?getri
根据?getrf得到的LU分解结果计算逆矩阵。
接口定义
C Interface：
void sgetri_(const int *n, float *a, const int *lda, const int *ipiv, float *work, const int *lwork, int *info);
void dgetri_(const int *n, double *a, const int *lda, const int *ipiv, double *work, const int *lwork, int *info);
void cgetri_(const int *n, float _Complex *a, const int *lda, const int *ipiv, float _Complex *work, const int *lwork, int *info);
void zgetri_(const int *n, double _Complex *a, const int *lda, const int *ipiv, double _Complex *work, const int *lwork, int *info);
Fortran Interface：
SGETRI(n, a, lda, ipiv, work, lwork, info)
DGETRI(n, a, lda, ipiv, work, lwork, info)
CGETRI(n, a, lda, ipiv, work, lwork, info)
ZGETRI(n, a, lda, ipiv, work, lwork, info)
参数
参数名 |
类型 |
描述 |
输入/输出 |
|---|---|---|---|
n |
整数型 |
矩阵A的行数或列数。 |
输入 |
a |
|
|
输入/输出 |
lda |
整数型 |
A的leading dimension大小，要求lda ≥ max(1, n)。 |
输入 |
ipiv |
整数型数组 |
?getrf得到的主元索引，长度为n：1 ≤ ipiv ≤ n，表示分解中矩阵第i行与第ipiv[i-1]行交换。 |
输入 |
work |
|
临时存储空间，使用lwork=-1调用后work[0]为最优的lwork值。 |
输出 |
lwork |
整数型 |
work数组的长度。 lwork=-1时查询最优work大小，结果保存在work[0]中，否则要求lwork≥n。 |
输入 |
info |
整数型 |
执行结果：
|
输出 |
依赖
#include "klapack.h"
示例
C Interface：
int n = 4;
int lda = 4;
int info = 0;
double *work = NULL;
double qwork;
int lwork = -1;
/*
* Origin A:
* 1.80 2.88 2.05 -0.89
* 5.25 -2.95 -0.95 -3.80
* 1.58 -2.69 -2.90 -1.04
* -1.11 -0.66 -0.59 0.80
* After LU factorization (via getrf, stored in column-major):
* 5.2500 -2.9500 -0.9500 -3.8000
* 0.3429 3.8914 2.3757 0.4129
* 0.3010 -0.4631 -1.5139 0.2948
* -0.2114 -0.3299 0.0047 0.1314
*/
double a[] = {5.2500, 0.3429, 0.3010, -0.2114,
-2.9500, 3.8914, -0.4631, -0.3299,
-0.9500, 2.3757, -1.5139, 0.0047,
-3.8000, 0.4129, 0.2948, 0.1314};
int ipiv[] = {2, 2, 3, 4};
/* Query optimal work size */
dgetri_(&n, a, &lda, ipiv, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate inversion */
dgetri_(&n, a, &lda, ipiv, work, &lwork, &info);
free(work);
/*
* Output:
* 1.7718 0.5753 0.0844 4.8145
* -0.1174 -0.4455 0.4113 -1.7122
* 0.1798 0.4526 -0.6675 1.4820
* 2.4941 0.7644 -0.0358 7.6104
*/
Fortran Interface：
PARAMETER (n = 4)
PARAMETER (lda = 4)
INTEGER :: info = 0
REAL(8) qwork(1)
REAL(8), ALLOCATABLE :: work(:)
INTEGER :: lwork = -1
* Origin A:
* 1.80 2.88 2.05 -0.89
* 5.25 -2.95 -0.95 -3.80
* 1.58 -2.69 -2.90 -1.04
* -1.11 -0.66 -0.59 0.80
* After LU factorization (via getrf, stored in column-major):
* 5.2500 -2.9500 -0.9500 -3.8000
* 0.3429 3.8914 2.3757 0.4129
* 0.3010 -0.4631 -1.5139 0.2948
* -0.2114 -0.3299 0.0047 0.1314
REAL(8) :: a(n, n)
DATA a / 5.2500, 0.3429, 0.3010, -0.2114,
$ -2.9500, 3.8914, -0.4631, -0.3299,
$ -0.9500, 2.3757, -1.5139, 0.0047,
$ -3.8000, 0.4129, 0.2948, 0.1314 /
INTEGER :: ipiv(n)
DATA ipiv / 2, 2, 3, 4 /
* Query optimal work size
EXTERNAL DGETRI
CALL DGETRI(n, a, lda, ipiv, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
* Calculate inversion
CALL DGETRI(n, a, lda, ipiv, work, lwork, info)
DEALLOCATE(work)
* Output:
* 1.7718 0.5753 0.0844 4.8145
* -0.1174 -0.4455 0.4113 -1.7122
* 0.1798 0.4526 -0.6675 1.4820
* 2.4941 0.7644 -0.0358 7.6104