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1 SUBROUTINE ZGTTS2( ITRANS, N, NRHS, DL, D, DU, DU2, IPIV, B, LDB ) |
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2 * |
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3 * -- LAPACK auxiliary routine (version 3.1) -- |
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4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
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5 * November 2006 |
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6 * |
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7 * .. Scalar Arguments .. |
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8 INTEGER ITRANS, LDB, N, NRHS |
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9 * .. |
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10 * .. Array Arguments .. |
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11 INTEGER IPIV( * ) |
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12 COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ), DU2( * ) |
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13 * .. |
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14 * |
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15 * Purpose |
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16 * ======= |
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17 * |
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18 * ZGTTS2 solves one of the systems of equations |
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19 * A * X = B, A**T * X = B, or A**H * X = B, |
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20 * with a tridiagonal matrix A using the LU factorization computed |
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21 * by ZGTTRF. |
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22 * |
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23 * Arguments |
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24 * ========= |
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25 * |
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26 * ITRANS (input) INTEGER |
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27 * Specifies the form of the system of equations. |
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28 * = 0: A * X = B (No transpose) |
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29 * = 1: A**T * X = B (Transpose) |
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30 * = 2: A**H * X = B (Conjugate transpose) |
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31 * |
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32 * N (input) INTEGER |
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33 * The order of the matrix A. |
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34 * |
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35 * NRHS (input) INTEGER |
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36 * The number of right hand sides, i.e., the number of columns |
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37 * of the matrix B. NRHS >= 0. |
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38 * |
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39 * DL (input) COMPLEX*16 array, dimension (N-1) |
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40 * The (n-1) multipliers that define the matrix L from the |
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41 * LU factorization of A. |
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42 * |
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43 * D (input) COMPLEX*16 array, dimension (N) |
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44 * The n diagonal elements of the upper triangular matrix U from |
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45 * the LU factorization of A. |
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46 * |
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47 * DU (input) COMPLEX*16 array, dimension (N-1) |
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48 * The (n-1) elements of the first super-diagonal of U. |
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49 * |
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50 * DU2 (input) COMPLEX*16 array, dimension (N-2) |
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51 * The (n-2) elements of the second super-diagonal of U. |
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52 * |
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53 * IPIV (input) INTEGER array, dimension (N) |
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54 * The pivot indices; for 1 <= i <= n, row i of the matrix was |
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55 * interchanged with row IPIV(i). IPIV(i) will always be either |
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56 * i or i+1; IPIV(i) = i indicates a row interchange was not |
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57 * required. |
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58 * |
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59 * B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
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60 * On entry, the matrix of right hand side vectors B. |
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61 * On exit, B is overwritten by the solution vectors X. |
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62 * |
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63 * LDB (input) INTEGER |
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64 * The leading dimension of the array B. LDB >= max(1,N). |
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65 * |
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66 * ===================================================================== |
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67 * |
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68 * .. Local Scalars .. |
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69 INTEGER I, J |
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70 COMPLEX*16 TEMP |
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71 * .. |
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72 * .. Intrinsic Functions .. |
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73 INTRINSIC DCONJG |
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74 * .. |
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75 * .. Executable Statements .. |
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76 * |
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77 * Quick return if possible |
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78 * |
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79 IF( N.EQ.0 .OR. NRHS.EQ.0 ) |
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80 $ RETURN |
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81 * |
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82 IF( ITRANS.EQ.0 ) THEN |
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83 * |
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84 * Solve A*X = B using the LU factorization of A, |
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85 * overwriting each right hand side vector with its solution. |
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86 * |
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87 IF( NRHS.LE.1 ) THEN |
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88 J = 1 |
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89 10 CONTINUE |
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90 * |
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91 * Solve L*x = b. |
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92 * |
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93 DO 20 I = 1, N - 1 |
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94 IF( IPIV( I ).EQ.I ) THEN |
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95 B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) |
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96 ELSE |
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97 TEMP = B( I, J ) |
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98 B( I, J ) = B( I+1, J ) |
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99 B( I+1, J ) = TEMP - DL( I )*B( I, J ) |
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100 END IF |
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101 20 CONTINUE |
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102 * |
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103 * Solve U*x = b. |
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104 * |
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105 B( N, J ) = B( N, J ) / D( N ) |
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106 IF( N.GT.1 ) |
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107 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / |
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108 $ D( N-1 ) |
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109 DO 30 I = N - 2, 1, -1 |
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110 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )* |
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111 $ B( I+2, J ) ) / D( I ) |
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112 30 CONTINUE |
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113 IF( J.LT.NRHS ) THEN |
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114 J = J + 1 |
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115 GO TO 10 |
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116 END IF |
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117 ELSE |
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118 DO 60 J = 1, NRHS |
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119 * |
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120 * Solve L*x = b. |
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121 * |
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122 DO 40 I = 1, N - 1 |
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123 IF( IPIV( I ).EQ.I ) THEN |
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124 B( I+1, J ) = B( I+1, J ) - DL( I )*B( I, J ) |
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125 ELSE |
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126 TEMP = B( I, J ) |
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127 B( I, J ) = B( I+1, J ) |
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128 B( I+1, J ) = TEMP - DL( I )*B( I, J ) |
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129 END IF |
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130 40 CONTINUE |
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131 * |
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132 * Solve U*x = b. |
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133 * |
