?gesv

Solve a system of linear equations , where is an matrix. and are matrices. In the solving process, LU factorization with partial rotation and row interchange is performed on to factor the LU into a form of , where is a transpose matrix, is a unit lower triangular matrix, and is an upper triangular matrix. The system of linear equations is solved by the result of LU factorization.

Interface Definition

C interface:

void sgesv_(const int *n,const int *nrhs,float *a,const int *lda,int *ipiv, float *b, const int *ldb,int *info);

void dgesv_(const int *n,const int *nrhs,double *a,const int *lda,int *ipiv, double *b, const int *ldb,int *info);

void cgesv_(const int *n,const int *nrhs,float_Complex *a,const int *lda,int *ipiv, float_Complex *b, const int *ldb,int *info);

void zgesv_(const int *n,const int *nrhs, double_Complex *a,const int *lda,int *ipiv, double_Complex *b, const int *ldb,int *info);

Fortran interface:

SGESV(n, nrhs, a, lda, ipiv, b, ldb, info);

DGESV(n, nrhs, a, lda, ipiv, b, ldb, info);

CGESV(n, nrhs, a, lda, ipiv, b, ldb, info);

ZGESV(n, nrhs, a, lda, ipiv, b, ldb, info);

Parameters

Parameter	Type	Description	Input/Output
n	Integer	Order of matrix A. The value of n must be greater than or equal to 0.	Input
nrhs	Integer	Number of items on the right, that is, the number of columns in matrix B. nrhs >= 0.	Input
a	A single-precision floating-point array in sgesv. A double-precision floating-point array in dgesv. A single-precision complex number array in cgesv. A double-precision complex number array in zgesv.	The matrix dimension is (lda, n). Input: n*n coefficient matrix A. Output: and in are stored. The unit diagonal element of is not stored.	Input/Output
lda	Integer	Leading dimension of the matrix A. lda >= max(1, n).	Input
ipiv	Integer array	The array dimension is n. Array storing the pivot indices of the permutation matrix P. The ith row and is interchanged with the ipiv(i)th row of the matrix.	Output
b	A single-precision floating-point array in sgesv. A double-precision floating-point array in dgesv. A single-precision complex number array in cgesv. A double-precision complex number array in zgesv.	The matrix dimension is (ldb, nrhs). Input: matrix B on the right of . Output: When info = 0, is the solution matrix X of .	Input/Output
ldb	Integer	Leading dimension of the matrix B. ldb >= max(1, n).	Input
info	Integer	Execution result: 0: The execution is successful. Smaller than 0: The value of the -info-th parameter is invalid. Greater than 0: . The factorization is complete, but the solution cannot be completed due to the singularity of .	Output

Dependencies

#include "klapack.h"

Examples

C interface:

int n = 5; 
int nrhs = 2; 
int lda = 5; 
int ldb = 5; 
int ipiv[5]; 
int info = 0; 
double a[]={72.1673 , 66.1857 , 64.7644 , 28.0199 , 91.4151, 
            6.5180 , 62.8483 , 72.4323 , 46.5760 ,  8.6928, 
            28.9821 , 42.1828 , 18.6437 , 99.8612 , 35.6972, 
            67.9812 ,  5.0880 , 85.5035 ,79.2945 , 54.5920, 
            28.6869 , 49.7512 ,  7.5186 ,28.6929 , 84.6041}; 
double b[]={ 9.4532 ,  1.5204 ,  2.2127 ,  0.9891, 7.1778, 
             6.8955 ,   7.2465,  3.5019 ,  8.2268, 3.5287}; 
dgesv_(&n,&nrhs,a,&lda,ipiv,b,&ldb,&info); 
/* 
* Output: 
* 0.17538061067669766        0.16637572403098155 
* -0.11183914210321674       -3.7758100714851153E-002 
* 5.5415093265516101E-002    0.15550950667724139 
* -1.4901096204948673E-002   -7.3593964815566168E-002 
* -0.10693481055391466       -0.15230871441871899 
*/

Fortran interface:

PARAMETER(n=5) 
PARAMETER(nrhs=2) 
PARAMETER(lda=5) 
PARAMETER(ldb=5) 
INTEGER::info =0 
INTEGER :: ipiv(n) 
REAL(8) :: a(n*n) 
        DATA a / 72.1673 , 66.1857 , 64.7644 , 28.0199 , 91.4151, 
     $           6.5180 , 62.8483 , 72.4323 , 46.5760 ,  8.6928, 
     $           28.9821 , 42.1828 , 18.6437 , 99.8612 , 35.6972, 
     $           67.9812 ,  5.0880 , 85.5035 ,79.2945 , 54.5920, 
     $           28.6869 , 49.7512 ,  7.5186 ,28.6929 , 84.6041 / 
        REAL(8) :: b(n, nrhs) 
        DATA b /9.4532 ,  1.5204 ,  2.2127 ,  0.9891, 7.1778, 
     $           6.8955 ,   7.2465,  3.5019 ,  8.2268, 3.5287 / 
        EXTERNAL DGESV 
        CALL DGESV(n, nrhs, a, lda, ipiv, b, ldb, info); 
*       Output: 
*       0.17538061067669766        0.16637572403098155 
*       -0.11183914210321674       -3.7758100714851153E-002 
*       5.5415093265516101E-002    0.15550950667724139  
 *      -1.4901096204948673E-002   -7.3593964815566168E-002 
*       -0.10693481055391466       -0.15230871441871899

Parent topic: Solving a Linear Equation System