LAPACK: SRC/clagtm.f Source File

Go to the documentation of this file.
00001       SUBROUTINE CLAGTM( 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       COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * ),
00016      $                   X( LDX, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  CLAGTM 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**T * X + beta * B
00037 *          = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B
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) COMPLEX array, dimension (N-1)
00051 *          The (n-1) sub-diagonal elements of T.
00052 *
00053 *  D       (input) COMPLEX array, dimension (N)
00054 *          The diagonal elements of T.
00055 *
00056 *  DU      (input) COMPLEX array, dimension (N-1)
00057 *          The (n-1) super-diagonal elements of T.
00058 *
00059 *  X       (input) COMPLEX 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) COMPLEX 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 *     .. Intrinsic Functions ..
00090       INTRINSIC          CONJG
00091 *     ..
00092 *     .. Executable Statements ..
00093 *
00094       IF( N.EQ.0 )
00095      $   RETURN
00096 *
00097 *     Multiply B by BETA if BETA.NE.1.
00098 *
00099       IF( BETA.EQ.ZERO ) THEN
00100          DO 20 J = 1, NRHS
00101             DO 10 I = 1, N
00102                B( I, J ) = ZERO
00103    10       CONTINUE
00104    20    CONTINUE
00105       ELSE IF( BETA.EQ.-ONE ) THEN
00106          DO 40 J = 1, NRHS
00107             DO 30 I = 1, N
00108                B( I, J ) = -B( I, J )
00109    30       CONTINUE
00110    40    CONTINUE
00111       END IF
00112 *
00113       IF( ALPHA.EQ.ONE ) THEN
00114          IF( LSAME( TRANS, 'N' ) ) THEN
00115 *
00116 *           Compute B := B + A*X
00117 *
00118             DO 60 J = 1, NRHS
00119                IF( N.EQ.1 ) THEN
00120                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
00121                ELSE
00122                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
00123      $                        DU( 1 )*X( 2, J )
00124                   B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
00125      $                        D( N )*X( N, J )
00126                   DO 50 I = 2, N - 1
00127                      B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
00128      $                           D( I )*X( I, J ) + DU( I )*X( I+1, J )
00129    50             CONTINUE
00130                END IF
00131    60       CONTINUE
00132          ELSE IF( LSAME( TRANS, 'T' ) ) THEN
00133 *
00134 *           Compute B := B + A**T * X
00135 *
00136             DO 80 J = 1, NRHS
00137                IF( N.EQ.1 ) THEN
00138                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
00139                ELSE
00140                   B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
00141      $                        DL( 1 )*X( 2, J )
00142                   B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
00143      $                        D( N )*X( N, J )
00144                   DO 70 I = 2, N - 1
00145                      B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
00146      $                           D( I )*X( I, J ) + DL( I )*X( I+1, J )
00147    70             CONTINUE
00148                END IF
00149    80       CONTINUE
00150          ELSE IF( LSAME( TRANS, 'C' ) ) THEN
00151 *
00152 *           Compute B := B + A**H * X
00153 *
00154             DO 100 J = 1, NRHS
00155                IF( N.EQ.1 ) THEN
00156                   B( 1, J ) = B( 1, J ) + CONJG( D( 1 ) )*X( 1, J )
00157                ELSE
00158                   B( 1, J ) = B( 1, J ) + CONJG( D( 1 ) )*X( 1, J ) +
00159      $                        CONJG( DL( 1 ) )*X( 2, J )
00160                   B( N, J ) = B( N, J ) + CONJG( DU( N-1 ) )*
00161      $                        X( N-1, J ) + CONJG( D( N ) )*X( N, J )
00162                   DO 90 I = 2, N - 1
00163                      B( I, J ) = B( I, J ) + CONJG( DU( I-1 ) )*
00164      $                           X( I-1, J ) + CONJG( D( I ) )*
00165      $                           X( I, J ) + CONJG( DL( I ) )*
00166      $                           X( I+1, J )
00167    90             CONTINUE
00168                END IF
00169   100       CONTINUE
00170          END IF
00171       ELSE IF( ALPHA.EQ.-ONE ) THEN
00172          IF( LSAME( TRANS, 'N' ) ) THEN
00173 *
00174 *           Compute B := B - A*X
00175 *
00176             DO 120 J = 1, NRHS
00177                IF( N.EQ.1 ) THEN
00178                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
00179                ELSE
00180                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
00181      $                        DU( 1 )*X( 2, J )
00182                   B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
00183      $                        D( N )*X( N, J )
00184                   DO 110 I = 2, N - 1
00185                      B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
00186      $                           D( I )*X( I, J ) - DU( I )*X( I+1, J )
00187   110             CONTINUE
00188                END IF
00189   120       CONTINUE
00190          ELSE IF( LSAME( TRANS, 'T' ) ) THEN
00191 *
00192 *           Compute B := B - A'*X
00193 *
00194             DO 140 J = 1, NRHS
00195                IF( N.EQ.1 ) THEN
00196                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
00197                ELSE
00198                   B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
00199      $                        DL( 1 )*X( 2, J )
00200                   B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
00201      $                        D( N )*X( N, J )
00202                   DO 130 I = 2, N - 1
00203                      B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
00204      $                           D( I )*X( I, J ) - DL( I )*X( I+1, J )
00205   130             CONTINUE
00206                END IF
00207   140       CONTINUE
00208          ELSE IF( LSAME( TRANS, 'C' ) ) THEN
00209 *
00210 *           Compute B := B - A'*X
00211 *
00212             DO 160 J = 1, NRHS
00213                IF( N.EQ.1 ) THEN
00214                   B( 1, J ) = B( 1, J ) - CONJG( D( 1 ) )*X( 1, J )
00215                ELSE
00216                   B( 1, J ) = B( 1, J ) - CONJG( D( 1 ) )*X( 1, J ) -
00217      $                        CONJG( DL( 1 ) )*X( 2, J )
00218                   B( N, J ) = B( N, J ) - CONJG( DU( N-1 ) )*
00219      $                        X( N-1, J ) - CONJG( D( N ) )*X( N, J )
00220                   DO 150 I = 2, N - 1
00221                      B( I, J ) = B( I, J ) - CONJG( DU( I-1 ) )*
00222      $                           X( I-1, J ) - CONJG( D( I ) )*
00223      $                           X( I, J ) - CONJG( DL( I ) )*
00224      $                           X( I+1, J )
00225   150             CONTINUE
00226                END IF
00227   160       CONTINUE
00228          END IF
00229       END IF
00230       RETURN
00231 *
00232 *     End of CLAGTM
00233 *
00234       END