NAME

STBCON - estimate 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

  —  LAPACK version 2.0  —  08 October 1994