slagtm.f

          SUBROUTINE SLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
         $                   B, LDB )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          TRANS
          INTEGER            LDB, LDX, N, NRHS
          REAL               ALPHA, BETA
    *     ..
    *     .. Array Arguments ..
          REAL               B( LDB, * ), D( * ), DL( * ), DU( * ),
         $                   X( LDX, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SLAGTM performs a matrix-vector product of the form
    *
    *     B := alpha * A * X + beta * B
    *
    *  where A is a tridiagonal matrix of order N, B and X are N by NRHS
    *  matrices, and alpha and beta are real scalars, each of which may be
    *  0., 1., or -1.
    *
    *  Arguments
    *  =========
    *
    *  TRANS   (input) CHARACTER*1
    *          Specifies the operation applied to A.
    *          = 'N':  No transpose, B := alpha * A * X + beta * B
    *          = 'T':  Transpose,    B := alpha * A'* X + beta * B
    *          = 'C':  Conjugate transpose = Transpose
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrices X and B.
    *
    *  ALPHA   (input) REAL
    *          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
    *          it is assumed to be 0.
    *
    *  DL      (input) REAL array, dimension (N-1)
    *          The (n-1) sub-diagonal elements of T.
    *
    *  D       (input) REAL array, dimension (N)
    *          The diagonal elements of T.
    *
    *  DU      (input) REAL array, dimension (N-1)
    *          The (n-1) super-diagonal elements of T.
    *
    *  X       (input) REAL array, dimension (LDX,NRHS)
    *          The N by NRHS matrix X.
    *  LDX     (input) INTEGER
    *          The leading dimension of the array X.  LDX >= max(N,1).
    *
    *  BETA    (input) REAL
    *          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
    *          it is assumed to be 1.
    *
    *  B       (input/output) REAL array, dimension (LDB,NRHS)
    *          On entry, the N by NRHS matrix B.
    *          On exit, B is overwritten by the matrix expression
    *          B := alpha * A * X + beta * B.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(N,1).
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, J
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Executable Statements ..
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Multiply B by BETA if BETA.NE.1.
    *
          IF( BETA.EQ.ZERO ) THEN
             DO 20 J = 1, NRHS
                DO 10 I = 1, N
                   B( I, J ) = ZERO
       10       CONTINUE
       20    CONTINUE
          ELSE IF( BETA.EQ.-ONE ) THEN
             DO 40 J = 1, NRHS
                DO 30 I = 1, N
                   B( I, J ) = -B( I, J )
       30       CONTINUE
       40    CONTINUE
          END IF
    *
          IF( ALPHA.EQ.ONE ) THEN
             IF( LSAME( TRANS, 'N' ) ) THEN
    *
    *           Compute B := B + A*X
    *
                DO 60 J = 1, NRHS
                   IF( N.EQ.1 ) THEN
                      B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
                   ELSE
                      B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
         $                        DU( 1 )*X( 2, J )
                      B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
         $                        D( N )*X( N, J )
                      DO 50 I = 2, N - 1
                         B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
         $                           D( I )*X( I, J ) + DU( I )*X( I+1, J )
       50             CONTINUE
                   END IF
       60       CONTINUE
             ELSE
    *
    *           Compute B := B + A'*X
    *
                DO 80 J = 1, NRHS
                   IF( N.EQ.1 ) THEN
                      B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
                   ELSE
                      B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
         $                        DL( 1 )*X( 2, J )
                      B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
         $                        D( N )*X( N, J )
                      DO 70 I = 2, N - 1
                         B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
         $                           D( I )*X( I, J ) + DL( I )*X( I+1, J )
       70             CONTINUE
                   END IF
       80       CONTINUE
             END IF
          ELSE IF( ALPHA.EQ.-ONE ) THEN
             IF( LSAME( TRANS, 'N' ) ) THEN
    *
    *           Compute B := B - A*X
    *
                DO 100 J = 1, NRHS
                   IF( N.EQ.1 ) THEN
                      B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
                   ELSE
                      B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
         $                        DU( 1 )*X( 2, J )
                      B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
         $                        D( N )*X( N, J )
                      DO 90 I = 2, N - 1
                         B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
         $                           D( I )*X( I, J ) - DU( I )*X( I+1, J )
       90             CONTINUE
                   END IF
      100       CONTINUE
             ELSE
    *
    *           Compute B := B - A'*X
    *
                DO 120 J = 1, NRHS
                   IF( N.EQ.1 ) THEN
                      B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
                   ELSE
                      B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
         $                        DL( 1 )*X( 2, J )
                      B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
         $                        D( N )*X( N, J )
                      DO 110 I = 2, N - 1
                         B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
         $                           D( I )*X( I, J ) - DL( I )*X( I+1, J )
      110             CONTINUE
                   END IF
      120       CONTINUE
             END IF
          END IF
          RETURN
    *
    *     End of SLAGTM
    *
          END