spoequ

NAME

spoequ - 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 SPOEQU( N, A, LDA, SCALE, SCOND, AMAX, INFO)
  INTEGER N, LDA, INFO
  REAL SCOND, AMAX
  REAL A(LDA,*), SCALE(*)
 
  SUBROUTINE SPOEQU_64( N, A, LDA, SCALE, SCOND, AMAX, INFO)
  INTEGER*8 N, LDA, INFO
  REAL SCOND, AMAX
  REAL A(LDA,*), SCALE(*)

F95 INTERFACE

  SUBROUTINE POEQU( [N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
  INTEGER :: N, LDA, INFO
  REAL :: SCOND, AMAX
  REAL, DIMENSION(:) :: SCALE
  REAL, DIMENSION(:,:) :: A
 
  SUBROUTINE POEQU_64( [N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
  INTEGER(8) :: N, LDA, INFO
  REAL :: SCOND, AMAX
  REAL, DIMENSION(:) :: SCALE
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void spoequ(int n, float *a, int lda, float *scale, float *scond, float *amax, int *info);

void spoequ_64(long n, float *a, long lda, float *scale, float *scond, float *amax, long *info);

PURPOSE

spoequ computes row and column scalings intended to equilibrate a symmetric 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 condition number over all possible diagonal scalings.

ARGUMENTS

* N (input): The order of the matrix A. N >= 0.
* A (input): 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): The leading dimension of the array A. LDA >= max(1,N).
* SCALE (output): If INFO = 0, SCALE contains the scale factors for A.
* SCOND (output): If INFO = 0, SCALE contains the ratio of the smallest SCALE(i) to the largest SCALE(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by SCALE.
* AMAX (output): 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)