zgtts2.f

          SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            ITRANS, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          INTEGER            IPIV( * )
          COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZGTTS2 solves one of the systems of equations
    *     A * X = B,  A**T * X = B,  or  A**H * X = B,
    *  with a tridiagonal matrix A using the LU factorization computed
    *  by ZGTTRF.
    *
    *  Arguments
    *  =========
    *
    *  ITRANS  (input) INTEGER
    *          Specifies the form of the system of equations.
    *          = 0:  A * X = B     (No transpose)
    *          = 1:  A**T * X = B  (Transpose)
    *          = 2:  A**H * X = B  (Conjugate transpose)
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrix B.  NRHS >= 0.
    *
    *  DL      (input) COMPLEX*16 array, dimension (N-1)
    *          The (n-1) multipliers that define the matrix L from the
    *          LU factorization of A.
    *
    *  D       (input) COMPLEX*16 array, dimension (N)
    *          The n diagonal elements of the upper triangular matrix U from
    *          the LU factorization of A.
    *
    *  DU      (input) COMPLEX*16 array, dimension (N-1)
    *          The (n-1) elements of the first super-diagonal of U.
    *
    *  DU2     (input) COMPLEX*16 array, dimension (N-2)
    *          The (n-2) elements of the second super-diagonal of U.
    *
    *  IPIV    (input) INTEGER array, dimension (N)
    *          The pivot indices; for 1 <= i <= n, row i of the matrix was
    *          interchanged with row IPIV(i).  IPIV(i) will always be either
    *          i or i+1; IPIV(i) = i indicates a row interchange was not
    *          required.
    *
    *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
    *          On entry, the matrix of right hand side vectors B.
    *          On exit, B is overwritten by the solution vectors X.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,N).
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          INTEGER            I, J
          COMPLEX*16         TEMP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          DCONJG
    *     ..
    *     .. Executable Statements ..
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 .OR. NRHS.EQ.0 )
         $   RETURN
    *
          IF( ITRANS.EQ.0 ) THEN
    *
    *        Solve A*X = B using the LU factorization of A,
    *        overwriting each right hand side vector with its solution.
    *
             IF( NRHS.LE.1 ) THEN
                J = 1
       10       CONTINUE
    *
    *           Solve L*x = b.
    *
                DO 20 I = 1, N - 1
                   IF( IPIV( I ).EQ.I ) THEN
                      B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
                   ELSE
                      TEMP = B( I, J )
                      B( I, J ) = B( I+1, J )
                      B( I+1, J ) = TEMP - DL( I )*B( I, J )
                   END IF
       20       CONTINUE
    *
    *           Solve U*x = b.
    *
                B( N, J ) = B( N, J ) / D( N )
                IF( N.GT.1 )
         $         B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
         $                       D( N-1 )
                DO 30 I = N - 2, 1, -1
                   B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
         $                     B( I+2, J ) ) / D( I )
       30       CONTINUE
                IF( J.LT.NRHS ) THEN
                   J = J + 1
                   GO TO 10
                END IF
             ELSE
                DO 60 J = 1, NRHS
    *
    *           Solve L*x = b.
    *
                   DO 40 I = 1, N - 1
                      IF( IPIV( I ).EQ.I ) THEN
                         B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
                      ELSE
                         TEMP = B( I, J )
                         B( I, J ) = B( I+1, J )
                         B( I+1, J ) = TEMP - DL( I )*B( I, J )
                      END IF
       40          CONTINUE
    *
    *           Solve U*x = b.
    *
                   B( N, J ) = B( N, J ) / D( N )
                   IF( N.GT.1 )
         $            B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
         $                          D( N-1 )
                   DO 50 I = N - 2, 1, -1
                      B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
         $                        B( I+2, J ) ) / D( I )
       50          CONTINUE
       60       CONTINUE
             END IF
          ELSE IF( ITRANS.EQ.1 ) THEN
    *
    *        Solve A**T * X = B.
    *
             IF( NRHS.LE.1 ) THEN
                J = 1
       70       CONTINUE
    *
    *           Solve U**T * x = b.
    *
                B( 1, J ) = B( 1, J ) / D( 1 )
                IF( N.GT.1 )
         $         B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
                DO 80 I = 3, N
                   B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
         $                     B( I-2, J ) ) / D( I )
       80       CONTINUE
    *
    *           Solve L**T * x = b.
    *
                DO 90 I = N - 1, 1, -1
                   IF( IPIV( I ).EQ.I ) THEN
                      B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
                   ELSE
                      TEMP = B( I+1, J )
                      B( I+1, J ) = B( I, J ) - DL( I )*TEMP
                      B( I, J ) = TEMP
                   END IF
       90       CONTINUE
                IF( J.LT.NRHS ) THEN
                   J = J + 1
                   GO TO 70
                END IF
             ELSE
                DO 120 J = 1, NRHS
    *
    *           Solve U**T * x = b.
    *
                   B( 1, J ) = B( 1, J ) / D( 1 )
                   IF( N.GT.1 )
         $            B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
                   DO 100 I = 3, N
                      B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
         $                        DU2( I-2 )*B( I-2, J ) ) / D( I )
      100          CONTINUE
    *
    *           Solve L**T * x = b.
    *
                   DO 110 I = N - 1, 1, -1
                      IF( IPIV( I ).EQ.I ) THEN
                         B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
                      ELSE
                         TEMP = B( I+1, J )
                         B( I+1, J ) = B( I, J ) - DL( I )*TEMP
                         B( I, J ) = TEMP
                      END IF
      110          CONTINUE
      120       CONTINUE
             END IF
          ELSE
    *
    *        Solve A**H * X = B.
    *
             IF( NRHS.LE.1 ) THEN
                J = 1
      130       CONTINUE
    *
    *           Solve U**H * x = b.
    *
                B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
                IF( N.GT.1 )
         $         B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) /
         $                     DCONJG( D( 2 ) )
                DO 140 I = 3, N
                   B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )-
         $                     DCONJG( DU2( I-2 ) )*B( I-2, J ) ) /
         $                     DCONJG( D( I ) )
      140       CONTINUE
    *
    *           Solve L**H * x = b.
    *
                DO 150 I = N - 1, 1, -1
                   IF( IPIV( I ).EQ.I ) THEN
                      B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J )
                   ELSE
                      TEMP = B( I+1, J )
                      B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
                      B( I, J ) = TEMP
                   END IF
      150       CONTINUE
                IF( J.LT.NRHS ) THEN
                   J = J + 1
                   GO TO 130
                END IF
             ELSE
                DO 180 J = 1, NRHS
    *
    *           Solve U**H * x = b.
    *
                   B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) )
                   IF( N.GT.1 )
         $            B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) )
         $                         / DCONJG( D( 2 ) )
                   DO 160 I = 3, N
                      B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*
         $                        B( I-1, J )-DCONJG( DU2( I-2 ) )*
         $                        B( I-2, J ) ) / DCONJG( D( I ) )
      160          CONTINUE
    *
    *           Solve L**H * x = b.
    *
                   DO 170 I = N - 1, 1, -1
                      IF( IPIV( I ).EQ.I ) THEN
                         B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*
         $                           B( I+1, J )
                      ELSE
                         TEMP = B( I+1, J )
                         B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP
                         B( I, J ) = TEMP
                      END IF
      170          CONTINUE
      180       CONTINUE
             END IF
          END IF
    *
    *     End of ZGTTS2
    *
          END