut < ncut; ++icut ) {
|
||||||
|
Cut *c = &cut[icut];
|
||||||
|
creal dfmin = SINGTOL*c->df;
|
||||||
|
creal sol = c->sol/div;
|
||||||
|
real df = c->f - c->fold;
|
||||||
|
df = (fabs(sol) < BIG*fabs(df)) ? df/sol : 1;
|
||||||
|
c->df = (fabs(df) < fabs(dfmin)) ? dfmin : df;
|
||||||
|
fmax = Max(fmax, fabs(c->f));
|
||||||
|
c->fold = c->f;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( lhssqnew < Sq((1 + fmax)*LHSTOL) ) break;
|
||||||
|
lhssq = lhssqnew;
|
||||||
|
goto repeat;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( icut = 0; icut < ncut; ++icut ) {
|
||||||
|
Cut *c = &cut[icut];
|
||||||
|
real *b = (real *)bounds + c->i;
|
||||||
|
c->save = *b;
|
||||||
|
*b = xmajor[Dim(c->i)] + SignedDelta(c->i);
|
||||||
|
}
|
||||||
|
|
||||||
|
return ncut;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Split(count iregion, int depth)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
|
||||||
|
Cut cut[2*NDIM];
|
||||||
|
Errors errors[NCOMP];
|
||||||
|
count comp, ncut, nsplit, xregion, ireg, xreg;
|
||||||
|
real tmp;
|
||||||
|
|
||||||
|
{
|
||||||
|
Region *const region = region_ + iregion;
|
||||||
|
selectedcomp_ = region->cutcomp;
|
||||||
|
neval_cut_ -= neval_;
|
||||||
|
ncut = FindCuts(cut, region->bounds, region->vol,
|
||||||
|
(real *)region->result + region->xmajor, region->fmajor,
|
||||||
|
region->fmajor - region->fminor);
|
||||||
|
neval_cut_ += neval_;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Errors *e = &errors[comp];
|
||||||
|
e->diff = region->result[comp].avg;
|
||||||
|
e->spread = e->err = 0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
xregion = nregions_;
|
||||||
|
|
||||||
|
depth -= ncut;
|
||||||
|
if( Explore(iregion, &samples_[0], depth, 1) ) {
|
||||||
|
Cut *c;
|
||||||
|
for( c = cut; ncut--; ++c ) {
|
||||||
|
real *b = (real *)region_[iregion].bounds;
|
||||||
|
ccount c0 = c->i, c1 = c0 ^ 1;
|
||||||
|
creal tmp = b[c1];
|
||||||
|
b[c1] = b[c0];
|
||||||
|
b[c0] = c->save;
|
||||||
|
if( !Explore(iregion, &samples_[0], depth++, ncut != 0) ) break;
|
||||||
|
if( ncut ) ((real *)region_[iregion].bounds)[c1] = tmp;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
nsplit = nregions_ - xregion + 1;
|
||||||
|
|
||||||
|
for( ireg = iregion, xreg = xregion; ireg < nregions_; ireg = xreg++ ) {
|
||||||
|
cResult *result = region_[ireg].result;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = &result[comp];
|
||||||
|
Errors *e = &errors[comp];
|
||||||
|
e->diff -= r->avg;
|
||||||
|
e->err += r->err;
|
||||||
|
e->spread += Sq(r->spread);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
tmp = 1./nsplit;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Errors *e = &errors[comp];
|
||||||
|
e->diff = tmp*fabs(e->diff);
|
||||||
|
e->err = (e->err == 0) ? 1 : 1 + e->diff/e->err;
|
||||||
|
e->spread = (e->spread == 0) ? 1 : 1 + e->diff/sqrt(e->spread);
|
||||||
|
}
|
||||||
|
|
||||||
|
tmp = 1 - tmp;
|
||||||
|
for( ireg = iregion, xreg = xregion; ireg < nregions_; ireg = xreg++ ) {
|
||||||
|
Result *result = region_[ireg].result;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Result *r = &result[comp];
|
||||||
|
cErrors *e = &errors[comp];
|
||||||
|
creal c = tmp*e->diff;
|
||||||
|
if( r->err > 0 ) r->err = r->err*e->err + c;
|
||||||
|
r->spread = r->spread*e->spread + c*samples_[0].neff;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
62
src/external/libCuba/src/divonne/common.c
vendored
Normal file
62
src/external/libCuba/src/divonne/common.c
vendored
Normal file
@ -0,0 +1,62 @@
|
|||||||
|
/*
|
||||||
|
common.c
|
||||||
|
includes most of the modules
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 5 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
static bool Explore(count iregion, cSamples *samples, cint depth, cint flags);
|
||||||
|
|
||||||
|
static void Split(count iregion, int depth);
|
||||||
|
|
||||||
|
#include "Random.c"
|
||||||
|
#include "ChiSquare.c"
|
||||||
|
#include "Rule.c"
|
||||||
|
#include "Sample.c"
|
||||||
|
#include "FindMinimum.c"
|
||||||
|
#include "Explore.c"
|
||||||
|
#include "Split.c"
|
||||||
|
#include "Integrate.c"
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadDimension(ccount ndim, cint flags, ccount key)
|
||||||
|
{
|
||||||
|
#if NDIM > 0
|
||||||
|
if( ndim > NDIM ) return true;
|
||||||
|
#endif
|
||||||
|
if( IsSobol(key) ) return
|
||||||
|
ndim < SOBOL_MINDIM || (!PSEUDORNG && ndim > SOBOL_MAXDIM);
|
||||||
|
if( IsRule(key, ndim) ) return ndim < 1;
|
||||||
|
return ndim < KOROBOV_MINDIM || ndim > KOROBOV_MAXDIM;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadComponent(cint ncomp)
|
||||||
|
{
|
||||||
|
#if NCOMP > 0
|
||||||
|
if( ncomp > NCOMP ) return true;
|
||||||
|
#endif
|
||||||
|
return ncomp < 1;
|
||||||
|
}
|
||||||
|
|
||||||
91
src/external/libCuba/src/divonne/decl.h
vendored
Normal file
91
src/external/libCuba/src/divonne/decl.h
vendored
Normal file
@ -0,0 +1,91 @@
|
|||||||
|
/*
|
||||||
|
decl.h
|
||||||
|
Type declarations
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 25 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "stddecl.h"
|
||||||
|
|
||||||
|
#define EXTRAPOLATE_EPS (.25*border_.lower)
|
||||||
|
/*#define EXTRAPOLATE_EPS 0x1p-26*/
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real lower, upper;
|
||||||
|
} Bounds;
|
||||||
|
|
||||||
|
typedef const Bounds cBounds;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real avg, spreadsq;
|
||||||
|
real spread, secondspread;
|
||||||
|
real nneed, maxerrsq, mindevsq;
|
||||||
|
int iregion;
|
||||||
|
} Totals;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
void *first, *last;
|
||||||
|
real errcoeff[3];
|
||||||
|
count n;
|
||||||
|
} Rule;
|
||||||
|
|
||||||
|
typedef const Rule cRule;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct samples {
