NAME

dpbcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF

SYNOPSIS

SUBROUTINE DPBCON(
UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO )

void dpbcon(char uplo, long int n, long int kd, double ∗dab,
long int ldab, double anorm, double ∗drcond, long int ∗info)

CHARACTER UPLO

INTEGER INFO, KD, LDAB, N

DOUBLE PRECISION ANORM, RCOND

INTEGER IWORK( ∗ )

DOUBLE PRECISION AB( LDAB, ∗ ), WORK( ∗ )

PURPOSE

DPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T computed by DPBTRF. 
 
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 subdiagonals if UPLO = ’L’.  KD >= 0.

AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A = U∗∗T∗U or A = L∗L∗∗T 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) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the symmetric 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) computed in this routine.

WORK    (workspace) DOUBLE PRECISION array, dimension (3∗N)

IWORK   (workspace) INTEGER array, dimension (N)

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

Sun, Inc.  —  Last change: 20 Sep 1996