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Merge branch 'master' into maverick

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koennecke
2016-01-26 10:56:19 +01:00
parent cdb9a8fba2 73d6c5f5fb
commit 1149227685
116 changed files with 7295 additions and 1935 deletions
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40
matrix/DEMO.DAT
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1.1 2 3 4 5 6 7 8 9 9
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3 4 5.1 6 7 8 9 9 8 7
3 4 5 6.1 7 8 9 9 8 7
1 2 3 4 5 7.2 7 8 9 9
1 2 3 4 1 6 7 8.3 9 9
6 2 3 4 5 6 7 8 9.8 9
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1 2 3 4 6 6 7 8 9 9
6 2 3 4 5 4 7 8 9 9
3
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1.1 2 3 4 5 6 7 8 9 9
2 3.1 4 5 6 7 8 9 9 8
3 4 5.1 6 7 8 9 9 8 7
3 4 5 6.1 7 8 9 9 8 7
1 2 3 4 5 7.2 7 8 9 9
1 2 3 4 1 6 7 8.3 9 9
6 2 3 4 5 6 7 8 9.8 9
1 2 3 3 5 6 7 8 9 9.8
1 2 3 4 6 6 7 8 9 9
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matrix/MAKEFILE.MSC
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#------------------------------------------------------------------------------
# file: makefile.msc
# desc: makefile for matrix library package under Microsoft C/C++ v7.0
# by: patrick ko
# date: 16 Apr 94
#
# note: a slim matrix library matrix.lib will be generated
#------------------------------------------------------------------------------
OBJS = matcreat.obj matdump.obj materr.obj matadd.obj matsub.obj \
matmul.obj matinv.obj matsolve.obj matdet.obj mattran.obj matdurbn.obj \
mattoepz.obj matsubx.obj
CC = cl -c
C = cl
demo.exe: demo.c matrix.lib
$(C) demo.c matrix.lib
matrix.lib: $(OBJS)
lib matrix +matcreat +matdump +materr +matadd.obj ,,
lib matrix +matsub +matmul +matinv +matsolve +matdet.obj ,,
lib matrix +mattran +matdurbn +mattoepz +matsubx ,,
matcreat.obj: matcreat.c matrix.h
$(CC) matcreat.c
matdump.obj: matdump.c matrix.h
$(CC) matdump.c
materr.obj: materr.c matrix.h
$(CC) materr.c
matadd.obj: matadd.c matrix.h
$(CC) matadd.c
matsub.obj: matsub.c matrix.h
$(CC) matsub.c
matmul.obj: matmul.c matrix.h
$(CC) matmul.c
matinv.obj: matinv.c matrix.h
$(CC) matinv.c
matsolve.obj: matsolve.c matrix.h
$(CC) matsolve.c
mattran.obj: mattran.c matrix.h
$(CC) mattran.c
matdet.obj: matdet.c matrix.h
$(CC) matdet.c
matdurbn.obj: matdurbn.c matrix.h
$(CC) matdurbn.c
mattoepz.obj: mattoepz.c matrix.h
$(CC) mattoepz.c
matsubx.obj: matsubx.c matrix.h
$(CC) matsubx.c
#------------------------------------------------------------------------------
# file: makefile.msc
# desc: makefile for matrix library package under Microsoft C/C++ v7.0
# by: patrick ko
# date: 16 Apr 94
#
# note: a slim matrix library matrix.lib will be generated
#------------------------------------------------------------------------------
OBJS = matcreat.obj matdump.obj materr.obj matadd.obj matsub.obj \
matmul.obj matinv.obj matsolve.obj matdet.obj mattran.obj matdurbn.obj \
mattoepz.obj matsubx.obj
CC = cl -c
C = cl
demo.exe: demo.c matrix.lib
$(C) demo.c matrix.lib
matrix.lib: $(OBJS)
lib matrix +matcreat +matdump +materr +matadd.obj ,,
lib matrix +matsub +matmul +matinv +matsolve +matdet.obj ,,
lib matrix +mattran +matdurbn +mattoepz +matsubx ,,