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134 B( N, J ) = B( N, J ) / D( N ) |
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135 IF( N.GT.1 ) |
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136 $ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / |
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137 $ D( N-1 ) |
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138 DO 50 I = N - 2, 1, -1 |
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139 B( I, J ) = ( B( I, J )-DU( I )*B( I+1, J )-DU2( I )* |
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140 $ B( I+2, J ) ) / D( I ) |
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141 50 CONTINUE |
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142 60 CONTINUE |
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143 END IF |
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144 ELSE IF( ITRANS.EQ.1 ) THEN |
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145 * |
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146 * Solve A**T * X = B. |
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147 * |
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148 IF( NRHS.LE.1 ) THEN |
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149 J = 1 |
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150 70 CONTINUE |
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151 * |
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152 * Solve U**T * x = b. |
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153 * |
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154 B( 1, J ) = B( 1, J ) / D( 1 ) |
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155 IF( N.GT.1 ) |
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156 $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) |
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157 DO 80 I = 3, N |
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158 B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )-DU2( I-2 )* |
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159 $ B( I-2, J ) ) / D( I ) |
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160 80 CONTINUE |
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161 * |
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162 * Solve L**T * x = b. |
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163 * |
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164 DO 90 I = N - 1, 1, -1 |
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165 IF( IPIV( I ).EQ.I ) THEN |
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166 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) |
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167 ELSE |
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168 TEMP = B( I+1, J ) |
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169 B( I+1, J ) = B( I, J ) - DL( I )*TEMP |
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170 B( I, J ) = TEMP |
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171 END IF |
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172 90 CONTINUE |
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173 IF( J.LT.NRHS ) THEN |
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174 J = J + 1 |
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175 GO TO 70 |
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176 END IF |
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177 ELSE |
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178 DO 120 J = 1, NRHS |
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179 * |
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180 * Solve U**T * x = b. |
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181 * |
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182 B( 1, J ) = B( 1, J ) / D( 1 ) |
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183 IF( N.GT.1 ) |
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184 $ B( 2, J ) = ( B( 2, J )-DU( 1 )*B( 1, J ) ) / D( 2 ) |
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185 DO 100 I = 3, N |
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186 B( I, J ) = ( B( I, J )-DU( I-1 )*B( I-1, J )- |
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187 $ DU2( I-2 )*B( I-2, J ) ) / D( I ) |
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188 100 CONTINUE |
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189 * |
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190 * Solve L**T * x = b. |
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191 * |
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192 DO 110 I = N - 1, 1, -1 |
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193 IF( IPIV( I ).EQ.I ) THEN |
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194 B( I, J ) = B( I, J ) - DL( I )*B( I+1, J ) |
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195 ELSE |
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196 TEMP = B( I+1, J ) |
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197 B( I+1, J ) = B( I, J ) - DL( I )*TEMP |
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198 B( I, J ) = TEMP |
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199 END IF |
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200 110 CONTINUE |
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201 120 CONTINUE |
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202 END IF |
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203 ELSE |
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204 * |
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205 * Solve A**H * X = B. |
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206 * |
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207 IF( NRHS.LE.1 ) THEN |
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208 J = 1 |
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209 130 CONTINUE |
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210 * |
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211 * Solve U**H * x = b. |
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212 * |
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213 B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) ) |
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214 IF( N.GT.1 ) |
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215 $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) / |
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216 $ DCONJG( D( 2 ) ) |
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217 DO 140 I = 3, N |
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218 B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )*B( I-1, J )- |
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219 $ DCONJG( DU2( I-2 ) )*B( I-2, J ) ) / |
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220 $ DCONJG( D( I ) ) |
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221 140 CONTINUE |
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222 * |
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223 * Solve L**H * x = b. |
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224 * |
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225 DO 150 I = N - 1, 1, -1 |
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226 IF( IPIV( I ).EQ.I ) THEN |
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227 B( I, J ) = B( I, J ) - DCONJG( DL( I ) )*B( I+1, J ) |
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228 ELSE |
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229 TEMP = B( I+1, J ) |
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230 B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP |
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231 B( I, J ) = TEMP |
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232 END IF |
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233 150 CONTINUE |
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234 IF( J.LT.NRHS ) THEN |
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235 J = J + 1 |
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236 GO TO 130 |
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237 END IF |
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238 ELSE |
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239 DO 180 J = 1, NRHS |
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240 * |
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241 * Solve U**H * x = b. |
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242 * |
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243 B( 1, J ) = B( 1, J ) / DCONJG( D( 1 ) ) |
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244 IF( N.GT.1 ) |
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245 $ B( 2, J ) = ( B( 2, J )-DCONJG( DU( 1 ) )*B( 1, J ) ) |
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246 $ / DCONJG( D( 2 ) ) |
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247 DO 160 I = 3, N |
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248 B( I, J ) = ( B( I, J )-DCONJG( DU( I-1 ) )* |
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249 $ B( I-1, J )-DCONJG( DU2( I-2 ) )* |
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250 $ B( I-2, J ) ) / DCONJG( D( I ) ) |
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251 160 CONTINUE |
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252 * |
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253 * Solve L**H * x = b. |
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254 * |
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255 DO 170 I = N - 1, 1, -1 |
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256 IF( IPIV( I ).EQ.I ) THEN |
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257 B( I, J ) = B( I, J ) - DCONJG( DL( I ) )* |
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258 $ B( I+1, J ) |
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259 ELSE |
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260 TEMP = B( I+1, J ) |
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261 B( I+1, J ) = B( I, J ) - DCONJG( DL( I ) )*TEMP |
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262 B( I, J ) = TEMP |
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263 END IF |
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264 170 CONTINUE |
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265 180 CONTINUE |
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266 END IF |
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267 END IF |
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268 * |
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269 * End of ZGTTS2 |
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270 * |
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271 END |
