dpbequ(3P) Sun Performance Library dpbequ(3P)NAMEdpbequ - compute row and column scalings intended to equilibrate a sym‐
metric positive definite band matrix A and reduce its condition number
(with respect to the two-norm)
SYNOPSIS
SUBROUTINE DPBEQU(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
INTEGER N, KD, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
SUBROUTINE DPBEQU_64(UPLO, N, KD, A, LDA, SCALE, SCOND, AMAX,
INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, KD, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
F95 INTERFACE
SUBROUTINE PBEQU(UPLO, [N], KD, A, [LDA], SCALE, SCOND, AMAX,
[INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, KD, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE PBEQU_64(UPLO, [N], KD, A, [LDA], SCALE, SCOND, AMAX,
[INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, KD, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dpbequ(char uplo, int n, int kd, double *a, int lda, double
*scale, double *scond, double *amax, int *info);
void dpbequ_64(char uplo, long n, long kd, double *a, long lda, double
*scale, double *scond, double *amax, long *info);
PURPOSEdpbequ computes row and column scalings intended to equilibrate a sym‐
metric 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 condi‐
tion 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.
KD (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KD >= 0.
A (input) The upper or lower triangle of the symmetric band matrix A,
stored in the first KD+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 >= KD+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.
6 Mar 2009 dpbequ(3P)
