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

NAME

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

SYNOPSIS

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

  SUBROUTINE SPBEQU_64( UPLO, N, NDIAG, A, LDA, SCALE, SCOND, AMAX, 
 *      INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, NDIAG, LDA, INFO
  REAL SCOND, AMAX
  REAL A(LDA,*), SCALE(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

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

void spbequ_64(char uplo, long n, long ndiag, float *a, long lda, float *scale, float *scond, float *amax, long *info);

PURPOSE

spbequ computes row and column scalings intended to equilibrate a symmetric 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)
  

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

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

• 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 symmetric 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)
  

   = 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.