sggesx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 701 行 · 第 1/4 页

</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VSR     (output) REAL array, dimension (LDVSR,N)
</span><span class="comment">*</span><span class="comment">          If JOBVSR = 'V', VSR will contain the right Schur vectors.
</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">  RCONDE  (output) REAL array, dimension ( 2 )
</span><span class="comment">*</span><span class="comment">          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
</span><span class="comment">*</span><span class="comment">          reciprocal condition numbers for the average of the selected
</span><span class="comment">*</span><span class="comment">          eigenvalues.
</span><span class="comment">*</span><span class="comment">          Not referenced if SENSE = 'N' or 'V'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RCONDV  (output) REAL array, dimension ( 2 )
</span><span class="comment">*</span><span class="comment">          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
</span><span class="comment">*</span><span class="comment">          reciprocal condition numbers for the selected deflating
</span><span class="comment">*</span><span class="comment">          subspaces.
</span><span class="comment">*</span><span class="comment">          Not referenced if SENSE = 'N' or 'E'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL 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.
</span><span class="comment">*</span><span class="comment">          If N = 0, LWORK &gt;= 1, else if SENSE = 'E', 'V', or 'B',
</span><span class="comment">*</span><span class="comment">          LWORK &gt;= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else
</span><span class="comment">*</span><span class="comment">          LWORK &gt;= max( 8*N, 6*N+16 ).
</span><span class="comment">*</span><span class="comment">          Note that 2*SDIM*(N-SDIM) &lt;= N*N/2.
</span><span class="comment">*</span><span class="comment">          Note also that an error is only returned if
</span><span class="comment">*</span><span class="comment">          LWORK &lt; max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B'
</span><span class="comment">*</span><span class="comment">          this may not be large enough.
</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 bound on the optimal size of the WORK
</span><span class="comment">*</span><span class="comment">          array and the minimum size of the IWORK array, returns these
</span><span class="comment">*</span><span class="comment">          values as the first entries of the WORK and IWORK arrays, and
</span><span class="comment">*</span><span class="comment">          no error message related to LWORK or LIWORK is issued by
</span><span class="comment">*</span><span class="comment">          <a name="XERBLA.197"></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">  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LIWORK  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array IWORK.
</span><span class="comment">*</span><span class="comment">          If SENSE = 'N' or N = 0, LIWORK &gt;= 1, otherwise
</span><span class="comment">*</span><span class="comment">          LIWORK &gt;= N+6.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment">          routine only calculates the bound on the optimal size of the
</span><span class="comment">*</span><span class="comment">          WORK array and the minimum size of the IWORK array, returns
</span><span class="comment">*</span><span class="comment">          these values as the first entries of the WORK and IWORK
</span><span class="comment">*</span><span class="comment">          arrays, and no error message related to LWORK or LIWORK is
</span><span class="comment">*</span><span class="comment">          issued by <a name="XERBLA.212"></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">  BWORK   (workspace) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          Not referenced if SORT = '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 ALPHAR(j), ALPHAI(j), and BETA(j) should
</span><span class="comment">*</span><span class="comment">                be correct for j=INFO+1,...,N.
</span><span class="comment">*</span><span class="comment">          &gt; N:  =N+1: other than QZ iteration failed in <a name="SHGEQZ.224"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>
</span><span class="comment">*</span><span class="comment">                =N+2: after reordering, roundoff changed values of
</span><span class="comment">*</span><span class="comment">                      some complex eigenvalues so that leading
</span><span class="comment">*</span><span class="comment">                      eigenvalues in the Generalized Schur form no
</span><span class="comment">*</span><span class="comment">                      longer satisfy SELCTG=.TRUE.  This could also
</span><span class="comment">*</span><span class="comment">                      be caused due to scaling.
</span><span class="comment">*</span><span class="comment">                =N+3: reordering failed in <a name="STGSEN.230"></a><a href="stgsen.f.html#STGSEN.1">STGSEN</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An approximate (asymptotic) bound on the average absolute error of
</span><span class="comment">*</span><span class="comment">  the selected eigenvalues is
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">       EPS * norm((A, B)) / RCONDE( 1 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  An approximate (asymptotic) bound on the maximum angular error in
</span><span class="comment">*</span><span class="comment">  the computed deflating subspaces is
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">       EPS * norm((A, B)) / RCONDV( 2 ).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  See LAPACK User's Guide, section 4.11 for more information.
