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1 SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
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2 * |
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3 * -- LAPACK routine (version 3.0) -- |
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2329
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4 * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., |
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5 * Courant Institute, Argonne National Lab, and Rice University |
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6 * March 31, 1993 |
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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, LDA, 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 A( LDA, * ), B( LDB, * ) |
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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 * DGETRS solves a system of linear equations |
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21 * A * X = B or A' * X = B |
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22 * with a general N-by-N matrix A using the LU factorization computed |
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23 * by DGETRF. |
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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. N >= 0. |
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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 * A (input) DOUBLE PRECISION array, dimension (LDA,N) |
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42 * The factors L and U from the factorization A = P*L*U |
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43 * as computed by DGETRF. |
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44 * |
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45 * LDA (input) INTEGER |
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46 * The leading dimension of the array A. LDA >= max(1,N). |
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47 * |
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48 * IPIV (input) INTEGER array, dimension (N) |
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49 * The pivot indices from DGETRF; for 1<=i<=N, row i of the |
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50 * matrix was interchanged with row IPIV(i). |
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51 * |
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52 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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53 * On entry, the right hand side matrix B. |
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54 * On exit, the solution matrix X. |
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55 * |
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56 * LDB (input) INTEGER |
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57 * The leading dimension of the array B. LDB >= max(1,N). |
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58 * |
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59 * INFO (output) INTEGER |
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60 * = 0: successful exit |
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61 * < 0: if INFO = -i, the i-th argument had an illegal value |
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62 * |
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63 * ===================================================================== |
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64 * |
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65 * .. Parameters .. |
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66 DOUBLE PRECISION ONE |
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67 PARAMETER ( ONE = 1.0D+0 ) |
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68 * .. |
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69 * .. Local Scalars .. |
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70 LOGICAL NOTRAN |
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71 * .. |
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72 * .. External Functions .. |
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73 LOGICAL LSAME |
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74 EXTERNAL LSAME |
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75 * .. |
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76 * .. External Subroutines .. |
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77 EXTERNAL DLASWP, DTRSM, XERBLA |
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78 * .. |
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79 * .. Intrinsic Functions .. |
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80 INTRINSIC MAX |
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81 * .. |
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82 * .. Executable Statements .. |
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83 * |
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84 * Test the input parameters. |
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85 * |
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86 INFO = 0 |
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87 NOTRAN = LSAME( TRANS, 'N' ) |
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88 IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. |
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89 $ LSAME( TRANS, 'C' ) ) THEN |
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90 INFO = -1 |
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91 ELSE IF( N.LT.0 ) THEN |
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92 INFO = -2 |
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93 ELSE IF( NRHS.LT.0 ) THEN |
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94 INFO = -3 |
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95 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN |
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96 INFO = -5 |
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97 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN |
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98 INFO = -8 |
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99 END IF |
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100 IF( INFO.NE.0 ) THEN |
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101 CALL XERBLA( 'DGETRS', -INFO ) |
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102 RETURN |
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103 END IF |
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104 * |
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105 * Quick return if possible |
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106 * |
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107 IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
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108 $ RETURN |
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109 * |
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110 IF( NOTRAN ) THEN |
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111 * |
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112 * Solve A * X = B. |
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113 * |
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114 * Apply row interchanges to the right hand sides. |
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115 * |
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116 CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 ) |
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117 * |
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118 * Solve L*X = B, overwriting B with X. |
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119 * |
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120 CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS, |
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121 $ ONE, A, LDA, B, LDB ) |
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122 * |
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123 * Solve U*X = B, overwriting B with X. |
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124 * |
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125 CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, |
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126 $ NRHS, ONE, A, LDA, B, LDB ) |
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127 ELSE |
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128 * |
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129 * Solve A' * X = B. |
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130 * |
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131 * Solve U'*X = B, overwriting B with X. |
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132 * |
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133 CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, |
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134 $ ONE, A, LDA, B, LDB ) |
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135 * |
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136 * Solve L'*X = B, overwriting B with X. |
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137 * |
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138 CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE, |
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139 $ A, LDA, B, LDB ) |
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140 * |
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141 * Apply row interchanges to the solution vectors. |
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142 * |
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143 CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 ) |
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144 END IF |
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145 * |
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146 RETURN |
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147 * |
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148 * End of DGETRS |
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149 * |
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150 END |