|
||||||
|
real weight;
|
||||||
|
real *x, *f, *avg, *err;
|
||||||
|
void (*sampler)(const struct samples *, cBounds *, creal);
|
||||||
|
cRule *rule;
|
||||||
|
count coeff;
|
||||||
|
number n, neff;
|
||||||
|
} Samples;
|
||||||
|
|
||||||
|
typedef const Samples cSamples;
|
||||||
|
|
||||||
|
|
||||||
|
#define TYPEDEFREGION \
|
||||||
|
typedef struct { \
|
||||||
|
real avg, err, spread, chisq; \
|
||||||
|
real fmin, fmax; \
|
||||||
|
real xmin[NDIM], xmax[NDIM]; \
|
||||||
|
} Result; \
|
||||||
|
typedef const Result cResult; \
|
||||||
|
typedef struct region { \
|
||||||
|
count cutcomp, depth, xmajor; \
|
||||||
|
real fmajor, fminor, vol; \
|
||||||
|
Bounds bounds[NDIM]; \
|
||||||
|
Result result[NCOMP]; \
|
||||||
|
} Region
|
||||||
|
|
||||||
|
#define CHUNKSIZE 4096
|
||||||
|
|
||||||
|
|
||||||
|
typedef void (*Integrand)(ccount *, creal *, ccount *, real *, cint *);
|
||||||
|
|
||||||
|
typedef void (*PeakFinder)(ccount *, cBounds *, number *, real *);
|
||||||
|
|
||||||
51
src/external/libCuba/src/divonne/util.c
vendored
Normal file
51
src/external/libCuba/src/divonne/util.c
vendored
Normal file
@ -0,0 +1,51 @@
|
|||||||
|
/*
|
||||||
|
util.c
|
||||||
|
Utility functions
|
||||||
|
this file is part of Divonne
|
||||||
|
last modified 9 Apr 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "decl.h"
|
||||||
|
|
||||||
|
static count ndim_, ncomp_, selectedcomp_, nregions_;
|
||||||
|
static number neval_, neval_opt_, neval_cut_;
|
||||||
|
static int sign_, phase_;
|
||||||
|
|
||||||
|
static Bounds border_;
|
||||||
|
|
||||||
|
static Samples samples_[3];
|
||||||
|
static Rule rule7_, rule9_, rule11_, rule13_;
|
||||||
|
static real *xgiven_, *fgiven_, *xextra_, *fextra_;
|
||||||
|
static count ldxgiven_;
|
||||||
|
static number ngiven_, nextra_;
|
||||||
|
|
||||||
|
static Totals *totals_;
|
||||||
|
|
||||||
|
static void *voidregion_;
|
||||||
|
#define region_ ((Region *)voidregion_)
|
||||||
|
static count size_;
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
#include "debug.c"
|
||||||
|
#endif
|
||||||
|
|
||||||
82
src/external/libCuba/src/suave/Fluct.c
vendored
Normal file
82
src/external/libCuba/src/suave/Fluct.c
vendored
Normal file
@ -0,0 +1,82 @@
|
|||||||
|
/*
|
||||||
|
Fluct.c
|
||||||
|
compute the fluctuation in the left and right half
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#if defined(HAVE_LONG_DOUBLE) && defined(HAVE_POWL)
|
||||||
|
|
||||||
|
typedef long double xdouble;
|
||||||
|
#define XDBL_MAX_EXP LDBL_MAX_EXP
|
||||||
|
#define XDBL_MAX LDBL_MAX
|
||||||
|
#define powx powl
|
||||||
|
|
||||||
|
#else
|
||||||
|
|
||||||
|
typedef double xdouble;
|
||||||
|
#define XDBL_MAX_EXP DBL_MAX_EXP
|
||||||
|
#define XDBL_MAX DBL_MAX
|
||||||
|
#define powx pow
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
xdouble fluct;
|
||||||
|
number n;
|
||||||
|
} Var;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Fluct(Var *var, real flatness,
|
||||||
|
cBounds *b, creal *w, number n, ccount comp, creal avg, creal err)
|
||||||
|
{
|
||||||
|
creal *x = w + n, *f = x + n*ndim_ + comp;
|
||||||
|
creal max = ldexp(1., (int)((XDBL_MAX_EXP - 2)/flatness));
|
||||||
|
creal norm = 1/(err*Max(fabs(avg), err));
|
||||||
|
count nvar = 2*ndim_;
|
||||||
|
|
||||||
|
Clear(var, nvar);
|
||||||
|
|
||||||
|
while( n-- ) {
|
||||||
|
count dim;
|
||||||
|
const xdouble t =
|
||||||
|
powx(Min(1 + fabs(*w++)*Sq(*f - avg)*norm, max), flatness);
|
||||||
|
|
||||||
|
f += ncomp_;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
Var *v = &var[2*dim + (*x++ >= b[dim].mid)];
|
||||||
|
const xdouble f = v->fluct + t;
|
||||||
|
v->fluct = (f > XDBL_MAX/2) ? XDBL_MAX/2 : f;
|
||||||
|
++v->n;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
flatness = 2/3./flatness;
|
||||||
|
while( nvar-- ) {
|
||||||
|
var->fluct = powx(var->fluct, flatness);
|
||||||
|
++var;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
156
src/external/libCuba/src/suave/Grid.c
vendored
Normal file
156
src/external/libCuba/src/suave/Grid.c
vendored
Normal file
@ -0,0 +1,156 @@
|
|||||||
|
/*
|
||||||
|
Grid.c
|
||||||
|
utility functions for the Vegas grid
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 15 Feb 08 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
static void RefineGrid(Grid grid, Grid margsum, cint flags)
|
||||||
|
{
|
||||||
|
real avgperbin, thisbin, newcur, delta;
|
||||||
|
Grid imp, newgrid;
|
||||||
|
int bin, newbin;
|
||||||
|
|
||||||
|
/* smooth the f^2 value stored for each bin */
|
||||||
|
real prev = margsum[0];
|
||||||
|
real cur = margsum[1];
|
||||||
|
real norm = margsum[0] = .5*(prev + cur);
|
||||||
|
for( bin = 1; bin < NBINS - 1; ++bin ) {
|
||||||
|
creal s = prev + cur;
|
||||||
|
prev = cur;
|
||||||
|
cur = margsum[bin + 1];
|
||||||
|
norm += margsum[bin] = (s + cur)/3.;
|
||||||
|
}
|
||||||
|
norm += margsum[NBINS - 1] = .5*(prev + cur);
|
||||||
|
|
||||||
|
if( norm == 0 ) return;
|
||||||
|
norm = 1/norm;
|
||||||
|
|
||||||
|
/* compute the importance function for each bin */
|
||||||
|
avgperbin = 0;
|
||||||
|
for( bin = 0; bin < NBINS; ++bin ) {
|
||||||
|
real impfun = 0;
|
||||||
|
if( margsum[bin] > 0 ) {
|
||||||
|
creal r = margsum[bin]*norm;
|
||||||
|
avgperbin += impfun = pow((r - 1)/log(r), 1.5);
|
||||||
|
}
|
||||||
|
imp[bin] = impfun;
|
||||||
|
}
|
||||||
|
avgperbin /= NBINS;
|
||||||
|
|
||||||
|
/* redefine the size of each bin */
|
||||||
|
cur = newcur = 0;
|
||||||
|
thisbin = 0;
|
||||||
|
bin = -1;
|
||||||
|
for( newbin = 0; newbin < NBINS - 1; ++newbin ) {
|
||||||
|
while( thisbin < avgperbin ) {
|
||||||
|
thisbin += imp[++bin];
|
||||||
|
prev = cur;
|
||||||
|
cur = grid[bin];
|
||||||
|
}
|
||||||
|
thisbin -= avgperbin;
|
||||||
|
delta = (cur - prev)*thisbin;
|
||||||
|
newgrid[newbin] = SHARPEDGES ?
