1 | /* |
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2 | * ----------------------------------------------------------------- |
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3 | * $Revision$ |
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4 | * $Date$ |
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5 | * ----------------------------------------------------------------- |
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6 | * Programmer(s): Aaron Collier @ LLNL |
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7 | * ----------------------------------------------------------------- |
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8 | * LLNS Copyright Start |
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9 | * Copyright (c) 2014, Lawrence Livermore National Security |
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10 | * This work was performed under the auspices of the U.S. Department |
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11 | * of Energy by Lawrence Livermore National Laboratory in part under |
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12 | * Contract W-7405-Eng-48 and in part under Contract DE-AC52-07NA27344. |
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13 | * Produced at the Lawrence Livermore National Laboratory. |
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14 | * All rights reserved. |
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15 | * For details, see the LICENSE file. |
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16 | * LLNS Copyright End |
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17 | * ----------------------------------------------------------------- |
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18 | * This is the header file for the implementation of the scaled |
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19 | * preconditioned Transpose-Free Quasi-Minimal Residual (SPTFQMR) |
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20 | * linear solver. |
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21 | * |
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22 | * The SPTFQMR algorithm solves a linear system of the form Ax = b. |
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23 | * Preconditioning is allowed on the left (PREC_LEFT), right |
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24 | * (PREC_RIGHT), or both (PREC_BOTH). Scaling is allowed on both |
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25 | * sides. We denote the preconditioner and scaling matrices as |
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26 | * follows: |
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27 | * P1 = left preconditioner |
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28 | * P2 = right preconditioner |
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29 | * S1 = diagonal matrix of scale factors for P1-inverse b |
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30 | * S2 = diagonal matrix of scale factors for P2 x |
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31 | * The matrices A, P1, and P2 are not required explicitly; only |
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32 | * routines that provide A, P1-inverse, and P2-inverse as operators |
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33 | * are required. |
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34 | * |
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35 | * In this notation, SPTFQMR applies the underlying TFQMR method to |
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36 | * the equivalent transformed system: |
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37 | * Abar xbar = bbar, where |
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38 | * Abar = S1 (P1-inverse) A (P2-inverse) (S2-inverse), |
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39 | * bbar = S1 (P1-inverse) b, and |
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40 | * xbar = S2 P2 x. |
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41 | * |
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42 | * The scaling matrices must be chosen so that vectors |
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43 | * S1 P1-inverse b and S2 P2 x have dimensionless components. If |
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44 | * preconditioning is done on the left only (P2 = I), by a matrix P, |
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45 | * then S2 must be a scaling for x, while S1 is a scaling for |
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46 | * P-inverse b, and so may also be taken as a scaling for x. |
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47 | * Similarly, if preconditioning is done on the right only (P1 = I, |
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48 | * P2 = P), then S1 must be a scaling for b, while S2 is a scaling |
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49 | * for P x, and may also be taken as a scaling for b. |
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50 | * |
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51 | * The stopping test for the SPTFQMR iterations is on the L2-norm of |
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52 | * the scaled preconditioned residual: |
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53 | * || bbar - Abar xbar ||_2 < delta |
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54 | * with an input test constant delta. |
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55 | * |
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56 | * The usage of this SPTFQMR solver involves supplying two routines |
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57 | * and making three calls. The user-supplied routines are: |
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58 | * atimes(A_data, x, y) to compute y = A x, given x, |
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59 | * and |
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60 | * psolve(P_data, y, x, lr) to solve P1 x = y or P2 x = y for x, |
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61 | * given y. |
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62 | * The three user calls are: |
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63 | * mem = SptfqmrMalloc(lmax, vec_tmpl); |
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64 | * to initialize memory |
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65 | * flag = SptfqmrSolve(mem, A_data, x, b, pretype, delta, P_data, |
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66 | * sx, sb, atimes, psolve, res_norm, nli, nps); |
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67 | * to solve the system, and |
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68 | * SptfqmrFree(mem); |
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69 | * to free the memory allocated by SptfqmrMalloc(). |
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70 | * Complete details for specifying atimes() and psolve() and for the |
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71 | * usage calls are given in the paragraphs below and in the header |
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72 | * file sundials_iterative.h. |
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73 | * ----------------------------------------------------------------- |
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74 | */ |
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75 | |
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76 | #ifndef _SPTFQMR_H |
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77 | #define _SPTFQMR_H |
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78 | |
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79 | #include <sundials/sundials_iterative.h> |
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80 | |
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81 | #ifdef __cplusplus /* wrapper to enable C++ usage */ |
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82 | extern "C" { |
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83 | #endif |
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84 | |
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85 | /* |
