zhbgst.f.html

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     $                             RWORK( I-K+KA-M )*AB( KA1, I-K )
                  RA1 = RA
               END IF
            END IF
            J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1
            NR = ( N-J2+KA ) / KA1
            J1 = J2 + ( NR-1 )*KA1
            IF( UPDATE ) THEN
               J2T = MAX( J2, I+2*KA-K+1 )
            ELSE
               J2T = J2
            END IF
            NRT = ( N-J2T+KA ) / KA1
            DO 320 J = J2T, J1, KA1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              create nonzero element a(j+1,j-ka) outside the band
</span><span class="comment">*</span><span class="comment">              and store it in WORK(j-m)
</span><span class="comment">*</span><span class="comment">
</span>               WORK( J-M ) = WORK( J-M )*AB( KA1, J-KA+1 )
               AB( KA1, J-KA+1 ) = RWORK( J-M )*AB( KA1, J-KA+1 )
  320       CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           generate rotations in 1st set to annihilate elements which
</span><span class="comment">*</span><span class="comment">           have been created outside the band
</span><span class="comment">*</span><span class="comment">
</span>            IF( NRT.GT.0 )
     $         CALL <a name="ZLARGV.620"></a><a href="zlargv.f.html#ZLARGV.1">ZLARGV</a>( NRT, AB( KA1, J2T-KA ), INCA, WORK( J2T-M ),
     $                      KA1, RWORK( J2T-M ), KA1 )
            IF( NR.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              apply rotations in 1st set from the left
</span><span class="comment">*</span><span class="comment">
</span>               DO 330 L = 1, KA - 1
                  CALL <a name="ZLARTV.627"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NR, AB( L+1, J2-L ), INCA,
     $                         AB( L+2, J2-L ), INCA, RWORK( J2-M ),
     $                         WORK( J2-M ), KA1 )
  330          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              apply rotations in 1st set from both sides to diagonal
</span><span class="comment">*</span><span class="comment">              blocks
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLAR2V.635"></a><a href="zlar2v.f.html#ZLAR2V.1">ZLAR2V</a>( NR, AB( 1, J2 ), AB( 1, J2+1 ), AB( 2, J2 ),
     $                      INCA, RWORK( J2-M ), WORK( J2-M ), KA1 )
<span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLACGV.638"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( NR, WORK( J2-M ), KA1 )
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           start applying rotations in 1st set from the right
</span><span class="comment">*</span><span class="comment">
</span>            DO 340 L = KA - 1, KB - K + 1, -1
               NRT = ( N-J2+L ) / KA1
               IF( NRT.GT.0 )
     $            CALL <a name="ZLARTV.646"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NRT, AB( KA1-L+1, J2 ), INCA,
     $                         AB( KA1-L, J2+1 ), INCA, RWORK( J2-M ),
     $                         WORK( J2-M ), KA1 )
  340       CONTINUE
<span class="comment">*</span><span class="comment">
</span>            IF( WANTX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              post-multiply X by product of rotations in 1st set
</span><span class="comment">*</span><span class="comment">
</span>               DO 350 J = J2, J1, KA1
                  CALL <a name="ZROT.656"></a><a href="zrot.f.html#ZROT.1">ZROT</a>( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1,
     $                       RWORK( J-M ), WORK( J-M ) )
  350          CONTINUE
            END IF
  360    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         IF( UPDATE ) THEN
            IF( I2.LE.N .AND. KBT.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              create nonzero element a(i-kbt+ka+1,i-kbt) outside the
</span><span class="comment">*</span><span class="comment">              band and store it in WORK(i-kbt)
</span><span class="comment">*</span><span class="comment">
</span>               WORK( I-KBT ) = -BB( KBT+1, I-KBT )*RA1
            END IF
         END IF
<span class="comment">*</span><span class="comment">
</span>         DO 400 K = KB, 1, -1
            IF( UPDATE ) THEN
               J2 = I - K - 1 + MAX( 2, K-I0+1 )*KA1
            ELSE
               J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           finish applying rotations in 2nd set from the right
</span><span class="comment">*</span><span class="comment">
</span>            DO 370 L = KB - K, 1, -1
               NRT = ( N-J2+KA+L ) / KA1
               IF( NRT.GT.0 )
     $            CALL <a name="ZLARTV.684"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NRT, AB( KA1-L+1, J2-KA ), INCA,
     $                         AB( KA1-L, J2-KA+1 ), INCA,
     $                         RWORK( J2-KA ), WORK( J2-KA ), KA1 )
  370       CONTINUE
            NR = ( N-J2+KA ) / KA1
            J1 = J2 + ( NR-1 )*KA1
            DO 380 J = J1, J2, -KA1
               WORK( J ) = WORK( J-KA )
               RWORK( J ) = RWORK( J-KA )
  380       CONTINUE
            DO 390 J = J2, J1, KA1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              create nonzero element a(j+1,j-ka) outside the band
</span><span class="comment">*</span><span class="comment">              and store it in WORK(j)
</span><span class="comment">*</span><span class="comment">
