zheequb.f (3)  Linux Man Pages
NAME
zheequb.f 
SYNOPSIS
Functions/Subroutines
subroutine zheequb (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)
ZHEEQUB
Function/Subroutine Documentation
subroutine zheequb (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, double precisionSCOND, double precisionAMAX, complex*16, dimension( * )WORK, integerINFO)
ZHEEQUB
Purpose:

ZHEEQUB computes row and column scalings intended to equilibrate a Hermitian matrix A and reduce its condition number (with respect to the twonorm). 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.
Parameters:

UPLO
UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.
NN is INTEGER The order of the matrix A. N >= 0.
AA is COMPLEX*16 array, dimension (LDA,N) The NbyN Hermitian matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
LDALDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
SS is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.
SCONDSCOND is DOUBLE PRECISION If INFO = 0, S contains the ratio of the smallest S(i) to the largest S(i). If SCOND >= 0.1 and AMAX is neither too large nor too small, it is not worth scaling by S.
AMAXAMAX is DOUBLE PRECISION Absolute value of largest matrix element. If AMAX is very close to overflow or very close to underflow, the matrix should be scaled.
WORKWORK is COMPLEX*16 array, dimension (3*N)
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, the ith diagonal element is nonpositive.
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 April 2012
Definition at line 127 of file zheequb.f.
Author
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