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# zpbcon

```
NAME
ZPBCON - estimate 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

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 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))).

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangular factor stored in AB;
= 'L':  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
= 'U', or the number of sub-diagonals if UPLO = 'L'.
KD >= 0.

AB      (input) COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky fac-
torization 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
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    (input) INTEGER
The leading dimension of the array AB.  LDAB >=
KD+1.

ANORM   (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) 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 1-norm of inv(A) com-
puted 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 i-th argument had an illegal
value
```