</span>               WORK( J ) = WORK( J )*AB( KA1, J-KA+1 )
               AB( KA1, J-KA+1 ) = RWORK( J )*AB( KA1, J-KA+1 )
  390       CONTINUE
            IF( UPDATE ) THEN
               IF( I-K.LT.N-KA .AND. K.LE.KBT )
     $            WORK( I-K+KA ) = WORK( I-K )
            END IF
  400    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         DO 440 K = KB, 1, -1
            J2 = I - K - 1 + MAX( 1, K-I0+1 )*KA1
            NR = ( N-J2+KA ) / KA1
            J1 = J2 + ( NR-1 )*KA1
            IF( NR.GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              generate rotations in 2nd set to annihilate elements
</span><span class="comment">*</span><span class="comment">              which have been created outside the band
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLARGV.717"></a><a href="zlargv.f.html#ZLARGV.1">ZLARGV</a>( NR, AB( KA1, J2-KA ), INCA, WORK( J2 ), KA1,
     $                      RWORK( J2 ), KA1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              apply rotations in 2nd set from the left
</span><span class="comment">*</span><span class="comment">
</span>               DO 410 L = 1, KA - 1
                  CALL <a name="ZLARTV.723"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NR, AB( L+1, J2-L ), INCA,
     $                         AB( L+2, J2-L ), INCA, RWORK( J2 ),
     $                         WORK( J2 ), KA1 )
  410          CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              apply rotations in 2nd set from both sides to diagonal
</span><span class="comment">*</span><span class="comment">              blocks
</span><span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLAR2V.731"></a><a href="zlar2v.f.html#ZLAR2V.1">ZLAR2V</a>( NR, AB( 1, J2 ), AB( 1, J2+1 ), AB( 2, J2 ),
     $                      INCA, RWORK( J2 ), WORK( J2 ), KA1 )
<span class="comment">*</span><span class="comment">
</span>               CALL <a name="ZLACGV.734"></a><a href="zlacgv.f.html#ZLACGV.1">ZLACGV</a>( NR, WORK( J2 ), KA1 )
            END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           start applying rotations in 2nd set from the right
</span><span class="comment">*</span><span class="comment">
</span>            DO 420 L = KA - 1, KB - K + 1, -1
               NRT = ( N-J2+L ) / KA1
               IF( NRT.GT.0 )
     $            CALL <a name="ZLARTV.742"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NRT, AB( KA1-L+1, J2 ), INCA,
     $                         AB( KA1-L, J2+1 ), INCA, RWORK( J2 ),
     $                         WORK( J2 ), KA1 )
  420       CONTINUE
<span class="comment">*</span><span class="comment">
</span>            IF( WANTX ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">              post-multiply X by product of rotations in 2nd set
</span><span class="comment">*</span><span class="comment">
</span>               DO 430 J = J2, J1, KA1
                  CALL <a name="ZROT.752"></a><a href="zrot.f.html#ZROT.1">ZROT</a>( N-M, X( M+1, J ), 1, X( M+1, J+1 ), 1,
     $                       RWORK( J ), WORK( J ) )
  430          CONTINUE
            END IF
  440    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         DO 460 K = 1, KB - 1
            J2 = I - K - 1 + MAX( 1, K-I0+2 )*KA1
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           finish applying rotations in 1st set from the right
</span><span class="comment">*</span><span class="comment">
</span>            DO 450 L = KB - K, 1, -1
               NRT = ( N-J2+L ) / KA1
               IF( NRT.GT.0 )
     $            CALL <a name="ZLARTV.766"></a><a href="zlartv.f.html#ZLARTV.1">ZLARTV</a>( NRT, AB( KA1-L+1, J2 ), INCA,
     $                         AB( KA1-L, J2+1 ), INCA, RWORK( J2-M ),
     $                         WORK( J2-M ), KA1 )
  450       CONTINUE
  460    CONTINUE
<span class="comment">*</span><span class="comment">
</span>         IF( KB.GT.1 ) THEN
            DO 470 J = N - 1, I2 + KA, -1
               RWORK( J-M ) = RWORK( J-KA-M )
               WORK( J-M ) = WORK( J-KA-M )
  470       CONTINUE
         END IF
<span class="comment">*</span><span class="comment">
</span>      END IF
<span class="comment">*</span><span class="comment">
</span>      GO TO 10
<span class="comment">*</span><span class="comment">
</span>  480 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     **************************** Phase 2 *****************************
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     The logical structure of this phase is:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     UPDATE = .TRUE.
</span><span class="comment">*</span><span class="comment">     DO I = 1, M
</span><span class="comment">*</span><span class="comment">        use S(i) to update A and create a new bulge
</span><span class="comment">*</span><span class="comment">        apply rotations to push all bulges KA positions upward
</span><span class="comment">*</span><span class="comment">     END DO
</span><span class="comment">*</span><span class="comment">     UPDATE = .FALSE.
</span><span class="comment">*</span><span class="comment">     DO I = M - KA - 1, 2, -1
</span><span class="comment">*</span><span class="comment">        apply rotations to push all bulges KA positions upward
</span><span class="comment">*</span><span class="comment">     END DO
12345

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