zgbbrd.f

famous linear algebra library (LAPACK) ports to windows

                  END IF
                  IF( NRT.GT.0 )
     $               CALL ZLARTV( NRT, AB( KLU1-L, J1-KLM+L-1 ), INCA,
     $                            AB( KLU1-L+1, J1-KLM+L-1 ), INCA,
     $                            RWORK( J1 ), WORK( J1 ), KB1 )
   10          CONTINUE
*
               IF( ML.GT.ML0 ) THEN
                  IF( ML.LE.M-I+1 ) THEN
*
*                    generate plane rotation to annihilate a(i+ml-1,i)
*                    within the band, and apply rotation from the left
*
                     CALL ZLARTG( AB( KU+ML-1, I ), AB( KU+ML, I ),
     $                            RWORK( I+ML-1 ), WORK( I+ML-1 ), RA )
                     AB( KU+ML-1, I ) = RA
                     IF( I.LT.N )
     $                  CALL ZROT( MIN( KU+ML-2, N-I ),
     $                             AB( KU+ML-2, I+1 ), LDAB-1,
     $                             AB( KU+ML-1, I+1 ), LDAB-1,
     $                             RWORK( I+ML-1 ), WORK( I+ML-1 ) )
                  END IF
                  NR = NR + 1
                  J1 = J1 - KB1
               END IF
*
               IF( WANTQ ) THEN
*
*                 accumulate product of plane rotations in Q
*
                  DO 20 J = J1, J2, KB1
                     CALL ZROT( M, Q( 1, J-1 ), 1, Q( 1, J ), 1,
     $                          RWORK( J ), DCONJG( WORK( J ) ) )
   20             CONTINUE
               END IF
*
               IF( WANTC ) THEN
*
*                 apply plane rotations to C
*
                  DO 30 J = J1, J2, KB1
                     CALL ZROT( NCC, C( J-1, 1 ), LDC, C( J, 1 ), LDC,
     $                          RWORK( J ), WORK( J ) )
   30             CONTINUE
               END IF
*
               IF( J2+KUN.GT.N ) THEN
*
*                 adjust J2 to keep within the bounds of the matrix
*
                  NR = NR - 1
                  J2 = J2 - KB1
               END IF
*
               DO 40 J = J1, J2, KB1
*
*                 create nonzero element a(j-1,j+ku) above the band
*                 and store it in WORK(n+1:2*n)
*
                  WORK( J+KUN ) = WORK( J )*AB( 1, J+KUN )
                  AB( 1, J+KUN ) = RWORK( J )*AB( 1, J+KUN )
   40          CONTINUE
*
*              generate plane rotations to annihilate nonzero elements
*              which have been generated above the band
*
               IF( NR.GT.0 )
     $            CALL ZLARGV( NR, AB( 1, J1+KUN-1 ), INCA,
     $                         WORK( J1+KUN ), KB1, RWORK( J1+KUN ),
     $                         KB1 )
*
*              apply plane rotations from the right
*
               DO 50 L = 1, KB
                  IF( J2+L-1.GT.M ) THEN
                     NRT = NR - 1
                  ELSE
                     NRT = NR
                  END IF
                  IF( NRT.GT.0 )
     $               CALL ZLARTV( NRT, AB( L+1, J1+KUN-1 ), INCA,
     $                            AB( L, J1+KUN ), INCA,
     $                            RWORK( J1+KUN ), WORK( J1+KUN ), KB1 )
   50          CONTINUE
*
               IF( ML.EQ.ML0 .AND. MU.GT.MU0 ) THEN
                  IF( MU.LE.N-I+1 ) THEN
*
*                    generate plane rotation to annihilate a(i,i+mu-1)
*                    within the band, and apply rotation from the right
*
                     CALL ZLARTG( AB( KU-MU+3, I+MU-2 ),
     $                            AB( KU-MU+2, I+MU-1 ),
     $                            RWORK( I+MU-1 ), WORK( I+MU-1 ), RA )
                     AB( KU-MU+3, I+MU-2 ) = RA
                     CALL ZROT( MIN( KL+MU-2, M-I ),
     $                          AB( KU-MU+4, I+MU-2 ), 1,
     $                          AB( KU-MU+3, I+MU-1 ), 1,
     $                          RWORK( I+MU-1 ), WORK( I+MU-1 ) )
                  END IF
                  NR = NR + 1
                  J1 = J1 - KB1
