Functions/Subroutines
subroutine	dspevx (JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO)
	DSPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Function/Subroutine Documentation

subroutine dspevx	(	character	JOBZ,
		character	RANGE,
		character	UPLO,
		integer	N,
		double precision, dimension( * )	AP,
		double precision	VL,
		double precision	VU,
		integer	IL,
		integer	IU,
		double precision	ABSTOL,
		integer	M,
		double precision, dimension( * )	W,
		double precision, dimension( ldz, * )	Z,
		integer	LDZ,
		double precision, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer, dimension( * )	IFAIL,
		integer	INFO
	)

DSPEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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Purpose:

 DSPEVX computes selected eigenvalues and, optionally, eigenvectors
 of a real symmetric matrix A in packed storage.  Eigenvalues/vectors
 can be selected by specifying either a range of values or a range of
 indices for the desired eigenvalues.

Parameters:

[in]	JOBZ	JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
[in]	RANGE	RANGE is CHARACTER*1 = 'A': all eigenvalues will be found; = 'V': all eigenvalues in the half-open interval (VL,VU] will be found; = 'I': the IL-th through IU-th eigenvalues will be found.
[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	AP	AP is DOUBLE PRECISION array, dimension (N(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)(2n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.
[in]	VL	VL is DOUBLE PRECISION
[in]	VU	VU is DOUBLE PRECISION If RANGE='V', the lower and upper bounds of the interval to be searched for eigenvalues. VL < VU. Not referenced if RANGE = 'A' or 'I'.
[in]	IL	IL is INTEGER
[in]	IU	IU is INTEGER If RANGE='I', the indices (in ascending order) of the smallest and largest eigenvalues to be returned. 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if RANGE = 'A' or 'V'.
[in]	ABSTOL	ABSTOL is DOUBLE PRECISION The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to ABSTOL + EPS * max( \|a\|,\|b\| ) , where EPS is the machine precision. If ABSTOL is less than or equal to zero, then EPS\|T\| will be used in its place, where \|T\| is the 1-norm of the tridiagonal matrix obtained by reducing AP to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold 2DLAMCH('S'), not zero. If this routine returns with INFO>0, indicating that some eigenvectors did not converge, try setting ABSTOL to 2*DLAMCH('S'). See "Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK Working Note #3.
[out]	M	M is INTEGER The total number of eigenvalues found. 0 <= M <= N. If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
[out]	W	W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the selected eigenvalues in ascending order.
[out]	Z	Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of Z holding the eigenvector associated with W(i). If an eigenvector fails to converge, then that column of Z contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in IFAIL. If JOBZ = 'N', then Z is not referenced. Note: the user must ensure that at least max(1,M) columns are supplied in the array Z; if RANGE = 'V', the exact value of M is not known in advance and an upper bound must be used.
[in]	LDZ	LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
[out]	WORK	WORK is DOUBLE PRECISION array, dimension (8*N)
[out]	IWORK	IWORK is INTEGER array, dimension (5*N)
[out]	IFAIL	IFAIL is INTEGER array, dimension (N) If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL are zero. If INFO > 0, then IFAIL contains the indices of the eigenvectors that failed to converge. If JOBZ = 'N', then IFAIL is not referenced.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, then i eigenvectors failed to converge. Their indices are stored in array IFAIL.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: November 2011

Definition at line 226 of file dspevx.f.

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