dtgevc.f.html

来自「famous linear algebra library (LAPACK) p」· HTML 代码 · 共 1,038 行 · 第 1/5 页

            TEMP = TEMP + ABS( S( I, J ) )
            TEMP2 = TEMP2 + ABS( P( I, J ) )
   40    CONTINUE
         ANORM = MAX( ANORM, TEMP )
         BNORM = MAX( BNORM, TEMP2 )
   50 CONTINUE
<span class="comment">*</span><span class="comment">
</span>      ASCALE = ONE / MAX( ANORM, SAFMIN )
      BSCALE = ONE / MAX( BNORM, SAFMIN )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Left eigenvectors
</span><span class="comment">*</span><span class="comment">
</span>      IF( COMPL ) THEN
         IEIG = 0
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Main loop over eigenvalues
</span><span class="comment">*</span><span class="comment">
</span>         ILCPLX = .FALSE.
         DO 220 JE = 1, N
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Skip this iteration if (a) HOWMNY='S' and SELECT=.FALSE., or
</span><span class="comment">*</span><span class="comment">           (b) this would be the second of a complex pair.
</span><span class="comment">*</span><span class="comment">           Check for complex eigenvalue, so as to be sure of which
</span><span class="comment">*</span><span class="comment">           entry(-ies) of SELECT to look at.
</span><span class="comment">*</span><span class="comment">
</span>            IF( ILCPLX ) THEN
               ILCPLX = .FALSE.
               GO TO 220
            END IF
            NW = 1
            IF( JE.LT.N ) THEN
               IF( S( JE+1, JE ).NE.ZERO ) THEN
                  ILCPLX = .TRUE.
                  NW = 2
               END IF
            END IF
            IF( ILALL ) THEN
               ILCOMP = .TRUE.
            ELSE IF( ILCPLX ) THEN
               ILCOMP = SELECT( JE ) .OR. SELECT( JE+1 )
            ELSE
               ILCOMP = SELECT( JE )
            END IF
            IF( .NOT.ILCOMP )
     $         GO TO 220
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Decide if (a) singular pencil, (b) real eigenvalue, or
</span><span class="comment">*</span><span class="comment">           (c) complex eigenvalue.
</span><span class="comment">*</span><span class="comment">
</span>            IF( .NOT.ILCPLX ) THEN
               IF( ABS( S( JE, JE ) ).LE.SAFMIN .AND.
     $             ABS( P( JE, JE ) ).LE.SAFMIN ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                 Singular matrix pencil -- return unit eigenvector
</span><span class="comment">*</span><span class="comment">
</span>                  IEIG = IEIG + 1
                  DO 60 JR = 1, N
                     VL( JR, IEIG ) = ZERO
   60             CONTINUE
                  VL( IEIG, IEIG ) = ONE
                  GO TO 220
               END IF
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Clear vector
</span><span class="comment">*</span><span class="comment">
</span>            DO 70 JR = 1, NW*N
               WORK( 2*N+JR ) = ZERO
   70       CONTINUE
<span class="comment">*</span><span class="comment">                                                 T
</span><span class="comment">*</span><span class="comment">           Compute coefficients in  ( a A - b B )  y = 0
</span><span class="comment">*</span><span class="comment">              a  is  ACOEF
</span><span class="comment">*</span><span class="comment">              b  is  BCOEFR + i*BCOEFI
</span><span class="comment">*</span><span class="comment">
</span>            IF( .NOT.ILCPLX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Real eigenvalue
</span><span class="comment">*</span><span class="comment">
</span>               TEMP = ONE / MAX( ABS( S( JE, JE ) )*ASCALE,
     $                ABS( P( JE, JE ) )*BSCALE, SAFMIN )
               SALFAR = ( TEMP*S( JE, JE ) )*ASCALE
               SBETA = ( TEMP*P( JE, JE ) )*BSCALE
               ACOEF = SBETA*ASCALE
               BCOEFR = SALFAR*BSCALE
               BCOEFI = ZERO
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Scale to avoid underflow
</span><span class="comment">*</span><span class="comment">
</span>               SCALE = ONE
               LSA = ABS( SBETA ).GE.SAFMIN .AND. ABS( ACOEF ).LT.SMALL
               LSB = ABS( SALFAR ).GE.SAFMIN .AND. ABS( BCOEFR ).LT.
