zpoequb.f - Online Linux Manual Page

Section : 3
Updated : Tue Nov 14 2017
Source : Version 3.8.0
Note : LAPACK
NAMEzpoequb.f
SYNOPSIS
Functions/Subroutinessubroutine zpoequb (N, A, LDA, S, SCOND, AMAX, INFO)
ZPOEQUB
Function/Subroutine Documentation
subroutine zpoequb (integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) S, double precision SCOND, double precision AMAX, integer INFO)ZPOEQUB Purpose: ZPOEQUB computes row and column scalings intended to equilibrate a Hermitian 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. This routine differs from ZPOEQU by restricting the scaling factors to a power of the radix. Barring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled diagonal entries are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).Parameters: N N is INTEGER The order of the matrix A. N >= 0.
A A is COMPLEX*16 array, dimension (LDA,N) The N-by-N Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.
LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
S S is DOUBLE PRECISION array, dimension (N) If INFO = 0, S contains the scale factors for A.
SCOND SCOND 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.
AMAX AMAX 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.
INFO INFO is INTEGER = 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.Author: Univ​. of Tennessee Univ​. of California Berkeley Univ​. of Colorado Denver NAG Ltd​. Date: December 2016 Definition at line 121 of file zpoequb​.f​.
AuthorGenerated automatically by Doxygen for LAPACK from the source code​. 0
Johanes Gumabo
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