?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 it into a form of , where is a permutation matrix, is a unit lower triangular matrix, and is an upper triangular matrix. The system of linear equations is solved based on the result of LU factorization.

Interface Definition

C interface:

void dsgesv_(const int *n, const int *nrhs, double *a, const int *lda, int *ipiv, const double *b, const int *ldb, double *x, const int *ldx, double *work, float *swork, int *iter, int *info);

void zcgesv_( const int *n, const int *nrhs, double _Complex *a, const int *lda, int *ipiv, const double _Complex *b, const int *ldb, double _Complex *x, const int *ldx, double _Complex *work, float _Complex *swork, double *rwork, int *iter, int *info);

Fortran interface:

DSGESV(N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, info);

ZCGESV(N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, info);

Parameters

Parameter	Type	Description	Input/Output
n	Integer	Order of matrix A. n ≥ 0.	Input
nrhs	Integer	Number of items on the right, that is, the number of columns in matrix B. nrhs ≥ 0.	Input
a	A double-precision floating-point array for dsgesv A complex double-precision array for zcgesv	Matrix with a size of (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 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 i-th row of the matrix is interchanged with the ipiv(i)-th row.	Output
b	A double-precision floating-point array for dsgesv A complex double-precision array for zcgesv	The matrix dimension is (ldb, nrhs). Input: right-hand side matrix B.	Input
ldb	Integer	Leading dimension of matrix B. ldb ≥ max(1, n).	Input
x	A double-precision floating-point array for dsgesv A complex double-precision array for zcgesv	Array with a size of ldxnrhs. If info=0, it contains the nnrhs solution matrix.	Output
ldx	Integer	Leading dimension of matrix X. ldx ≥ max(1, n).	Input
work	A double-precision floating-point array for dsgesv A complex double-precision array for zcgesv	Array with a size of n*nrhs. It is used to store residual vectors.	Output
swork	A single-precision floating-point array for dsgesv A complex single-precision array for zcgesv	Array with a size of n*(n+nrhs). Stores the single-precision matrix and single-precision solution results.	Output
rwork (only available for the complex type)	Double-precision floating-point array	Work array, with a size of n.	Output
iter	Integer	< 0: Iterative refinement fails and double precision factorization is performed. > 0: Iterative refinement is successfully performed and the number of iterations is returned.	Output
info	Integer	Execution results: 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

Dependency

#include "klapack.h"

Examples

C interface:

const int n = 4;
const int nrhs = 2;
const int lda = 4;
const int ldb = 4;
const int ldx = 4;

int info = 0;
int iter = 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}; 
int *ipiv = (int*)malloc(n * sizeof(int));
double b[] = {9.4532, 1.5204, 2.2127, 0.9891, 7.1778,
              6.8955, 7.2465, 3.5019, 8.2268, 3.5287};

double *x = (double*)malloc(ldx * nrhs * sizeof(double));
double *work = (double*)malloc(n * nrhs * sizeof(double));
float *swork = (float*)malloc(n * (n + nrhs) * sizeof(float));

dsgesv_(&n, &nrhs, a, &lda, ipiv, b, &ldb, x, &ldx, work, swork, &iter, &info);
if (info != 0) {
    printf("ERROR, info = %d\n", info);
}

if (iter < 0) {
    printf("Iterative refinement failed, iter = %d\n", iter);
}
/* output */
* x
* 0.153366        0.083995
* -0.538653       0.096517
* 1.080726        -0.174382
* -0.145340       0.022261
* iter
* 2

Fortran interface:

PARAMETER (n = 4) 
PARAMETER (nrhs = 2) 
PARAMETER (lda = 4)
PARAMETER (ldb = 4)
PARAMETER (ldx = 4)
REAL(8) :: a(lda, n)  
REAL(8) :: b(ldb, n)
REAL(8) :: b(ldx, n)
REAL(8) :: work(nrhs, n)
REAL(4) :: swork(n+nrhs, n)
INTERGER::ipiv(n)

INTEGER :: info = 0
INTEGER :: iter = 0
  
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 /
 EXTERNAL DSGESV
 CALL DSGESV(n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info);
IF (info.NE.0) THEN 
    CALL EXIT(1) 
END IF
IF (iter.LT.0) THEN 
    CALL EXIT(1) 
END IF
* 
* Output: 
* 0.153366        0.083995
* -0.538653       0.096517
* 1.080726        -0.174382
* -0.145340       0.022261
* iter
* 2

Parent topic: Mixed Precision Functions