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## Arguments

AB
(input/output) REAL or COMPLEX array, shape with (AB,1) and (AB,2) , where is the number of subdiagonals or superdiagonals in the band and is the order of .
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') triangle of matrix in band storage. The diagonals of are stored in the rows of AB so that the column of is stored in the column of as follows:

On exit, is overwritten by values generated during the reduction of to a tridiagonal matrix . If 'U' the first superdiagonal and the diagonal of are returned in rows and of . If 'L', the diagonal and first subdiagonal of are returned in the first two rows of .

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

Q
Optional (output) REAL or COMPLEX square array, shape with .
The unitary matrix used in the reduction to tridiagonal form. This is computed only if Z is 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.
References: [1] and [17,9,20,21].

Next: Example 1 (from Program Up: Standard Symmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19