               END IF
*
               IF( WANTPT ) THEN
*
*                 accumulate product of plane rotations in P'
*
                  DO 60 J = J1, J2, KB1
                     CALL ZROT( N, PT( J+KUN-1, 1 ), LDPT,
     $                          PT( J+KUN, 1 ), LDPT, RWORK( J+KUN ),
     $                          DCONJG( WORK( J+KUN ) ) )
   60             CONTINUE
               END IF
*
               IF( J2+KB.GT.M ) THEN
*
*                 adjust J2 to keep within the bounds of the matrix
*
                  NR = NR - 1
                  J2 = J2 - KB1
               END IF
*
               DO 70 J = J1, J2, KB1
*
*                 create nonzero element a(j+kl+ku,j+ku-1) below the
*                 band and store it in WORK(1:n)
*
                  WORK( J+KB ) = WORK( J+KUN )*AB( KLU1, J+KUN )
                  AB( KLU1, J+KUN ) = RWORK( J+KUN )*AB( KLU1, J+KUN )
   70          CONTINUE
*
               IF( ML.GT.ML0 ) THEN
                  ML = ML - 1
               ELSE
                  MU = MU - 1
               END IF
   80       CONTINUE
   90    CONTINUE
      END IF
*
      IF( KU.EQ.0 .AND. KL.GT.0 ) THEN
*
*        A has been reduced to complex lower bidiagonal form
*
*        Transform lower bidiagonal form to upper bidiagonal by applying
*        plane rotations from the left, overwriting superdiagonal
*        elements on subdiagonal elements
*
         DO 100 I = 1, MIN( M-1, N )
            CALL ZLARTG( AB( 1, I ), AB( 2, I ), RC, RS, RA )
            AB( 1, I ) = RA
            IF( I.LT.N ) THEN
               AB( 2, I ) = RS*AB( 1, I+1 )
               AB( 1, I+1 ) = RC*AB( 1, I+1 )
            END IF
            IF( WANTQ )
     $         CALL ZROT( M, Q( 1, I ), 1, Q( 1, I+1 ), 1, RC,
     $                    DCONJG( RS ) )
            IF( WANTC )
     $         CALL ZROT( NCC, C( I, 1 ), LDC, C( I+1, 1 ), LDC, RC,
     $                    RS )
  100    CONTINUE
      ELSE
*
*        A has been reduced to complex upper bidiagonal form or is
*        diagonal
*
         IF( KU.GT.0 .AND. M.LT.N ) THEN
*
*           Annihilate a(m,m+1) by applying plane rotations from the
*           right
*
            RB = AB( KU, M+1 )
            DO 110 I = M, 1, -1
               CALL ZLARTG( AB( KU+1, I ), RB, RC, RS, RA )
               AB( KU+1, I ) = RA
               IF( I.GT.1 ) THEN
                  RB = -DCONJG( RS )*AB( KU, I )
                  AB( KU, I ) = RC*AB( KU, I )
               END IF
               IF( WANTPT )
     $            CALL ZROT( N, PT( I, 1 ), LDPT, PT( M+1, 1 ), LDPT,
     $                       RC, DCONJG( RS ) )
  110       CONTINUE
         END IF
      END IF
*
*     Make diagonal and superdiagonal elements real, storing them in D
*     and E
*
      T = AB( KU+1, 1 )
      DO 120 I = 1, MINMN
         ABST = ABS( T )
         D( I ) = ABST
         IF( ABST.NE.ZERO ) THEN
            T = T / ABST
         ELSE
            T = CONE
         END IF
         IF( WANTQ )
     $      CALL ZSCAL( M, T, Q( 1, I ), 1 )
         IF( WANTC )
     $      CALL ZSCAL( NCC, DCONJG( T ), C( I, 1 ), LDC )
         IF( I.LT.MINMN ) THEN
            IF( KU.EQ.0 .AND. KL.EQ.0 ) THEN
               E( I ) = ZERO
               T = AB( 1, I+1 )
            ELSE
               IF( KU.EQ.0 ) THEN
                  T = AB( 2, I )*DCONJG( T )
               ELSE
                  T = AB( KU, I+1 )*DCONJG( T )
               END IF
               ABST = ABS( T )
               E( I ) = ABST
               IF( ABST.NE.ZERO ) THEN
                  T = T / ABST
               ELSE
                  T = CONE
               END IF
               IF( WANTPT )
     $            CALL ZSCAL( N, T, PT( I+1, 1 ), LDPT )
               T = AB( KU+1, I+1 )*DCONJG( T )
            END IF
         END IF
  120 CONTINUE
      RETURN
*
*     End of ZGBBRD
*
      END