cpbcon-f(3)

cpbcon.f –

Synopsis

Functions/Subroutines

subroutine cpbcon (UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO)
CPBCON

Function/Subroutine Documentation

subroutine cpbcon (characterUPLO, integerN, integerKD, complex, dimension( ldab, * )AB, integerLDAB, realANORM, realRCOND, complex, dimension( * )WORK, real, dimension( * )RWORK, integerINFO)

CPBCON

Purpose:

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

 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 is COMPLEX 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 REAL
 The 1-norm (or infinity-norm) of the Hermitian band matrix A.

RCOND

 RCOND is REAL
 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 array, dimension (2*N)

RWORK

 RWORK is REAL 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:

November 2011

Definition at line 133 of file cpbcon.f.

Author

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