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 )
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 >=
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 ille
gal value
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