added test for the confluent hypergeometric function 1F1(m,n,z) of the GSL lib

src/tests/hypergeometricFcn/README

@@ -0,0 +1,15 @@
+hypergeometricFcn is a test to verify that Mathematica and the GSL lib
+produce the same output for the confluent hypergeometric function 1F1(m,n,z).
+The file erfi.dat is a file generate by Mathematica with the following commands
+
+f = Erfi[z]
+tt = Table[{z, f}, {z, 0, 3, 0.01}]
+Export["erfi.dat", tt]
+
+and Erfi[z] can be written in terms of 1F1(m,n,z) as
+
+Erfi[z] = 2 z / Sqrt[Pi] Hypergeometric1F1[1/2, 3/2, z^2]
+
+The only thing hypergeometricFcn does is to read erfi.dat, calculate Erfi[z]
+according to the above equation and save both data sets in a file called
+erfi_gsl.dat.

src/tests/hypergeometricFcn/erfi.dat

@@ -0,0 +1,301 @@
+0   0
+0.01   0.01128416780862822
+0.02   0.02257059271413823
+0.02999999999999999   0.03386153316791828
+0.04   0.04515925033172434
+0.05   0.05646600943625297
+0.05999999999999999   0.06778408114378643
+0.07   0.07911574291627587
+0.08   0.09046328039023708
+0.08999999999999999   0.1018289887598418
+0.1   0.1132151741695998
+0.11   0.1246241551180391
+0.12   0.1360582638738105
+0.13   0.1475198479056553
+0.14   0.1590112713276985
+0.1499999999999999   0.1705349163615497
+0.16   0.1820931848167174
+0.17   0.1936884995908712
+0.1799999999999999   0.2053233061915081
+0.19   0.2170000742806184
+0.2   0.2287212992439713
+0.2099999999999999   0.2404895037866808
+0.22   0.252307239556747
+0.23   0.2641770887983099
+0.2399999999999999   0.2761016660363946
+0.25   0.288083619794972
+0.26   0.300125634350208
+0.27   0.3122304315208248
+0.28   0.3244007724975507
+0.2899999999999999   0.3366394597136943
+0.2999999999999999   0.3489493387589361
+0.31   0.3613333003384971
+0.32   0.3737942822799063
+0.33   0.3863352715896648
+0.34   0.3989593065621741
+0.35   0.4116694789433721
+0.3599999999999999   0.4244689361516121
+0.37   0.4373608835583889
+0.38   0.4503485868316228
+0.39   0.4634353743442958
+0.4   0.4766246396513396
+0.41   0.4899198440377719
+0.4199999999999999   0.5033245191411938
+0.4299999999999999   0.5168422696518704
+0.44   0.5304767760937363
+0.45   0.5442317976897957
+0.46   0.5581111753155144
+0.47   0.5721188345439376
+0.4799999999999999   0.5862587887864184
+0.4899999999999999   0.6005351425329815
+0.5   0.614952094696511
+0.51   0.629513942065115
+0.52   0.6442250828671904
+0.53   0.659090020453895
+0.54   0.6741133671039147
+0.55   0.6892998479556272
+0.56   0.7046543050719494
+0.57   0.7201817016433922
+0.5799999999999999   0.7358871263350611
+0.5899999999999999   0.7517757977835818
+0.5999999999999999   0.7678530692501769
+0.6099999999999999   0.7841244334363807
+0.62   0.800595527469159
+0.63   0.8172721380624627
+0.64   0.834160206862572
+0.65   0.8512658359848793
+0.66   0.8685952937500885
+0.67   0.8861550206281582
+0.68   0.9039516353986728
+0.69   0.9219919415366877
+0.7   0.9402829338335074
+0.7099999999999999   0.9588318052622525
+0.7199999999999999   0.9776459540985063
+0.7299999999999999   0.9967329913067852
+0.7399999999999999   1.01610074820405
+0.75   1.035757284411963
+0.76   1.055710896110123
+0.77   1.075970124603062
+0.78   1.096543765214321
+0.79   1.117440876521578
+0.8   1.138670789947371
+0.81   1.16024311972064
+0.82   1.182167773225021
+0.83   1.204454961750493
+0.8399999999999999   1.227115211665787
+0.8499999999999999   1.250159376029729
+0.8599999999999999   1.273598646660546
+0.87   1.297444566682988
+0.88   1.321709043574109
+0.89   1.346404362729431
+0.9   1.371543201572287
+0.91   1.397138644230154
+0.92   1.423204196802919
+0.93   1.449753803249173
+0.94   1.476801861917867
+0.95   1.504363242753928
+0.9599999999999999   1.532453305207788
+0.9699999999999999   1.561087916880205
+0.9799999999999999   1.590283472935232
+0.9899999999999999   1.620056916315735
+1.   1.650425758797542
+1.01   1.681408102919991
+1.02   1.713022664832454
+1.03   1.74528879809836
+1.04   1.778226518500184
+1.05   1.811856529891002
+1.06   1.84620025114042
+1.07   1.881279844224987
+1.08   1.917118243515681
+1.09   1.953739186317573
+1.1   1.991167244719524
+1.11   2.029427858814586
+1.12   2.068547371354753
+1.13   2.108553063906904
+1.14   2.149473194580001
+1.15   2.191337037397191
+1.159999999999999   2.234174923390037
+1.169999999999999   2.278018283496002
+1.179999999999999   2.322899693344363
+1.189999999999999   2.368852920020018
+1.2   2.415912970899116
+1.21   2.464116144655226
+1.22   2.513500084539712
+1.23   2.564103834045282
+1.24   2.615967895067185
+1.25   2.669134288682375
+1.26   2.723646618673162
+1.27   2.779550137928277
+1.28   2.836891817861157
+1.29   2.895720420992494
+1.3   2.956086576851622
+1.31   3.018042861359369
+1.32   3.081643879863457
+1.33   3.146946354006425
+1.34   3.214009212615456
