SRC/zpbcon.f(3) Library Functions Manual SRC/zpbcon.f(3)

SRC/zpbcon.f


subroutine zpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info)
ZPBCON

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.

Definition at line 131 of file zpbcon.f.

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