- AP
- (
*input/output*)**REAL**or**COMPLEX**array, shape with , where is the order of .

On entry, the upper or lower triangle of matrix in packed storage. The elements are stored columnwise as follows:

On exit, is overwritten by values generated during the reduction of to a tridiagonal matrix . If 'U', the diagonal and first superdiagonal of T overwrite the corresponding diagonals of . If 'L', the diagonal and first subdiagonal of T overwrite the corresponding diagonals of . - W
- (
*output*)**REAL**array, shape with .

The eigenvalues in ascending order. - UPLO
*Optional*(*input*)**CHARACTER(LEN=1)**.

Default value: 'U'.- Z
*Optional*(*output*)**REAL**or**COMPLEX**array, shape with (**Z**,1) and (**Z**,2)**M**.

The first**M**columns of**Z**contain the orthonormal eigenvectors of the matrix corresponding to the selected eigenvalues, with the column of**Z**containing the eigenvector associated with the eigenvalue in**W**. 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**.

Note: The user must ensure that at least**M**columns are supplied in the array**Z**. When the exact value of**M**is not known in advance, an upper bound must be used. In all cases**M**.- 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**) .

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: If**Z**is present then**IFAIL**should also be present.- 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. 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.