sggevx.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 741 行 · 第 1/4 页

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<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute workspace
</span><span class="comment">*</span><span class="comment">      (Note: Comments in the code beginning &quot;Workspace:&quot; describe the
</span><span class="comment">*</span><span class="comment">       minimal amount of workspace needed at that point in the code,
</span><span class="comment">*</span><span class="comment">       as well as the preferred amount for good performance.
</span><span class="comment">*</span><span class="comment">       NB refers to the optimal block size for the immediately
</span><span class="comment">*</span><span class="comment">       following subroutine, as returned by <a name="ILAENV.360"></a><a href="hfy-index.html#ILAENV">ILAENV</a>. The workspace is
</span><span class="comment">*</span><span class="comment">       computed assuming ILO = 1 and IHI = N, the worst case.)
</span><span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         IF( N.EQ.0 ) THEN
            MINWRK = 1
            MAXWRK = 1
         ELSE
            IF( NOSCL .AND. .NOT.ILV ) THEN
               MINWRK = 2*N
            ELSE
               MINWRK = 6*N
            END IF
            IF( WANTSE ) THEN
               MINWRK = 10*N
            ELSE IF( WANTSV .OR. WANTSB ) THEN
               MINWRK = 2*N*( N + 4 ) + 16
            END IF
            MAXWRK = MINWRK
            MAXWRK = MAX( MAXWRK,
     $                    N + N*<a name="ILAENV.380"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SGEQRF.380"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 ) )
            MAXWRK = MAX( MAXWRK,
     $                    N + N*<a name="ILAENV.382"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORMQR.382"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 ) )
            IF( ILVL ) THEN
               MAXWRK = MAX( MAXWRK, N +
     $                       N*<a name="ILAENV.385"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( 1, <span class="string">'<a name="SORGQR.385"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>'</span>, <span class="string">' '</span>, N, 1, N, 0 ) )
            END IF
         END IF
         WORK( 1 ) = MAXWRK
<span class="comment">*</span><span class="comment">
</span>         IF( LWORK.LT.MINWRK .AND. .NOT.LQUERY ) THEN
            INFO = -26
         END IF
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.396"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="SGGEVX.396"></a><a href="sggevx.f.html#SGGEVX.1">SGGEVX</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">
</span><span class="comment">*</span><span class="comment">     Get machine constants
</span><span class="comment">*</span><span class="comment">
</span>      EPS = <a name="SLAMCH.410"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'P'</span> )
      SMLNUM = <a name="SLAMCH.411"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>( <span class="string">'S'</span> )
      BIGNUM = ONE / SMLNUM
      CALL <a name="SLABAD.413"></a><a href="slabad.f.html#SLABAD.1">SLABAD</a>( SMLNUM, BIGNUM )
      SMLNUM = SQRT( SMLNUM ) / EPS
      BIGNUM = ONE / SMLNUM
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale A if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      ANRM = <a name="SLANGE.419"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, N, N, A, LDA, WORK )
      ILASCL = .FALSE.
      IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
         ANRMTO = SMLNUM
         ILASCL = .TRUE.
      ELSE IF( ANRM.GT.BIGNUM ) THEN
         ANRMTO = BIGNUM
         ILASCL = .TRUE.
      END IF
      IF( ILASCL )
     $   CALL <a name="SLASCL.429"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRM, ANRMTO, N, N, A, LDA, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Scale B if max element outside range [SMLNUM,BIGNUM]
</span><span class="comment">*</span><span class="comment">
</span>      BNRM = <a name="SLANGE.433"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'M'</span>, N, N, B, LDB, WORK )
      ILBSCL = .FALSE.
      IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN
         BNRMTO = SMLNUM
         ILBSCL = .TRUE.
      ELSE IF( BNRM.GT.BIGNUM ) THEN
         BNRMTO = BIGNUM
         ILBSCL = .TRUE.
