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SUBROUTINE <a name="DSBGVX.1"></a><a href="dsbgvx.f.html#DSBGVX.1">DSBGVX</a>( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
$ LDZ, WORK, IWORK, IFAIL, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, KA, KB, LDAB, LDBB, LDQ, LDZ, M,
$ N
DOUBLE PRECISION ABSTOL, VL, VU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IFAIL( * ), IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
$ W( * ), WORK( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DSBGVX.24"></a><a href="dsbgvx.f.html#DSBGVX.1">DSBGVX</a> computes selected eigenvalues, and optionally, eigenvectors
</span><span class="comment">*</span><span class="comment"> of a real generalized symmetric-definite banded eigenproblem, of
</span><span class="comment">*</span><span class="comment"> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
</span><span class="comment">*</span><span class="comment"> and banded, and B is also positive definite. Eigenvalues and
</span><span class="comment">*</span><span class="comment"> eigenvectors can be selected by specifying either all eigenvalues,
</span><span class="comment">*</span><span class="comment"> a range of values or a range of indices for the desired eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RANGE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'A': all eigenvalues will be found.
</span><span class="comment">*</span><span class="comment"> = 'V': all eigenvalues in the half-open interval (VL,VU]
</span><span class="comment">*</span><span class="comment"> will be found.
</span><span class="comment">*</span><span class="comment"> = 'I': the IL-th through IU-th eigenvalues will be found.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangles of A and B are stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangles of A and B are stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals of the matrix A if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> KB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of superdiagonals of the matrix B if UPLO = 'U',
</span><span class="comment">*</span><span class="comment"> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment"> matrix A, stored in the first ka+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of A is stored in the j-th column of the array AB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the contents of AB are destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= KA+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric band
</span><span class="comment">*</span><span class="comment"> matrix B, stored in the first kb+1 rows of the array. The
</span><span class="comment">*</span><span class="comment"> j-th column of B is stored in the j-th column of the array BB
</span><span class="comment">*</span><span class="comment"> as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the factor S from the split Cholesky factorization
</span><span class="comment">*</span><span class="comment"> B = S**T*S, as returned by <a name="DPBSTF.81"></a><a href="dpbstf.f.html#DPBSTF.1">DPBSTF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDBB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array BB. LDBB >= KB+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (output) DOUBLE PRECISION array, dimension (LDQ, N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', the n-by-n matrix used in the reduction of
</span><span class="comment">*</span><span class="comment"> A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
</span><span class="comment">*</span><span class="comment"> and consequently C to tridiagonal form.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', the array Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. If JOBZ = 'N',
</span><span class="comment">*</span><span class="comment"> LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VL (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> VU (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> If RANGE='V', the lower and upper bounds of the interval to
</span><span class="comment">*</span><span class="comment"> be searched for eigenvalues. VL < VU.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'I'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IL (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> If RANGE='I', the indices (in ascending order) of the
</span><span class="comment">*</span><span class="comment"> smallest and largest eigenvalues to be returned.
</span><span class="comment">*</span><span class="comment"> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'V'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL (input) DOUBLE PRECISION
</span><span class="comment">*</span><span class="comment"> The absolute error tolerance for the eigenvalues.
</span><span class="comment">*</span><span class="comment"> An approximate eigenvalue is accepted as converged
</span><span class="comment">*</span><span class="comment"> when it is determined to lie in an interval [a,b]
</span><span class="comment">*</span><span class="comment"> of width less than or equal to
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL + EPS * max( |a|,|b| ) ,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where EPS is the machine precision. If ABSTOL is less than
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