zgegv.f.html

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</span><span class="comment">*</span><span class="comment">  form[*] of the &quot;balanced&quot; versions of A and B.  If no eigenvectors
</span><span class="comment">*</span><span class="comment">  are computed, then only the diagonal blocks will be correct.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  [*] In other words, upper triangular form.
</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   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
      COMPLEX*16         CZERO, CONE
      PARAMETER          ( CZERO = ( 0.0D0, 0.0D0 ),
     $                   CONE = ( 1.0D0, 0.0D0 ) )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            ILIMIT, ILV, ILVL, ILVR, LQUERY
      CHARACTER          CHTEMP
      INTEGER            ICOLS, IHI, IINFO, IJOBVL, IJOBVR, ILEFT, ILO,
     $                   IN, IRIGHT, IROWS, IRWORK, ITAU, IWORK, JC, JR,
     $                   LOPT, LWKMIN, LWKOPT, NB, NB1, NB2, NB3
      DOUBLE PRECISION   ABSAI, ABSAR, ABSB, ANRM, ANRM1, ANRM2, BNRM,
     $                   BNRM1, BNRM2, EPS, SAFMAX, SAFMIN, SALFAI,
     $                   SALFAR, SBETA, SCALE, TEMP
      COMPLEX*16         X
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Arrays ..
</span>      LOGICAL            LDUMMA( 1 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.220"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZGEQRF.220"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>, <a name="ZGGBAK.220"></a><a href="zggbak.f.html#ZGGBAK.1">ZGGBAK</a>, <a name="ZGGBAL.220"></a><a href="zggbal.f.html#ZGGBAL.1">ZGGBAL</a>, <a name="ZGGHRD.220"></a><a href="zgghrd.f.html#ZGGHRD.1">ZGGHRD</a>, <a name="ZHGEQZ.220"></a><a href="zhgeqz.f.html#ZHGEQZ.1">ZHGEQZ</a>,
     $                   <a name="ZLACPY.221"></a><a href="zlacpy.f.html#ZLACPY.1">ZLACPY</a>, <a name="ZLASCL.221"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>, <a name="ZLASET.221"></a><a href="zlaset.f.html#ZLASET.1">ZLASET</a>, <a name="ZTGEVC.221"></a><a href="ztgevc.f.html#ZTGEVC.1">ZTGEVC</a>, <a name="ZUNGQR.221"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>, <a name="ZUNMQR.221"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.224"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.225"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      DOUBLE PRECISION   <a name="DLAMCH.226"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.226"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
      EXTERNAL           <a name="LSAME.227"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.227"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, <a name="DLAMCH.227"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>, <a name="ZLANGE.227"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, INT, MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Functions ..
</span>      DOUBLE PRECISION   ABS1
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Statement Function definitions ..
</span>      ABS1( X ) = ABS( DBLE( X ) ) + ABS( DIMAG( X ) )
<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.242"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVL, <span class="string">'N'</span> ) ) THEN
         IJOBVL = 1
         ILVL = .FALSE.
      ELSE IF( <a name="LSAME.245"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVL, <span class="string">'V'</span> ) ) THEN
         IJOBVL = 2
         ILVL = .TRUE.
      ELSE
         IJOBVL = -1
         ILVL = .FALSE.
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( <a name="LSAME.253"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVR, <span class="string">'N'</span> ) ) THEN
         IJOBVR = 1
         ILVR = .FALSE.
      ELSE IF( <a name="LSAME.256"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBVR, <span class="string">'V'</span> ) ) THEN
         IJOBVR = 2
         ILVR = .TRUE.
      ELSE
         IJOBVR = -1
         ILVR = .FALSE.
