zheequb - compute row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE ZHEEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) DOUBLE PRECISION S(*) SUBROUTINE ZHEEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER*8 INFO, LDA, N DOUBLE PRECISION AMAX, SCOND CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) DOUBLE PRECISION S(*) F95 INTERFACE SUBROUTINE HEEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: SCOND, AMAX SUBROUTINE HEEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: SCOND, AMAX C INTERFACE #include <sunperf.h> void zheequb (char uplo, int n, doublecomplex *a, int lda, double *s, double *scond, double *amax, int *info); void zheequb_64 (char uplo, long n, doublecomplex *a, long lda, double *s, double *scond, double *amax, long *info);
Oracle Solaris Studio Performance Library zheequb(3P) NAME zheequb - compute row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the two-norm) SYNOPSIS SUBROUTINE ZHEEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) DOUBLE PRECISION S(*) SUBROUTINE ZHEEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER*8 INFO, LDA, N DOUBLE PRECISION AMAX, SCOND CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), WORK(*) DOUBLE PRECISION S(*) F95 INTERFACE SUBROUTINE HEEQUB(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: SCOND, AMAX SUBROUTINE HEEQUB_64(UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A COMPLEX(8), DIMENSION(:) :: WORK REAL(8) :: SCOND, AMAX C INTERFACE #include <sunperf.h> void zheequb (char uplo, int n, doublecomplex *a, int lda, double *s, double *scond, double *amax, int *info); void zheequb_64 (char uplo, long n, doublecomplex *a, long lda, double *s, double *scond, double *amax, long *info); PURPOSE zheequb computes row and column scalings intended to equilibrate a Her- mitian 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 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) N is INTEGER The order of the matrix A. N >= 0. A (input) A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian 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 DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A. SCOND (output) SCOND is DOUBLE PRECISION 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 DOUBLE PRECISION 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 COMPLEX*16 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 zheequb(3P)