zhegst.f.html

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      SUBROUTINE <a name="ZHEGST.1"></a><a href="zhegst.f.html#ZHEGST.1">ZHEGST</a>( ITYPE, UPLO, N, A, LDA, B, LDB, 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>      CHARACTER          UPLO
      INTEGER            INFO, ITYPE, LDA, LDB, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      COMPLEX*16         A( LDA, * ), B( LDB, * )
<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="ZHEGST.18"></a><a href="zhegst.f.html#ZHEGST.1">ZHEGST</a> reduces a complex Hermitian-definite generalized
</span><span class="comment">*</span><span class="comment">  eigenproblem to standard form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If ITYPE = 1, the problem is A*x = lambda*B*x,
</span><span class="comment">*</span><span class="comment">  and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
</span><span class="comment">*</span><span class="comment">  B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B must have been previously factorized as U**H*U or L*L**H by <a name="ZPOTRF.27"></a><a href="zpotrf.f.html#ZPOTRF.1">ZPOTRF</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">  ITYPE   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
</span><span class="comment">*</span><span class="comment">          = 2 or 3: compute U*A*U**H or L**H*A*L.
</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 and B is factored as
</span><span class="comment">*</span><span class="comment">                  U**H*U;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored and B is factored as
</span><span class="comment">*</span><span class="comment">                  L*L**H.
</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">  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment">          N-by-N upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the transformed matrix, stored in the
</span><span class="comment">*</span><span class="comment">          same format as A.
</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">  B       (input) COMPLEX*16 array, dimension (LDB,N)
</span><span class="comment">*</span><span class="comment">          The triangular factor from the Cholesky factorization of B,
</span><span class="comment">*</span><span class="comment">          as returned by <a name="ZPOTRF.62"></a><a href="zpotrf.f.html#ZPOTRF.1">ZPOTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &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">
</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>      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
      COMPLEX*16         CONE, HALF
      PARAMETER          ( CONE = ( 1.0D+0, 0.0D+0 ),
     $                   HALF = ( 0.5D+0, 0.0D+0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            K, KB, NB
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.85"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZHEGS2.85"></a><a href="zhegs2.f.html#ZHEGS2.1">ZHEGS2</a>, ZHEMM, ZHER2K, ZTRMM, ZTRSM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.91"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.92"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.93"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<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
      UPPER = <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
         INFO = -1
      ELSE IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.103"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -2
      ELSE IF( N.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -5
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -7
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.113"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZHEGST.113"></a><a href="zhegst.f.html#ZHEGST.1">ZHEGST</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><span class="comment">*</span><span class="comment">     Determine the block size for this environment.
</span><span class="comment">*</span><span class="comment">
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