</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 = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            CURSL, ILASCL, ILBSCL, ILVSL, ILVSR, LASTSL,
     $                   LQUERY, LST2SL, WANTSB, WANTSE, WANTSN, WANTST,
     $                   WANTSV
      INTEGER            I, ICOLS, IERR, IHI, IJOB, IJOBVL, IJOBVR,
     $                   ILEFT, ILO, IP, IRIGHT, IROWS, ITAU, IWRK,
     $                   LIWMIN, LWRK, MAXWRK, MINWRK
      REAL               ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS, PL,
     $                   PR, SAFMAX, SAFMIN, SMLNUM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      REAL               DIF( 2 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SGEQRF.267"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>, <a name="SGGBAK.267"></a><a href="sggbak.f.html#SGGBAK.1">SGGBAK</a>, <a name="SGGBAL.267"></a><a href="sggbal.f.html#SGGBAL.1">SGGBAL</a>, <a name="SGGHRD.267"></a><a href="sgghrd.f.html#SGGHRD.1">SGGHRD</a>, <a name="SHGEQZ.267"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>, <a name="SLABAD.267"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>,
     $                   <a name="SLACPY.268"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>, <a name="SLASCL.268"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>, <a name="SLASET.268"></a><a href="slaset.f.html#SLASET.1">SLASET</a>, <a name="SORGQR.268"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>, <a name="SORMQR.268"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>, <a name="STGSEN.268"></a><a href="stgsen.f.html#STGSEN.1">STGSEN</a>,
     $                   <a name="XERBLA.269"></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">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.272"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.273"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      REAL               <a name="SLAMCH.274"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.274"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
      EXTERNAL           <a name="LSAME.275"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.275"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="SLAMCH.275"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANGE.275"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, SQRT
<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">     Decode the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.284"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSL, <span class="string">'N'</span> ) ) THEN
         IJOBVL = 1
         ILVSL = .FALSE.
      ELSE IF( <a name="LSAME.287"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSL, <span class="string">'V'</span> ) ) THEN
         IJOBVL = 2
         ILVSL = .TRUE.
      ELSE
         IJOBVL = -1
         ILVSL = .FALSE.
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.295"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSR, <span class="string">'N'</span> ) ) THEN
         IJOBVR = 1
         ILVSR = .FALSE.
      ELSE IF( <a name="LSAME.298"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVSR, <span class="string">'V'</span> ) ) THEN
         IJOBVR = 2
         ILVSR = .TRUE.
      ELSE
         IJOBVR = -1
         ILVSR = .FALSE.
      END IF
<span class="comment">*</span><span class="comment">
</span>      WANTST = <a name="LSAME.306"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'S'</span> )
      WANTSN = <a name="LSAME.307"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'N'</span> )
      WANTSE = <a name="LSAME.308"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'E'</span> )
      WANTSV = <a name="LSAME.309"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'V'</span> )
      WANTSB = <a name="LSAME.310"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SENSE, <span class="string">'B'</span> )
      LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
      IF( WANTSN ) THEN
         IJOB = 0
      ELSE IF( WANTSE ) THEN
         IJOB = 1
      ELSE IF( WANTSV ) THEN
         IJOB = 2
      ELSE IF( WANTSB ) THEN
         IJOB = 4
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( IJOBVL.LE.0 ) THEN
         INFO = -1
      ELSE IF( IJOBVR.LE.0 ) THEN
         INFO = -2
      ELSE IF( ( .NOT.WANTST ) .AND. ( .NOT.<a name="LSAME.329"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( SORT, <span class="string">'N'</span> ) ) ) THEN
         INFO = -3
      ELSE IF( .NOT.( WANTSN .OR. WANTSE .OR. WANTSV .OR. WANTSB ) .OR.
     $         ( .NOT.WANTST .AND. .NOT.WANTSN ) ) THEN
         INFO = -5