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1 SUBROUTINE DGTTRS( TRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB, |
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2 $ INFO ) |
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3 * |
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4 * -- LAPACK routine (version 3.1) -- |
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5 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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6 * November 2006 |
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7 * |
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8 * .. Scalar Arguments .. |
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9 CHARACTER TRANS |
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10 INTEGER INFO, LDB, N, NRHS |
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11 * .. |
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12 * .. Array Arguments .. |
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13 INTEGER IPIV( * ) |
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14 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
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15 * .. |
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16 * |
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17 * Purpose |
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18 * ======= |
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19 * |
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20 * DGTTRS solves one of the systems of equations |
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21 * A*X = B or A'*X = B, |
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22 * with a tridiagonal matrix A using the LU factorization computed |
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23 * by DGTTRF. |
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24 * |
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25 * Arguments |
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26 * ========= |
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27 * |
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28 * TRANS (input) CHARACTER*1 |
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29 * Specifies the form of the system of equations. |
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30 * = 'N': A * X = B (No transpose) |
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31 * = 'T': A'* X = B (Transpose) |
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32 * = 'C': A'* X = B (Conjugate transpose = Transpose) |
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33 * |
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34 * N (input) INTEGER |
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35 * The order of the matrix A. |
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36 * |
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37 * NRHS (input) INTEGER |
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38 * The number of right hand sides, i.e., the number of columns |
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39 * of the matrix B. NRHS >= 0. |
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40 * |
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41 * DL (input) DOUBLE PRECISION array, dimension (N-1) |
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42 * The (n-1) multipliers that define the matrix L from the |
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43 * LU factorization of A. |
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44 * |
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45 * D (input) DOUBLE PRECISION array, dimension (N) |
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46 * The n diagonal elements of the upper triangular matrix U from |
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47 * the LU factorization of A. |
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48 * |
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49 * DU (input) DOUBLE PRECISION array, dimension (N-1) |
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50 * The (n-1) elements of the first super-diagonal of U. |
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51 * |
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52 * DU2 (input) DOUBLE PRECISION array, dimension (N-2) |
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53 * The (n-2) elements of the second super-diagonal of U. |
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54 * |
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55 * IPIV (input) INTEGER array, dimension (N) |
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56 * The pivot indices; for 1 <= i <= n, row i of the matrix was |
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57 * interchanged with row IPIV(i). IPIV(i) will always be either |
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58 * i or i+1; IPIV(i) = i indicates a row interchange was not |
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59 * required. |
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60 * |
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61 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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62 * On entry, the matrix of right hand side vectors B. |
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63 * On exit, B is overwritten by the solution vectors X. |
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64 * |
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65 * LDB (input) INTEGER |
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66 * The leading dimension of the array B. LDB >= max(1,N). |
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67 * |
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68 * INFO (output) INTEGER |
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69 * = 0: successful exit |
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70 * < 0: if INFO = -i, the i-th argument had an illegal value |
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71 * |
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72 * ===================================================================== |
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73 * |
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74 * .. Local Scalars .. |
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75 LOGICAL NOTRAN |
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76 INTEGER ITRANS, J, JB, NB |
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77 * .. |
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78 * .. External Functions .. |
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79 INTEGER ILAENV |
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80 EXTERNAL ILAENV |
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81 * .. |
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82 * .. External Subroutines .. |
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83 EXTERNAL DGTTS2, XERBLA |
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84 * .. |
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85 * .. Intrinsic Functions .. |
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86 INTRINSIC MAX, MIN |
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87 * .. |
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88 * .. Executable Statements .. |
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89 * |
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90 INFO = 0 |
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91 NOTRAN = ( TRANS.EQ.'N' .OR. TRANS.EQ.'n' ) |
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92 IF( .NOT.NOTRAN .AND. .NOT.( TRANS.EQ.'T' .OR. TRANS.EQ. |
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93 $ 't' ) .AND. .NOT.( TRANS.EQ.'C' .OR. TRANS.EQ.'c' ) ) THEN |
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94 INFO = -1 |
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95 ELSE IF( N.LT.0 ) THEN |
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96 INFO = -2 |
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97 ELSE IF( NRHS.LT.0 ) THEN |
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98 INFO = -3 |
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99 ELSE IF( LDB.LT.MAX( N, 1 ) ) THEN |
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100 INFO = -10 |
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101 END IF |
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102 IF( INFO.NE.0 ) THEN |
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103 CALL XERBLA( 'DGTTRS', -INFO ) |
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104 RETURN |
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105 END IF |
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106 * |
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107 * Quick return if possible |
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108 * |
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109 IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
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110 $ RETURN |
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111 * |
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112 * Decode TRANS |
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113 * |
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114 IF( NOTRAN ) THEN |
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115 ITRANS = 0 |
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116 ELSE |
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117 ITRANS = 1 |
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118 END IF |
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119 * |
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120 * Determine the number of right-hand sides to solve at a time. |
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121 * |
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122 IF( NRHS.EQ.1 ) THEN |
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123 NB = 1 |
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124 ELSE |
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125 NB = MAX( 1, ILAENV( 1, 'DGTTRS', TRANS, N, NRHS, -1, -1 ) ) |
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126 END IF |
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127 * |
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128 IF( NB.GE.NRHS ) THEN |
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129 CALL DGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) |
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130 ELSE |
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131 DO 10 J = 1, NRHS, NB |
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132 JB = MIN( NRHS-J+1, NB ) |
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133 CALL DGTTS2( ITRANS, N, JB, DL, D, DU, DU2, IPIV, B( 1, J ), |
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134 $ LDB ) |
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135 10 CONTINUE |
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136 END IF |
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137 * |
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138 * End of DGTTRS |
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139 * |
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140 END |