|
||||||
|
cur - delta/imp[bin] :
|
||||||
|
(newcur = Max(newcur + 0x1p-48,
|
||||||
|
cur - 2*delta/(imp[bin] + imp[IDim(bin - 1)])));
|
||||||
|
}
|
||||||
|
Copy(grid, newgrid, NBINS - 1);
|
||||||
|
grid[NBINS - 1] = 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Reweight(Bounds *b,
|
||||||
|
creal *w, creal *f, creal *lastf, cResult *total, cint flags)
|
||||||
|
{
|
||||||
|
Grid margsum[NDIM];
|
||||||
|
real scale[NCOMP];
|
||||||
|
cbin_t *bin = (cbin_t *)lastf;
|
||||||
|
count dim, comp;
|
||||||
|
|
||||||
|
if( ncomp_ == 1 ) scale[0] = 1;
|
||||||
|
else {
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
scale[comp] = (total[comp].avg == 0) ? 0 : 1/total[comp].avg;
|
||||||
|
}
|
||||||
|
|
||||||
|
Zap(margsum);
|
||||||
|
|
||||||
|
while( f < lastf ) {
|
||||||
|
real fsq = 0;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp )
|
||||||
|
fsq += Sq(*f++*scale[comp]);
|
||||||
|
fsq *= Sq(*w++);
|
||||||
|
if( fsq != 0 )
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
margsum[dim][bin[dim]] += fsq;
|
||||||
|
bin += ndim_;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
RefineGrid(b[dim].grid, margsum[dim], flags);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void StretchGrid(cGrid grid, Grid gridL, Grid gridR)
|
||||||
|
{
|
||||||
|
real prev = 0, cur, step, x;
|
||||||
|
count bin = 0;
|
||||||
|
|
||||||
|
while( bin < NBINS ) {
|
||||||
|
cur = grid[bin++];
|
||||||
|
if( cur >= .5 ) break;
|
||||||
|
prev = cur;
|
||||||
|
}
|
||||||
|
|
||||||
|
step = (bin - (cur - .5)/(cur - prev))/NBINS;
|
||||||
|
|
||||||
|
prev = x = 0;
|
||||||
|
cur = *grid;
|
||||||
|
|
||||||
|
for( bin = 0; bin < NBINS; ++bin ) {
|
||||||
|
x += step;
|
||||||
|
if( x > 1 ) {
|
||||||
|
--x;
|
||||||
|
prev = cur;
|
||||||
|
cur = *++grid;
|
||||||
|
}
|
||||||
|
gridL[bin] = 2*(prev + (cur - prev)*x);
|
||||||
|
}
|
||||||
|
|
||||||
|
step = 1 - step;
|
||||||
|
for( bin = 0; bin < NBINS - 1; ++bin ) {
|
||||||
|
x += step;
|
||||||
|
if( x > 1 ) {
|
||||||
|
--x;
|
||||||
|
prev = cur;
|
||||||
|
cur = *++grid;
|
||||||
|
}
|
||||||
|
gridR[bin] = 2*(prev + (cur - prev)*x) - 1;
|
||||||
|
}
|
||||||
|
gridR[NBINS - 1] = 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
298
src/external/libCuba/src/suave/Integrate.c
vendored
Normal file
298
src/external/libCuba/src/suave/Integrate.c
vendored
Normal file
@ -0,0 +1,298 @@
|
|||||||
|
/*
|
||||||
|
Integrate.c
|
||||||
|
integrate over the unit hypercube
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 2 Jan 08 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
static int Integrate(creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
cnumber nnew, creal flatness,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
|
||||||
|
count dim, comp, df;
|
||||||
|
int fail = 1;
|
||||||
|
Result totals[NCOMP];
|
||||||
|
Region *anchor = NULL, *region = NULL;
|
||||||
|
|
||||||
|
if( VERBOSE > 1 ) {
|
||||||
|
char s[256];
|
||||||
|
sprintf(s, "Suave input parameters:\n"
|
||||||
|
" ndim " COUNT "\n ncomp " COUNT "\n"
|
||||||
|
" epsrel " REAL "\n epsabs " REAL "\n"
|
||||||
|
" flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n"
|
||||||
|
" nnew " NUMBER "\n flatness " REAL,
|
||||||
|
ndim_, ncomp_,
|
||||||
|
epsrel, epsabs,
|
||||||
|
flags, mineval, maxeval,
|
||||||
|
nnew, flatness);
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( setjmp(abort_) ) goto abort;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
IniRandom(2*maxeval, flags);
|
||||||
|
|
||||||
|
RegionAlloc(anchor, nnew, nnew);
|
||||||
|
anchor->next = NULL;
|
||||||
|
anchor->div = 0;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
Bounds *b = &anchor->bounds[dim];
|
||||||
|
b->lower = 0;
|
||||||
|
b->upper = 1;
|
||||||
|
b->mid = .5;
|
||||||
|
|
||||||
|
if( dim == 0 ) {
|
||||||
|
count bin;
|
||||||
|
/* define the initial distribution of bins */
|
||||||
|
for( bin = 0; bin < NBINS; ++bin )
|
||||||
|
b->grid[bin] = (bin + 1)/(real)NBINS;
|
||||||
|
}
|
||||||
|
else Copy(b->grid, anchor->bounds[0].grid, NBINS);
|
||||||
|
}
|
||||||
|
|
||||||
|
Sample(nnew, anchor, anchor->w,
|
||||||
|
anchor->w + nnew, anchor->w + (ndim_ + 1)*nnew, flags);
|
||||||
|
df = anchor->df;
|
||||||
|
ResCopy(totals, anchor->result);
|
||||||
|
|
||||||
|
for( nregions_ = 1; ; ++nregions_ ) {
|
||||||
|
Var var[NDIM][2], *vLR;
|
||||||
|
real maxratio, maxerr, minfluct, bias, mid;
|
||||||
|
Region *regionL, *regionR, *reg, **parent, **par;
|
||||||
|
Bounds *bounds, *boundsL, *boundsR;
|
||||||
|
count maxcomp, bisectdim;
|
||||||
|
number n, nL, nR, nnewL, nnewR;
|
||||||
|
real *w, *wL, *wR, *x, *xL, *xR, *f, *fL, *fR, *wlast, *flast;
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[128 + 128*NCOMP], *p = s;
|
||||||
|
|
||||||
|
p += sprintf(p, "\n"
|
||||||
|
"Iteration " COUNT ": " NUMBER " integrand evaluations so far",
|
||||||
|
nregions_, neval_);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *tot = &totals[comp];
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)",
|
||||||
|
comp + 1, tot->avg, tot->err, tot->chisq, df);
|
||||||
|
}
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
maxratio = -INFTY;
|
||||||
|
maxcomp = 0;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
creal ratio = totals[comp].err/MaxErr(totals[comp].avg);
|
||||||
|
if( ratio > maxratio ) {
|
||||||
|
maxratio = ratio;
|
||||||
|
maxcomp = comp;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( maxratio <= 1 && neval_ >= mineval ) {
|
||||||
|
fail = 0;
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( neval_ >= maxeval ) break;
|
||||||
|
|
||||||
|
maxerr = -INFTY;
|
||||||
|
parent = &anchor;
|
||||||
|
region = anchor;
|
||||||
|
for( par = &anchor; (reg = *par); par = ®->next ) {
|
||||||
|
creal err = reg->result[maxcomp].err;
|
||||||
|
if( err > maxerr ) {
|
||||||
|
maxerr = err;
|
||||||
|
parent = par;
|
||||||
|
region = reg;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
Fluct(var[0], flatness,
|
||||||
|
region->bounds, region->w, region->n, maxcomp,
|
||||||
|
region->result[maxcomp].avg, Max(maxerr, epsabs));
|
||||||
|
|
||||||
|
bias = (epsrel < 1e-50) ? 2 :
|
||||||
|
Max(pow(2., -(real)region->div/ndim_)/epsrel, 2.);
|
||||||
|
minfluct = INFTY;
|
||||||
|
bisectdim = 0;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
creal fluct = (var[dim][0].fluct + var[dim][1].fluct)*
|
||||||
|
(bias - b->upper + b->lower);
|
||||||
|
if( fluct < minfluct ) {
|
||||||
|
minfluct = fluct;
|
||||||
|
bisectdim = dim;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
vLR = var[bisectdim];
|
||||||
|
minfluct = vLR[0].fluct + vLR[1].fluct;
|
||||||
|
nnewL = IMax(
|
||||||
|
(minfluct == 0) ? nnew/2 : (count)(vLR[0].fluct/minfluct*nnew),
|
||||||
|
MINSAMPLES );
|
||||||
|
nL = vLR[0].n + nnewL;
|
||||||
|
nnewR = IMax(nnew - nnewL, MINSAMPLES);
|
||||||
|
nR = vLR[1].n + nnewR;
