SYNOPSIS

SUBROUTINE ZTBCON(

NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK, INFO )

    

CHARACTER DIAG, NORM, UPLO

    

INTEGER INFO, KD, LDAB, N

    

DOUBLE PRECISION RCOND

    

DOUBLE PRECISION RWORK( * )

    

COMPLEX*16 AB( LDAB, * ), WORK( * )

PURPOSE

ZTBCON 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*16 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) COMPLEX*16 array, dimension (2*N)

RWORK (workspace) DOUBLE PRECISION array, dimension (N)

INFO (output) INTEGER

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