cpoequb.f man page

cpoequb.f

Synopsis

Functions/Subroutines

subroutine cpoequb (N, A, LDA, S, SCOND, AMAX, INFO)
CPOEQUB

Function/Subroutine Documentation

subroutine cpoequb (integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) S, real SCOND, real AMAX, integer INFO)

CPOEQUB

Purpose:

CPOEQUB 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 CPOEQU 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
Parameters:

N

N is INTEGER
The order of the matrix A.  N >= 0.

A

A is COMPLEX 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 REAL array, dimension (N)
If INFO = 0, S contains the scale factors for A.

SCOND

SCOND is REAL
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 REAL
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 cpoequb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page cpoequb(3) is an alias of cpoequb.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK