cheev.f.html

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      SUBROUTINE <a name="CHEEV.1"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a>( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
     $                  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, UPLO
      INTEGER            INFO, LDA, LWORK, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               RWORK( * ), W( * )
      COMPLEX            A( LDA, * ), WORK( * )
<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="CHEEV.20"></a><a href="cheev.f.html#CHEEV.1">CHEEV</a> computes all eigenvalues and, optionally, eigenvectors of a
</span><span class="comment">*</span><span class="comment">  complex Hermitian matrix A.
</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">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is 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 matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment">          On entry, the Hermitian matrix A.  If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N upper triangular part of A contains the
</span><span class="comment">*</span><span class="comment">          upper triangular part of the matrix A.  If UPLO = 'L',
</span><span class="comment">*</span><span class="comment">          the leading N-by-N lower triangular part of A contains
</span><span class="comment">*</span><span class="comment">          the lower triangular part of the matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
</span><span class="comment">*</span><span class="comment">          orthonormal eigenvectors of the matrix A.
</span><span class="comment">*</span><span class="comment">          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
</span><span class="comment">*</span><span class="comment">          or the upper triangle (if UPLO='U') of A, including the
</span><span class="comment">*</span><span class="comment">          diagonal, is destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  W       (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The length of the array WORK.  LWORK &gt;= max(1,2*N-1).
</span><span class="comment">*</span><span class="comment">          For optimal efficiency, LWORK &gt;= (NB+1)*N,
</span><span class="comment">*</span><span class="comment">          where NB is the blocksize for <a name="CHETRD.61"></a><a href="chetrd.f.html#CHETRD.1">CHETRD</a> returned by <a name="ILAENV.61"></a><a href="hfy-index.html#ILAENV">ILAENV</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment">          only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment">          this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment">          message related to LWORK is issued by <a name="XERBLA.66"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (max(1, 3*N-2))
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, the algorithm failed to converge; i
</span><span class="comment">*</span><span class="comment">                off-diagonal elements of an intermediate tridiagonal
</span><span class="comment">*</span><span class="comment">                form did not converge to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
      COMPLEX            CONE
      PARAMETER          ( CONE = ( 1.0E0, 0.0E0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LOWER, LQUERY, WANTZ
      INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
     $                   LLWORK, LWKOPT, NB
      REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
     $                   SMLNUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.94"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      REAL               <a name="CLANHE.95"></a><a href="clanhe.f.html#CLANHE.1">CLANHE</a>, <a name="SLAMCH.95"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           <a name="ILAENV.96"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="LSAME.96"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="CLANHE.96"></a><a href="clanhe.f.html#CLANHE.1">CLANHE</a>, <a name="SLAMCH.96"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CHETRD.99"></a><a href="chetrd.f.html#CHETRD.1">CHETRD</a>, <a name="CLASCL.99"></a><a href="clascl.f.html#CLASCL.1">CLASCL</a>, <a name="CSTEQR.99"></a><a href="csteqr.f.html#CSTEQR.1">CSTEQR</a>, <a name="CUNGTR.99"></a><a href="cungtr.f.html#CUNGTR.1">CUNGTR</a>, SSCAL, <a name="SSTERF.99"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a>,
     $                   <a name="XERBLA.100"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, SQRT
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