     $               SMALL
               IF( LSA )
     $            SCALE = ( SMALL / ABS( SBETA ) )*MIN( ANORM, BIG )
               IF( LSB )
     $            SCALE = MAX( SCALE, ( SMALL / ABS( SALFAR ) )*
     $                    MIN( BNORM, BIG ) )
               IF( LSA .OR. LSB ) THEN
                  SCALE = MIN( SCALE, ONE /
     $                    ( SAFMIN*MAX( ONE, ABS( ACOEF ),
     $                    ABS( BCOEFR ) ) ) )
                  IF( LSA ) THEN
                     ACOEF = ASCALE*( SCALE*SBETA )
                  ELSE
                     ACOEF = SCALE*ACOEF
                  END IF
                  IF( LSB ) THEN
                     BCOEFR = BSCALE*( SCALE*SALFAR )
                  ELSE
                     BCOEFR = SCALE*BCOEFR
                  END IF
               END IF
               ACOEFA = ABS( ACOEF )
               BCOEFA = ABS( BCOEFR )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              First component is 1
</span><span class="comment">*</span><span class="comment">
</span>               WORK( 2*N+JE ) = ONE
               XMAX = ONE
            ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Complex eigenvalue
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="DLAG2.521"></a><a href="dlag2.f.html#DLAG2.1">DLAG2</a>( S( JE, JE ), LDS, P( JE, JE ), LDP,
     $                     SAFMIN*SAFETY, ACOEF, TEMP, BCOEFR, TEMP2,
     $                     BCOEFI )
               BCOEFI = -BCOEFI
               IF( BCOEFI.EQ.ZERO ) THEN
                  INFO = JE
                  RETURN
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Scale to avoid over/underflow
</span><span class="comment">*</span><span class="comment">
</span>               ACOEFA = ABS( ACOEF )
               BCOEFA = ABS( BCOEFR ) + ABS( BCOEFI )
               SCALE = ONE
               IF( ACOEFA*ULP.LT.SAFMIN .AND. ACOEFA.GE.SAFMIN )
     $            SCALE = ( SAFMIN / ULP ) / ACOEFA
               IF( BCOEFA*ULP.LT.SAFMIN .AND. BCOEFA.GE.SAFMIN )
     $            SCALE = MAX( SCALE, ( SAFMIN / ULP ) / BCOEFA )
               IF( SAFMIN*ACOEFA.GT.ASCALE )
     $            SCALE = ASCALE / ( SAFMIN*ACOEFA )
               IF( SAFMIN*BCOEFA.GT.BSCALE )
     $            SCALE = MIN( SCALE, BSCALE / ( SAFMIN*BCOEFA ) )
               IF( SCALE.NE.ONE ) THEN
                  ACOEF = SCALE*ACOEF
                  ACOEFA = ABS( ACOEF )
                  BCOEFR = SCALE*BCOEFR
                  BCOEFI = SCALE*BCOEFI
                  BCOEFA = ABS( BCOEFR ) + ABS( BCOEFI )
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Compute first two components of eigenvector
</span><span class="comment">*</span><span class="comment">
</span>               TEMP = ACOEF*S( JE+1, JE )
               TEMP2R = ACOEF*S( JE, JE ) - BCOEFR*P( JE, JE )
               TEMP2I = -BCOEFI*P( JE, JE )
               IF( ABS( TEMP ).GT.ABS( TEMP2R )+ABS( TEMP2I ) ) THEN
                  WORK( 2*N+JE ) = ONE
                  WORK( 3*N+JE ) = ZERO
                  WORK( 2*N+JE+1 ) = -TEMP2R / TEMP
                  WORK( 3*N+JE+1 ) = -TEMP2I / TEMP
               ELSE
                  WORK( 2*N+JE+1 ) = ONE
                  WORK( 3*N+JE+1 ) = ZERO
                  TEMP = ACOEF*S( JE, JE+1 )
                  WORK( 2*N+JE ) = ( BCOEFR*P( JE+1, JE+1 )-ACOEF*
     $                             S( JE+1, JE+1 ) ) / TEMP
                  WORK( 3*N+JE ) = BCOEFI*P( JE+1, JE+1 ) / TEMP
               END IF
               XMAX = MAX( ABS( WORK( 2*N+JE ) )+ABS( WORK( 3*N+JE ) ),
     $                ABS( WORK( 2*N+JE+1 ) )+ABS( WORK( 3*N+JE+1 ) ) )
            END IF
<span class="comment">*</span><span class="comment">
</span>            DMIN = MAX( ULP*ACOEFA*ANORM, ULP*BCOEFA*BNORM, SAFMIN )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                                           T
</span><span class="comment">*</span><span class="comment">           Triangular solve of  (a A - b B)  y = 0
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">                                   T
</span><span class="comment">*</span><span class="comment">           (rowwise in  (a A - b B) , or columnwise in (a A - b B) )
</span><span class="comment">*</span><span class="comment">
</span>            IL2BY2 = .FALSE.
<span class="comment">*</span><span class="comment">
</span>            DO 160 J = JE + NW, N
               IF( IL2BY2 ) THEN
                  IL2BY2 = .FALSE.
                  GO TO 160
               END IF
<span class="comment">*</span><span class="comment">
</span>               NA = 1
               BDIAG( 1 ) = P( J, J )
               IF( J.LT.N ) THEN
                  IF( S( J+1, J ).NE.ZERO ) THEN
                     IL2BY2 = .TRUE.
                     BDIAG( 2 ) = P( J+1, J+1 )
                     NA = 2
                  END IF
               END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              Check whether scaling is necessary for dot products
</span><span class="comment">*</span><span class="comment">
</span>               XSCALE = ONE / MAX( ONE, XMAX )
               TEMP = MAX( WORK( J ), WORK( N+J ),
     $                ACOEFA*WORK( J )+BCOEFA*WORK( N+J ) )
               IF( IL2BY2 )
     $            TEMP = MAX( TEMP, WORK( J+1 ), WORK( N+J+1 ),