matcreat.obj: matcreat.c matrix.h
$(CC) matcreat.c
matdump.obj: matdump.c matrix.h
$(CC) matdump.c
materr.obj: materr.c matrix.h
$(CC) materr.c
matadd.obj: matadd.c matrix.h
$(CC) matadd.c
matsub.obj: matsub.c matrix.h
$(CC) matsub.c
matmul.obj: matmul.c matrix.h
$(CC) matmul.c
matinv.obj: matinv.c matrix.h
$(CC) matinv.c
matsolve.obj: matsolve.c matrix.h
$(CC) matsolve.c
mattran.obj: mattran.c matrix.h
$(CC) mattran.c
matdet.obj: matdet.c matrix.h
$(CC) matdet.c
matdurbn.obj: matdurbn.c matrix.h
$(CC) matdurbn.c
mattoepz.obj: mattoepz.c matrix.h
$(CC) mattoepz.c
matsubx.obj: matsubx.c matrix.h
$(CC) matsubx.c

148
matrix/MAKEFILE.TC
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@ -1,74 +1,74 @@
#------------------------------------------------------------------------------
# file: makefile.tc
# desc: makefile for matrix library package under Turbo C v2.0
# by: patrick ko
# date: 16 Apr 94
#
# note: a slim matrix library matrix.lib will be generated
#------------------------------------------------------------------------------
DRIVE = C:
OBJS = matcreat.obj matdump.obj materr.obj matadd.obj matsub.obj \
matmul.obj matinv.obj matsolve.obj matdet.obj mattran.obj matdurbn.obj \
mattoepz.obj matsubx.obj
LIB = -L$(DRIVE)\TC\LIB
INC = -I$(DRIVE)\TC\INCLUDE
CC = tcc -c -mh $(INC)
C = tcc -mh $(LIB) $(INC)
LL = tlib matrix.lib
demo.exe: demo.c $(OBJS)
$(C) demo.c matrix.lib
matcreat.obj: matcreat.c matrix.h
$(CC) matcreat.c
$(LL) -+matcreat.obj
matdump.obj: matdump.c matrix.h
$(CC) matdump.c
$(LL) -+matdump.obj
materr.obj: materr.c matrix.h
$(CC) materr.c
$(LL) -+materr.obj
matadd.obj: matadd.c matrix.h
$(CC) matadd.c
$(LL) -+matadd.obj
matsub.obj: matsub.c matrix.h
$(CC) matsub.c
$(LL) -+matsub.obj
matmul.obj: matmul.c matrix.h
$(CC) matmul.c
$(LL) -+matmul.obj
matinv.obj: matinv.c matrix.h
$(CC) matinv.c
$(LL) -+matinv.obj
matsolve.obj: matsolve.c matrix.h
$(CC) matsolve.c
$(LL) -+matsolve.obj
mattran.obj: mattran.c matrix.h
$(CC) mattran.c
$(LL) -+mattran.obj
matdet.obj: matdet.c matrix.h
$(CC) matdet.c
$(LL) -+matdet.obj
matdurbn.obj: matdurbn.c matrix.h
$(CC) matdurbn.c
$(LL) -+matdurbn.obj
mattoepz.obj: mattoepz.c matrix.h
$(CC) mattoepz.c
$(LL) -+mattoepz.obj
matsubx.obj: matsubx.c matrix.h
$(CC) matsubx.c
$(LL) -+matsubx.obj
#------------------------------------------------------------------------------
# file: makefile.tc
# desc: makefile for matrix library package under Turbo C v2.0
# by: patrick ko
# date: 16 Apr 94
#
# note: a slim matrix library matrix.lib will be generated
#------------------------------------------------------------------------------
DRIVE = C:
OBJS = matcreat.obj matdump.obj materr.obj matadd.obj matsub.obj \
matmul.obj matinv.obj matsolve.obj matdet.obj mattran.obj matdurbn.obj \
mattoepz.obj matsubx.obj
LIB = -L$(DRIVE)\TC\LIB
INC = -I$(DRIVE)\TC\INCLUDE
CC = tcc -c -mh $(INC)
C = tcc -mh $(LIB) $(INC)
LL = tlib matrix.lib
demo.exe: demo.c $(OBJS)
$(C) demo.c matrix.lib
matcreat.obj: matcreat.c matrix.h
$(CC) matcreat.c
$(LL) -+matcreat.obj
matdump.obj: matdump.c matrix.h
$(CC) matdump.c
$(LL) -+matdump.obj
materr.obj: materr.c matrix.h
$(CC) materr.c
$(LL) -+materr.obj
matadd.obj: matadd.c matrix.h
$(CC) matadd.c
$(LL) -+matadd.obj
matsub.obj: matsub.c matrix.h
$(CC) matsub.c
$(LL) -+matsub.obj
matmul.obj: matmul.c matrix.h
$(CC) matmul.c
$(LL) -+matmul.obj
matinv.obj: matinv.c matrix.h
$(CC) matinv.c
$(LL) -+matinv.obj
matsolve.obj: matsolve.c matrix.h
$(CC) matsolve.c
$(LL) -+matsolve.obj
mattran.obj: mattran.c matrix.h
$(CC) mattran.c
$(LL) -+mattran.obj
matdet.obj: matdet.c matrix.h
$(CC) matdet.c
$(LL) -+matdet.obj
matdurbn.obj: matdurbn.c matrix.h
$(CC) matdurbn.c
$(LL) -+matdurbn.obj
mattoepz.obj: mattoepz.c matrix.h
$(CC) mattoepz.c
$(LL) -+mattoepz.obj
matsubx.obj: matsubx.c matrix.h
$(CC) matsubx.c
$(LL) -+matsubx.obj

108
matrix/MAKEFILE.UX
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@ -1,54 +1,54 @@
#------------------------------------------------------------------------------
# file: makefile.ux
# desc: makefile for matrix library package under Unix
# by: patrick ko
# date: 16 Apr 94
#------------------------------------------------------------------------------
OBJS = matcreat.o matdump.o materr.o matadd.o matsub.o \
matmul.o matinv.o matsolve.o mattran.o matdet.o mattoepz.o matdurbn.o
CC = cc -c
C = cc
CO = -lm -g
demo: demo.c $(OBJS)
$(C) demo.c -o demo $(OBJS) $(CO)
matcreat.o: matcreat.c matrix.h
$(CC) matcreat.c
matdump.o: matdump.c matrix.h
$(CC) matdump.c
materr.o: materr.c matrix.h
$(CC) materr.c
matadd.o: matadd.c matrix.h
$(CC) matadd.c
matsub.o: matsub.c matrix.h
$(CC) matsub.c
matmul.o: matmul.c matrix.h
$(CC) matmul.c
matinv.o: matinv.c matrix.h
$(CC) matinv.c
matsolve.o: matsolve.c matrix.h
$(CC) matsolve.c
mattran.o: mattran.c matrix.h
$(CC) mattran.c
matdet.o: matdet.c matrix.h
$(CC) matdet.c
mattoepz.o: mattoepz.c matrix.h
$(CC) mattoepz.c
matdurbn.o: matdurbn.c matrix.h
$(CC) matdurbn.c
matsubx.o: matsubx.c matrix.h
$(CC) matsubx.c
#------------------------------------------------------------------------------
# file: makefile.ux
# desc: makefile for matrix library package under Unix
# by: patrick ko
# date: 16 Apr 94
#------------------------------------------------------------------------------
OBJS = matcreat.o matdump.o materr.o matadd.o matsub.o \
matmul.o matinv.o matsolve.o mattran.o matdet.o mattoepz.o matdurbn.o
CC = cc -c
C = cc
CO = -lm -g
demo: demo.c $(OBJS)
$(C) demo.c -o demo $(OBJS) $(CO)
matcreat.o: matcreat.c matrix.h
$(CC) matcreat.c
matdump.o: matdump.c matrix.h
$(CC) matdump.c
materr.o: materr.c matrix.h
$(CC) materr.c
matadd.o: matadd.c matrix.h
$(CC) matadd.c
matsub.o: matsub.c matrix.h
$(CC) matsub.c
matmul.o: matmul.c matrix.h
$(CC) matmul.c
matinv.o: matinv.c matrix.h
$(CC) matinv.c
matsolve.o: matsolve.c matrix.h
$(CC) matsolve.c
mattran.o: mattran.c matrix.h
$(CC) mattran.c
matdet.o: matdet.c matrix.h
$(CC) matdet.c
mattoepz.o: mattoepz.c matrix.h
$(CC) mattoepz.c
matdurbn.o: matdurbn.c matrix.h
$(CC) matdurbn.c
matsubx.o: matsubx.c matrix.h
$(CC) matsubx.c

224
matrix/READ.ME
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@ -1,112 +1,112 @@
-------------------------------------------------------------------------------
Small Matrix Toolbox for C programmers
version 0.42
(Support Unix and DOS)
by Patrick KO Shu-pui
Copyright (c) 1992, 1993, 1994 All Rights Reserved.
