stbcon.f −

**Functions/Subroutines**

subroutine **stbcon** (NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, IWORK, INFO)

STBCON

**subroutine stbcon (characterNORM, characterUPLO, characterDIAG, integerN, integerKD, real, dimension( ldab, * )AB, integerLDAB, realRCOND, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
STBCON**

**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)) ).

**Parameters:**

*NORM*

NORM is 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*

UPLO is CHARACTER*1

= ’U’: A is upper triangular;

= ’L’: A is lower triangular.

*DIAG*

DIAG is CHARACTER*1

= ’N’: A is non-unit triangular;

= ’U’: A is unit triangular.

*N*

N is INTEGER

The order of the matrix A. N >= 0.

*KD*

KD is INTEGER

The number of superdiagonals or subdiagonals of the

triangular band matrix A. KD >= 0.

*AB*

AB is 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*

LDAB is INTEGER

The leading dimension of the array AB. LDAB >= KD+1.

*RCOND*

RCOND is REAL

The reciprocal of the condition number of the matrix A,

computed as RCOND = 1/(norm(A) * norm(inv(A))).

*WORK*

WORK is REAL array, dimension (3*N)

*IWORK*

IWORK is INTEGER array, dimension (N)

*INFO*

INFO is INTEGER

= 0: successful exit

< 0: if INFO = -i, the i-th argument had an illegal value

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 143 of file stbcon.f.

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