◆ zstein()

void zstein	(	int	n,
		double	d[],
		double	e[],
		int	m,
		double	w[],
		int	iblock[],
		int	isplit[],
		int	ldz,
		doublecomplex	z[],
		double	work[],
		int	iwork[],
		int	ifail[],
		int *	info
	)

Eigenvectors of symmetric tridiagonal matrix to which a Hermitian matrix was reduced (Inverse iteration method)

Purpose: This routine computes the eigenvectors of a real symmetric tridiagonal matrix T to which a Hermitian matrix was reduced, corresponding to specified eigenvalues, using inverse iteration.
The maximum number of iterations allowed for each eigenvector is specified by an internal parameter maxits (currently set to 5).
Although the eigenvectors are real, they are stored in a complex array, which may be passed to zunmtr or zupmtr for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form.

Parameters

[in]	n	Order of the tridiagonal matrix. (n >= 0) (If n = 0, returns without computation)
[in]	d[]	Array d[ld] (ld >= n) The n diagonal elements of the tridiagonal matrix T.
[in]	e[]	Array e[le] (le >= n) The (n - 1) subdiagonal elements of the tridiagonal matrix T.
[in]	m	The number of eigenvectors to be found. (0 <= m <= n)
[in]	w[]	Array w[lw] (lw >= n) The first m elements of w[] contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array w from dstebz with order = 'B' is expected here.)
[in]	iblock[]	Array iblock[liblock] (liblock >= n) The submatrix indices associated with the corresponding eigenvalues in w[]. iblock[i] = 1 if eigenvalue w[i] belongs to the first submatrix from the top, = 2 if w[i] belongs to the second submatrix, etc. (The output array iblock from dstebz is expected here.)
[in]	isplit[]	Array isplit[lisplit] (lisplit >= n) The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to isplit[0], the second of rows/columns isplit[0] + 1 through isplit[1], etc. (The output array isplit from dstebz is expected here.)
[in]	ldz	Leading dimension of the two dimensional array z[][]. (ldz >= max(1, n))
[out]	z[][]	Array z[lz][ldz] (lz >= max(1, m)) The computed eigenvectors. The eigenvector associated with the eigenvalue w[i] is stored in the i-th row of z. Any vector which fails to converge is set to its current iterate after maxits iterations. The imaginary parts of the eigenvectors are set to zero.
[out]	work[]	Array work[lwork] (lwork >= 5*n) Work array.
[out]	iwork[]	Array iwork[liwork] (liwork >= n) Integer work array.
[out]	ifail[]	Array ifail[lifail] (lifail >= m) On normal exit, all elements of ifail are zero. If one or more eigenvectors fail to converge after maxits iterations, then their indices are stored in array ifail.
[out]	info	= 0: Successful exit. = -1: The argument n had an illegal value. (n < 0) = -4: The argument m had an illegal value. (m < 0 or m > n) = -5: The argument w had an illegal value. (an element not in ascending order) = -6: The argument iblock had an illegal value. (an element not in ascending order) = -8: The argument ldz had an illegal value. (ldz too small) = i > 0: Eigenvectors failed to converge in maxits iterations. Their indices are stored in array ifail.

Reference: LAPACK