◆ ztbcon()

Condition number of a complex triangular band matrix

Purpose: This routine 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

[in]	norm	Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm. = 'I': Infinity-norm.
[in]	uplo	= 'U': A is upper triangular. = 'L': A is lower triangular.
[in]	diag	= 'N': A is non-unit triangular. = 'U': A is unit triangular. (Diagonal elements of ab[][] are not referenced and are assumed to be 1)
[in]	n	Order of the matrix A. (n >= 0) (If n = 0, returns rcond = 1)
[in]	kd	Number of super-diagonals or sub-diagonals of the triangular band matrix A. (kd >= 0)
[in]	ldab	Leading dimension of the two dimensional array ab[][]. (ldab >= kd + 1)
[in]	ab[][]	Array ab[lab][ldab] (lab >= n) n x n triangular band matrix A in kd+1 x n symmetric band matrix form. Upper or lower part is to be stored in accordance with uplo.
[out]	rcond	The reciprocal of the condition number of the matrix A, computed as rcond = 1/(norm(A) * norm(inv(A))).
[out]	work[]	Array work[lwork] (lwork >= 2*n) Work array.
[out]	rwork[]	Array rwork[lrwork] (lrwork >= n) Work array.
[out]	info	= 0: Successful exit = -1: The argument norm had an illegal value (norm != '1', 'O' nor 'I') = -2: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -3: The argument diag had an illegal value (diag != 'N' nor 'U') = -4: The argument n had an illegal value (n < 0) = -5: The argument kd had an illegal value (kd < 0) = -6: The argument ldab had an illegal value (ldab < kd+1)