1 | /* |
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2 | * ----------------------------------------------------------------- |
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3 | * Programmer(s): Daniel Reynolds @ SMU |
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4 | * Based on code sundials_spfgmr.h by: Daniel R. Reynolds and |
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5 | * Hilari C. Tiedeman @ SMU |
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6 | * ----------------------------------------------------------------- |
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7 | * LLNS/SMU Copyright Start |
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8 | * Copyright (c) 2017, Southern Methodist University and |
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9 | * Lawrence Livermore National Security |
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10 | * |
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11 | * This work was performed under the auspices of the U.S. Department |
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12 | * of Energy by Southern Methodist University and Lawrence Livermore |
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13 | * National Laboratory under Contract DE-AC52-07NA27344. |
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14 | * Produced at Southern Methodist University and the Lawrence |
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15 | * Livermore National Laboratory. |
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16 | * |
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17 | * All rights reserved. |
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18 | * For details, see the LICENSE file. |
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19 | * LLNS/SMU Copyright End |
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20 | * ----------------------------------------------------------------- |
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21 | * This is the header file for the SPFGMR implementation of the |
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22 | * SUNLINSOL module. The SPFGMR algorithm is based on the |
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23 | * Scaled Preconditioned FGMRES (Flexible Generalized Minimal |
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24 | * Residual) method [Y. Saad, SIAM J. Sci. Comput., 1993]. |
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25 | * |
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26 | * The SPFGMR algorithm solves a linear system A x = b. |
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27 | * Preconditioning is only allowed on the right. Scaling is allowed |
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28 | * on both sides, and restarts are also allowed. We denote the |
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29 | * preconditioner and scaling matrices as follows: |
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30 | * P = right preconditioner |
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31 | * S1 = diagonal matrix of scale factors for P-inverse b |
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32 | * S2 = diagonal matrix of scale factors for x |
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33 | * The matrices A and P are not required explicitly; only routines |
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34 | * that provide A and P-inverse as operators are required. |
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35 | * |
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36 | * In this notation, SPFGMR applies the underlying GMRES method to |
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37 | * the equivalent transformed system |
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38 | * Abar xbar = bbar , where |
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39 | * Abar = S1 A (P-inverse) (S2-inverse) , |
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40 | * bbar = S1 b , and xbar = S2 P x . |
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41 | * |
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42 | * The scaling matrices must be chosen so that vectors S1 b and |
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43 | * S2 P x have dimensionless components. If preconditioning is not |
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44 | * performed (P = I), then S2 must be a scaling for x, while S1 is a |
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45 | * scaling for b. Similarly, if preconditioning is performed, then |
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46 | * S1 must be a scaling for b, while S2 is a scaling for P x, and may |
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47 | * also be taken as a scaling for b. |
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48 | * |
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49 | * The stopping test for the SPFGMR iterations is on the L2 norm of |
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50 | * the scaled preconditioned residual: |
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51 | * || bbar - Abar xbar ||_2 < delta |
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52 | * with an input test constant delta. |
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53 | * |
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54 | * The usage of this SPFGMR solver involves supplying up to three |
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55 | * routines and making a variety of calls. The user-supplied routines are |
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56 | * atimes (A_data, x, y) to compute y = A x, given x, |
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57 | * psolve (P_data, y, x, lr) to solve P1 x = y or P2 x = y for |
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58 | * x, given y, |
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59 | * psetup (P_data) to perform any 'setup' operations in |
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60 | * preparation for calling psolve. |
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61 | * The three user calls are: |
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62 | * SUNLinearSolver LS = SUNSPFGMR(y, pretype, maxl); |
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63 | * to create the linear solver structure, |
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64 | * flag = SUNLinSolSetATimes(LS, A_data, atimes); |
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65 | * to set the matrix-vector product setup/apply routines, |
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66 | * flag = SUNLinSolSetPreconditioner(LS, P_data, psetup, psolve); |
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67 | * to *optionally* set the preconditioner setup/apply routines, |
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68 | * flag = SUNLinSolInitialize(LS); |
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69 | * to perform internal solver memory allocations, |
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70 | * flag = SUNLinSolSetup(LS, NULL); |
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71 | * to call the psetup routine (if non-NULL); |
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72 | * flag = SUNLinSolSolve(LS, NULL, x, b, w, tol); |
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73 | * to solve the linear system to the tolerance 'tol' |
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74 | * long int nli = SUNLinSolNumIters(LS); |
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75 | * to *optionally* retrieve the number of linear iterations |
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76 | * performed by the solver, |
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77 | * long int lastflag = SUNLinSolLastFlag(LS); |
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78 | * to *optionally* retrieve the last internal solver error flag, |
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79 | * flag = SUNLinSolFree(LS); |
