zlaed0.f.html

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      SUBROUTINE <a name="ZLAED0.1"></a><a href="zlaed0.f.html#ZLAED0.1">ZLAED0</a>( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK,
     $                   IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK 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>      INTEGER            INFO, LDQ, LDQS, N, QSIZ
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IWORK( * )
      DOUBLE PRECISION   D( * ), E( * ), RWORK( * )
      COMPLEX*16         Q( LDQ, * ), QSTORE( LDQS, * )
<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">  Using the divide and conquer method, <a name="ZLAED0.20"></a><a href="zlaed0.f.html#ZLAED0.1">ZLAED0</a> computes all eigenvalues
</span><span class="comment">*</span><span class="comment">  of a symmetric tridiagonal matrix which is one diagonal block of
</span><span class="comment">*</span><span class="comment">  those from reducing a dense or band Hermitian matrix and
</span><span class="comment">*</span><span class="comment">  corresponding eigenvectors of the dense or band matrix.
</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">  QSIZ   (input) INTEGER
</span><span class="comment">*</span><span class="comment">         The dimension of the unitary matrix used to reduce
</span><span class="comment">*</span><span class="comment">         the full matrix to tridiagonal form.  QSIZ &gt;= N if ICOMPQ = 1.
</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 dimension of the symmetric tridiagonal matrix.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D      (input/output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment">         On entry, the diagonal elements of the tridiagonal matrix.
</span><span class="comment">*</span><span class="comment">         On exit, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E      (input/output) DOUBLE PRECISION array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">         On entry, the off-diagonal elements of the tridiagonal matrix.
</span><span class="comment">*</span><span class="comment">         On exit, E has been destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Q      (input/output) COMPLEX*16 array, dimension (LDQ,N)
</span><span class="comment">*</span><span class="comment">         On entry, Q must contain an QSIZ x N matrix whose columns
</span><span class="comment">*</span><span class="comment">         unitarily orthonormal. It is a part of the unitary matrix
</span><span class="comment">*</span><span class="comment">         that reduces the full dense Hermitian matrix to a
</span><span class="comment">*</span><span class="comment">         (reducible) symmetric tridiagonal matrix.
</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.  LDQ &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK  (workspace) INTEGER array,
</span><span class="comment">*</span><span class="comment">         the dimension of IWORK must be at least
</span><span class="comment">*</span><span class="comment">                      6 + 6*N + 5*N*lg N
</span><span class="comment">*</span><span class="comment">                      ( lg( N ) = smallest integer k
</span><span class="comment">*</span><span class="comment">                                  such that 2^k &gt;= N )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK  (workspace) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment">                               dimension (1 + 3*N + 2*N*lg N + 3*N**2)
</span><span class="comment">*</span><span class="comment">                        ( lg( N ) = smallest integer k
</span><span class="comment">*</span><span class="comment">                                    such that 2^k &gt;= N )
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N)
</span><span class="comment">*</span><span class="comment">         Used to store parts of
</span><span class="comment">*</span><span class="comment">         the eigenvector matrix when the updating matrix multiplies
</span><span class="comment">*</span><span class="comment">         take place.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDQS   (input) INTEGER
</span><span class="comment">*</span><span class="comment">         The leading dimension of the array QSTORE.
</span><span class="comment">*</span><span class="comment">         LDQS &gt;= max(1,N).
</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:  The algorithm failed to compute an eigenvalue while
</span><span class="comment">*</span><span class="comment">                working on the submatrix lying in rows and columns
</span><span class="comment">*</span><span class="comment">                INFO/(N+1) through mod(INFO,N+1).
</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">  Warning:      N could be as big as QSIZ!
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   TWO
      PARAMETER          ( TWO = 2.D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            CURLVL, CURPRB, CURR, I, IGIVCL, IGIVNM,
     $                   IGIVPT, INDXQ, IPERM, IPRMPT, IQ, IQPTR, IWREM,
     $                   J, K, LGN, LL, MATSIZ, MSD2, SMLSIZ, SMM1,
     $                   SPM1, SPM2, SUBMAT, SUBPBS, TLVLS
      DOUBLE PRECISION   TEMP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DCOPY, <a name="DSTEQR.95"></a><a href="dsteqr.f.html#DSTEQR.1">DSTEQR</a>, <a name="XERBLA.95"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, ZCOPY, <a name="ZLACRM.95"></a><a href="zlacrm.f.html#ZLACRM.1">ZLACRM</a>, <a name="ZLAED7.95"></a><a href="zlaed7.f.html#ZLAED7.1">ZLAED7</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            <a name="ILAENV.98"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="ILAENV.99"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, DBLE, INT, LOG, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     IF( ICOMPQ .LT. 0 .OR. ICOMPQ .GT. 2 ) THEN
</span><span class="comment">*</span><span class="comment">        INFO = -1
</span><span class="comment">*</span><span class="comment">     ELSE IF( ( ICOMPQ .EQ. 1 ) .AND. ( QSIZ .LT. MAX( 0, N ) ) )
</span><span class="comment">*</span><span class="comment">    $        THEN
</span>      IF( QSIZ.LT.MAX( 0, N ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
         INFO = -6
      ELSE IF( LDQS.LT.MAX( 1, N ) ) THEN
         INFO = -8
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.124"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZLAED0.124"></a><a href="zlaed0.f.html#ZLAED0.1">ZLAED0</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      SMLSIZ = <a name="ILAENV.133"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 9, <span class="string">'<a name="ZLAED0.133"></a><a href="zlaed0.f.html#ZLAED0.1">ZLAED0</a>'</span>, <span class="string">' '</span>, 0, 0, 0, 0 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Determine the size and placement of the submatrices, and save in
</span><span class="comment">*</span><span class="comment">     the leading elements of IWORK.
</span><span class="comment">*</span><span class="comment">
</span>      IWORK( 1 ) = N
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