+1.35   3.282893686813416
+1.36   3.353663409560882
+1.37   3.426384519849983
+1.38   3.501125771782464
+1.39   3.577958648776878
+1.4   3.656957483162535
+1.409999999999999   3.738199581431794
+1.419999999999999   3.821765355436631
+1.429999999999999   3.907738459830743
+1.439999999999999   3.996205936074648
+1.45   4.087258363338228
+1.46   4.1809900166533
+1.47   4.277499032687774
+1.48   4.376887583533097
+1.49   4.479262058918055
+1.5   4.584733257284428
+1.51   4.693416586183766
+1.52   4.8054322724798
+1.53   4.920905582867543
+1.54   5.039967055248233
+1.55   5.162752741529169
+1.56   5.289404462448803
+1.57   5.420070075060937
+1.58   5.554903753546978
+1.59   5.694066284062637
+1.6   5.837725374364937
+1.61   5.986055979007075
+1.62   6.13924064093324
+1.63   6.297469850352028
+1.64   6.46094242181703
+1.65   6.629865890495652
+1.66   6.804456928662892
+1.669999999999999   6.984941783515976
+1.679999999999999   7.171556737468155
+1.689999999999999   7.364548592146415
+1.7   7.564175177387984
+1.71   7.770705886605176
+1.72   7.984422239966907
+1.73   8.205618476929244
+1.74   8.43460217973579
+1.75   8.671694929603422
+1.76   8.917232997408376
+1.77   9.171568070794009
+1.78   9.435068019734107
+1.79   9.708117702704745
+1.8   9.991119815744896
+1.81   10.28449578682015
+1.82   10.58868671804708
+1.83   10.90415437848731
+1.84   11.23138225038145
+1.85   11.57087663186459
+1.86   11.92316779938606
+1.87   12.28881123325021
+1.88   12.66838890989962
+1.89   13.06251066478044
+1.9   13.47181562986157
+1.91   13.89697375012563
+1.919999999999999   14.33868738361188
+1.929999999999999   14.79769298987001
+1.939999999999999   15.27476291197971
+1.95   15.77070725760681
+1.96   16.28637588490131
+1.97   16.82266049940022
+1.98   17.38049686847747
+1.99   17.96086716028695
+2.   18.56480241457556
+2.01   19.19338515320039
+2.02   19.84775213867227
+2.03   20.52909728956656
+2.04   21.23867476219554
+2.049999999999999   21.97780220852527
+2.06   22.74786422094802
+2.069999999999999   23.5503159751887
+2.08   24.38668708333797
+2.089999999999999   25.25858566976229
+2.1   26.16770268345233
+2.109999999999999   27.11581646123231
+2.12   28.10479755717558
+2.129999999999999   29.13661385454958
+2.14   30.21333597766457
+2.149999999999999   31.3371430221117
+2.16   32.51032862307257
+2.169999999999999   33.73530738264912
+2.18   35.01462167852244
+2.189999999999999   36.35094887769473
+2.2   37.74710898061626
+2.21   39.2060727226474
+2.22   40.73097016157087
+2.23   42.3250997817479
+2.24   43.99193814752662
+2.25   45.73515014065391
+2.26   47.55859981874191
+2.27   49.46636193428724
+2.28   51.46273415636842
+2.29   53.55225003994006
+2.3   55.73969279064824
+2.31   58.03010987628351
+2.319999999999999   60.42882853942212
+2.33   62.94147226946333
+2.339999999999999   65.57397829619274
+2.35   68.33261617119417
+2.359999999999999   71.22400750791783
+2.37   74.255146956017
+2.379999999999999   77.43342449070178
+2.39   80.76664910336438
+2.399999999999999   84.26307398561921
+2.41   87.93142330521251
+2.419999999999999   91.78092067900989
+2.43   95.82131945551353
+2.439999999999999   100.0629349271087
+2.45   104.516678600558
+2.46   109.1940946631549
+2.47   114.107398791505
+2.48   119.2695194601261
+2.49   124.6941419180349
+2.5   130.395755013247
+2.51   136.3897010577407
+2.52   142.6922289389604
+2.53   149.3205506984623
+2.54   156.2929018138786
+2.55   163.6286054371017
+2.56   171.3481408595211
+2.569999999999999   179.4732164944314
+2.58   188.0268476873872
+2.589999999999999   197.0334396875008
+2.6   206.5188761365411
+2.609999999999999   216.510613458281
+2.62   227.0377815581046
+2.629999999999999   238.1312912724161
+2.64   249.8239490392179
+2.649999999999999   262.1505792953359
+2.66   275.1481551425377
+2.669999999999999   288.8559378642276
+2.68   303.3156259168774
+2.689999999999999   318.5715140659986
+2.7   334.6706633855801
+2.71   351.6630828927222
+2.72   369.601923646089
+2.73   388.5436861979171
+2.74   408.5484423552258
+2.75   429.6800722766929
+2.76   452.0065180080196
+2.77   475.6000546407463
+2.78   500.537580368018
+2.79   526.9009268060783
+2.8   554.777191053032
+2.81   584.2590910670118
+2.819999999999999   615.4453460651943
+2.83   648.4410837736076
+2.839999999999999   683.358276496242
+2.85   720.3162081214007
+2.859999999999999   759.4419743442698
+2.87   800.871018558486
+2.879999999999999   844.7477060568625
+2.89   891.2259393836651
+2.899999999999999   940.469817898963
+2.91   992.6543448510879
+2.919999999999999   1047.966185507326
+2.93   1106.6044801674
+2.939999999999999   1168.781716180411
+2.95   1234.724663405969
+2.96   1304.675377905578
+2.97   1378.89227902371
+2.98   1457.651305421107
+2.99   1541.247156058746
+3.   1629.994622601567

