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.

Generated automatically by Doxygen for LAPACK from the source code.

Version 3.12.0 LAPACK