zpbcon (l)  Linux Man Pages
zpbcon: estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
Command to display zpbcon
manual in Linux: $ man l zpbcon
NAME
ZPBCON  estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
SYNOPSIS
 SUBROUTINE ZPBCON(

UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
RWORK, INFO )

CHARACTER
UPLO

INTEGER
INFO, KD, LDAB, N

DOUBLE
PRECISION ANORM, RCOND

DOUBLE
PRECISION RWORK( * )

COMPLEX*16
AB( LDAB, * ), WORK( * )
PURPOSE
ZPBCON estimates the reciprocal of the condition number (in the
1norm) 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))).
ARGUMENTS
 UPLO (input) CHARACTER*1

= aqUaq: Upper triangular factor stored in AB;
= aqLaq: Lower triangular factor stored in AB.
 N (input) INTEGER

The order of the matrix A. N >= 0.
 KD (input) INTEGER

The number of superdiagonals of the matrix A if UPLO = aqUaq,
or the number of subdiagonals if UPLO = aqLaq. KD >= 0.
 AB (input) 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 jth column of U or L is
stored in the jth column of the array AB as follows:
if UPLO =aqUaq, AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j;
if UPLO =aqLaq, AB(1+ij,j) = L(i,j) for j<=i<=min(n,j+kd).
 LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >= KD+1.
 ANORM (input) DOUBLE PRECISION

The 1norm (or infinitynorm) of the Hermitian band matrix A.
 RCOND (output) 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 1norm of inv(A) computed in this routine.
 WORK (workspace) COMPLEX*16 array, dimension (2*N)

 RWORK (workspace) DOUBLE PRECISION array, dimension (N)

 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
Pages related to zpbcon
 zpbcon (3)
 zpbequ (l)  computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the twonorm)
 zpbrfs (l)  improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution
 zpbstf (l)  computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A
 zpbsv (l)  computes the solution to a complex system of linear equations A * X = B,
 zpbsvx (l)  uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B,
 zpbtf2 (l)  computes the Cholesky factorization of a complex Hermitian positive definite band matrix A
 zpbtrf (l)  computes the Cholesky factorization of a complex Hermitian positive definite band matrix A