src/tests/hypergeometricFcn/hypergeometricFcn.cpp

@@ -0,0 +1,60 @@
+#include <iostream>
+#include <fstream>
+using namespace std;
+
+#include <cmath>
+
+#include <gsl_sf_hyperg.h>
+
+#define PI 3.14159265359
+
+extern "C" {
+  double gsl_sf_hyperg_1F1(double a, double b, double x);
+}
+
+int main(int argc, char *argv[])
+{
+  // load Mathematica test file
+  ifstream fin;
+
+  fin.open("erfi.dat", iostream::in);
+  if (!fin.is_open()) {
+    return -1;
+  }
+
+  int max=0;
+  char str[256];
+  double t, fval;
+  double data[3][1000];
+  while (!fin.eof()) {
+    fin.getline(str, sizeof(str));
+    sscanf(str, "%lf %lf", &t, &fval);
+    data[0][max] = t;
+    data[1][max] = fval;
+    max++;
+  }
+
+  fin.close();
+
+  // evaluate gsl function
+  for (int i=0; i<max; i++) {
+    t = i*0.01;
+    data[2][i] = 2*t/sqrt(PI)*gsl_sf_hyperg_1F1(1.0/2.0,3.0/2.0,t*t);
+  }
+
+  // save everything together in an output file
+  ofstream fout;
+
+  fout.open("erfi_gsl.dat", iostream::out);
+  if (!fout.is_open()) {
+    return -1;
+  }
+
+  for (int i=0; i<max; i++) {
+    fout << data[0][i] << ", " << data[1][i] << ", " << data[2][i] << endl;
+  }
+
+  fout.close();
+
+  return 0;
+}

src/tests/hypergeometricFcn/hypergeometricFcn.pro

@@ -0,0 +1,24 @@
+#------------------------------------------------------
+# hypergeometricFcn.pro
+# qmake file for hypergeometricFcn
+#
+# Andreas Suter, 2008/02/12
+#
+# $Id$
+#
+#------------------------------------------------------
+
+MAKEFILE = Makefile
+
+CONFIG += warn_on debug
+
+HEADERS =
+
+SOURCES = hypergeometricFcn.cpp
+
+INCLUDEPATH += /usr/include/gsl
+
+unix:LIBS += -lgslcblas -lgsl -lbsd -lm -ldl -lutil
+
+TARGET = hypergeometricFcn
+

src/tests/spirit/PFunctionGrammar.h

@@ -35,7 +35,7 @@
 #include <iostream>
 using namespace std;
 
-//#define BOOST_SPIRIT_DEBUG
+#define BOOST_SPIRIT_DEBUG
 
 #include <boost/spirit/core.hpp>
 #include <boost/spirit/tree/ast.hpp>

src/tests/spirit/fcnInput.txt

@@ -18,7 +18,7 @@ PAR 1.0 2.1 3.5 -0.87 0.87
 MAP 2 1 4 5
 FUNCTIONS
 #fun0 = sin(par3/(par1+map2))
-fun1 = 1.0+(((sin(par1))))
+fun1 = 1.0+(sin(par1))
 #fun0 = par1 + map3 * cos(cos(par2 - map1))
 #fun8 = log(sin(par1)) + exp(-1.0*map2)
 #fun1 = par1 + map1 * (0.01355+par1*(2.1 - (-2.3 / 3.4)))