dpoequ
dpoequ - compute row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm)
SUBROUTINE DPOEQU( N, A, LDA, SCALE, SCOND, AMAX, INFO)
INTEGER N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
SUBROUTINE DPOEQU_64( N, A, LDA, SCALE, SCOND, AMAX, INFO)
INTEGER*8 N, LDA, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION A(LDA,*), SCALE(*)
SUBROUTINE POEQU( [N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
INTEGER :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE POEQU_64( [N], A, [LDA], SCALE, SCOND, AMAX, [INFO])
INTEGER(8) :: N, LDA, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
REAL(8), DIMENSION(:,:) :: A
#include <sunperf.h>
void dpoequ(int n, double *a, int lda, double *scale, double *scond, double *amax, int *info);
void dpoequ_64(long n, double *a, long lda, double *scale, double *scond, double *amax, long *info);
dpoequ computes row and column scalings intended to equilibrate a
symmetric positive definite 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.
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* N (input)
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The order of the matrix A. N >= 0.
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* A (input)
-
The N-by-N symmetric positive definite matrix whose scaling
factors are to be computed. Only the diagonal elements of A
are referenced.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,N).
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* SCALE (output)
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If INFO = 0, SCALE contains the scale factors for A.
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* SCOND (output)
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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.
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* AMAX (output)
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Absolute value of largest matrix element. If AMAX is very
close to overflow or very close to underflow, the matrix
should be scaled.
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* INFO (output)
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