zpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm
SUBROUTINE ZPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND DOUBLE COMPLEX A(LDA,*) DOUBLE PRECISION S(*) SUBROUTINE ZPOEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER*8 INFO, LDA, N DOUBLE PRECISION AMAX, SCOND DOUBLE COMPLEX A(LDA,*) DOUBLE PRECISION S(*) F95 INTERFACE SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER :: N, LDA, INFO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A REAL(8) :: SCOND, AMAX SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER(8) :: N, LDA, INFO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A REAL(8) :: SCOND, AMAX C INTERFACE #include <sunperf.h> void zpoequb (int n, doublecomplex *a, int lda, double *s, double *scond, double *amax, int *info); void zpoequb_64 (long n, doublecomplex *a, long lda, double *s, double *scond, double *amax, long *info);
Oracle Solaris Studio Performance Library zpoequb(3P) NAME zpoequb - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number with respect to the two-norm SYNOPSIS SUBROUTINE ZPOEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER INFO, LDA, N DOUBLE PRECISION AMAX, SCOND DOUBLE COMPLEX A(LDA,*) DOUBLE PRECISION S(*) SUBROUTINE ZPOEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER*8 INFO, LDA, N DOUBLE PRECISION AMAX, SCOND DOUBLE COMPLEX A(LDA,*) DOUBLE PRECISION S(*) F95 INTERFACE SUBROUTINE POEQUB(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER :: N, LDA, INFO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A REAL(8) :: SCOND, AMAX SUBROUTINE POEQUB_64(N, A, LDA, S, SCOND, AMAX, INFO) INTEGER(8) :: N, LDA, INFO REAL(8), DIMENSION(:) :: S COMPLEX(8), DIMENSION(:,:) :: A REAL(8) :: SCOND, AMAX C INTERFACE #include <sunperf.h> void zpoequb (int n, doublecomplex *a, int lda, double *s, double *scond, double *amax, int *info); void zpoequb_64 (long n, doublecomplex *a, long lda, double *s, double *scond, double *amax, long *info); PURPOSE zpoequb computes row and column scalings intended to equilibrate a sym- metric positive definite 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 condi- tion number over all possible diagonal scalings. ARGUMENTS 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 symmetric positive definite 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. 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 zpoequb(3P)