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zpbcon.f(3) LAPACK zpbcon.f(3)

NAME

zpbcon.f

SYNOPSIS

Functions/Subroutines


subroutine zpbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO)
ZPBCON

Function/Subroutine Documentation

subroutine zpbcon (character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)

ZPBCON

Purpose:


ZPBCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by
ZPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).

Parameters:

UPLO


UPLO is CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.

N


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

KD


KD is INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0.

AB


AB is COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A, stored in the
first KD+1 rows of the array. The j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).

LDAB


LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

ANORM


ANORM is DOUBLE PRECISION
The 1-norm (or infinity-norm) of the Hermitian band matrix A.

RCOND


RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK


WORK is COMPLEX*16 array, dimension (2*N)

RWORK


RWORK is DOUBLE PRECISION array, dimension (N)

INFO


INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 135 of file zpbcon.f.

Author

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Tue Nov 14 2017 Version 3.8.0