-------------------------------------------------------------------------------
ADDRESS TO CONTACT:
fidonet: 6:700/132 BiG Programming Club
[852] 663-0223 19.2 kbps
[852] 663-0236 16.8 kbps
internet: pko@hk.super.net
mailing: Patrick Ko
G.P.O. Box 7468
Hong Kong
-------------------------------------------------------------------------------
MATRX042.ZIP contains
READ .ME - this file
DEMO .C - demo how to use this package
DEMO .DAT - demo data
DEMO .EXE - demo executable for DOS
MAKEFILE.MSC - makefile for Microsoft C/C++ 7.0 on DOS
MAKEFILE.TC - makefile for Turbo C 2.0 on DOS
MAKEFILE.UX - makefile for Unix
MATRIX .DOC - matrix toolbox interface document
MATRIX .H - matrix header file (must include it)
MATADD .C - matrix addition
MATCREAT.C - matrix creation
MATDET .C - find minor, cofactor, determinant
MATDUMP .C - matrix dump
MATERR .C - matrix error handling routine
MATINV .C - matrix inversion
MATMUL .C - matrix multiplication
MATSOLVE.C - linear equations solver
MATSUB .C - matrix substraction
MATSUBX .C - submatrix operation
MATTOEPZ.C - create symmetric Toeplitz matrix
MATDURBN.C - Symmetrix Toeplitz matrix fast solving algorithm
MATTRAN .C - matrix transpose
-------------------------------------------------------------------------------
WHATS NEW in v0.1:
- +, -, *, inverse matrix operations
WHATS NEW in v0.2:
- Linear equation solver
- C-programmer-friendly C sources
WHATS NEW in v0.3:
- better data structure (more Object-Oriented)
- finding minors, cofactors, determinants
- Levinson-Durbin algorithm for symmetric Toeplitz matrix
WHATS NEW in v0.4:
- Revised method for minors, cofactors and determinants
whose time complexity is T(n^3) instead of nearly T(n!).
This is important when you want to find the determinant
of a matrix whose size is over 10 x 10.
- submatrix operator
- matrix formmated dump function
- brief matrix toolbox interface document included
WHATS NEW in v0.41:
- bug fix for unit matrix creation
WHATS NEW in v0.42:
- support Microsoft C/C++ 7.0
HOW TO COMPILE:
1. All Unix environment - make -f makefile.ux
2. DOS (Turbo C v2.0) - make -fmakefile.tc
3. DOS (Microsoft C/C++ v7.0) - nmake -fmakefile.msc
REFERENCES
[1] Mary L.Boas, "Mathematical Methods in the Physical Sciene,"
John Wiley & Sons, 2nd Ed., 1983. Chap 3.
[2] Kendall E.Atkinson, "An Introduction to Numberical Analysis,"
John Wiley & Sons, 1978.
[3] Shuzo Saito, Kazuo Nakata, "Fundamentals of Speech Signal
Processing," Academic Press, 1985.
[4] Alfred V.Aho, John E.Hopcroft, Jeffrey D.Ullman, "The Design
and Analysis of Computer Algorithms," 1974.
AUTHOR
All the sources are written by Patrick KO Shu Pui
BiG Programming Club (6:700/132, fidonet)
===============================================================================
AUTHORIZATION NOTICE
This C source package MATRX042.ZIP is FREE for ACADEMIC purpose only.
For COMMERCIAL use, authorization is required from the author.
Please send US$25 for registration.
===============================================================================
DISCLAIMER (I hate this but I have to do that)
You are on your own risk - the author is not responsible for any lost due
to the use of this toolbox.
===============================================================================
-------------------------------------------------------------------------------
Small Matrix Toolbox for C programmers
version 0.42
(Support Unix and DOS)
by Patrick KO Shu-pui
Copyright (c) 1992, 1993, 1994 All Rights Reserved.
