slagtm.f.html

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      SUBROUTINE <a name="SLAGTM.1"></a><a href="slagtm.f.html#SLAGTM.1">SLAGTM</a>( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
     $                   B, LDB )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          TRANS
      INTEGER            LDB, LDX, N, NRHS
      REAL               ALPHA, BETA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               B( LDB, * ), D( * ), DL( * ), DU( * ),
     $                   X( LDX, * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="SLAGTM.21"></a><a href="slagtm.f.html#SLAGTM.1">SLAGTM</a> performs a matrix-vector product of the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     B := alpha * A * X + beta * B
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where A is a tridiagonal matrix of order N, B and X are N by NRHS
</span><span class="comment">*</span><span class="comment">  matrices, and alpha and beta are real scalars, each of which may be
</span><span class="comment">*</span><span class="comment">  0., 1., or -1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TRANS   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the operation applied to A.
</span><span class="comment">*</span><span class="comment">          = 'N':  No transpose, B := alpha * A * X + beta * B
</span><span class="comment">*</span><span class="comment">          = 'T':  Transpose,    B := alpha * A'* X + beta * B
</span><span class="comment">*</span><span class="comment">          = 'C':  Conjugate transpose = Transpose
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrices X and B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ALPHA   (input) REAL
</span><span class="comment">*</span><span class="comment">          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
</span><span class="comment">*</span><span class="comment">          it is assumed to be 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DL      (input) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) sub-diagonal elements of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The diagonal elements of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DU      (input) REAL array, dimension (N-1)
</span><span class="comment">*</span><span class="comment">          The (n-1) super-diagonal elements of T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  X       (input) REAL array, dimension (LDX,NRHS)
</span><span class="comment">*</span><span class="comment">          The N by NRHS matrix X.
</span><span class="comment">*</span><span class="comment">  LDX     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array X.  LDX &gt;= max(N,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  BETA    (input) REAL
</span><span class="comment">*</span><span class="comment">          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
</span><span class="comment">*</span><span class="comment">          it is assumed to be 1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) REAL array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the N by NRHS matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, B is overwritten by the matrix expression
</span><span class="comment">*</span><span class="comment">          B := alpha * A * X + beta * B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(N,1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.85"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Multiply B by BETA if BETA.NE.1.
</span><span class="comment">*</span><span class="comment">
</span>      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
<span class="comment">*</span><span class="comment">
</span>      IF( ALPHA.EQ.ONE ) THEN
         IF( <a name="LSAME.110"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute B := B + A*X
</span><span class="comment">*</span><span class="comment">
</span>            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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute B := B + A'*X
</span><span class="comment">*</span><span class="comment">
</span>            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( <a name="LSAME.148"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( TRANS, <span class="string">'N'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute B := B - A*X
</span><span class="comment">*</span><span class="comment">
</span>            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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute B := B - A'*X
</span><span class="comment">*</span><span class="comment">
</span>            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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLAGTM.188"></a><a href="slagtm.f.html#SLAGTM.1">SLAGTM</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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