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

NAME

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

SYNOPSIS

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

  SUBROUTINE CPPEQU_64( UPLO, N, A, SCALE, SCOND, AMAX, INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(*)
  INTEGER*8 N, INFO
  REAL SCOND, AMAX
  REAL SCALE(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void cppequ_64(char uplo, long n, complex *a, float *scale, float *scond, float *amax, long *info);

PURPOSE

cppequ computes row and column scalings intended to equilibrate a Hermitian 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 Hermitian 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.