Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3 - estimates the reciprocal of the condition number of a triangular band matrix A,
in either the 1-norm or the infinity-norm

```

#### SYNOPSIS

```       SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK, INFO )

CHARACTER      DIAG, NORM, UPLO

INTEGER        INFO, KD, LDAB, N

REAL           RCOND

REAL           RWORK( * )

COMPLEX        AB( LDAB, * ), WORK( * )

```

#### PURPOSE

```       CTBCON 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) COMPLEX 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) COMPLEX array, dimension (2*N)

RWORK   (workspace) REAL array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

LAPACK routine (version 3.2)               April 2011                            CTBCON(3lapack)
```