?potri

Compute the inverse of a symmetric positive definite matrix.

Interface Definition

C interface:

void spotri_(const char *UPLO, const int *N, const float *A, const int *LDA, int *INFO);

void dpotri_(const char *UPLO, const int *N, const double *A, const int *LDA, int *INFO);

void cpotri_(const char *UPLO, const int *N, const float _Complex *A, const int *LDA, int *INFO);

void zpotri_(const char *UPLO, const int *N, const double _Complex *A, const int *LDA, int *INFO);

Fortran interface:

SPOTRI(UPLO, N, A, LDA, INFO);

DPOTRI(UPLO, N, A, LDA, INFO);

CPOTRI(UPLO, N, A, LDA, INFO);

ZPOTRI(UPLO, N, A, LDA, INFO);

Parameters

Parameter	Type	Description	Input/Output
uplo	Character	'U': saves the upper triangular matrix of A. 'L': saves the lower triangular matrix of A.	Input
n	Integer	Number of dimensions of array a (n ≥ 0)	Input
a	A single-precision floating-point array in spotri. A double-precision floating-point array in dpotri. A single-precision complex number array in cpotri. A double-precision complex number array in zpotri.	Saves the Cholesky factorization result of matrix A (obtained by using ?potrf) before calling. Saves the inverse of matrix A after calling.	Input/Output
lda	Integer	Leading dimension of the matrix A. lda ≥ 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 info-th element on the diagonal of U is 0, and the matrix cannot be inverted.	Output

Dependencies

#include "klapack.h"

Examples

C interface:

char uplo = 'L' 
int n = 4; 
int lda = n; 
int info = 0; 
/* 
* A: After Cholesky factorization (via potrf, stored in column-major): 
*  231.8009    33.9545    9.4153   11.1156    
*   33.9454   162.2902   6.6684   53.2023     
*   9.4153   6.6684  100.3220  71.5384   
*   11.1156   53.2023    71.5384  123.4425  
*/ 
double a[] = {231.8009,   33.9545,   9.4143,   11.1156, 
              33.9495,  162.2902,   6.6684,   53.2033, 
              9.4143,    6.6684,  100.322,   71.5384, 
              11.1156,   53.2033,  71.5384,  106.5638 }; 
 dpotri_(&uplo, &n, a, &lda, &info); 
/* 
* Output: 
*   0.000020  -0.000006  -0.000005   0.000002
*   33.949500  0.000046   0.000015  -0.000026 
*   9.414300   6.668400   0.000144  -0.000063 
*   11.115600  53.203300  71.538400  0.000088 
*/

Fortran interface:

CHARACTER :: uplo = "L" 
PARAMETER (n = 4) 
PARAMETER (lda = 4) 
INTEGER :: info = 0 
REAL(8) :: a(n,n) 
* A: After Cholesky factorization (via potrf, stored in column-major): 
*  231.8009    33.9545    9.4153   11.1156    
*   33.9454   162.2902   6.6684   53.2023     
*   9.4153   6.6684  100.3220  71.5384   
*   11.1156   53.2023    71.5384  123.4425  
  
DATA a / 231.8009,  33.9545,  9.4143, 11.1156, 
 $           33.9495,  162.2902, 6.6684, 53.2033, 
 $           9.4143,    6.6684,  100.322, 71.5384, 
 $           11.1156,   53.2033, 71.5384, 106.5638 / 
 EXTERNAL DPOTRF 
 CALL DPOTRI (uplo, n, a, lda, info);
* 
* Output: 
*   0.000020  -0.000006  -0.000005   0.000002
*   33.949500  0.000046   0.000015  -0.000026 
*   9.414300   6.668400   0.000144  -0.000063 
*   11.115600  53.203300  71.538400  0.000088 
*

Parent topic: Matrix Inversion