LAPACK: SRC/cgtts2.f Source File

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00001       SUBROUTINE CGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            ITRANS, LDB, N, NRHS
00010 *     ..
00011 *     .. Array Arguments ..
00012       INTEGER            IPIV( * )
00013       COMPLEX            B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  CGTTS2 solves one of the systems of equations
00020 *     A * X = B,  A**T * X = B,  or  A**H * X = B,
00021 *  with a tridiagonal matrix A using the LU factorization computed
00022 *  by CGTTRF.
00023 *
00024 *  Arguments
00025 *  =========
00026 *
00027 *  ITRANS  (input) INTEGER
00028 *          Specifies the form of the system of equations.
00029 *          = 0:  A * X = B     (No transpose)
00030 *          = 1:  A**T * X = B  (Transpose)
00031 *          = 2:  A**H * X = B  (Conjugate transpose)
00032 *
00033 *  N       (input) INTEGER
00034 *          The order of the matrix A.
00035 *
00036 *  NRHS    (input) INTEGER
00037 *          The number of right hand sides, i.e., the number of columns
00038 *          of the matrix B.  NRHS >= 0.
00039 *
00040 *  DL      (input) COMPLEX array, dimension (N-1)
00041 *          The (n-1) multipliers that define the matrix L from the
00042 *          LU factorization of A.
00043 *
00044 *  D       (input) COMPLEX array, dimension (N)
00045 *          The n diagonal elements of the upper triangular matrix U from
00046 *          the LU factorization of A.
00047 *
00048 *  DU      (input) COMPLEX array, dimension (N-1)
00049 *          The (n-1) elements of the first super-diagonal of U.
00050 *
00051 *  DU2     (input) COMPLEX array, dimension (N-2)
00052 *          The (n-2) elements of the second super-diagonal of U.
00053 *
00054 *  IPIV    (input) INTEGER array, dimension (N)
00055 *          The pivot indices; for 1 <= i <= n, row i of the matrix was
00056 *          interchanged with row IPIV(i).  IPIV(i) will always be either
00057 *          i or i+1; IPIV(i) = i indicates a row interchange was not
00058 *          required.
00059 *
00060 *  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
00061 *          On entry, the matrix of right hand side vectors B.
00062 *          On exit, B is overwritten by the solution vectors X.
00063 *
00064 *  LDB     (input) INTEGER
00065 *          The leading dimension of the array B.  LDB >= max(1,N).
00066 *
00067 *  =====================================================================
00068 *
00069 *     .. Local Scalars ..
00070       INTEGER            I, J
00071       COMPLEX            TEMP
00072 *     ..
00073 *     .. Intrinsic Functions ..
00074       INTRINSIC          CONJG
00075 *     ..
00076 *     .. Executable Statements ..
00077 *
00078 *     Quick return if possible
00079 *
00080       IF( N.EQ.0 .OR. NRHS.EQ.0 )
00081      $   RETURN
00082 *
00083       IF( ITRANS.EQ.0 ) THEN
00084 *
00085 *        Solve A*X = B using the LU factorization of A,
00086 *        overwriting each right hand side vector with its solution.
00087 *
00088          IF( NRHS.LE.1 ) THEN
00089             J = 1
00090    10       CONTINUE
00091 *
00092 *           Solve L*x = b.
00093 *
00094             DO 20 I = 1, N - 1
00095                IF( IPIV( I ).EQ.I ) THEN
00096                   B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
00097                ELSE
00098                   TEMP = B( I, J )
00099                   B( I, J ) = B( I+1, J )
00100                   B( I+1, J ) = TEMP - DL( I )*B( I, J )
00101                END IF
00102    20       CONTINUE
00103 *
00104 *           Solve U*x = b.
00105 *
00106             B( N, J ) = B( N, J ) / D( N )
00107             IF( N.GT.1 )
00108      $         B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
00109      $                       D( N-1 )
00110             DO 30 I = N - 2, 1, -1
00111                B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
00112      $                     B( I+2, J ) ) / D( I )
00113    30       CONTINUE
00114             IF( J.LT.NRHS ) THEN
00115                J = J + 1
00116                GO TO 10
00117             END IF
00118          ELSE
00119             DO 60 J = 1, NRHS
00120 *
00121 *           Solve L*x = b.
00122 *
00123                DO 40 I = 1, N - 1
00124                   IF( IPIV( I ).EQ.I ) THEN
00125                      B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J )
00126                   ELSE
00127                      TEMP = B( I, J )
00128                      B( I, J ) = B( I+1, J )
00129                      B( I+1, J ) = TEMP - DL( I )*B( I, J )
00130                   END IF
00131    40          CONTINUE
00132 *
00133 *           Solve U*x = b.