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86 | * ----------------------------------------------------------------- |
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87 | * Types: struct SptfqmrMemRec and struct *SptfqmrMem |
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88 | * ----------------------------------------------------------------- |
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89 | * A variable declaration of type struct *SptfqmrMem denotes a pointer |
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90 | * to a data structure of type struct SptfqmrMemRec. The SptfqmrMemRec |
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91 | * structure contains numerous fields that must be accessed by the |
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92 | * SPTFQMR linear solver module. |
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93 | * |
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94 | * l_max maximum Krylov subspace dimension that SptfqmrSolve will |
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95 | * be permitted to use |
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96 | * |
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97 | * r_star vector (type N_Vector) which holds the initial scaled, |
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98 | * preconditioned linear system residual |
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99 | * |
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100 | * q/d/v/p/u/r vectors (type N_Vector) used for workspace by |
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101 | * the SPTFQMR algorithm |
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102 | * |
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103 | * vtemp1/vtemp2/vtemp3 scratch vectors (type N_Vector) used as |
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104 | * temporary storage |
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105 | * ----------------------------------------------------------------- |
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106 | */ |
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107 | |
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108 | typedef struct { |
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109 | |
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110 | int l_max; |
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111 | |
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112 | N_Vector r_star; |
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113 | N_Vector q; |
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114 | N_Vector d; |
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115 | N_Vector v; |
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116 | N_Vector p; |
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117 | N_Vector *r; |
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118 | N_Vector u; |
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119 | N_Vector vtemp1; |
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120 | N_Vector vtemp2; |
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121 | N_Vector vtemp3; |
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122 | |
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123 | } SptfqmrMemRec, *SptfqmrMem; |
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124 | |
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125 | /* |
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126 | * ----------------------------------------------------------------- |
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127 | * Function : SptfqmrMalloc |
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128 | * ----------------------------------------------------------------- |
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129 | * SptfqmrMalloc allocates additional memory needed by the SPTFQMR |
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130 | * linear solver module. |
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131 | * |
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132 | * l_max maximum Krylov subspace dimension that SptfqmrSolve will |
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133 | * be permitted to use |
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134 | * |
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135 | * vec_tmpl implementation-specific template vector (type N_Vector) |
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136 | * (created using either N_VNew_Serial or N_VNew_Parallel) |
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137 | * |
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138 | * If successful, SptfqmrMalloc returns a non-NULL memory pointer. If |
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139 | * an error occurs, then a NULL pointer is returned. |
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140 | * ----------------------------------------------------------------- |
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141 | */ |
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142 | |
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143 | SUNDIALS_EXPORT SptfqmrMem SptfqmrMalloc(int l_max, N_Vector vec_tmpl); |
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144 | |
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145 | /* |
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146 | * ----------------------------------------------------------------- |
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147 | * Function : SptfqmrSolve |
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148 | * ----------------------------------------------------------------- |
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149 | * SptfqmrSolve solves the linear system Ax = b by means of a scaled |
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150 | * preconditioned Transpose-Free Quasi-Minimal Residual (SPTFQMR) |
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151 | * method. |
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152 | * |
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153 | * mem pointer to an internal memory block allocated during a |
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154 | * prior call to SptfqmrMalloc |
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155 | * |
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156 | * A_data pointer to a data structure containing information |
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157 | * about the coefficient matrix A (passed to user-supplied |
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158 | * function referenced by atimes (function pointer)) |
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159 | * |
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160 | * x vector (type N_Vector) containing initial guess x_0 upon |
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161 | * entry, but which upon return contains an approximate solution |
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162 | * of the linear system Ax = b (solution only valid if return |
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163 | * value is either SPTFQMR_SUCCESS or SPTFQMR_RES_REDUCED) |
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164 | * |
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165 | * b vector (type N_Vector) set to the right-hand side vector b |
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166 | * of the linear system (undisturbed by function) |
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167 | * |
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168 | * pretype variable (type int) indicating the type of |
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169 | * preconditioning to be used (see sundials_iterative.h) |
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170 | * |
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171 | * delta tolerance on the L2 norm of the scaled, preconditioned |
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172 | * residual (if return value == SPTFQMR_SUCCESS, then |
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173 | * ||sb*P1_inv*(b-Ax)||_L2 <= delta) |
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174 | * |
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175 | * P_data pointer to a data structure containing preconditioner |
