?getri

Compute the inverse matrix based on the LU factorization result obtained using ?getrf.

Interface Definition

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)

Parameters

Parameter	Type	Description	Input/Output
n	Integer	Number of rows or columns in matrix A.	Input
a	A single-precision floating-point array for sgetri A double-precision floating-point array for dgetri A single-precision complex array for cgetri A double-precision complex array for zgetri	Saves the LU factorization result of matrix A (obtained using ?getrf) before the function is called. Saves the inverse matrix of matrix A after the function is called.	Input/Output
lda	Integer	Leading dimension of matrix A. lda ≥ max(1, n).	Input
ipiv	Integer array	An array containing pivot indices obtained from ?getrf. Its length is n. For 1 ≤ ipiv ≤ n, row i and row ipiv[i-1] of the matrix are interchanged during factorization.	Input
work	A single-precision floating-point array for sgetri A double-precision floating-point array for dgetri A single-precision complex array for cgetri A double-precision complex array for zgetri	Temporary storage space. After lwork=-1 is called, work[0] is the optimal lwork value.	Output
lwork	Integer	Length of the work array. If lwork = -1, the optimal work size is queried and the result is saved in work[0]. If lwork ≠ -1, the value of lwork must be greater than or equal to 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 info-th element on the diagonal of U is 0, and the matrix cannot be inverted.	Output

Dependency

#include "klapack.h"

Examples

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

Parent topic: Matrix Inversion Functions