      END IF
      ILV = ILVL .OR. ILVR
<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>      LWKMIN = MAX( 2*N, 1 )
      LWKOPT = LWKMIN
      WORK( 1 ) = LWKOPT
      LQUERY = ( LWORK.EQ.-1 )
      INFO = 0
      IF( IJOBVL.LE.0 ) THEN
         INFO = -1
      ELSE IF( IJOBVR.LE.0 ) 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
      ELSE IF( LDVL.LT.1 .OR. ( ILVL .AND. LDVL.LT.N ) ) THEN
         INFO = -11
      ELSE IF( LDVR.LT.1 .OR. ( ILVR .AND. LDVR.LT.N ) ) THEN
         INFO = -13
      ELSE IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
         INFO = -15
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         NB1 = <a name="ILAENV.291"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZGEQRF.291"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>'</span>, <span class="string">' '</span>, N, N, -1, -1 )
         NB2 = <a name="ILAENV.292"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNMQR.292"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>'</span>, <span class="string">' '</span>, N, N, N, -1 )
         NB3 = <a name="ILAENV.293"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="ZUNGQR.293"></a><a href="zungqr.f.html#ZUNGQR.1">ZUNGQR</a>'</span>, <span class="string">' '</span>, N, N, N, -1 )
         NB = MAX( NB1, NB2, NB3 )
         LOPT = MAX( 2*N, N*( NB+1 ) )
         WORK( 1 ) = LOPT
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.300"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZGEGV.300"></a><a href="zgegv.f.html#ZGEGV.1">ZGEGV</a> '</span>, -INFO )
         RETURN
      ELSE IF( LQUERY ) THEN
         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">     Get machine constants
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="DLAMCH.313"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'E'</span> )*<a name="DLAMCH.313"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'B'</span> )
      SAFMIN = <a name="DLAMCH.314"></a><a href="dlamch.f.html#DLAMCH.1">DLAMCH</a>( <span class="string">'S'</span> )
      SAFMIN = SAFMIN + SAFMIN
      SAFMAX = ONE / SAFMIN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="ZLANGE.320"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, RWORK )
      ANRM1 = ANRM
      ANRM2 = ONE
      IF( ANRM.LT.ONE ) THEN
         IF( SAFMAX*ANRM.LT.ONE ) THEN
            ANRM1 = SAFMIN
            ANRM2 = SAFMAX*ANRM
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( ANRM.GT.ZERO ) THEN
         CALL <a name="ZLASCL.331"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>( <span class="string">'G'</span>, -1, -1, ANRM, ONE, N, N, A, LDA, IINFO )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 10
            RETURN
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale B
</span><span class="comment">*</span><span class="comment">
</span>      BNRM = <a name="ZLANGE.340"></a><a href="zlange.f.html#ZLANGE.1">ZLANGE</a>( <span class="string">'M'</span>, N, N, B, LDB, RWORK )
      BNRM1 = BNRM
      BNRM2 = ONE
      IF( BNRM.LT.ONE ) THEN
         IF( SAFMAX*BNRM.LT.ONE ) THEN
            BNRM1 = SAFMIN
            BNRM2 = SAFMAX*BNRM
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( BNRM.GT.ZERO ) THEN
         CALL <a name="ZLASCL.351"></a><a href="zlascl.f.html#ZLASCL.1">ZLASCL</a>( <span class="string">'G'</span>, -1, -1, BNRM, ONE, N, N, B, LDB, IINFO )
         IF( IINFO.NE.0 ) THEN
            INFO = N + 10
            RETURN
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Permute the matrix to make it more nearly triangular
</span><span class="comment">*</span><span class="comment">     Also &quot;balance&quot; the matrix.
</span><span class="comment">*</span><span class="comment">
</span>      ILEFT = 1
      IRIGHT = N + 1
      IRWORK = IRIGHT + N
      CALL <a name="ZGGBAL.364"></a><a href="zggbal.f.html#ZGGBAL.1">ZGGBAL</a>( <span class="string">'P'</span>, N, A, LDA, B, LDB, ILO, IHI, RWORK( ILEFT ),
     $             RWORK( IRIGHT ), RWORK( IRWORK ), IINFO )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 1
         GO TO 80
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce B to triangular form, and initialize VL and/or VR
</span><span class="comment">*</span><span class="comment">
</span>      IROWS = IHI + 1 - ILO
      IF( ILV ) THEN
         ICOLS = N + 1 - ILO
      ELSE
         ICOLS = IROWS
      END IF
      ITAU = 1
      IWORK = ITAU + IROWS
      CALL <a name="ZGEQRF.381"></a><a href="zgeqrf.f.html#ZGEQRF.1">ZGEQRF</a>( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
     $             WORK( IWORK ), LWORK+1-IWORK, IINFO )
      IF( IINFO.GE.0 )
     $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 2
         GO TO 80
      END IF
<span class="comment">*</span><span class="comment">
</span>      CALL <a name="ZUNMQR.390"></a><a href="zunmqr.f.html#ZUNMQR.1">ZUNMQR</a>( <span class="string">'L'</span>, <span class="string">'C'</span>, IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWORK ),
     $             LWORK+1-IWORK, IINFO )
      IF( IINFO.GE.0 )
     $   LWKOPT = MAX( LWKOPT, INT( WORK( IWORK ) )+IWORK-1 )
      IF( IINFO.NE.0 ) THEN
         INFO = N + 3
         GO TO 80
      END IF
<span class="comment">*</span><span class="comment">
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