zhbgvx.f.html

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      SUBROUTINE <a name="ZHBGVX.1"></a><a href="zhbgvx.f.html#ZHBGVX.1">ZHBGVX</a>( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
     $                   LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
     $                   LDZ, WORK, RWORK, 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   RWORK( * ), W( * )
      COMPLEX*16         AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
     $                   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="ZHBGVX.25"></a><a href="zhbgvx.f.html#ZHBGVX.1">ZHBGVX</a> computes all the eigenvalues, and optionally, the eigenvectors
</span><span class="comment">*</span><span class="comment">  of a complex generalized Hermitian-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 Hermitian
</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 &gt;= 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 &gt;= 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 &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AB      (input/output) COMPLEX*16 array, dimension (LDAB, N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the Hermitian 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)&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j&lt;=i&lt;=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 &gt;= KA+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BB      (input/output) COMPLEX*16 array, dimension (LDBB, N)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the Hermitian 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(kb+1+i-j,j) = B(i,j) for max(1,j-kb)&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j&lt;=i&lt;=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**H*S, as returned by <a name="ZPBSTF.82"></a><a href="zpbstf.f.html#ZPBSTF.1">ZPBSTF</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 &gt;= KB+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q       (output) COMPLEX*16 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 &gt;= 1. If JOBZ = 'V', LDQ &gt;= 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 &lt; 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 &lt;= IL &lt;= IU &lt;= N, if N &gt; 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
</span><span class="comment">*</span><span class="comment">          or equal to zero, then  EPS*|T|  will be used in its place,
</span><span class="comment">*</span><span class="comment">          where |T| is the 1-norm of the tridiagonal matrix obtained
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