- 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.