?gesv
Solve a system of linear equations 
, where 
is an 
matrix, and 
and 
are 
matrices. The routine computes the LU factorization of 
with partial pivoting and row interchanges, factoring as 
, where 
is a permutation matrix, 
is a unit lower triangular matrix, and 
is an upper triangular matrix. It then uses the LU factorization results to solve the system of linear equations.
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. n ≥ 0. |
Input |
|
nrhs |
Integer |
Number of items on the right, that is, the number of columns in matrix B. nrhs ≥ 0. |
Input |
|
a |
|
The matrix dimension is (lda, n).
|
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 |
|
The matrix dimension is (ldb, nrhs).
|
Input/Output |
|
ldb |
Integer |
Leading dimension of matrix B. ldb ≥ max(1, n). |
Input |
|
info |
Integer |
Execution result:
|
Output |
Dependency
#include "klapack.h"
Examples
C interface:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 |
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