|
||||||
|
|
||||||
|
RegionAlloc(regionL, nL, nnewL);
|
||||||
|
RegionAlloc(regionR, nR, nnewR);
|
||||||
|
|
||||||
|
*parent = regionL;
|
||||||
|
regionL->next = regionR;
|
||||||
|
regionR->next = region->next;
|
||||||
|
regionL->div = regionR->div = region->div + 1;
|
||||||
|
|
||||||
|
bounds = ®ion->bounds[bisectdim];
|
||||||
|
mid = bounds->mid;
|
||||||
|
n = region->n;
|
||||||
|
w = wlast = region->w; x = w + n; f = flast = x + n*ndim_;
|
||||||
|
wL = regionL->w; xL = wL + nL; fL = xL + nL*ndim_;
|
||||||
|
wR = regionR->w; xR = wR + nR; fR = xR + nR*ndim_;
|
||||||
|
|
||||||
|
while( n-- ) {
|
||||||
|
cbool final = (*w < 0);
|
||||||
|
if( x[bisectdim] < mid ) {
|
||||||
|
if( final && wR > regionR->w ) *(wR - 1) = -fabs(*(wR - 1));
|
||||||
|
*wL++ = *w++;
|
||||||
|
VecCopy(xL, x);
|
||||||
|
xL += ndim_;
|
||||||
|
ResCopy(fL, f);
|
||||||
|
fL += ncomp_;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
if( final && wL > regionL->w ) *(wL - 1) = -fabs(*(wL - 1));
|
||||||
|
*wR++ = *w++;
|
||||||
|
VecCopy(xR, x);
|
||||||
|
xR += ndim_;
|
||||||
|
ResCopy(fR, f);
|
||||||
|
fR += ncomp_;
|
||||||
|
}
|
||||||
|
x += ndim_;
|
||||||
|
f += ncomp_;
|
||||||
|
if( n && final ) wlast = w, flast = f;
|
||||||
|
}
|
||||||
|
|
||||||
|
Reweight(region->bounds, wlast, flast, f, totals, flags);
|
||||||
|
VecCopy(regionL->bounds, region->bounds);
|
||||||
|
VecCopy(regionR->bounds, region->bounds);
|
||||||
|
|
||||||
|
boundsL = ®ionL->bounds[bisectdim];
|
||||||
|
boundsR = ®ionR->bounds[bisectdim];
|
||||||
|
boundsL->mid = .5*(boundsL->lower + (boundsL->upper = mid));
|
||||||
|
boundsR->mid = .5*((boundsR->lower = mid) + boundsR->upper);
|
||||||
|
|
||||||
|
StretchGrid(bounds->grid, boundsL->grid, boundsR->grid);
|
||||||
|
|
||||||
|
Sample(nnewL, regionL, wL, xL, fL, flags);
|
||||||
|
Sample(nnewR, regionR, wR, xR, fR, flags);
|
||||||
|
|
||||||
|
df += regionL->df + regionR->df - region->df;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
Result *rL = ®ionL->result[comp];
|
||||||
|
Result *rR = ®ionR->result[comp];
|
||||||
|
Result *tot = &totals[comp];
|
||||||
|
real diff, sigsq;
|
||||||
|
|
||||||
|
tot->avg += diff = rL->avg + rR->avg - r->avg;
|
||||||
|
|
||||||
|
diff = Sq(.25*diff);
|
||||||
|
sigsq = rL->sigsq + rR->sigsq;
|
||||||
|
if( sigsq > 0 ) {
|
||||||
|
creal c = Sq(1 + sqrt(diff/sigsq));
|
||||||
|
rL->sigsq *= c;
|
||||||
|
rR->sigsq *= c;
|
||||||
|
}
|
||||||
|
rL->err = sqrt(rL->sigsq += diff);
|
||||||
|
rR->err = sqrt(rR->sigsq += diff);
|
||||||
|
|
||||||
|
tot->sigsq += rL->sigsq + rR->sigsq - r->sigsq;
|
||||||
|
tot->err = sqrt(tot->sigsq);
|
||||||
|
|
||||||
|
tot->chisq += rL->chisq + rR->chisq - r->chisq;
|
||||||
|
}
|
||||||
|
|
||||||
|
free(region);
|
||||||
|
region = NULL;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *tot = &totals[comp];
|
||||||
|
integral[comp] = tot->avg;
|
||||||
|
error[comp] = tot->err;
|
||||||
|
prob[comp] = ChiSquare(tot->chisq, df);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( REGIONS ) {
|
||||||
|
MLPutFunction(stdlink, "List", 2);
|
||||||
|
MLPutFunction(stdlink, "List", nregions_);
|
||||||
|
for( region = anchor; region; region = region->next ) {
|
||||||
|
real lower[NDIM], upper[NDIM];
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
lower[dim] = b->lower;
|
||||||
|
upper[dim] = b->upper;
|
||||||
|
}
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "Cuba`Suave`region", 4);
|
||||||
|
MLPutRealList(stdlink, lower, ndim_);
|
||||||
|
MLPutRealList(stdlink, upper, ndim_);
|
||||||
|
|
||||||
|
MLPutFunction(stdlink, "List", ncomp_);
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
real res[] = {r->avg, r->err, r->chisq};
|
||||||
|
MLPutRealList(stdlink, res, Elements(res));
|
||||||
|
}
|
||||||
|
|
||||||
|
MLPutInteger(stdlink, region->df);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
abort:
|
||||||
|
#endif
|
||||||
|
|
||||||
|
if( region ) free(region);
|
||||||
|
|
||||||
|
while( (region = anchor) ) {
|
||||||
|
anchor = anchor->next;
|
||||||
|
free(region);
|
||||||
|
}
|
||||||
|
|
||||||
|
return fail;
|
||||||
|
}
|
||||||
|
|
||||||
191
src/external/libCuba/src/suave/Sample.c
vendored
Normal file
191
src/external/libCuba/src/suave/Sample.c
vendored
Normal file
@ -0,0 +1,191 @@
|
|||||||
|
/*
|
||||||
|
Sample.c
|
||||||
|
the sampling step of Suave
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real sum, sqsum;
|
||||||
|
real weight, weightsum, avg, avgsum;
|
||||||
|
real guess, chisum, chisqsum;
|
||||||
|
} Cumulants;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void Sample(cnumber nnew, void *voidregion,
|
||||||
|
real *lastw, real *lastx, real *lastf, cint flags)
|
||||||
|
{
|
||||||
|
TYPEDEFREGION;
|
||||||
|
|
||||||
|
Region *const region = (Region *)voidregion;
|
||||||
|
count comp, dim, df;
|
||||||
|
number n;
|
||||||
|
Cumulants cumul[NCOMP];
|
||||||
|
char **ss, *s;
|
||||||
|
ccount chars = 128*(region->div + 1);
|
||||||
|
|
||||||
|
creal jacobian = 1/ldexp((real)nnew, region->div);
|
||||||
|
real *w = lastw, *f = lastx;
|
||||||
|
bin_t *bin = (bin_t *)(lastf + nnew*ncomp_);
|
||||||
|
|
||||||
|
for( n = nnew; n; --n ) {
|
||||||
|
real weight = jacobian;
|
||||||
|
|
||||||
|
GetRandom(f);
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
creal pos = *f*NBINS;
|
||||||
|
ccount ipos = (count)pos;
|
||||||
|
creal prev = (ipos == 0) ? 0 : b->grid[ipos - 1];
|
||||||
|
creal diff = b->grid[ipos] - prev;
|
||||||
|
*f++ = b->lower + (prev + (pos - ipos)*diff)*(b->upper - b->lower);
|
||||||
|
*bin++ = ipos;
|
||||||
|
weight *= diff*NBINS;
|
||||||
|
}
|
||||||
|
|
||||||
|
*w++ = weight;
|
||||||
|
}
|
||||||
|
|
||||||
|
DoSample(nnew, lastw, lastx, lastf);
|
||||||
|
|
||||||
|
*(w - 1) = -*(w - 1);
|
||||||
|
lastw = w;
|
||||||
|
w = region->w;
|
||||||
|
region->n = lastw - w;
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
char *p0;
|
||||||
|
MemAlloc(ss, ndim_*64 + ncomp_*(sizeof(char *) + chars));
|
||||||
|
s = (char *)(ss + ncomp_);
|
||||||
|
p0 = s + ndim_*64;
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
ss[comp] = p0;
|
||||||
|
p0 += chars;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
Zap(cumul);
|
||||||
|
df = n = 0;
|
||||||
|
|
||||||
|
while( w < lastw ) {
|
||||||
|
cbool final = (*w < 0);
|
||||||
|
creal weight = fabs(*w++);
|
||||||
|
++n;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Cumulants *c = &cumul[comp];
|
||||||
|
|
||||||
|
creal wfun = weight*(*f++);
|
||||||
|
c->sum += wfun;
|
||||||
|
c->sqsum += Sq(wfun);
|
||||||
|
|
||||||
|
if( final ) {
|
||||||
|
if( n > 1 ) {
|
||||||
|
real w = Weight(c->sum, c->sqsum, n);
|
||||||
|
c->weightsum += c->weight = w;
|
||||||
|
c->avgsum += c->avg = w*c->sum;
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
creal sig = sqrt(1/w);
|
||||||
|
ss[comp] += (df == 0) ?