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80 | * to free the solver memory. |
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81 | * Complete details for specifying atimes, psetup and psolve |
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82 | * and for the usage calls are given below. |
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83 | * |
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84 | * ----------------------------------------------------------------- |
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85 | * |
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86 | * Part I contains declarations specific to the SPFGMR implementation |
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87 | * of the supplied SUNLINSOL module. |
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88 | * |
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89 | * Part II contains the prototype for the constructor |
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90 | * SUNSPFGMR as well as implementation-specific prototypes |
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91 | * for various useful solver operations. |
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92 | * |
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93 | * Notes: |
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94 | * |
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95 | * - The definition of the generic SUNLinearSolver structure can |
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96 | * be found in the header file sundials_linearsolver.h. |
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97 | * |
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98 | * ----------------------------------------------------------------- |
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99 | */ |
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100 | |
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101 | #ifndef _SUNLINSOL_SPFGMR_H |
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102 | #define _SUNLINSOL_SPFGMR_H |
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103 | |
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104 | #include <sundials/sundials_linearsolver.h> |
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105 | #include <sundials/sundials_matrix.h> |
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106 | #include <sundials/sundials_nvector.h> |
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107 | #include <sundials/sundials_spfgmr.h> |
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108 | |
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109 | #ifdef __cplusplus /* wrapper to enable C++ usage */ |
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110 | extern "C" { |
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111 | #endif |
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112 | |
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113 | /* Default SPFGMR solver parameters */ |
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114 | #define SUNSPFGMR_MAXL_DEFAULT 5 |
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115 | #define SUNSPFGMR_MAXRS_DEFAULT 0 |
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116 | #define SUNSPFGMR_GSTYPE_DEFAULT MODIFIED_GS |
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117 | |
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118 | /* |
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119 | * ----------------------------------------------------------------- |
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120 | * PART I: SPFGMR implementation of SUNLinearSolver |
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121 | * |
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122 | * The SPFGMR implementation of the SUNLinearSolver 'content' |
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123 | * structure contains: |
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124 | * maxl -- number of GMRES basis vectors to use |
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125 | * pretype -- flag for type of preconditioning to employ |
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126 | * gstype -- flag for type of Gram-Schmidt orthogonalization |
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127 | * max_restarts -- number of GMRES restarts to allow |
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128 | * last_flag -- last error return flag from internal setup/solve |
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129 | * ATimes -- function pointer to ATimes routine |
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130 | * ATData -- pointer to structure for ATimes |
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131 | * Psetup -- function pointer to preconditioner setup routine |
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132 | * Psolve -- function pointer to preconditioner solve routine |
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133 | * PData -- pointer to structure for Psetup/Psolve |
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134 | * V -- the array of Krylov basis vectors v_1, ..., v_(maxl+1), |
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135 | * stored in V[0], ..., V[l_max]. Each v_i is a vector of |
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136 | * type N_Vector. |
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137 | * Z -- the array of preconditioned basis vectors z_1, ..., |
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138 | * z_(maxl+1), stored in Z[0], ..., Z[l_max]. Each z_i |
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139 | * is a vector of type N_Vector. |
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140 | * Hes -- the (maxl+1) x maxl Hessenberg matrix. It is stored |
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141 | * row-wise so that the (i,j)th element is given by Hes[i][j]. |
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142 | * givens -- a length 2*max array which represents the Givens |
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143 | * rotation matrices that arise in the algorithm. The Givens |
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144 | * rotation matrices F_0, F_1, ..., F_j, where F_i is |
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145 | * |
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146 | * 1 |
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147 | * 1 |
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148 | * c_i -s_i <--- row i |
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149 | * s_i c_i |
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150 | * 1 |
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151 | * 1 |
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152 | * |
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153 | * are represented in the givens vector as |
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154 | * givens[0]=c_0, givens[1]=s_0, givens[2]=c_1, givens[3]=s_1, |
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155 | * ..., givens[2j]=c_j, givens[2j+1]=s_j. |
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156 | * xcor -- a vector (type N_Vector) which holds the scaled, |
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157 | * preconditioned correction to the initial guess |
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158 | * yg -- a length (maxl+1) array of realtype used to hold "short" |
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159 | * vectors (e.g. y and g). |
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160 | * vtemp -- a vector (type N_Vector) used as temporary vector |
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161 | * storage during calculations. |
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162 | * ----------------------------------------------------------------- |
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163 | */ |
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164 | |
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165 | struct _SUNLinearSolverContent_SPFGMR { |
