LAPACK: SRC/slagtm.f Source File

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00001       SUBROUTINE SLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
00002      $                   B, LDB )
00003 *
00004 *  -- LAPACK auxiliary routine (version 3.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     November 2006
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          TRANS
00011       INTEGER            LDB, LDX, N, NRHS
00012       REAL               ALPHA, BETA
00013 *     ..
00014 *     .. Array Arguments ..
00015       REAL               B( LDB, * ), D( * ), DL( * ), DU( * ),
00016      $                   X( LDX, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  SLAGTM performs a matrix-vector product of the form
00023 *
00024 *     B := alpha * A * X + beta * B
00025 *
00026 *  where A is a tridiagonal matrix of order N, B and X are N by NRHS
00027 *  matrices, and alpha and beta are real scalars, each of which may be
00028 *  0., 1., or -1.
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  TRANS   (input) CHARACTER*1
00034 *          Specifies the operation applied to A.
00035 *          = 'N':  No transpose, B := alpha * A * X + beta * B
00036 *          = 'T':  Transpose,    B := alpha * A'* X + beta * B
00037 *          = 'C':  Conjugate transpose = Transpose
00038 *
00039 *  N       (input) INTEGER
00040 *          The order of the matrix A.  N >= 0.
00041 *
00042 *  NRHS    (input) INTEGER
00043 *          The number of right hand sides, i.e., the number of columns
00044 *          of the matrices X and B.
00045 *
00046 *  ALPHA   (input) REAL
00047 *          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
00048 *          it is assumed to be 0.
00049 *
00050 *  DL      (input) REAL array, dimension (N-1)
00051 *          The (n-1) sub-diagonal elements of T.
00052 *
00053 *  D       (input) REAL array, dimension (N)
00054 *          The diagonal elements of T.
00055 *
00056 *  DU      (input) REAL array, dimension (N-1)
00057 *          The (n-1) super-diagonal elements of T.
00058 *
00059 *  X       (input) REAL array, dimension (LDX,NRHS)
00060 *          The N by NRHS matrix X.
00061 *  LDX     (input) INTEGER
00062 *          The leading dimension of the array X.  LDX >= max(N,1).
00063 *
00064 *  BETA    (input) REAL
00065 *          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
00066 *          it is assumed to be 1.
00067 *
00068 *  B       (input/output) REAL array, dimension (LDB,NRHS)
00069 *          On entry, the N by NRHS matrix B.
00070 *          On exit, B is overwritten by the matrix expression
00071 *          B := alpha * A * X + beta * B.
00072 *
00073 *  LDB     (input) INTEGER
00074 *          The leading dimension of the array B.  LDB >= max(N,1).
00075 *
00076 *  =====================================================================
00077 *
00078 *     .. Parameters ..
00079       REAL               ONE, ZERO
00080       PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
00081 *     ..
00082 *     .. Local Scalars ..
00083       INTEGER            I, J
00084 *     ..
00085 *     .. External Functions ..
00086       LOGICAL            LSAME
00087       EXTERNAL           LSAME
00088 *     ..
00089 *     .. Executable Statements ..
00090 *
00091       IF( N.EQ.0 )
00092      $   RETURN
00093 *
00094 *     Multiply B by BETA if BETA.NE.1.
00095 *
00096       IF( BETA.EQ.ZERO ) THEN
00097          DO 20 J = 1, NRHS
00098             DO 10 I = 1, N
00099                B( I, J ) = ZERO
00100    10       CONTINUE
00101    20    CONTINUE
00102       ELSE IF( BETA.EQ.-ONE ) THEN
00103          DO 40 J = 1, NRHS
00104             DO 30 I = 1, N
00105                B( I, J ) = -B( I, J )
00106    30       CONTINUE
00107    40    CONTINUE
00108       END IF
00109 *
00110       IF( ALPHA.EQ.ONE ) THEN
00111          IF( LSAME( TRANS, 'N' ) ) THEN
00112 *
00113 *           Compute B := B + A*X
00114 *
00115             DO 60 J = 1, NRHS
00116                IF( N.EQ.1 ) THEN
00117                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
00118                ELSE
00119                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
00120      $                        DU( 1 )*X( 2, J )
00121                   B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
00122      $                        D( N )*X( N, J )
00123                   DO 50 I = 2, N - 1
00124                      B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
00125      $                           D( I )*X( I, J ) + DU( I )*X( I+1, J )
00126    50             CONTINUE
00127                END IF
00128    60       CONTINUE
00129          ELSE
00130 *
00131 *           Compute B := B + A'*X
00132 *
00133             DO 80 J = 1, NRHS
00134                IF( N.EQ.1 ) THEN
00135                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
00136                ELSE
00137                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
00138      $                        DL( 1 )*X( 2, J )
00139                   B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
00140      $                        D( N )*X( N, J )
00141                   DO 70 I = 2, N - 1
00142                      B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
00143      $                           D( I )*X( I, J ) + DL( I )*X( I+1, J )
00144    70             CONTINUE
00145                END IF
00146    80       CONTINUE
00147          END IF
00148       ELSE IF( ALPHA.EQ.-ONE ) THEN
00149          IF( LSAME( TRANS, 'N' ) ) THEN
00150 *
00151 *           Compute B := B - A*X
00152 *
00153             DO 100 J = 1, NRHS
00154                IF( N.EQ.1 ) THEN
00155                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
00156                ELSE
00157                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
00158      $                        DU( 1 )*X( 2, J )
00159                   B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
00160      $                        D( N )*X( N, J )
00161                   DO 90 I = 2, N - 1
00162                      B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
00163      $                           D( I )*X( I, J ) - DU( I )*X( I+1, J )
00164    90             CONTINUE
00165                END IF
00166   100       CONTINUE
00167          ELSE
00168 *
00169 *           Compute B := B - A'*X
00170 *
00171             DO 120 J = 1, NRHS
00172                IF( N.EQ.1 ) THEN
00173                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
00174                ELSE
00175                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
00176      $                        DL( 1 )*X( 2, J )
00177                   B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
00178      $                        D( N )*X( N, J )
00179                   DO 110 I = 2, N - 1
00180                      B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
00181      $                           D( I )*X( I, J ) - DL( I )*X( I+1, J )
00182   110             CONTINUE
00183                END IF
00184   120       CONTINUE
00185          END IF
00186       END IF
00187       RETURN
00188 *
00189 *     End of SLAGTM
00190 *
00191       END