|
||||||
|
sprintf(ss[comp], "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL " (" NUMBER ")", comp + 1,
|
||||||
|
c->sum, sig, n) :
|
||||||
|
sprintf(ss[comp], "\n "
|
||||||
|
REAL " +- " REAL " (" NUMBER ")",
|
||||||
|
c->sum, sig, n);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( df == 0 ) c->guess = c->sum;
|
||||||
|
else {
|
||||||
|
c->chisum += w *= c->sum - c->guess;
|
||||||
|
c->chisqsum += w*c->sum;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
c->sum = c->sqsum = 0;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if( final ) ++df, n = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
region->df = --df;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Result *r = ®ion->result[comp];
|
||||||
|
Cumulants *c = &cumul[comp];
|
||||||
|
creal sigsq = 1/c->weightsum;
|
||||||
|
creal avg = sigsq*c->avgsum;
|
||||||
|
|
||||||
|
if( LAST ) {
|
||||||
|
r->sigsq = 1/c->weight;
|
||||||
|
r->avg = r->sigsq*c->avg;
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
r->sigsq = sigsq;
|
||||||
|
r->avg = avg;
|
||||||
|
}
|
||||||
|
r->err = sqrt(r->sigsq);
|
||||||
|
|
||||||
|
r->chisq = (sigsq < .9*NOTZERO) ? 0 : c->chisqsum - avg*c->chisum;
|
||||||
|
/* This catches the special case where the integrand is constant
|
||||||
|
over the entire region. Unless that constant is zero, only the
|
||||||
|
first set of samples will have zero variance, and hence weight
|
||||||
|
(n - 1) 1e30 (see above). All other sets have been sampled
|
||||||
|
from a non-constant weight function and therefore inevitably
|
||||||
|
show some variance. This is an artificial effect, brought about
|
||||||
|
by the fact that the constancy of the integrand in the region is
|
||||||
|
seen only in this subdivision, and can degrade the chi-square
|
||||||
|
score quite a bit. If the constancy was determined from more
|
||||||
|
than two samples (hence .9*NOTZERO), the chi-squares from the
|
||||||
|
other sets are removed here. */
|
||||||
|
}
|
||||||
|
|
||||||
|
if( VERBOSE > 2 ) {
|
||||||
|
char *p = s;
|
||||||
|
char *p0 = p + ndim_*64;
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
cBounds *b = ®ion->bounds[dim];
|
||||||
|
p += sprintf(p,
|
||||||
|
(dim == 0) ? "\nRegion (" REALF ") - (" REALF ")" :
|
||||||
|
"\n (" REALF ") - (" REALF ")",
|
||||||
|
b->lower, b->upper);
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cResult *r = ®ion->result[comp];
|
||||||
|
p += sprintf(p, "%s \tchisq " REAL " (" COUNT " df)",
|
||||||
|
p0, r->chisq, df);
|
||||||
|
p0 += chars;
|
||||||
|
}
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
free(ss);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
92
src/external/libCuba/src/suave/Suave.c
vendored
Normal file
92
src/external/libCuba/src/suave/Suave.c
vendored
Normal file
@ -0,0 +1,92 @@
|
|||||||
|
/*
|
||||||
|
Suave.c
|
||||||
|
Subregion-adaptive Vegas Monte-Carlo integration
|
||||||
|
by Thomas Hahn
|
||||||
|
last modified 30 Aug 07 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "util.c"
|
||||||
|
|
||||||
|
#define Print(s) puts(s); fflush(stdout)
|
||||||
|
|
||||||
|
static Integrand integrand_;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void DoSample(number n, creal *w, creal *x, real *f)
|
||||||
|
{
|
||||||
|
neval_ += n;
|
||||||
|
while( n-- ) {
|
||||||
|
integrand_(&ndim_, x, &ncomp_, f, w++);
|
||||||
|
x += ndim_;
|
||||||
|
f += ncomp_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
#include "common.c"
|
||||||
|
|
||||||
|
Extern void EXPORT(Suave)(ccount ndim, ccount ncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
cnumber nnew, creal flatness,
|
||||||
|
count *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
ndim_ = ndim;
|
||||||
|
ncomp_ = ncomp;
|
||||||
|
|
||||||
|
if( BadComponent(ncomp) || BadDimension(ndim, flags) ) *pfail = -1;
|
||||||
|
else {
|
||||||
|
neval_ = 0;
|
||||||
|
integrand_ = integrand;
|
||||||
|
|
||||||
|
*pfail = Integrate(epsrel, Max(epsabs, NOTZERO),
|
||||||
|
flags, mineval, maxeval, nnew, flatness,
|
||||||
|
integral, error, prob);
|
||||||
|
*pnregions = nregions_;
|
||||||
|
*pneval = neval_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
Extern void EXPORT(suave)(ccount *pndim, ccount *pncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal *pepsrel, creal *pepsabs,
|
||||||
|
cint *pflags, cnumber *pmineval, cnumber *pmaxeval,
|
||||||
|
cnumber *pnnew, creal *pflatness,
|
||||||
|
count *pnregions, number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
EXPORT(Suave)(*pndim, *pncomp,
|
||||||
|
integrand,
|
||||||
|
*pepsrel, *pepsabs,
|
||||||
|
*pflags, *pmineval, *pmaxeval,
|
||||||
|
*pnnew, *pflatness,
|
||||||
|
pnregions, pneval, pfail,
|
||||||
|
integral, error, prob);
|
||||||
|
}
|
||||||
|
|
||||||
53
src/external/libCuba/src/suave/common.c
vendored
Normal file
53
src/external/libCuba/src/suave/common.c
vendored
Normal file
@ -0,0 +1,53 @@
|
|||||||
|
/*
|
||||||
|
common.c
|
||||||
|
includes most of the modules
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 14 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "Random.c"
|
||||||
|
#include "ChiSquare.c"
|
||||||
|
#include "Grid.c"
|
||||||
|
#include "Sample.c"
|
||||||
|
#include "Fluct.c"
|
||||||
|
#include "Integrate.c"
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadDimension(cint ndim, cint flags)
|
||||||
|
{
|
||||||
|
#if NDIM > 0
|
||||||
|
if( ndim > NDIM ) return true;
|
||||||
|
#endif
|
||||||
|
return ndim < SOBOL_MINDIM || (!PSEUDORNG && ndim > SOBOL_MAXDIM);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadComponent(cint ncomp)
|
||||||
|
{
|
||||||
|
#if NCOMP > 0
|
||||||
|
if( ncomp > NCOMP ) return true;
|
||||||
|
#endif
|
||||||
|
return ncomp < 1;
|
||||||
|
}
|
||||||
|
|
||||||
71
src/external/libCuba/src/suave/decl.h
vendored
Normal file
71
src/external/libCuba/src/suave/decl.h
vendored
Normal file
@ -0,0 +1,71 @@
|
|||||||
|
/*
|
||||||
|
decl.h
|
||||||
|
Type declarations
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 30 Aug 07 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "stddecl.h"
|
||||||
|
|
||||||
|
#define MINSAMPLES 10
|
||||||
|
|
||||||
|
#define NBINS 64
|
||||||
|
|
||||||
|
typedef unsigned char bin_t;
|
||||||
|
/* Note: bin_t must be wide enough to hold the numbers 0..NBINS */
|
||||||
|
|
||||||
|
typedef const bin_t cbin_t;
|
||||||
|
|
||||||
|
typedef real Grid[NBINS];
|
||||||
|
|
||||||
|
typedef const Grid cGrid;
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real avg, err, sigsq, chisq;
|
||||||
|
} Result;
|
||||||
|
|
||||||
|
typedef const Result cResult;
|
||||||
|
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real lower, upper, mid;
|
||||||
|
Grid grid;
|
||||||
|
} Bounds;
|
||||||
|
|
||||||
|
typedef const Bounds cBounds;
|
||||||
|
|
||||||
|
|
||||||
|
#define TYPEDEFREGION \
