zppequ
zppequ - 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)
SUBROUTINE ZPPEQU( UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*)
INTEGER N, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)
SUBROUTINE ZPPEQU_64( UPLO, N, A, SCALE, SCOND, AMAX, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(*)
INTEGER*8 N, INFO
DOUBLE PRECISION SCOND, AMAX
DOUBLE PRECISION SCALE(*)
SUBROUTINE PPEQU( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A
INTEGER :: N, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
SUBROUTINE PPEQU_64( UPLO, [N], A, SCALE, SCOND, AMAX, [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: A
INTEGER(8) :: N, INFO
REAL(8) :: SCOND, AMAX
REAL(8), DIMENSION(:) :: SCALE
#include <sunperf.h>
void zppequ(char uplo, int n, doublecomplex *a, double *scale, double *scond, double *amax, int *info);
void zppequ_64(char uplo, long n, doublecomplex *a, double *scale, double *scond, double *amax, long *info);
zppequ 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.
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* UPLO (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* A (input)
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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.
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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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