NAME
STBCON - estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
SYNOPSIS
- SUBROUTINE STBCON(
-
NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, IWORK, INFO )
- CHARACTER
-
DIAG, NORM, UPLO
- INTEGER
-
INFO, KD, LDAB, N
- REAL
-
RCOND
- INTEGER
-
IWORK( * )
- REAL
-
AB( LDAB, * ), WORK( * )
PURPOSE
STBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
ARGUMENTS
- NORM (input) CHARACTER*1
-
Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
- UPLO (input) CHARACTER*1
-
= 'U': A is upper triangular;
= 'L': A is lower triangular.
- DIAG (input) CHARACTER*1
-
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
- N (input) INTEGER
-
The order of the matrix A. N >= 0.
- KD (input) INTEGER
-
The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
- AB (input) REAL array, dimension (LDAB,N)
-
The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
- LDAB (input) INTEGER
-
The leading dimension of the array AB. LDAB >= KD+1.
- RCOND (output) REAL
-
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
- 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