|
||||||
|
typedef struct region { \
|
||||||
|
struct region *next; \
|
||||||
|
count div, df; \
|
||||||
|
number n; \
|
||||||
|
Result result[NCOMP]; \
|
||||||
|
Bounds bounds[NDIM]; \
|
||||||
|
real fluct[NCOMP][NDIM][2]; \
|
||||||
|
real w[]; \
|
||||||
|
} Region
|
||||||
|
|
||||||
|
|
||||||
|
typedef void (*Integrand)(ccount *, creal *, ccount *, real *, creal *);
|
||||||
|
|
||||||
43
src/external/libCuba/src/suave/util.c
vendored
Normal file
43
src/external/libCuba/src/suave/util.c
vendored
Normal file
@ -0,0 +1,43 @@
|
|||||||
|
/*
|
||||||
|
util.c
|
||||||
|
Utility functions
|
||||||
|
this file is part of Suave
|
||||||
|
last modified 9 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "decl.h"
|
||||||
|
|
||||||
|
static count ndim_, ncomp_, nregions_;
|
||||||
|
static number neval_;
|
||||||
|
|
||||||
|
|
||||||
|
#define RegionAlloc(p, n, nnew) \
|
||||||
|
MemAlloc(p, sizeof(Region) + \
|
||||||
|
(n)*(ndim_ + ncomp_ + 1)*sizeof(real) + \
|
||||||
|
(nnew)*ndim_*sizeof(bin_t))
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
#include "debug.c"
|
||||||
|
#endif
|
||||||
|
|
||||||
121
src/external/libCuba/src/vegas/Grid.c
vendored
Normal file
121
src/external/libCuba/src/vegas/Grid.c
vendored
Normal file
@ -0,0 +1,121 @@
|
|||||||
|
/*
|
||||||
|
Grid.c
|
||||||
|
utility functions for the Vegas grid
|
||||||
|
this file is part of Vegas
|
||||||
|
last modified 29 May 09 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
static inline void GetGrid(Grid *grid)
|
||||||
|
{
|
||||||
|
count bin, dim;
|
||||||
|
unsigned const int slot = abs(EXPORT(vegasgridno)) - 1;
|
||||||
|
|
||||||
|
if( EXPORT(vegasgridno) < 0 ) {
|
||||||
|
EXPORT(vegasgridno) = -EXPORT(vegasgridno);
|
||||||
|
if( slot < MAXGRIDS ) griddim_[slot] = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( slot < MAXGRIDS && gridptr_[slot] ) {
|
||||||
|
if( griddim_[slot] == ndim_ ) {
|
||||||
|
VecCopy(grid, gridptr_[slot]);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
free(gridptr_[slot]);
|
||||||
|
gridptr_[slot] = NULL;
|
||||||
|
}
|
||||||
|
|
||||||
|
for( bin = 0; bin < NBINS; ++bin )
|
||||||
|
grid[0][bin] = (bin + 1)/(real)NBINS;
|
||||||
|
for( dim = 1; dim < ndim_; ++dim )
|
||||||
|
Copy(&grid[dim], &grid[0], 1);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void PutGrid(Grid *grid)
|
||||||
|
{
|
||||||
|
unsigned const int slot = EXPORT(vegasgridno) - 1;
|
||||||
|
|
||||||
|
if( slot < MAXGRIDS ) {
|
||||||
|
if( gridptr_[slot] == NULL ) Alloc(gridptr_[slot], ndim_);
|
||||||
|
griddim_[slot] = ndim_;
|
||||||
|
VecCopy(gridptr_[slot], grid);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static void RefineGrid(Grid grid, Grid margsum, cint flags)
|
||||||
|
{
|
||||||
|
real avgperbin, thisbin, newcur, delta;
|
||||||
|
Grid imp, newgrid;
|
||||||
|
int bin, newbin;
|
||||||
|
|
||||||
|
/* smooth the f^2 value stored for each bin */
|
||||||
|
real prev = margsum[0];
|
||||||
|
real cur = margsum[1];
|
||||||
|
real norm = margsum[0] = .5*(prev + cur);
|
||||||
|
for( bin = 1; bin < NBINS - 1; ++bin ) {
|
||||||
|
creal s = prev + cur;
|
||||||
|
prev = cur;
|
||||||
|
cur = margsum[bin + 1];
|
||||||
|
norm += margsum[bin] = (s + cur)/3.;
|
||||||
|
}
|
||||||
|
norm += margsum[NBINS - 1] = .5*(prev + cur);
|
||||||
|
|
||||||
|
if( norm == 0 ) return;
|
||||||
|
norm = 1/norm;
|
||||||
|
|
||||||
|
/* compute the importance function for each bin */
|
||||||
|
avgperbin = 0;
|
||||||
|
for( bin = 0; bin < NBINS; ++bin ) {
|
||||||
|
real impfun = 0;
|
||||||
|
if( margsum[bin] > 0 ) {
|
||||||
|
creal r = margsum[bin]*norm;
|
||||||
|
avgperbin += impfun = pow((r - 1)/log(r), 1.5);
|
||||||
|
}
|
||||||
|
imp[bin] = impfun;
|
||||||
|
}
|
||||||
|
avgperbin /= NBINS;
|
||||||
|
|
||||||
|
/* redefine the size of each bin */
|
||||||
|
cur = newcur = 0;
|
||||||
|
thisbin = 0;
|
||||||
|
bin = -1;
|
||||||
|
for( newbin = 0; newbin < NBINS - 1; ++newbin ) {
|
||||||
|
while( thisbin < avgperbin ) {
|
||||||
|
thisbin += imp[++bin];
|
||||||
|
prev = cur;
|
||||||
|
cur = grid[bin];
|
||||||
|
}
|
||||||
|
thisbin -= avgperbin;
|
||||||
|
delta = (cur - prev)*thisbin;
|
||||||
|
newgrid[newbin] = SHARPEDGES ?
|
||||||
|
cur - delta/imp[bin] :
|
||||||
|
(newcur = Max(newcur,
|
||||||
|
cur - 2*delta/(imp[bin] + imp[IDim(bin - 1)])));
|
||||||
|
}
|
||||||
|
Copy(grid, newgrid, NBINS - 1);
|
||||||
|
grid[NBINS - 1] = 1;
|
||||||
|
}
|
||||||
|
|
||||||
257
src/external/libCuba/src/vegas/Integrate.c
vendored
Normal file
257
src/external/libCuba/src/vegas/Integrate.c
vendored
Normal file
@ -0,0 +1,257 @@
|
|||||||
|
/*
|
||||||
|
Integrate.c
|
||||||
|
integrate over the unit hypercube
|
||||||
|
this file is part of Vegas
|
||||||
|
last modified 17 Dec 07 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
static int Integrate(creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
cnumber nstart, cnumber nincrease,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
real *sample;
|
||||||
|
count dim, comp;
|
||||||
|
int fail = 1;
|
||||||
|
struct {
|
||||||
|
count niter;
|
||||||
|
number nsamples, neval;
|
||||||
|
Cumulants cumul[NCOMP];
|
||||||
|
Grid grid[NDIM];
|
||||||
|
} state;
|
||||||
|
int statemsg = VERBOSE;
|
||||||
|
struct stat st;
|
||||||
|
|
||||||
|
if( VERBOSE > 1 ) {
|
||||||
|
char s[256];
|
||||||
|
sprintf(s, "Vegas input parameters:\n"
|
||||||
|
" ndim " COUNT "\n ncomp " COUNT "\n"
|
||||||
|
" epsrel " REAL "\n epsabs " REAL "\n"
|
||||||
|
" flags %d\n mineval " NUMBER "\n maxeval " NUMBER "\n"
|
||||||
|
" nstart " NUMBER "\n nincrease " NUMBER "\n"
|
||||||
|
" vegasgridno %d\n vegasstate \"%s\"\n",
|
||||||
|
ndim_, ncomp_,
|
||||||
|
epsrel, epsabs,
|
||||||
|
flags, mineval, maxeval,
|
||||||
|
nstart, nincrease,
|
||||||
|
EXPORT(vegasgridno), EXPORT(vegasstate));
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
if( setjmp(abort_) ) goto abort;
|
||||||
|
#endif
|
||||||
|
|
||||||
|
IniRandom(2*maxeval, flags);
|
||||||
|
|
||||||
|
if( *EXPORT(vegasstate) && stat(EXPORT(vegasstate), &st) == 0 &&
|
||||||
|
st.st_size == sizeof(state) && (st.st_mode & 0400) ) {
|
||||||
|
cint h = open(EXPORT(vegasstate), O_RDONLY);
|
||||||
|
read(h, &state, sizeof(state));
|
||||||
|
close(h);
|
||||||
|
SkipRandom(neval_ = state.neval);
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[256];
|
||||||
|
sprintf(s, "\nRestoring state from %s.", EXPORT(vegasstate));
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
else {
|
||||||
|
state.niter = 0;
|
||||||
|
state.nsamples = nstart;
|
||||||
|
Zap(state.cumul);
|
||||||
|
GetGrid(state.grid);
|
||||||
|
}
|
||||||
|
|
||||||
|
SamplesAlloc(sample, EXPORT(vegasnbatch));
|
||||||
|
|
||||||
|
/* main iteration loop */
|
||||||
|
|
||||||
|
for( ; ; ) {
|
||||||
|
number nsamples = state.nsamples;
