NAME

sppequ - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage and reduce its condition number (with respect to the two-norm)

SYNOPSIS

  SUBROUTINE SPPEQU( UPLO, N, A, SCALE, SCOND, AMAX, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, INFO
  REAL SCOND, AMAX
  REAL A(*), SCALE(*)

  SUBROUTINE SPPEQU_64( UPLO, N, A, SCALE, SCOND, AMAX, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INFO
  REAL SCOND, AMAX
  REAL A(*), SCALE(*)

F95 INTERFACE

  SUBROUTINE PPEQU( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, INFO
  REAL :: SCOND, AMAX
  REAL, DIMENSION(:) :: A, SCALE

  SUBROUTINE PPEQU_64( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, INFO
  REAL :: SCOND, AMAX
  REAL, DIMENSION(:) :: A, SCALE

C INTERFACE

#include <sunperf.h>

void sppequ(char uplo, int n, float *a, float *scale, float *scond, float *amax, int *info);

void sppequ_64(char uplo, long n, float *a, float *scale, float *scond, float *amax, long *info);

PURPOSE

sppequ computes row and column scalings intended to equilibrate a symmetric positive definite matrix A in packed storage 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)

 = 'U':  Upper triangle of A is stored;

 = 'L':  Lower triangle of A is stored.

N (input)
The order of the matrix A. N > = 0.
A (input)
The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j < =i < =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.