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Arguments

A
(input/output) REAL or COMPLEX square array, shape .
On entry, the matrix .
If UPLO 'U', the upper triangular part of A contains the upper triangular part of the matrix . If UPLO 'L', the lower triangular part of A contains the lower triangular part of the matrix .
On exit:
If JOBZ = 'V', then the first M columns of A contain the orthonormal eigenvectors of the matrix corresponding to the selected eigenvalues, with the column of A containing the eigenvector associated with the eigenvalue in .
If JOBZ = 'N', the upper triangle (if UPLO = 'U') or the lower triangle (if UPLO = 'L') of A, including the diagonal, is destroyed.

W
(output) REAL array, shape with .
The first M elements contain the selected eigenvalues in ascending order.

JOBZ
Optional (input) CHARACTER(LEN=1).

Default value: 'N'.

UPLO
Optional (input) CHARACTER(LEN=1).

Default value: 'U'.

VL,VU
Optional (input) REAL.
The lower and upper bounds of the interval to be searched for eigenvalues. VL VU.
Default values: VL -HUGE(wp) and VU HUGE(wp), where wp ::= KIND(1.0) KIND(1.0D0).
Note: Neither VL nor VU may be present if IL and/or IU is present.

IL,IU
Optional (input) INTEGER.
The indices of the smallest and largest eigenvalues to be returned. The through eigenvalues will be found. .
Default values: IL and IU (A,1).
Note: Neither IL nor IU may be present if VL and/or VU is present.
Note: All eigenvalues are calculated if none of the arguments VL, VU, IL and IU are present.

M
Optional (output) INTEGER.
The total number of eigenvalues found. .
Note: If and are present then .

ISUPPZ
Optional (output) INTEGER array, shape with size(ISUPPZ) ,M).
The support of the eigenvectors in A, i.e., the indices indicating the nonzero elements. The eigenvector is nonzero only in elements ISUPPZ through ISUPPZ.
Note: ISUPPZ must be absent if JOBZ = 'N'.

ABSTOL
Optional (input) REAL.
The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval of width less than or equal to

where wp is the working precision. If ABSTOL , then will be used in its place, where is the norm of the tridiagonal matrix obtained by reducing to tridiagonal form.
Default value: .
Note: Eigenvalues are computed most accurately if ABSTOL is set to LA_LAMCH( 1.0_wp, 'Safe minimum'), not zero.

INFO
Optional (output) INTEGER

If INFO is not present and an error occurs, then the program is terminated with an error message.
References: [1] and [17,9,20].

Next: Example (from Program LA_SYEVR_EXAMPLE) Up: Standard Symmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19