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# stbcon

```
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
```