spbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A
SUBROUTINE SPBSTF(UPLO, N, KD, AB, LDAB, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDAB, INFO REAL AB(LDAB,*) SUBROUTINE SPBSTF_64(UPLO, N, KD, AB, LDAB, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDAB, INFO REAL AB(LDAB,*) F95 INTERFACE SUBROUTINE PBSTF(UPLO, N, KD, AB, LDAB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDAB, INFO REAL, DIMENSION(:,:) :: AB SUBROUTINE PBSTF_64(UPLO, N, KD, AB, LDAB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDAB, INFO REAL, DIMENSION(:,:) :: AB C INTERFACE #include <sunperf.h> void spbstf(char uplo, int n, int kd, float *ab, int ldab, int *info); void spbstf_64(char uplo, long n, long kd, float *ab, long ldab, long *info);
Oracle Solaris Studio Performance Library spbstf(3P) NAME spbstf - compute a split Cholesky factorization of a real symmetric positive definite band matrix A SYNOPSIS SUBROUTINE SPBSTF(UPLO, N, KD, AB, LDAB, INFO) CHARACTER*1 UPLO INTEGER N, KD, LDAB, INFO REAL AB(LDAB,*) SUBROUTINE SPBSTF_64(UPLO, N, KD, AB, LDAB, INFO) CHARACTER*1 UPLO INTEGER*8 N, KD, LDAB, INFO REAL AB(LDAB,*) F95 INTERFACE SUBROUTINE PBSTF(UPLO, N, KD, AB, LDAB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, KD, LDAB, INFO REAL, DIMENSION(:,:) :: AB SUBROUTINE PBSTF_64(UPLO, N, KD, AB, LDAB, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, KD, LDAB, INFO REAL, DIMENSION(:,:) :: AB C INTERFACE #include <sunperf.h> void spbstf(char uplo, int n, int kd, float *ab, int ldab, int *info); void spbstf_64(char uplo, long n, long kd, float *ab, long ldab, long *info); PURPOSE spbstf computes a split Cholesky factorization of a real symmetric pos- itive definite band matrix A. This routine is designed to be used in conjunction with SSBGST. The factorization has the form A = S**T*S where S is a band matrix of the same bandwidth as A and the following structure: S = ( U ) ( M L ) where U is upper triangular of order m = (n+kd)/2, and L is lower tri- angular of order n-m. ARGUMENTS UPLO (input) = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) The order of the matrix A. N >= 0. KD (input) The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0. AB (input/output) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, if INFO = 0, the factor S from the split Cholesky factorization A=S**T*S. See Further Details. LDAB (input) The leading dimension of the array AB. LDAB >= KD+1. INFO (output) = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, the factorization could not be completed, because the updated element a(i,i) was negative; the matrix A is not positive definite. FURTHER DETAILS The band storage scheme is illustrated by the following example, when N = 7, KD = 2: S = ( s11 s12 s13 ) ( s22 s23 s24 ) ( s33 s34 ) ( s44 ) ( s53 s54 s55 ) ( s64 s65 s66 ) ( s75 s76 s77 ) If UPLO = 'U', the array AB holds: on entry: on exit: * * a13 a24 a35 a46 a57 * * s13 s24 s53 s64 s75 * a12 a23 a34 a45 a56 a67 * s12 s23 s34 s54 s65 s76 a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 If UPLO = 'L', the array AB holds: on entry: on exit: a11 a22 a33 a44 a55 a66 a77 s11 s22 s33 s44 s55 s66 s77 a21 a32 a43 a54 a65 a76 * s12 s23 s34 s54 s65 s76 * a31 a42 a53 a64 a64 * * s13 s24 s53 s64 s75 * * Array elements marked * are not used by the routine. 7 Nov 2015 spbstf(3P)