P?POTRF

Calculate the Cholesky factorization of a symmetric positive definite matrix or a Hermitian positive definite matrix, that is, or . is an upper triangular matrix, and is a lower triangular matrix.

Interface Definition

C interface:

void pspotrf_(const char *uplo, const int *n, float *a, const int *ia, const int *ja, const int *desca, int *info)

void pdpotrf_(const char *uplo, const int *n, double *a, const int *ia, const int *ja, const int *desca, int *info)

void pcpotrf_(const char *uplo, const int *n, float _Complex *a, const int *ia, const int *ja, const int *desca, int *info)

void pzpotrf_(const char *uplo, const int *n, double _Complex *a, const int *ia, const int *ja, const int *desca, int *info)

Fortran interface:

PSPOTRF(uplo, n, a, ia, ja, desca, info)

PDPOTRF(uplo, n, a, ia, ja, desca, info)

PCPOTRF(uplo, n, a, ia, ja, desca, info)

PZPOTRF(uplo, n, a, ia, ja, desca, info)

Parameters

Parameter	Type	Scope	Description	Input/Output
uplo	Character	Global	U indicates the upper triangular matrix is stored, and L indicates the lower triangular matrix is stored.	Input
n	Integer	Global	Number of columns to be operated, for example, the number of columns in a submatrix	Input
a	A single-precision floating-point array for pspotrf A double-precision floating-point array for pdpotrf A single-precision complex number array for pcpotrf A double-precision complex number array for pzpotrf	Local	Stores the local part of distributed matrix A to be factorized before this function is called. If uplo = 'U', the upper triangular matrix U is stored for the diagonal and the part above the diagonal after the function is called. If uplo = 'L', the lower triangular matrix L is stored for the diagonal and the part above the diagonal after the function is called.	Input/Output
ia	Integer	Global	Row indices of the submatrix in the global matrix	Input
ja	Integer	Global	Column indices of the submatrix in the global matrix	Input
desca	Integer array	Local and global	Descriptor of distributed matrix A	Input
info	Integer	Global	Execution result: 0: The exit is successful. Smaller than 0: The value of the -info-th parameter is invalid. Greater than 0: The principal minor of order info in matrix A is not positive definite, and the factorization cannot be completed.	Output

Dependencies

#include <kscalapack.h>

Examples

C interface:

    int n = 8;       // (Global) Matrix size
    int nprow = 2;   // Number of row procs
    int npcol = 2;   // Number of column procs
    int nb = 4;      // (Global) Block size
    char uplo='L';   // Matrix is lower triangular
    char layout='R'; // Block cyclic, Row major processor mapping
    int descA[9];
    int info;
    int lddA = mpA > 1 ? mpA : 1;
    descinit_( descA,  &n, &n, &nb, &nb, &izero, &izero, &ictxt, &lddA, &info);     
    np = 4;
    /* 
     * Origin A: 
     *  
    *16 1 2 3 4 5 6 7
    *1 16 3 4 5 6 7 8
    *2 3 16 5 6 7 8 9
    *3 4 5 16 7 8 9 10
    *4 5 6 7 16 9 10 11
    *5 6 7 8 9 16 11 12
    *6 7 8 9 10 11 16 13
    *7 8 9 10 11 12 13 16


    /* Query optimal work size */ 
    pdpotrf_(&uplo, &n, A, &ione, &ione, descA, &info);
    * After PDPOTRF: 
    *4.00000 1.00000 2.00000 3.00000 4.00000 5.00000 6.00000 7.00000
    *0.250000 3.99218 3.00000 4.00000 5.00000 6.00000 7.00000 8.00000
    *0.500000 0.720158 3.90274 5.00000 6.00000 7.00000 8.00000 9.00000
    *0.750000 0.954992 1.00884 3.67529 7.00000 8.00000 9.00000 10.0000
    *1.00000 1.18983 1.18971 1.06481 3.32191 9.00000 10.0000 11.0000
    *1.25000 1.42466 1.37058 1.17522 0.955149 2.86983 11.0000 12.0000
    *1.50000 1.65949 1.55145 1.28562 0.996646 0.756689 2.31741 13.0000
    *1.75000 1.89433 1.73232 1.39603 1.03814 0.734271 0.500013 1.59132

Parent topic: Matrix Factorization