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

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

On exit, the contents of**AP**are destroyed. - BP
- (
*input/output*)**REAL**or**COMPLEX**array, shape with (**BP**) (**AP**).

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

On exit, the triangular factor or of the Cholesky factorization or , in the same storage format as . - W
- (
*output*)**REAL**array, shape with .

The eigenvalues in ascending order. - ITYPE
*Optional*(*input*)**INTEGER**.

Specifies the problem type to be solved:

Default value: 1.- UPLO
*Optional*(*input*)**CHARACTER(LEN=1)**.

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

The first**M**columns of**Z**contain the orthonormal eigenvectors corresponding to the selected eigenvalues, with the column of**Z**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**Z**contains the latest approximation to the eigenvector and the index of the eigenvector is returned in**IFAIL**.- 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: 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 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.