DTBCON(3f)

NAME
DTBCON - the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

SUBROUTINE DTBCON(
    NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, IWORK, INFO )

CHARACTER
    DIAG, NORM, UPLO

INTEGER
    INFO, KD, LDAB, N

DOUBLE
    PRECISION RCOND

INTEGER
    IWORK( * )

DOUBLE
    PRECISION AB( LDAB, * ), WORK( * )

PURPOSE
DTBCON 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) DOUBLE PRECISION 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) DOUBLE PRECISION
    The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK    (workspace) DOUBLE PRECISION 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