SPBCON(3)
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 SPBTRF
SYNOPSIS
- SUBROUTINE SPBCON(
-
UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
IWORK, INFO )
-
CHARACTER
UPLO
-
INTEGER
INFO, KD, LDAB, N
-
REAL
ANORM, RCOND
-
INTEGER
IWORK( * )
-
REAL
AB( LDAB, * ), WORK( * )
PURPOSE
SPBCON 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 SPBTRF.
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) REAL 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) REAL
-
The 1-norm (or infinity-norm) of the symmetric 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) REAL 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