spstrf - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A
SUBROUTINE SPSTRF(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL TOL INTEGER INFO, LDA, N, RANK CHARACTER*1 UPLO REAL A(LDA,*), WORK(2*N) INTEGER PIV(N) SUBROUTINE SPSTRF_64(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL TOL INTEGER*8 INFO, LDA, N, RANK CHARACTER*1 UPLO REAL A(LDA,*), WORK(2*N) INTEGER*8 PIV(N) F95 INTERFACE SUBROUTINE PSTRF(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: PIV REAL, DIMENSION(:) :: WORK REAL :: TOL SUBROUTINE PSTRF_64(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: PIV REAL, DIMENSION(:) :: WORK REAL :: TOL C INTERFACE #include <sunperf.h> void spstrf (char uplo, int n, float *a, int lda, int *piv, int *rank, float tol, int *info); void spstrf_64 (char uplo, long n, float *a, long lda, long *piv, long *rank, float tol, long *info);
Oracle Solaris Studio Performance Library spstrf(3P) NAME spstrf - compute the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A SYNOPSIS SUBROUTINE SPSTRF(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL TOL INTEGER INFO, LDA, N, RANK CHARACTER*1 UPLO REAL A(LDA,*), WORK(2*N) INTEGER PIV(N) SUBROUTINE SPSTRF_64(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL TOL INTEGER*8 INFO, LDA, N, RANK CHARACTER*1 UPLO REAL A(LDA,*), WORK(2*N) INTEGER*8 PIV(N) F95 INTERFACE SUBROUTINE PSTRF(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: PIV REAL, DIMENSION(:) :: WORK REAL :: TOL SUBROUTINE PSTRF_64(UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, RANK, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: PIV REAL, DIMENSION(:) :: WORK REAL :: TOL C INTERFACE #include <sunperf.h> void spstrf (char uplo, int n, float *a, int lda, int *piv, int *rank, float tol, int *info); void spstrf_64 (char uplo, long n, float *a, long lda, long *piv, long *rank, float tol, long *info); PURPOSE spstrf computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. The factorization has the form P**T * A * P = U**T * U , if UPLO = 'U', P**T * A * P = L * L**T, if UPLO = 'L', where U is an upper tri- angular matrix and L is lower triangular, and P is stored as vector PIV. This algorithm does not attempt to check that A is positive semidefi- nite. This version of the algorithm calls level 3 BLAS. ARGUMENTS UPLO (input) UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored. = 'U': Upper triangular = 'L': Lower triangular N (input) N is INTEGER The order of the matrix A. N >= 0. A (input/output) A is REAL array, dimension (LDA,N) On entry, the symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangu- lar part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if INFO = 0, the factor U or L from the Cholesky factorization as above. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). PIV (output) PIV is INTEGER array, dimension (N) PIV is such that the nonzero entries are P( PIV(K), K ) = 1. RANK (output) RANK is INTEGER The rank of A given by the number of steps the algorithm com- pleted. TOL (input) TOL is REAL User defined tolerance. If TOL < 0, then N*U*MAX( A(K,K) ) will be used. The algorithm terminates at the (K-1)st step if the pivot <= TOL. WORK (output) WORK is REAL array, dimension (2*N) Work space. INFO (output) INFO is INTEGER < 0: If INFO = -K, the K-th argument had an illegal value, = 0: algorithm completed successfully, and > 0: the matrix A is either rank deficient with computed rank as returned in RANK, or is indefinite. See Section 7 of LAPACK Working Note #161 for further information. 7 Nov 2015 spstrf(3P)