zgegs.f.html

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      SUBROUTINE <a name="ZGEGS.1"></a><a href="zgegs.f.html#ZGEGS.1">ZGEGS</a>( JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHA, BETA,
     $                  VSL, LDVSL, VSR, LDVSR, 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          JOBVSL, JOBVSR
      INTEGER            INFO, LDA, LDB, LDVSL, LDVSR, LWORK, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ),
     $                   BETA( * ), VSL( LDVSL, * ), VSR( LDVSR, * ),
     $                   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">  This routine is deprecated and has been replaced by routine <a name="ZGGES.23"></a><a href="zgges.f.html#ZGGES.1">ZGGES</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZGEGS.25"></a><a href="zgegs.f.html#ZGEGS.1">ZGEGS</a> computes the eigenvalues, Schur form, and, optionally, the
</span><span class="comment">*</span><span class="comment">  left and or/right Schur vectors of a complex matrix pair (A,B).
</span><span class="comment">*</span><span class="comment">  Given two square matrices A and B, the generalized Schur
</span><span class="comment">*</span><span class="comment">  factorization has the form
</span><span class="comment">*</span><span class="comment">  
</span><span class="comment">*</span><span class="comment">     A = Q*S*Z**H,  B = Q*T*Z**H
</span><span class="comment">*</span><span class="comment">  
</span><span class="comment">*</span><span class="comment">  where Q and Z are unitary matrices and S and T are upper triangular.
</span><span class="comment">*</span><span class="comment">  The columns of Q are the left Schur vectors
</span><span class="comment">*</span><span class="comment">  and the columns of Z are the right Schur vectors.
</span><span class="comment">*</span><span class="comment">  
</span><span class="comment">*</span><span class="comment">  If only the eigenvalues of (A,B) are needed, the driver routine
</span><span class="comment">*</span><span class="comment">  <a name="ZGEGV.37"></a><a href="zgegv.f.html#ZGEGV.1">ZGEGV</a> should be used instead.  See <a name="ZGEGV.37"></a><a href="zgegv.f.html#ZGEGV.1">ZGEGV</a> for a description of the
</span><span class="comment">*</span><span class="comment">  eigenvalues of the generalized nonsymmetric eigenvalue problem
</span><span class="comment">*</span><span class="comment">  (GNEP).
</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">  JOBVSL   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  do not compute the left Schur vectors;
</span><span class="comment">*</span><span class="comment">          = 'V':  compute the left Schur vectors (returned in VSL).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBVSR   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'N':  do not compute the right Schur vectors;
</span><span class="comment">*</span><span class="comment">          = 'V':  compute the right Schur vectors (returned in VSR).
</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, B, VSL, and VSR.  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 matrix A.
</span><span class="comment">*</span><span class="comment">          On exit, the upper triangular matrix S from the generalized
</span><span class="comment">*</span><span class="comment">          Schur factorization.
</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 A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX*16 array, dimension (LDB, N)
</span><span class="comment">*</span><span class="comment">          On entry, the matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, the upper triangular matrix T from the generalized
</span><span class="comment">*</span><span class="comment">          Schur factorization.
</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 B.  LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ALPHA   (output) COMPLEX*16 array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The complex scalars alpha that define the eigenvalues of
</span><span class="comment">*</span><span class="comment">          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur
</span><span class="comment">*</span><span class="comment">          form of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BETA    (output) COMPLEX*16 array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The non-negative real scalars beta that define the
</span><span class="comment">*</span><span class="comment">          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element
</span><span class="comment">*</span><span class="comment">          of the triangular factor T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          Together, the quantities alpha = ALPHA(j) and beta = BETA(j)
</span><span class="comment">*</span><span class="comment">          represent the j-th eigenvalue of the matrix pair (A,B), in
</span><span class="comment">*</span><span class="comment">          one of the forms lambda = alpha/beta or mu = beta/alpha.
</span><span class="comment">*</span><span class="comment">          Since either lambda or mu may overflow, they should not,
</span><span class="comment">*</span><span class="comment">          in general, be computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VSL     (output) COMPLEX*16 array, dimension (LDVSL,N)
</span><span class="comment">*</span><span class="comment">          If JOBVSL = 'V', the matrix of left Schur vectors Q.
</span><span class="comment">*</span><span class="comment">          Not referenced if JOBVSL = 'N'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVSL   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix VSL. LDVSL &gt;= 1, and
</span><span class="comment">*</span><span class="comment">          if JOBVSL = 'V', LDVSL &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VSR     (output) COMPLEX*16 array, dimension (LDVSR,N)
</span><span class="comment">*</span><span class="comment">          If JOBVSR = 'V', the matrix of right Schur vectors Z.
</span><span class="comment">*</span><span class="comment">          Not referenced if JOBVSR = 'N'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVSR   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the matrix VSR. LDVSR &gt;= 1, and
</span><span class="comment">*</span><span class="comment">          if JOBVSR = 'V', LDVSR &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) COMPLEX*16 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 dimension of the array WORK.  LWORK &gt;= max(1,2*N).
</span><span class="comment">*</span><span class="comment">          For good performance, LWORK must generally be larger.
</span><span class="comment">*</span><span class="comment">          To compute the optimal value of LWORK, call <a name="ILAENV.110"></a><a href="hfy-index.html#ILAENV">ILAENV</a> to get
</span><span class="comment">*</span><span class="comment">          blocksizes (for <a name="ZGEQRF.111"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>, <a name="ZUNMQR.111"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>, and <a name="CUNGQR.111"></a><a href="cungqr.f.html#CUNGQR.1">CUNGQR</a>.)  Then compute:
</span><span class="comment">*</span><span class="comment">          NB  -- MAX of the blocksizes for <a name="ZGEQRF.112"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>, <a name="ZUNMQR.112"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>, and <a name="CUNGQR.112"></a><a href="cungqr.f.html#CUNGQR.1">CUNGQR</a>;
</span><span class="comment">*</span><span class="comment">          the optimal LWORK is N*(NB+1).
</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.118"></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) DOUBLE PRECISION array, dimension (3*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">          =1,...,N:
</span><span class="comment">*</span><span class="comment">                The QZ iteration failed.  (A,B) are not in Schur
</span><span class="comment">*</span><span class="comment">                form, but ALPHA(j) and BETA(j) should be correct for
</span><span class="comment">*</span><span class="comment">                j=INFO+1,...,N.
</span><span class="comment">*</span><span class="comment">          &gt; N:  errors that usually indicate LAPACK problems:
</span><span class="comment">*</span><span class="comment">                =N+1: error return from <a name="ZGGBAL.130"></a><a href="zggbal.f.html#ZGGBAL.1">ZGGBAL</a>
</span><span class="comment">*</span><span class="comment">                =N+2: error return from <a name="ZGEQRF.131"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>
</span><span class="comment">*</span><span class="comment">                =N+3: error return from <a name="ZUNMQR.132"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>
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