00134 *
00135                B( N, J ) = B( N, J ) / D( N )
00136                IF( N.GT.1 )
00137      $            B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) /
00138      $                          D( N-1 )
00139                DO 50 I = N - 2, 1, -1
00140                   B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )*
00141      $                        B( I+2, J ) ) / D( I )
00142    50          CONTINUE
00143    60       CONTINUE
00144          END IF
00145       ELSE IF( ITRANS.EQ.1 ) THEN
00146 *
00147 *        Solve A**T * X = B.
00148 *
00149          IF( NRHS.LE.1 ) THEN
00150             J = 1
00151    70       CONTINUE
00152 *
00153 *           Solve U**T * x = b.
00154 *
00155             B( 1, J ) = B( 1, J ) / D( 1 )
00156             IF( N.GT.1 )
00157      $         B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
00158             DO 80 I = 3, N
00159                B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )*
00160      $                     B( I-2, J ) ) / D( I )
00161    80       CONTINUE
00162 *
00163 *           Solve L**T * x = b.
00164 *
00165             DO 90 I = N - 1, 1, -1
00166                IF( IPIV( I ).EQ.I ) THEN
00167                   B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
00168                ELSE
00169                   TEMP = B( I+1, J )
00170                   B( I+1, J ) = B( I, J ) - DL( I )*TEMP
00171                   B( I, J ) = TEMP
00172                END IF
00173    90       CONTINUE
00174             IF( J.LT.NRHS ) THEN
00175                J = J + 1
00176                GO TO 70
00177             END IF
00178          ELSE
00179             DO 120 J = 1, NRHS
00180 *
00181 *           Solve U**T * x = b.
00182 *
00183                B( 1, J ) = B( 1, J ) / D( 1 )
00184                IF( N.GT.1 )
00185      $            B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 )
00186                DO 100 I = 3, N
00187                   B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-
00188      $                        DU2( I-2 )*B( I-2, J ) ) / D( I )
00189   100          CONTINUE
00190 *
00191 *           Solve L**T * x = b.
00192 *
00193                DO 110 I = N - 1, 1, -1
00194                   IF( IPIV( I ).EQ.I ) THEN
00195                      B( I, J ) = B( I, J ) - DL( I )*B( I+1, J )
00196                   ELSE
00197                      TEMP = B( I+1, J )
00198                      B( I+1, J ) = B( I, J ) - DL( I )*TEMP
00199                      B( I, J ) = TEMP
00200                   END IF
00201   110          CONTINUE
00202   120       CONTINUE
00203          END IF
00204       ELSE
00205 *
00206 *        Solve A**H * X = B.
00207 *
00208          IF( NRHS.LE.1 ) THEN
00209             J = 1
00210   130       CONTINUE
00211 *
00212 *           Solve U**H * x = b.
00213 *
00214             B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
00215             IF( N.GT.1 )
00216      $         B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
00217      $                     CONJG( D( 2 ) )
00218             DO 140 I = 3, N
00219                B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*B( I-1, J )-
00220      $                     CONJG( DU2( I-2 ) )*B( I-2, J ) ) /
00221      $                     CONJG( D( I ) )
00222   140       CONTINUE
00223 *
00224 *           Solve L**H * x = b.
00225 *
00226             DO 150 I = N - 1, 1, -1
00227                IF( IPIV( I ).EQ.I ) THEN
00228                   B( I, J ) = B( I, J ) - CONJG( DL( I ) )*B( I+1, J )
00229                ELSE
00230                   TEMP = B( I+1, J )
00231                   B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
00232                   B( I, J ) = TEMP
00233                END IF
00234   150       CONTINUE
00235             IF( J.LT.NRHS ) THEN
00236                J = J + 1
00237                GO TO 130
00238             END IF
00239          ELSE
00240             DO 180 J = 1, NRHS
00241 *
00242 *           Solve U**H * x = b.
00243 *
00244                B( 1, J ) = B( 1, J ) / CONJG( D( 1 ) )
00245                IF( N.GT.1 )
00246      $            B( 2, J ) = ( B( 2, J )-CONJG( DU( 1 ) )*B( 1, J ) ) /
00247      $                        CONJG( D( 2 ) )
00248                DO 160 I = 3, N
00249                   B( I, J ) = ( B( I, J )-CONJG( DU( I-1 ) )*
00250      $                        B( I-1, J )-CONJG( DU2( I-2 ) )*
00251      $                        B( I-2, J ) ) / CONJG( D( I ) )
00252   160          CONTINUE
00253 *
00254 *           Solve L**H * x = b.
00255 *
00256                DO 170 I = N - 1, 1, -1
00257                   IF( IPIV( I ).EQ.I ) THEN
00258                      B( I, J ) = B( I, J ) - CONJG( DL( I ) )*
00259      $                           B( I+1, J )
00260                   ELSE
00261                      TEMP = B( I+1, J )
00262                      B( I+1, J ) = B( I, J ) - CONJG( DL( I ) )*TEMP
00263                      B( I, J ) = TEMP
00264                   END IF
00265   170          CONTINUE
00266   180       CONTINUE
00267          END IF
00268       END IF
00269 *
00270 *     End of CGTTS2
00271 *
00272       END