-------------------------------------------------------------------------------
ADDRESS TO CONTACT:
fidonet: 6:700/132 BiG Programming Club
[852] 663-0223 19.2 kbps
[852] 663-0236 16.8 kbps
internet: pko@hk.super.net
mailing: Patrick Ko
G.P.O. Box 7468
Hong Kong
-------------------------------------------------------------------------------
MATRX042.ZIP contains
READ .ME - this file
DEMO .C - demo how to use this package
DEMO .DAT - demo data
DEMO .EXE - demo executable for DOS
MAKEFILE.MSC - makefile for Microsoft C/C++ 7.0 on DOS
MAKEFILE.TC - makefile for Turbo C 2.0 on DOS
MAKEFILE.UX - makefile for Unix
MATRIX .DOC - matrix toolbox interface document
MATRIX .H - matrix header file (must include it)
MATADD .C - matrix addition
MATCREAT.C - matrix creation
MATDET .C - find minor, cofactor, determinant
MATDUMP .C - matrix dump
MATERR .C - matrix error handling routine
MATINV .C - matrix inversion
MATMUL .C - matrix multiplication
MATSOLVE.C - linear equations solver
MATSUB .C - matrix substraction
MATSUBX .C - submatrix operation
MATTOEPZ.C - create symmetric Toeplitz matrix
MATDURBN.C - Symmetrix Toeplitz matrix fast solving algorithm
MATTRAN .C - matrix transpose
-------------------------------------------------------------------------------
WHATS NEW in v0.1:
- +, -, *, inverse matrix operations
WHATS NEW in v0.2:
- Linear equation solver
- C-programmer-friendly C sources
WHATS NEW in v0.3:
- better data structure (more Object-Oriented)
- finding minors, cofactors, determinants
- Levinson-Durbin algorithm for symmetric Toeplitz matrix
WHATS NEW in v0.4:
- Revised method for minors, cofactors and determinants
whose time complexity is T(n^3) instead of nearly T(n!).
This is important when you want to find the determinant
of a matrix whose size is over 10 x 10.
- submatrix operator
- matrix formmated dump function
- brief matrix toolbox interface document included
WHATS NEW in v0.41:
- bug fix for unit matrix creation
WHATS NEW in v0.42:
- support Microsoft C/C++ 7.0
HOW TO COMPILE:
1. All Unix environment - make -f makefile.ux
2. DOS (Turbo C v2.0) - make -fmakefile.tc
3. DOS (Microsoft C/C++ v7.0) - nmake -fmakefile.msc
REFERENCES
[1] Mary L.Boas, "Mathematical Methods in the Physical Sciene,"
John Wiley & Sons, 2nd Ed., 1983. Chap 3.
[2] Kendall E.Atkinson, "An Introduction to Numberical Analysis,"
John Wiley & Sons, 1978.
[3] Shuzo Saito, Kazuo Nakata, "Fundamentals of Speech Signal
Processing," Academic Press, 1985.
[4] Alfred V.Aho, John E.Hopcroft, Jeffrey D.Ullman, "The Design
and Analysis of Computer Algorithms," 1974.
AUTHOR
All the sources are written by Patrick KO Shu Pui
BiG Programming Club (6:700/132, fidonet)
===============================================================================
AUTHORIZATION NOTICE
This C source package MATRX042.ZIP is FREE for ACADEMIC purpose only.
For COMMERCIAL use, authorization is required from the author.
Please send US$25 for registration.
===============================================================================
DISCLAIMER (I hate this but I have to do that)
You are on your own risk - the author is not responsible for any lost due
to the use of this toolbox.
===============================================================================

182
matrix/demo.c
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@ -1,92 +1,92 @@
/*
*-----------------------------------------------------------------------------
* file: demo.c
* desc: demostrate how to use Patrick's matrix toolbox
* by: ko shu pui, patrick
* date: 24 nov 91 v0.1
* revi: 14 may 92 v0.2
* 24 may 92 v0.4
* ref:
* [1] Mary L.Boas, "Mathematical Methods in the Physical Sciene,"
* John Wiley & Sons, 2nd Ed., 1983. Chap 3.
*
* [2] Kendall E.Atkinson, "An Introduction to Numberical Analysis,"
* John Wiley & Sons, 1978.
*
* [3] Alfred V.Aho, John E.Hopcroft, Jeffrey D.Ullman, "The Design
* and Analysis of Computer Algorithms," 1974.
