Contents

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

NAME

     dpoequ - compute row and column scalings intended to equili-
     brate  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  equili-
     brate  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  con-
     dition 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 smal-
               lest  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 under-
               flow, the matrix should be scaled.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value
               > 0:  if INFO = i, the i-th  diagonal  element  is
               nonpositive.