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176 | * information (passed to user-supplied function referenced |
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177 | * by psolve (function pointer)) |
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178 | * |
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179 | * sx vector (type N_Vector) containing positive scaling factors |
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180 | * for x (pass sx == NULL if scaling NOT required) |
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181 | * |
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182 | * sb vector (type N_Vector) containing positive scaling factors |
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183 | * for b (pass sb == NULL if scaling NOT required) |
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184 | * |
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185 | * atimes user-supplied routine responsible for computing the |
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186 | * matrix-vector product Ax (see sundials_iterative.h) |
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187 | * |
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188 | * psolve user-supplied routine responsible for solving the |
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189 | * preconditioned linear system Pz = r (ignored if |
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190 | * pretype == PREC_NONE) (see sundials_iterative.h) |
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191 | * |
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192 | * res_norm pointer (type realtype*) to the L2 norm of the |
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193 | * scaled, preconditioned residual (if return value |
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194 | * is either SPTFQMR_SUCCESS or SPTFQMR_RES_REDUCED, then |
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195 | * *res_norm = ||sb*P1_inv*(b-Ax)||_L2, where x is |
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196 | * the computed approximate solution, sb is the diagonal |
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197 | * scaling matrix for the right-hand side b, and P1_inv |
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198 | * is the inverse of the left-preconditioner matrix) |
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199 | * |
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200 | * nli pointer (type int*) to the total number of linear |
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201 | * iterations performed |
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202 | * |
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203 | * nps pointer (type int*) to the total number of calls made |
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204 | * to the psolve routine |
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205 | * ----------------------------------------------------------------- |
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206 | */ |
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207 | |
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208 | SUNDIALS_EXPORT int SptfqmrSolve(SptfqmrMem mem, void *A_data, N_Vector x, N_Vector b, |
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209 | int pretype, realtype delta, void *P_data, N_Vector sx, |
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210 | N_Vector sb, ATimesFn atimes, PSolveFn psolve, |
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211 | realtype *res_norm, int *nli, int *nps); |
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212 | |
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213 | /* Return values for SptfqmrSolve */ |
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214 | |
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215 | #define SPTFQMR_SUCCESS 0 /* SPTFQMR algorithm converged */ |
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216 | #define SPTFQMR_RES_REDUCED 1 /* SPTFQMR did NOT converge, but the |
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217 | residual was reduced */ |
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218 | #define SPTFQMR_CONV_FAIL 2 /* SPTFQMR algorithm failed to converge */ |
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219 | #define SPTFQMR_PSOLVE_FAIL_REC 3 /* psolve failed recoverably */ |
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220 | #define SPTFQMR_ATIMES_FAIL_REC 4 /* atimes failed recoverably */ |
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221 | #define SPTFQMR_PSET_FAIL_REC 5 /* pset faild recoverably */ |
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222 | |
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223 | #define SPTFQMR_MEM_NULL -1 /* mem argument is NULL */ |
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224 | #define SPTFQMR_ATIMES_FAIL_UNREC -2 /* atimes returned failure flag */ |
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225 | #define SPTFQMR_PSOLVE_FAIL_UNREC -3 /* psolve failed unrecoverably */ |
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226 | #define SPTFQMR_PSET_FAIL_UNREC -4 /* pset failed unrecoverably */ |
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227 | |
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228 | /* |
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229 | * ----------------------------------------------------------------- |
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230 | * Function : SptfqmrFree |
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231 | * ----------------------------------------------------------------- |
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232 | * SptfqmrFree frees the memory allocated by a call to SptfqmrMalloc. |
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233 | * It is illegal to use the pointer mem after a call to SptfqmrFree. |
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234 | * ----------------------------------------------------------------- |
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235 | */ |
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236 | |
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237 | SUNDIALS_EXPORT void SptfqmrFree(SptfqmrMem mem); |
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238 | |
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239 | /* |
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240 | * ----------------------------------------------------------------- |
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241 | * Macro : SPTFQMR_VTEMP |
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242 | * ----------------------------------------------------------------- |
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243 | * This macro provides access to the work vector vtemp1 in the |
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244 | * memory block of the SPTFQMR module. The argument mem is the |
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245 | * memory pointer returned by SptfqmrMalloc, of type SptfqmrMem, |
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246 | * and the macro value is of type N_Vector. |
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247 | * |
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248 | * Note: Only used by IDA (vtemp1 contains P_inverse F if |
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249 | * nli_inc == 0). |
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250 | * ----------------------------------------------------------------- |
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251 | */ |
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252 | |
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253 | #define SPTFQMR_VTEMP(mem) (mem->vtemp1) |
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254 | |
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255 | #ifdef __cplusplus |
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256 | } |
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257 | #endif |
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258 | |
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259 | #endif |
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