|
||||||
|
creal jacobian = 1./nsamples;
|
||||||
|
Grid margsum[NCOMP][NDIM];
|
||||||
|
|
||||||
|
Zap(margsum);
|
||||||
|
|
||||||
|
for( ; nsamples > 0; nsamples -= EXPORT(vegasnbatch) ) {
|
||||||
|
cnumber nbatch = IMin(EXPORT(vegasnbatch), nsamples);
|
||||||
|
real *w = sample;
|
||||||
|
real *x = w + nbatch;
|
||||||
|
real *f = x + nbatch*ndim_;
|
||||||
|
real *lastf = f + nbatch*ncomp_;
|
||||||
|
bin_t *bin = (bin_t *)lastf;
|
||||||
|
|
||||||
|
while( x < f ) {
|
||||||
|
real weight = jacobian;
|
||||||
|
|
||||||
|
GetRandom(x);
|
||||||
|
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
creal pos = *x*NBINS;
|
||||||
|
ccount ipos = (count)pos;
|
||||||
|
creal prev = (ipos == 0) ? 0 : state.grid[dim][ipos - 1];
|
||||||
|
creal diff = state.grid[dim][ipos] - prev;
|
||||||
|
*x++ = prev + (pos - ipos)*diff;
|
||||||
|
*bin++ = ipos;
|
||||||
|
weight *= diff*NBINS;
|
||||||
|
}
|
||||||
|
|
||||||
|
*w++ = weight;
|
||||||
|
}
|
||||||
|
|
||||||
|
DoSample(nbatch, sample, w, f);
|
||||||
|
|
||||||
|
w = sample;
|
||||||
|
bin = (bin_t *)lastf;
|
||||||
|
|
||||||
|
while( f < lastf ) {
|
||||||
|
creal weight = *w++;
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
real wfun = weight*(*f++);
|
||||||
|
if( wfun ) {
|
||||||
|
Cumulants *c = &state.cumul[comp];
|
||||||
|
Grid *m = margsum[comp];
|
||||||
|
|
||||||
|
c->sum += wfun;
|
||||||
|
c->sqsum += wfun *= wfun;
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
m[dim][bin[dim]] += wfun;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
bin += ndim_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
fail = 0;
|
||||||
|
|
||||||
|
/* compute the integral and error values */
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
Cumulants *c = &state.cumul[comp];
|
||||||
|
real avg, sigsq;
|
||||||
|
real w = Weight(c->sum, c->sqsum, state.nsamples);
|
||||||
|
|
||||||
|
sigsq = 1/(c->weightsum += w);
|
||||||
|
avg = sigsq*(c->avgsum += w*c->sum);
|
||||||
|
|
||||||
|
c->avg = LAST ? (sigsq = 1/w, c->sum) : avg;
|
||||||
|
c->err = sqrt(sigsq);
|
||||||
|
fail |= (c->err > MaxErr(c->avg));
|
||||||
|
|
||||||
|
if( state.niter == 0 ) c->guess = c->sum;
|
||||||
|
else {
|
||||||
|
c->chisum += w *= c->sum - c->guess;
|
||||||
|
c->chisqsum += w*c->sum;
|
||||||
|
}
|
||||||
|
c->chisq = c->chisqsum - avg*c->chisum;
|
||||||
|
|
||||||
|
c->sum = c->sqsum = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( VERBOSE ) {
|
||||||
|
char s[128 + 128*NCOMP], *p = s;
|
||||||
|
|
||||||
|
p += sprintf(p, "\n"
|
||||||
|
"Iteration " COUNT ": " NUMBER " integrand evaluations so far",
|
||||||
|
state.niter + 1, neval_);
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cCumulants *c = &state.cumul[comp];
|
||||||
|
p += sprintf(p, "\n[" COUNT "] "
|
||||||
|
REAL " +- " REAL " \tchisq " REAL " (" COUNT " df)",
|
||||||
|
comp + 1, c->avg, c->err, c->chisq, state.niter);
|
||||||
|
}
|
||||||
|
|
||||||
|
Print(s);
|
||||||
|
}
|
||||||
|
|
||||||
|
if( fail == 0 && neval_ >= mineval ) {
|
||||||
|
if( *EXPORT(vegasstate) ) unlink(EXPORT(vegasstate));
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
|
||||||
|
if( neval_ >= maxeval && *EXPORT(vegasstate) == 0 ) break;
|
||||||
|
|
||||||
|
if( ncomp_ == 1 )
|
||||||
|
for( dim = 0; dim < ndim_; ++dim )
|
||||||
|
RefineGrid(state.grid[dim], margsum[0][dim], flags);
|
||||||
|
else {
|
||||||
|
for( dim = 0; dim < ndim_; ++dim ) {
|
||||||
|
Grid wmargsum;
|
||||||
|
Zap(wmargsum);
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
real w = state.cumul[comp].avg;
|
||||||
|
if( w != 0 ) {
|
||||||
|
creal *m = margsum[comp][dim];
|
||||||
|
count bin;
|
||||||
|
w = 1/Sq(w);
|
||||||
|
for( bin = 0; bin < NBINS; ++bin )
|
||||||
|
wmargsum[bin] += w*m[bin];
|
||||||
|
}
|
||||||
|
}
|
||||||
|
RefineGrid(state.grid[dim], wmargsum, flags);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
++state.niter;
|
||||||
|
state.nsamples += nincrease;
|
||||||
|
|
||||||
|
if( *EXPORT(vegasstate) ) {
|
||||||
|
cint h = creat(EXPORT(vegasstate), 0666);
|
||||||
|
if( h != -1 ) {
|
||||||
|
state.neval = neval_;
|
||||||
|
write(h, &state, sizeof(state));
|
||||||
|
close(h);
|
||||||
|
|
||||||
|
if( statemsg ) {
|
||||||
|
char s[256];
|
||||||
|
sprintf(s, "\nSaving state to %s.", EXPORT(vegasstate));
|
||||||
|
Print(s);
|
||||||
|
statemsg = false;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if( neval_ >= maxeval ) break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for( comp = 0; comp < ncomp_; ++comp ) {
|
||||||
|
cCumulants *c = &state.cumul[comp];
|
||||||
|
integral[comp] = c->avg;
|
||||||
|
error[comp] = c->err;
|
||||||
|
prob[comp] = ChiSquare(c->chisq, state.niter);
|
||||||
|
}
|
||||||
|
|
||||||
|
#ifdef MLVERSION
|
||||||
|
abort:
|
||||||
|
#endif
|
||||||
|
|
||||||
|
free(sample);
|
||||||
|
PutGrid(state.grid);
|
||||||
|
|
||||||
|
return fail;
|
||||||
|
}
|
||||||
|
|
||||||
100
src/external/libCuba/src/vegas/Vegas.c
vendored
Normal file
100
src/external/libCuba/src/vegas/Vegas.c
vendored
Normal file
@ -0,0 +1,100 @@
|
|||||||
|
/*
|
||||||
|
Vegas.c
|
||||||
|
Vegas Monte-Carlo integration
|
||||||
|
by Thomas Hahn
|
||||||
|
last modified 30 Aug 07 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "util.c"
|
||||||
|
|
||||||
|
#define Print(s) puts(s); fflush(stdout)
|
||||||
|
|
||||||
|
static Integrand integrand_;
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
static inline void DoSample(number n, creal *w, creal *x, real *f)
|
||||||
|
{
|
||||||
|
neval_ += n;
|
||||||
|
while( n-- ) {
|
||||||
|
integrand_(&ndim_, x, &ncomp_, f, w++);
|
||||||
|
x += ndim_;
|
||||||
|
f += ncomp_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
#include "common.c"
|
||||||
|
|
||||||
|
Extern void EXPORT(Vegas)(ccount ndim, ccount ncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal epsrel, creal epsabs,
|
||||||
|
cint flags, cnumber mineval, cnumber maxeval,
|
||||||
|
cnumber nstart, cnumber nincrease,
|
||||||
|
number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
ndim_ = ndim;
|
||||||
|
ncomp_ = ncomp;
|
||||||
|
|
||||||
|
if( BadComponent(ncomp) || BadDimension(ndim, flags) ) *pfail = -1;
|
||||||
|
else {
|
||||||
|
neval_ = 0;
|
||||||
|
integrand_ = integrand;
|
||||||
|
|
||||||
|
*pfail = Integrate(epsrel, epsabs,
|
||||||
|
flags, mineval, maxeval, nstart, nincrease,
|
||||||
|
integral, error, prob);
|
||||||
|
|
||||||
|
*pneval = neval_;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*********************************************************************/
|
||||||
|
|
||||||
|
Extern void EXPORT(vegas)(ccount *pndim, ccount *pncomp,
|
||||||
|
Integrand integrand,
|
||||||
|
creal *pepsrel, creal *pepsabs,
|
||||||
|
cint *pflags, cnumber *pmineval, cnumber *pmaxeval,
|
||||||
|
cnumber *pnstart, cnumber *pnincrease,
