i have two codes for solving linear equations, one from intel:
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/*
LAPACKE_dgesv Example.
======================
The program computes the solution to the system of linear
equations with a square matrix A and multiple
right-hand sides B, where A is the coefficient matrix:
6.80 -6.05 -0.45 8.32 -9.67
-2.11 -3.30 2.58 2.71 -5.14
5.66 5.36 -2.70 4.35 -7.26
5.97 -4.44 0.27 -7.17 6.08
8.23 1.08 9.04 2.14 -6.87
and B is the right-hand side matrix:
4.02 -1.56 9.81
6.19 4.00 -4.09
-8.22 -8.67 -4.57
-7.57 1.75 -8.61
-3.03 2.86 8.99
Description.
============
The routine solves for X the system of linear equations A*X = B,
where A is an n-by-n matrix, the columns of matrix B are individual
right-hand sides, and the columns of X are the corresponding
solutions.
The LU decomposition with partial pivoting and row interchanges is
used to factor A as A = P*L*U, where P is a permutation matrix, L
is unit lower triangular, and U is upper triangular. The factored
form of A is then used to solve the system of equations A*X = B.
Example Program Results.
========================
LAPACKE_dgesv (row-major, high-level) Example Program Results
Solution
-0.80 -0.39 0.96
-0.70 -0.55 0.22
0.59 0.84 1.90
1.32 -0.10 5.36
0.57 0.11 4.04
Details of LU factorization
8.23 1.08 9.04 2.14 -6.87
0.83 -6.94 -7.92 6.55 -3.99
0.69 -0.67 -14.18 7.24 -5.19
0.73 0.75 0.02 -13.82 14.19
-0.26 0.44 -0.59 -0.34 -3.43
Pivot indices
5 5 3 4 5
*/
#include <stdlib.h>
#include <stdio.h>
#include "mkl_lapacke.h"
/* Auxiliary routines prototypes */
extern void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda );
extern void print_int_vector( char* desc, MKL_INT n, MKL_INT* a );
/* Parameters */
#define N 3
#define NRHS 1
#define LDA N
#define LDB NRHS
/* Main program */
int main() {
/* Locals */
MKL_INT n = N, nrhs = NRHS, lda = LDA, ldb = LDB, info;
/* Local arrays */
MKL_INT ipiv[N];
double a[LDA*N] = {
1,1,1,
1,1,3,
2,1,1
};
double b[LDB*N] = {
1,
2,
3
};
/* Executable statements */
printf( "LAPACKE_dgesv (row-major, high-level) Example Program Results\n" );
/* Solve the equations A*X = B */
info = LAPACKE_dgesv( LAPACK_ROW_MAJOR, n, nrhs, a, lda, ipiv,
b, ldb );
/* Check for the exact singularity */
if( info > 0 ) {
printf( "The diagonal element of the triangular factor of A,\n" );
printf( "U(%i,%i) is zero, so that A is singular;\n", info, info );
printf( "the solution could not be computed.\n" );
exit( 1 );
}
/* Print solution */
print_matrix( "Solution", n, nrhs, b, ldb );
/* Print details of LU factorization */
print_matrix( "Details of LU factorization", n, n, a, lda );
/* Print pivot indices */
print_int_vector( "Pivot indices", n, ipiv );
exit( 0 );
} /* End of LAPACKE_dgesv Example */
/* Auxiliary routine: printing a matrix */
void print_matrix( char* desc, MKL_INT m, MKL_INT n, double* a, MKL_INT lda ) {
MKL_INT i, j;
printf( "\n %s\n", desc );
for( i = 0; i < m; i++ ) {
for( j = 0; j < n; j++ ) printf( " %6.2f", a[i*lda+j] );
printf( "\n" );
}
}
/* Auxiliary routine: printing a vector of integers */
void print_int_vector( char* desc, MKL_INT n, MKL_INT* a ) {
MKL_INT j;
printf( "\n %s\n", desc );
for( j = 0; j < n; j++ ) printf( " %6i", a[j] );
printf( "\n" );
}another which i created for gnu blas lapack :
#include<stdio.h>
#include<iostream>
#include "lapacke.h"
using namespace std;
int main()
{
// note, to understand this part take a look in the MAN pages, at section of parameters.
char TRANS = 'T';
int INFO=3;
int LDA = 3;
int LDB = 3;
int N = 3;
int NRHS = 1;
int IPIV[3] ;
/* double A[9]=
{
1,2,-1,
2,1,1,
-1,2,1,
};
double B[3]=
{
4,
-2,
2
};
*/
double A[9] =
{
1,1,1,
1,1,3,
2,1,1
};
double B[3] =
{
1,
2,
3
};
// end of declarations
cout << "compute the LU factorization..."<< endl << endl;
//void LAPACK_dgetrf( lapack_int* m, lapack_int* n, double* a, lapack_int* lda, lapack_int* ipiv, lapack_int *info );
LAPACK_dgetrf(&N,&N,A,&LDA,IPIV,&INFO);
// checks INFO, if INFO != 0 something goes wrong, for more information see the MAN page of dgetrf.
if(INFO)
{
cout << "an error occured : "<< INFO << endl << endl;
}else{
cout << "solving the system..."<< endl << endl;
// void LAPACK_dgetrs( char* trans, lapack_int* n, lapack_int* nrhs, const double* a, lapack_int* lda, const lapack_int* ipiv,double* b, lapack_int* ldb, lapack_int *info );
dgetrs_(&TRANS,&N,&NRHS,A,&LDA,IPIV,B,&LDB,&INFO);
printf("IPIV= %d %d %d \n",IPIV[0],IPIV[1],IPIV[2]);
if(INFO)
{
// checks INFO, if INFO != 0 something goes wrong, for more information see the MAN page of dgetrs.
cout << "an error occured : "<< INFO << endl << endl;
}else{
cout << "print the result : {";
int i;
for (i=0;i<N;i++)
{
cout << B[i] << "";
}
cout << "}"<< endl << endl;
}
}
cout << "program terminated."<< endl << endl;
return 0;
}compute the LU factorization...
solving the system...
IPIV= 1 3 3
print the result : {2 -1.5 0.5 }
program terminated.outputs are:
LAPACKE_dgesv (row-major, high-level) Example Program Results
Solution
2.00
-1.50
0.50
Details of LU factorization
2.00 1.00 1.00
0.50 0.50 2.50
0.50 1.00 -2.00
Pivot indices
3 2 3
can intel's ipiv differ from gnu's ipiv (different algorithm) or, there is some error in my code ?
Awaiting your reply
Regards
Puneet