ssyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm
SUBROUTINE SSYEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER INFO, LDA, N REAL AMAX, SCOND CHARACTER*1 UPLO REAL A(LDA,*), S(*), WORK(*) SUBROUTINE SSYEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER*8 INFO, LDA, N REAL AMAX, SCOND CHARACTER*1 UPLO REAL A(LDA,*), S(*), WORK(*) F95 INTERFACE SUBROUTINE SYEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL, DIMENSION(:) :: S, WORK REAL :: SCOND, AMAX SUBROUTINE SYEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL, DIMENSION(:) :: S, WORK REAL :: SCOND, AMAX C INTERFACE #include <sunperf.h> void ssyequb (char uplo, int n, float *a, int lda, float *s, float *scond, float *amax, int *info); void ssyequb_64 (char uplo, long n, float *a, long lda, float *s, float *scond, float *amax, long *info);
Oracle Solaris Studio Performance Library ssyequb(3P) NAME ssyequb - compute row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number with respect to the two-norm SYNOPSIS SUBROUTINE SSYEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER INFO, LDA, N REAL AMAX, SCOND CHARACTER*1 UPLO REAL A(LDA,*), S(*), WORK(*) SUBROUTINE SSYEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER*8 INFO, LDA, N REAL AMAX, SCOND CHARACTER*1 UPLO REAL A(LDA,*), S(*), WORK(*) F95 INTERFACE SUBROUTINE SYEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL, DIMENSION(:) :: S, WORK REAL :: SCOND, AMAX SUBROUTINE SYEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) REAL, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL, DIMENSION(:) :: S, WORK REAL :: SCOND, AMAX C INTERFACE #include <sunperf.h> void ssyequb (char uplo, int n, float *a, int lda, float *s, float *scond, float *amax, int *info); void ssyequb_64 (char uplo, long n, float *a, long lda, float *s, float *scond, float *amax, long *info); PURPOSE ssyequb computes row and column scalings intended to equilibrate a sym- metric matrix A and reduce its condition number (with respect to the two-norm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings. ARGUMENTS UPLO (input) UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T. N (input) N is INTEGER The order of the matrix A. N >= 0. A (input) A is REAL array, dimension (LDA,N) The N-by-N symmetric matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. LDA (input) LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). S (output) S is REAL array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) SCOND is REAL If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S. AMAX (output) AMAX is REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled. WORK (output) WORK is REAL array, dimension (3*N) INFO (output) INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value; > 0: if INFO = i, the i-th diagonal element is nonpositive. 7 Nov 2015 ssyequb(3P)