|
||||||
|
number *pneval, int *pfail,
|
||||||
|
real *integral, real *error, real *prob)
|
||||||
|
{
|
||||||
|
/* make sure the filename is null-terminated */
|
||||||
|
if( *EXPORT(vegasstate) ) {
|
||||||
|
char *p;
|
||||||
|
EXPORT(vegasstate)[sizeof(EXPORT(vegasstate)) - 1] = 0;
|
||||||
|
if( (p = strchr(EXPORT(vegasstate), ' ')) ) *p = 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
EXPORT(Vegas)(*pndim, *pncomp,
|
||||||
|
integrand,
|
||||||
|
*pepsrel, *pepsabs,
|
||||||
|
*pflags, *pmineval, *pmaxeval,
|
||||||
|
*pnstart, *pnincrease,
|
||||||
|
pneval, pfail,
|
||||||
|
integral, error, prob);
|
||||||
|
}
|
||||||
|
|
||||||
50
src/external/libCuba/src/vegas/common.c
vendored
Normal file
50
src/external/libCuba/src/vegas/common.c
vendored
Normal file
@ -0,0 +1,50 @@
|
|||||||
|
/*
|
||||||
|
common.c
|
||||||
|
include most of the modules
|
||||||
|
this file is part of Vegas
|
||||||
|
last modified 14 Feb 05 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "Random.c"
|
||||||
|
#include "ChiSquare.c"
|
||||||
|
#include "Grid.c"
|
||||||
|
#include "Integrate.c"
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadDimension(cint ndim, cint flags)
|
||||||
|
{
|
||||||
|
#if NDIM > 0
|
||||||
|
if( ndim > NDIM ) return true;
|
||||||
|
#endif
|
||||||
|
return ndim < SOBOL_MINDIM || (!PSEUDORNG && ndim > SOBOL_MAXDIM);
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
static inline bool BadComponent(cint ncomp)
|
||||||
|
{
|
||||||
|
#if NCOMP > 0
|
||||||
|
if( ncomp > NCOMP ) return true;
|
||||||
|
#endif
|
||||||
|
return ncomp < 1;
|
||||||
|
}
|
||||||
|
|
||||||
54
src/external/libCuba/src/vegas/decl.h
vendored
Normal file
54
src/external/libCuba/src/vegas/decl.h
vendored
Normal file
@ -0,0 +1,54 @@
|
|||||||
|
/*
|
||||||
|
decl.h
|
||||||
|
Type declarations
|
||||||
|
this file is part of Vegas
|
||||||
|
last modified 30 Aug 07 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
|
||||||
|
#include "stddecl.h"
|
||||||
|
|
||||||
|
#define MAXGRIDS 10
|
||||||
|
|
||||||
|
#define MAXSTATESIZE 128
|
||||||
|
|
||||||
|
#define NBINS 128
|
||||||
|
|
||||||
|
typedef unsigned char bin_t;
|
||||||
|
/* Note: bin_t must be wide enough to hold the numbers 0..NBINS */
|
||||||
|
|
||||||
|
typedef const bin_t cbin_t;
|
||||||
|
|
||||||
|
typedef real Grid[NBINS];
|
||||||
|
|
||||||
|
typedef struct {
|
||||||
|
real sum, sqsum;
|
||||||
|
real weightsum, avgsum;
|
||||||
|
real chisum, chisqsum, guess;
|
||||||
|
real avg, err, chisq;
|
||||||
|
} Cumulants;
|
||||||
|
|
||||||
|
typedef const Cumulants cCumulants;
|
||||||
|
|
||||||
|
typedef void (*Integrand)(ccount *, creal *, ccount *, real *, creal *);
|
||||||
|
|
||||||
46
src/external/libCuba/src/vegas/util.c
vendored
Normal file
46
src/external/libCuba/src/vegas/util.c
vendored
Normal file
@ -0,0 +1,46 @@
|
|||||||
|
/*
|
||||||
|
util.c
|
||||||
|
Utility functions
|
||||||
|
this file is part of Vegas
|
||||||
|
last modified 2 Mar 06 th
|
||||||
|
*/
|
||||||
|
|
||||||
|
/***************************************************************************
|
||||||
|
* Copyright (C) 2004-2009 by Thomas Hahn *
|
||||||
|
* hahn@feynarts.de *
|
||||||
|
* *
|
||||||
|
* This library is free software; you can redistribute it and/or *
|
||||||
|
* modify it under the terms of the GNU Library General Public *
|
||||||
|
* License as published by the Free Software Foundation; either *
|
||||||
|
* version 2 of the License, or (at your option) any later version. *
|
||||||
|
* *
|
||||||
|
* This library is distributed in the hope that it will be useful, *
|
||||||
|
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
|
||||||
|
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
|
||||||
|
* Library General Public License for more details. *
|
||||||
|
* *
|
||||||
|
* You should have received a copy of the GNU Library General Public *
|
||||||
|
* License along with this library; if not, write to the Free *
|
||||||
|
* Foundation, Inc., *
|
||||||
|
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA *
|
||||||
|
***************************************************************************/
|
||||||
|
|
||||||
|
#include "decl.h"
|
||||||
|
|
||||||
|
static count ndim_, ncomp_;
|
||||||
|
static number neval_;
|
||||||
|
static Grid *gridptr_[MAXGRIDS];
|
||||||
|
static count griddim_[MAXGRIDS];
|
||||||
|
int EXPORT(vegasnbatch) = 1000;
|
||||||
|
int EXPORT(vegasgridno) = 0;
|
||||||
|
char EXPORT(vegasstate)[MAXSTATESIZE] = "";
|
||||||
|
|
||||||
|
|
||||||
|
#define SamplesAlloc(p, n) \
|
||||||
|
MemAlloc(p, (n)*((ndim_ + ncomp_ + 1)*sizeof(real) + ndim_*sizeof(bin_t)))
|
||||||
|
|
||||||
|
|
||||||
|
#ifdef DEBUG
|
||||||
|
#include "debug.c"
|
||||||
|
#endif
|
||||||
|
|
||||||
@ -1677,10 +1677,10 @@ void PTextEdit::musrView()
|
|||||||
QString str;
|
QString str;
|
||||||
|
|
||||||
str = fAdmin->getExecPath() + "/musrview";
|
str = fAdmin->getExecPath() + "/musrview";
|
||||||
cmd = str + " ";
|
cmd = str + " \"";
|
||||||
|
|
||||||
str = *fFilenames.find( currentEditor() );
|
str = *fFilenames.find( currentEditor() );
|
||||||
cmd += str + " &";
|
cmd += str + "\" &";
|
||||||
|
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
}
|
}
|
||||||
@ -1708,10 +1708,10 @@ void PTextEdit::musrT0()
|
|||||||
QString str;
|
QString str;
|
||||||
|
|
||||||
str = fAdmin->getExecPath() + "/musrt0";
|
str = fAdmin->getExecPath() + "/musrt0";
|
||||||
cmd = str + " ";
|
cmd = str + " \"";
|
||||||
|
|
||||||
str = *fFilenames.find( currentEditor() );
|
str = *fFilenames.find( currentEditor() );
|
||||||
cmd += str + " &";
|
cmd += str + "\" &";
|
||||||
|
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
|
|
||||||
@ -1783,13 +1783,13 @@ void PTextEdit::musrSwapMsrMlog()
|
|||||||
|
|
||||||
// swap files
|
// swap files
|
||||||
QString cmd;
|
QString cmd;
|
||||||
cmd = QString("cp ") + currentFileName + QString(" ") + tempFileName;
|
cmd = QString("cp \"") + currentFileName + QString("\" \"") + tempFileName + QString("\"");
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
cmd = QString("cp ") + swapFileName + QString(" ") + currentFileName;
|
cmd = QString("cp \"") + swapFileName + QString("\" \"") + currentFileName + QString("\"");
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
cmd = QString("cp ") + tempFileName + QString(" ") + swapFileName;
|
cmd = QString("cp \"") + tempFileName + QString("\" \"") + swapFileName + QString("\"");
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
cmd = QString("rm ") + tempFileName;
|
cmd = QString("rm \"") + tempFileName + QString("\"");
|
||||||
system(cmd.latin1());
|
system(cmd.latin1());
|
||||||
|
|
||||||
int currentIdx = fTabWidget->currentPageIndex();
|
int currentIdx = fTabWidget->currentPageIndex();
|
||||||
|
|||||||
Loading…
x
Reference in New Issue
Block a user