• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

dpoequ - 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 DPOEQU( N, A, LDA, SCALE, SCOND, AMAX, INFO)
  INTEGER N, LDA, INFO
  DOUBLE PRECISION SCOND, AMAX
  DOUBLE PRECISION A(LDA,*), SCALE(*)

  SUBROUTINE DPOEQU_64( N, A, LDA, SCALE, SCOND, AMAX, INFO)
  INTEGER*8 N, LDA, INFO
  DOUBLE PRECISION SCOND, AMAX
  DOUBLE PRECISION A(LDA,*), SCALE(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void dpoequ(int n, double *a, int lda, double *scale, double *scond, double *amax, int *info);

void dpoequ_64(long n, double *a, long lda, double *scale, double *scond, double *amax, long *info);

PURPOSE

dpoequ 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)
  

   = 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.