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166 | int maxl; |
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167 | int pretype; |
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168 | int gstype; |
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169 | int max_restarts; |
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170 | int numiters; |
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171 | realtype resnorm; |
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172 | long int last_flag; |
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173 | |
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174 | ATimesFn ATimes; |
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175 | void* ATData; |
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176 | PSetupFn Psetup; |
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177 | PSolveFn Psolve; |
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178 | void* PData; |
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179 | |
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180 | N_Vector s1; |
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181 | N_Vector s2; |
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182 | N_Vector *V; |
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183 | N_Vector *Z; |
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184 | realtype **Hes; |
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185 | realtype *givens; |
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186 | N_Vector xcor; |
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187 | realtype *yg; |
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188 | N_Vector vtemp; |
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189 | }; |
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190 | |
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191 | typedef struct _SUNLinearSolverContent_SPFGMR *SUNLinearSolverContent_SPFGMR; |
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192 | |
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193 | /* |
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194 | * ----------------------------------------------------------------- |
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195 | * PART II: functions exported by sunlinsol_spfgmr |
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196 | * |
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197 | * CONSTRUCTOR: |
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198 | * SUNSPFGMR creates and allocates memory for a SPFGMR solver |
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199 | * |
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200 | * "SET" ROUTINES: |
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201 | * SUNSPFGMRSetPrecType updates whether to use preconditioning. |
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202 | * Since only right preconditioning is supported, the inputs |
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203 | * PREC_LEFT, PREC_RIGHT and PREC_BOTH all result in |
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204 | * PREC_RIGHT. All other input values default to PREC_NONE. |
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205 | * SUNSPFGMRSetGSType sets the type of Gram-Schmidt |
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206 | * orthogonalization to use. Supported values are MODIFIED_GS |
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207 | * and CLASSICAL_GS. |
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208 | * SUNSPFGMRSetMaxRestarts sets the number of FGMRES restarts to |
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209 | * allow. A negative input will result in the default of 0. |
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210 | * |
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211 | * ----------------------------------------------------------------- |
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212 | */ |
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213 | |
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214 | SUNDIALS_EXPORT SUNLinearSolver SUNSPFGMR(N_Vector y, int pretype, int maxl); |
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215 | SUNDIALS_EXPORT int SUNSPFGMRSetPrecType(SUNLinearSolver S, int pretype); |
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216 | SUNDIALS_EXPORT int SUNSPFGMRSetGSType(SUNLinearSolver S, int gstype); |
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217 | SUNDIALS_EXPORT int SUNSPFGMRSetMaxRestarts(SUNLinearSolver S, int maxrs); |
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218 | |
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219 | /* |
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220 | * ----------------------------------------------------------------- |
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221 | * SPFGMR implementations of various useful linear solver operations |
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222 | * ----------------------------------------------------------------- |
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223 | */ |
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224 | |
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225 | SUNDIALS_EXPORT SUNLinearSolver_Type SUNLinSolGetType_SPFGMR(SUNLinearSolver S); |
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226 | SUNDIALS_EXPORT int SUNLinSolInitialize_SPFGMR(SUNLinearSolver S); |
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227 | SUNDIALS_EXPORT int SUNLinSolSetATimes_SPFGMR(SUNLinearSolver S, void* A_data, |
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228 | ATimesFn ATimes); |
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229 | SUNDIALS_EXPORT int SUNLinSolSetPreconditioner_SPFGMR(SUNLinearSolver S, |
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230 | void* P_data, |
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231 | PSetupFn Pset, |
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232 | PSolveFn Psol); |
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233 | SUNDIALS_EXPORT int SUNLinSolSetScalingVectors_SPFGMR(SUNLinearSolver S, |
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234 | N_Vector s1, |
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235 | N_Vector s2); |
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236 | SUNDIALS_EXPORT int SUNLinSolSetup_SPFGMR(SUNLinearSolver S, SUNMatrix A); |
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237 | SUNDIALS_EXPORT int SUNLinSolSolve_SPFGMR(SUNLinearSolver S, SUNMatrix A, |
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238 | N_Vector x, N_Vector b, realtype tol); |
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239 | SUNDIALS_EXPORT int SUNLinSolNumIters_SPFGMR(SUNLinearSolver S); |
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240 | SUNDIALS_EXPORT realtype SUNLinSolResNorm_SPFGMR(SUNLinearSolver S); |
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241 | SUNDIALS_EXPORT N_Vector SUNLinSolResid_SPFGMR(SUNLinearSolver S); |
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242 | SUNDIALS_EXPORT long int SUNLinSolLastFlag_SPFGMR(SUNLinearSolver S); |
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243 | SUNDIALS_EXPORT int SUNLinSolSpace_SPFGMR(SUNLinearSolver S, |
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244 | long int *lenrwLS, |
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245 | long int *leniwLS); |
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246 | SUNDIALS_EXPORT int SUNLinSolFree_SPFGMR(SUNLinearSolver S); |
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247 | |
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248 | |
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249 | #ifdef __cplusplus |
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250 | } |
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251 | #endif |
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252 | |
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253 | #endif |
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