*
*-----------------------------------------------------------------------------
*/
#include <stdio.h>
#include <time.h>
#include "matrix.h"
int main()
{
MATRIX A, B, X, M;
FILE *fp;
double result;
time_t t1, t2;
int tinv, tdet, tmul;
A = mat_creat( 10, 10, UNDEFINED );
B = mat_creat( 10, 1, UNDEFINED );
if ((fp = fopen( "demo.dat", "r" )) == NULL)
{
fprintf( stderr, "file cannot be opened\n" );
exit (0);
}
fgetmat( A, fp );
printf( "|- Matrix A -|\n");
mat_dumpf( A, "%+06.1f " );
t1 = time(&t1);
result = mat_det(A);
t2 = time(&t2);
tdet = t2 - t1;
printf( "\n\nDet(A) = %f\n", result );
printf( "|- Inv A -|\n");
t1 = time(&t1);
X = mat_inv( A );
t2 = time(&t2);
tinv = t2 - t1;
if (X == NULL)
printf( "A is a singular matrix\n" );
else
{
mat_dumpf(X, "%+06.1f ");
printf( "|- A x Inv A -|\n");
t1 = time(&t1);
M = mat_mul( X, A );
t2 = time(&t2);
tmul = t2 - t1;
mat_dumpf( M, "%+06.1f " );
mat_free(M);
mat_free(X);
}
fgetmat( B, fp );
printf( "|- Matrix B -|\n");
mat_dumpf( B, "%+06.1f " );
printf( "|- A x B -|\n");
mat_free(mat_dumpf(mat_mul(A, B), "%+06.1f "));
printf( "time for finding 10 x 10 matrix inversion is less than %d secs\n", tinv );
printf( "time for finding 10 x 10 matrix determinant is less than %d secs\n", tdet );
printf( "time for finding 10 x 10 matrix multiplication is less than %d secs\n", tmul );
mat_free( A );
mat_free( B );
fclose(fp);
}
/*
*-----------------------------------------------------------------------------
* file: demo.c
* desc: demostrate how to use Patrick's matrix toolbox
* by: ko shu pui, patrick
* date: 24 nov 91 v0.1
* revi: 14 may 92 v0.2
* 24 may 92 v0.4
* ref:
* [1] Mary L.Boas, "Mathematical Methods in the Physical Sciene,"
* John Wiley & Sons, 2nd Ed., 1983. Chap 3.
*
* [2] Kendall E.Atkinson, "An Introduction to Numberical Analysis,"
* John Wiley & Sons, 1978.
*
* [3] Alfred V.Aho, John E.Hopcroft, Jeffrey D.Ullman, "The Design
* and Analysis of Computer Algorithms," 1974.
*
*-----------------------------------------------------------------------------
*/
#include <stdio.h>
#include <time.h>
#include "matrix.h"
int main()
{
MATRIX A, B, X, M;
FILE *fp;
double result;
time_t t1, t2;
int tinv, tdet, tmul;
A = mat_creat( 10, 10, UNDEFINED );
B = mat_creat( 10, 1, UNDEFINED );
if ((fp = fopen( "demo.dat", "r" )) == NULL)
{
fprintf( stderr, "file cannot be opened\n" );
exit (0);
}
fgetmat( A, fp );
printf( "|- Matrix A -|\n");
mat_dumpf( A, "%+06.1f " );
t1 = time(&t1);
result = mat_det(A);
t2 = time(&t2);
tdet = t2 - t1;
printf( "\n\nDet(A) = %f\n", result );
printf( "|- Inv A -|\n");
t1 = time(&t1);
X = mat_inv( A );
t2 = time(&t2);
tinv = t2 - t1;
if (X == NULL)
printf( "A is a singular matrix\n" );
else
{
mat_dumpf(X, "%+06.1f ");
printf( "|- A x Inv A -|\n");
t1 = time(&t1);
M = mat_mul( X, A );
t2 = time(&t2);
tmul = t2 - t1;
mat_dumpf( M, "%+06.1f " );
mat_free(M);
mat_free(X);
}
fgetmat( B, fp );
printf( "|- Matrix B -|\n");
mat_dumpf( B, "%+06.1f " );
printf( "|- A x B -|\n");
mat_free(mat_dumpf(mat_mul(A, B), "%+06.1f "));
printf( "time for finding 10 x 10 matrix inversion is less than %d secs\n", tinv );
printf( "time for finding 10 x 10 matrix determinant is less than %d secs\n", tdet );
printf( "time for finding 10 x 10 matrix multiplication is less than %d secs\n", tmul );
mat_free( A );
mat_free( B );
fclose(fp);
}