      END IF
      IF( ILBSCL )
     $   CALL <a name="SLASCL.443"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRM, BNRMTO, N, N, B, LDB, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Permute and/or balance the matrix pair (A,B)
</span><span class="comment">*</span><span class="comment">     (Workspace: need 6*N if BALANC = 'S' or 'B', 1 otherwise)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SGGBAL.448"></a><a href="sggbal.f.html#SGGBAL.1">SGGBAL</a>( BALANC, N, A, LDA, B, LDB, ILO, IHI, LSCALE, RSCALE,
     $             WORK, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute ABNRM and BBNRM
</span><span class="comment">*</span><span class="comment">
</span>      ABNRM = <a name="SLANGE.453"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'1'</span>, N, N, A, LDA, WORK( 1 ) )
      IF( ILASCL ) THEN
         WORK( 1 ) = ABNRM
         CALL <a name="SLASCL.456"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, ANRMTO, ANRM, 1, 1, WORK( 1 ), 1,
     $                IERR )
         ABNRM = WORK( 1 )
      END IF
<span class="comment">*</span><span class="comment">
</span>      BBNRM = <a name="SLANGE.461"></a><a href="slange.f.html#SLANGE.1">SLANGE</a>( <span class="string">'1'</span>, N, N, B, LDB, WORK( 1 ) )
      IF( ILBSCL ) THEN
         WORK( 1 ) = BBNRM
         CALL <a name="SLASCL.464"></a><a href="slascl.f.html#SLASCL.1">SLASCL</a>( <span class="string">'G'</span>, 0, 0, BNRMTO, BNRM, 1, 1, WORK( 1 ), 1,
     $                IERR )
         BBNRM = WORK( 1 )
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce B to triangular form (QR decomposition of B)
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB )
</span><span class="comment">*</span><span class="comment">
</span>      IROWS = IHI + 1 - ILO
      IF( ILV .OR. .NOT.WANTSN ) THEN
         ICOLS = N + 1 - ILO
      ELSE
         ICOLS = IROWS
      END IF
      ITAU = 1
      IWRK = ITAU + IROWS
      CALL <a name="SGEQRF.480"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>( IROWS, ICOLS, B( ILO, ILO ), LDB, WORK( ITAU ),
     $             WORK( IWRK ), LWORK+1-IWRK, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Apply the orthogonal transformation to A
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="SORMQR.486"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>( <span class="string">'L'</span>, <span class="string">'T'</span>, IROWS, ICOLS, IROWS, B( ILO, ILO ), LDB,
     $             WORK( ITAU ), A( ILO, ILO ), LDA, WORK( IWRK ),
     $             LWORK+1-IWRK, IERR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Initialize VL and/or VR
</span><span class="comment">*</span><span class="comment">     (Workspace: need N, prefer N*NB)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILVL ) THEN
         CALL <a name="SLASET.494"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, VL, LDVL )
         IF( IROWS.GT.1 ) THEN
            CALL <a name="SLACPY.496"></a><a href="slacpy.f.html#SLACPY.1">SLACPY</a>( <span class="string">'L'</span>, IROWS-1, IROWS-1, B( ILO+1, ILO ), LDB,
     $                   VL( ILO+1, ILO ), LDVL )
         END IF
         CALL <a name="SORGQR.499"></a><a href="sorgqr.f.html#SORGQR.1">SORGQR</a>( IROWS, IROWS, IROWS, VL( ILO, ILO ), LDVL,
     $                WORK( ITAU ), WORK( IWRK ), LWORK+1-IWRK, IERR )
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( ILVR )
     $   CALL <a name="SLASET.504"></a><a href="slaset.f.html#SLASET.1">SLASET</a>( <span class="string">'Full'</span>, N, N, ZERO, ONE, VR, LDVR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Reduce to generalized Hessenberg form
</span><span class="comment">*</span><span class="comment">     (Workspace: none needed)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILV .OR. .NOT.WANTSN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Eigenvectors requested -- work on whole matrix.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="SGGHRD.513"></a><a href="sgghrd.f.html#SGGHRD.1">SGGHRD</a>( JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB, VL,
     $                LDVL, VR, LDVR, IERR )
      ELSE
         CALL <a name="SGGHRD.516"></a><a href="sgghrd.f.html#SGGHRD.1">SGGHRD</a>( <span class="string">'N'</span>, <span class="string">'N'</span>, IROWS, 1, IROWS, A( ILO, ILO ), LDA,
     $                B( ILO, ILO ), LDB, VL, LDVL, VR, LDVR, IERR )
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Perform QZ algorithm (Compute eigenvalues, and optionally, the
</span><span class="comment">*</span><span class="comment">     Schur forms and Schur vectors)
</span><span class="comment">*</span><span class="comment">     (Workspace: need N)
</span><span class="comment">*</span><span class="comment">
</span>      IF( ILV .OR. .NOT.WANTSN ) THEN
         CHTEMP = <span class="string">'S'</span>
      ELSE
         CHTEMP = <span class="string">'E'</span>
      END IF
<span class="comment">*</span><span class="comment">
</span>      CALL <a name="SHGEQZ.530"></a><a href="shgeqz.f.html#SHGEQZ.1">SHGEQZ</a>( CHTEMP, JOBVL, JOBVR, N, ILO, IHI, A, LDA, B, LDB,
     $             ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK,
     $             LWORK, IERR )
      IF( IERR.NE.0 ) THEN
         IF( IERR.GT.0 .AND. IERR.LE.N ) THEN
            INFO = IERR
         ELSE IF( IERR.GT.N .AND. IERR.LE.2*N ) THEN
            INFO = IERR - N
         ELSE
            INFO = N + 1
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