◆ zgtcon()

Condition number of a complex tridiagonal matrix

Purpose: This routine estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by zgttrf.

An estimate is obtained for norm(inv(A)), and 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]	n	Order of the matrix A. (n >= 0) (If n = 0, returns rcond = 1)
[in]	dl[]	Array dl[ldl] (ldl >= n - 1) n-1 multipliers that define the matrix L from the LU factorization of A as computed by zgttrf.
[in]	d[]	Array d[ld] (ld >= n) n diagonal elements of the upper triangular matrix U from the LU factorization of A.
[in]	du[]	Array du[ldu] (ldu >= n - 1) n-1 elements of the first super-diagonal of U.
[in]	du2[]	Array du2[ldu2] (ldu2 >= n - 2) n-2 elements of the second super-diagonal of U.
[out]	ipiv[]	Array ipiv[lipiv] (lipiv >= n) Pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row ipiv[i-1]. ipiv[i-1] will always be either i or i+1; ipiv[i-1] = i indicates a row interchange was not required.
[in]	anorm	norm = '1' or 'O': The 1-norm of the original matrix A. (anorm >= 0) norm = 'I': The infinity-norm of the original matrix A. (anorm >= 0)
[out]	rcond	The reciprocal of the condition number of the matrix A, computed as rcond = 1/(anorm * ainvnm), where ainvnm is an estimate of the 1-norm of inv(A) computed in this routine.
[out]	work[]	Array work[lwork] (lwork >= 2*n) Work array.
[out]	info	= 0: Successful exit = -1: The argument norm had an illegal value (norm != '1', 'O' nor 'I') = -2: The argument n had an illegal value (n < 0) = -8: The argument anorm had an illegal value (anorm < 0)