NAME

cpbcon - 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 CPBTRF

SYNOPSIS

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

CHARACTER UPLO

INTEGER INFO, KD, LDAB, N

REAL ANORM, RCOND

REAL RWORK( ∗ )

COMPLEX AB( LDAB, ∗ ), WORK( ∗ )

#include <sunperf.h>

void cpbcon(char uplo, int n, int kd, complex ∗cab, int ldab, float anorm, float ∗srcond, int ∗info);

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))).
 

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

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

RCOND (output) 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 (workspace) COMPLEX array, dimension (2∗N)

RWORK (workspace) REAL array, dimension (N)

INFO (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunOS 5.0  —  Last change: 10 Dec 1998