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## Arguments

A
(input/output) REAL or COMPLEX square array, shape .
On entry, the matrix .
If 'U', the upper triangular part of contains the upper triangular part of matrix . If 'L', the lower triangular part of contains the lower triangular part of matrix .
On exit, if JOBZ = 'V', the first M columns of A contain the orthonormal eigenvectors corresponding to the selected eigenvalues, with the column of A holding the eigenvector associated with the eigenvalue in W .
The eigenvectors are normalized as follows: If an eigenvector fails to converge, then that column of A contains the latest approximation to the eigenvector and the index of the eigenvector is returned in IFAIL.
If JOBZ = 'N', then the upper triangle (if UPLO = 'U') or the lower triangle (if UPLO = 'L') of , including the diagonal, is destroyed.

B
(input/output) REAL or COMPLEX square array, shape with .
On entry, the matrix .
If 'U', the upper triangular part of contains the upper triangular part of matrix . If 'L', the lower triangular part of contains the lower triangular part of matrix .
On exit, the part of containing the matrix is overwritten by the triangular factor or of the Cholesky factorization or .

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

ITYPE
Optional (input) INTEGER.
Specifies the problem type to be solved: Default value: 1.

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 .

IFAIL
Optional (output) INTEGER array, shape with (IFAIL)  (A,1).
If INFO , the first M elements of IFAIL are zero.
If INFO , then IFAIL contains the indices of the eigenvectors that failed to converge. Note: IFAIL should be present if JOBZ = 'V'.

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 the generalized eigenvalue problem to tridiagonal form. Eigenvalues will be computed most accurately when ABSTOL is set to twice the underflow threshold , not zero.
Default value: .
Note: If this routine returns with , then some eigenvectors did not converge. Try setting ABSTOL to .

INFO
Optional (output) INTEGER. If INFO is not present and an error occurs, then the program is terminated with an error message.
References:  and [17,9,20,21].     Next: Example (from Program LA_SYGVX_EXAMPLE) Up: Generalized Symmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19