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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 of and is the order of and .
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') triangle of 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, the contents of AB are destroyed.

BB
(input/output) REAL or COMPLEX array, shape with (BB,1) and (BB,2) , where is the number of subdiagonals or superdiagonals in the band 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 BB so that the column of is stored in the column of as follows: On exit, the factor from the split Cholesky factorization .

W
(output) REAL array, shape with .
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 square array, shape with (Z,1) .
The first M columns of Z contain the orthonormal eigenvectors corresponding to the selected eigenvalues, with the i column of Z containing the eigenvector associated with the eigenvalue in W . The eigenvectors are normalized so that . 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) .
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 .
If Z is present, the matrix used in the reduction of to tridiagonal form.

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_SBGVX_EXAMPLE) Up: Generalized Symmetric Eigenvalue Problems Previous: Purpose   Contents   Index
Susan Blackford 2001-08-19