slasyf_rook - compute a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
SUBROUTINE SLASYF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER INFO, KB, LDA, LDW, N, NB INTEGER IPIV(*) REAL A(LDA,*), W(LDW,*) SUBROUTINE SLASYF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, KB, LDA, LDW, N, NB INTEGER*8 IPIV(*) REAL A(LDA,*), W(LDW,*) F95 INTERFACE SUBROUTINE LASYF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) REAL, DIMENSION(:,:) :: A, W INTEGER :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV SUBROUTINE LASYF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) REAL, DIMENSION(:,:) :: A, W INTEGER(8) :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV C INTERFACE #include <sunperf.h> void slasyf_rook (char uplo, int n, int nb, int *kb, float *a, int lda, int *ipiv, int ldw, int *info); void slasyf_rook_64 (char uplo, long n, long nb, long *kb, float *a, long lda, long *ipiv, long ldw, long *info);
Oracle Solaris Studio Performance Library slasyf_rook(3P) NAME slasyf_rook - compute a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method SYNOPSIS SUBROUTINE SLASYF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER INFO, KB, LDA, LDW, N, NB INTEGER IPIV(*) REAL A(LDA,*), W(LDW,*) SUBROUTINE SLASYF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, KB, LDA, LDW, N, NB INTEGER*8 IPIV(*) REAL A(LDA,*), W(LDW,*) F95 INTERFACE SUBROUTINE LASYF_ROOK(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) REAL, DIMENSION(:,:) :: A, W INTEGER :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV SUBROUTINE LASYF_ROOK_64(UPLO, N, NB, KB, A, LDA, IPIV, W, LDW, INFO) REAL, DIMENSION(:,:) :: A, W INTEGER(8) :: N, NB, KB, LDA, LDW, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV C INTERFACE #include <sunperf.h> void slasyf_rook (char uplo, int n, int nb, int *kb, float *a, int lda, int *ipiv, int ldw, int *info); void slasyf_rook_64 (char uplo, long n, long nb, long *kb, float *a, long lda, long *ipiv, long ldw, long *info); PURPOSE slasyf_rook computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ("rook") diagonal pivoting method. The partial factorization has the form: A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' ( L21 I ) ( 0 A22 ) ( 0 I ) where the order of D is at most NB. The actual order is returned in the argument KB, and is either NB or NB-1, or N if N <= NB. SLASYF_ROOK is an auxiliary routine called by SSYTRF_ROOK. It uses blocked code (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or A22 (if UPLO = 'L'). 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. NB (input) NB is INTEGER The maximum number of columns of the matrix A that should be factored. NB should be at least 2 to allow for 2-by-2 pivot blocks. KB (output) KB is INTEGER The number of columns of A that were actually factored. KB is either NB-1 or NB, or N if N <= NB. 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 triangular 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, A contains details of the partial factorization. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (output) IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D. If UPLO = 'U': Only the last KB elements of IPIV are set. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, D(k-1:k,k-1:k) is a 2-by-2 diago- nal block. If UPLO = 'L': Only the first KB elements of IPIV are set. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, D(k:k+1,k:k+1) is a 2-by-2 diago- nal block. W (output) W is REAL array, dimension (LDW,NB) LDW (input) LDW is INTEGER The leading dimension of the array W. LDW >= max(1,N). INFO (output) INFO is INTEGER = 0: successful exit, > 0: if INFO = k, D(k,k) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular. 7 Nov 2015 slasyf_rook(3P)