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1 SUBROUTINE DGTTRF( N, DL, D, DU, DU2, IPIV, INFO ) |
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2 * |
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3 * -- LAPACK 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 INFO, N |
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9 * .. |
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10 * .. Array Arguments .. |
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11 INTEGER IPIV( * ) |
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12 DOUBLE PRECISION 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 * DGTTRF computes an LU factorization of a real tridiagonal matrix A |
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19 * using elimination with partial pivoting and row interchanges. |
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20 * |
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21 * The factorization has the form |
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22 * A = L * U |
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23 * where L is a product of permutation and unit lower bidiagonal |
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24 * matrices and U is upper triangular with nonzeros in only the main |
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25 * diagonal and first two superdiagonals. |
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26 * |
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27 * Arguments |
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28 * ========= |
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29 * |
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30 * N (input) INTEGER |
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31 * The order of the matrix A. |
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32 * |
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33 * DL (input/output) DOUBLE PRECISION array, dimension (N-1) |
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34 * On entry, DL must contain the (n-1) sub-diagonal elements of |
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35 * A. |
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36 * |
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37 * On exit, DL is overwritten by the (n-1) multipliers that |
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38 * define the matrix L from the LU factorization of A. |
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39 * |
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40 * D (input/output) DOUBLE PRECISION array, dimension (N) |
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41 * On entry, D must contain the diagonal elements of A. |
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42 * |
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43 * On exit, D is overwritten by the n diagonal elements of the |
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44 * upper triangular matrix U from the LU factorization of A. |
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45 * |
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46 * DU (input/output) DOUBLE PRECISION array, dimension (N-1) |
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47 * On entry, DU must contain the (n-1) super-diagonal elements |
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48 * of A. |
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49 * |
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50 * On exit, DU is overwritten by the (n-1) elements of the first |
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51 * super-diagonal of U. |
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52 * |
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53 * DU2 (output) DOUBLE PRECISION array, dimension (N-2) |
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54 * On exit, DU2 is overwritten by the (n-2) elements of the |
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55 * second super-diagonal of U. |
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56 * |
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57 * IPIV (output) INTEGER array, dimension (N) |
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58 * The pivot indices; for 1 <= i <= n, row i of the matrix was |
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59 * interchanged with row IPIV(i). IPIV(i) will always be either |
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60 * i or i+1; IPIV(i) = i indicates a row interchange was not |
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61 * required. |
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62 * |
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63 * INFO (output) INTEGER |
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64 * = 0: successful exit |
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65 * < 0: if INFO = -k, the k-th argument had an illegal value |
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66 * > 0: if INFO = k, U(k,k) is exactly zero. The factorization |
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67 * has been completed, but the factor U is exactly |
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68 * singular, and division by zero will occur if it is used |
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69 * to solve a system of equations. |
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70 * |
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71 * ===================================================================== |
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72 * |
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73 * .. Parameters .. |
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74 DOUBLE PRECISION ZERO |
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75 PARAMETER ( ZERO = 0.0D+0 ) |
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76 * .. |
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77 * .. Local Scalars .. |
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78 INTEGER I |
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79 DOUBLE PRECISION FACT, TEMP |
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80 * .. |
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81 * .. Intrinsic Functions .. |
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82 INTRINSIC ABS |
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83 * .. |
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84 * .. External Subroutines .. |
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85 EXTERNAL XERBLA |
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86 * .. |
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87 * .. Executable Statements .. |
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88 * |
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89 INFO = 0 |
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90 IF( N.LT.0 ) THEN |
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91 INFO = -1 |
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92 CALL XERBLA( 'DGTTRF', -INFO ) |
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93 RETURN |
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94 END IF |
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95 * |
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96 * Quick return if possible |
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97 * |
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98 IF( N.EQ.0 ) |
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99 $ RETURN |
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100 * |
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101 * Initialize IPIV(i) = i and DU2(I) = 0 |
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102 * |
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103 DO 10 I = 1, N |
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104 IPIV( I ) = I |
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105 10 CONTINUE |
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106 DO 20 I = 1, N - 2 |
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107 DU2( I ) = ZERO |
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108 20 CONTINUE |
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109 * |
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110 DO 30 I = 1, N - 2 |
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111 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN |
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112 * |
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113 * No row interchange required, eliminate DL(I) |
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114 * |
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115 IF( D( I ).NE.ZERO ) THEN |
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116 FACT = DL( I ) / D( I ) |
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117 DL( I ) = FACT |
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118 D( I+1 ) = D( I+1 ) - FACT*DU( I ) |
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119 END IF |
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120 ELSE |
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121 * |
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122 * Interchange rows I and I+1, eliminate DL(I) |
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123 * |
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124 FACT = D( I ) / DL( I ) |
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125 D( I ) = DL( I ) |
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126 DL( I ) = FACT |
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127 TEMP = DU( I ) |
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128 DU( I ) = D( I+1 ) |
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129 D( I+1 ) = TEMP - FACT*D( I+1 ) |
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130 DU2( I ) = DU( I+1 ) |
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131 DU( I+1 ) = -FACT*DU( I+1 ) |
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132 IPIV( I ) = I + 1 |
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133 END IF |
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134 30 CONTINUE |
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135 IF( N.GT.1 ) THEN |
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136 I = N - 1 |
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137 IF( ABS( D( I ) ).GE.ABS( DL( I ) ) ) THEN |
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138 IF( D( I ).NE.ZERO ) THEN |
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139 FACT = DL( I ) / D( I ) |
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140 DL( I ) = FACT |
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141 D( I+1 ) = D( I+1 ) - FACT*DU( I ) |
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142 END IF |
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143 ELSE |
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144 FACT = D( I ) / DL( I ) |
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145 D( I ) = DL( I ) |
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146 DL( I ) = FACT |
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147 TEMP = DU( I ) |
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148 DU( I ) = D( I+1 ) |
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149 D( I+1 ) = TEMP - FACT*D( I+1 ) |
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150 IPIV( I ) = I + 1 |
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151 END IF |
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152 END IF |
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153 * |
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154 * Check for a zero on the diagonal of U. |
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155 * |
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156 DO 40 I = 1, N |
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157 IF( D( I ).EQ.ZERO ) THEN |
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158 INFO = I |
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159 GO TO 50 |
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160 END IF |
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161 40 CONTINUE |
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162 50 CONTINUE |
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163 * |
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164 RETURN |
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165 * |
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166 * End of DGTTRF |
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167 * |
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168 END |
