zpbequ

NAME

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

SYNOPSIS

  SUBROUTINE ZPBEQU( UPLO, N, NDIAG, A, LDA, SCALE, SCOND, AMAX, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*)
  INTEGER N, NDIAG, LDA, INFO
  DOUBLE PRECISION SCOND, AMAX
  DOUBLE PRECISION SCALE(*)
 
  SUBROUTINE ZPBEQU_64( UPLO, N, NDIAG, A, LDA, SCALE, SCOND, AMAX, 
 *      INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(LDA,*)
  INTEGER*8 N, NDIAG, LDA, INFO
  DOUBLE PRECISION SCOND, AMAX
  DOUBLE PRECISION SCALE(*)

F95 INTERFACE

  SUBROUTINE PBEQU( UPLO, [N], NDIAG, A, [LDA], SCALE, SCOND, AMAX, 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INFO
  REAL(8) :: SCOND, AMAX
  REAL(8), DIMENSION(:) :: SCALE
 
  SUBROUTINE PBEQU_64( UPLO, [N], NDIAG, A, [LDA], SCALE, SCOND, AMAX, 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INFO
  REAL(8) :: SCOND, AMAX
  REAL(8), DIMENSION(:) :: SCALE

C INTERFACE

#include <sunperf.h>

void zpbequ(char uplo, int n, int ndiag, doublecomplex *a, int lda, double *scale, double *scond, double *amax, int *info);

void zpbequ_64(char uplo, long n, long ndiag, doublecomplex *a, long lda, double *scale, double *scond, double *amax, long *info);

PURPOSE

zpbequ computes row and column scalings intended to equilibrate a Hermitian positive definite band 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

* UPLO (input)
* N (input): The order of the matrix A. N >= 0.
* NDIAG (input): The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. NDIAG >= 0.
* A (input): The upper or lower triangle of the Hermitian band matrix A, stored in the first NDIAG+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
* LDA (input): The leading dimension of the array A. LDA >= NDIAG+1.
* 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)