[16222] | 1 | /* |
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| 2 | * ----------------------------------------------------------------- |
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| 3 | * Programmer(s): Daniel Reynolds, Ashley Crawford @ SMU |
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| 4 | * ----------------------------------------------------------------- |
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| 5 | * LLNS/SMU Copyright Start |
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| 6 | * Copyright (c) 2017, Southern Methodist University and |
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| 7 | * Lawrence Livermore National Security |
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| 8 | * |
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| 9 | * This work was performed under the auspices of the U.S. Department |
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| 10 | * of Energy by Southern Methodist University and Lawrence Livermore |
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| 11 | * National Laboratory under Contract DE-AC52-07NA27344. |
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| 12 | * Produced at Southern Methodist University and the Lawrence |
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| 13 | * Livermore National Laboratory. |
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| 14 | * |
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| 15 | * All rights reserved. |
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| 16 | * For details, see the LICENSE file. |
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| 17 | * LLNS/SMU Copyright End |
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| 18 | * ----------------------------------------------------------------- |
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| 19 | * This is the header file for the PCG implementation of the |
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| 20 | * SUNLINSOL module. The PCG algorithm is based on the |
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| 21 | * Preconditioned Conjugate Gradient. |
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| 22 | * |
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| 23 | * The PCG algorithm solves a linear system A x = b where |
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| 24 | * A is a symmetric, real-valued matrix, i.e. A = A' (Matlab |
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| 25 | * notation for the transpose of A). Preconditioning is allowed, |
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| 26 | * and is applied in a symmetric fashion on both the right and left. |
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| 27 | * Scaling is also allowed and is applied symmetrically. We denote |
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| 28 | * the preconditioner and scaling matrices as follows: |
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| 29 | * P = preconditioner (assumed symmetric) |
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| 30 | * S = diagonal matrix of scale factors |
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| 31 | * The matrices A and P are not required explicitly; only routines |
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| 32 | * that provide A and P-inverse as operators are required. The |
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| 33 | * diagonal of the matrix S is held in a single N_Vector, supplied |
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| 34 | * by the user of this module. |
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| 35 | * |
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| 36 | * In this notation, PCG applies the underlying algorithm 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 = S (P-inverse) A (P-inverse) S , |
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| 40 | * bbar = S (P-inverse) b , and xbar = (S-inverse) P x . |
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| 41 | * |
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| 42 | * The scaling matrix must be chosen so that the vectors |
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| 43 | * (S P-inverse b) and (S-inverse P x) have dimensionless |
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| 44 | * components. |
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| 45 | * |
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| 46 | * The stopping test for the PCG iterations is on the L2 norm of |
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| 47 | * the scaled preconditioned residual: |
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| 48 | * || bbar - Abar xbar ||_2 < delta |
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| 49 | * <=> |
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| 50 | * || S (P-inverse) b - S (P-inverse) A x ||_2 < delta |
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| 51 | * <=> |
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| 52 | * || P-inverse b - (P-inverse) A x ||_S < delta |
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| 53 | * where || v ||_S = sqrt(v' S' S v) with an input test constant |
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| 54 | * delta. |
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| 55 | * |
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| 56 | * The usage of this PCG solver involves supplying up to three |
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| 57 | * routines and making a variety of calls. The user-supplied |
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| 58 | * routines are |
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| 59 | * atimes (A_data, x, y) to compute y = A x, given x, |
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| 60 | * psolve (P_data, y, x, lr) to solve P1 x = y or P2 x = y for |
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| 61 | * x, given y, |
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| 62 | * psetup (P_data) to perform any 'setup' operations in |
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| 63 | * preparation for calling psolve. |
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| 64 | * The user calls are: |
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| 65 | * SUNLinearSolver LS = SUNPCG(y, pretype, maxl); |
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| 66 | * to create the linear solver structure, |
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| 67 | * flag = SUNLinSolSetATimes(LS, A_data, atimes); |
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| 68 | * to set the matrix-vector product setup/apply routines, |
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| 69 | * flag = SUNLinSolSetPreconditioner(LS, P_data, psetup, psolve); |
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| 70 | * to *optionally* set the preconditioner setup/apply routines, |
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| 71 | * flag = SUNLinSolSetScalingVectors(LS, s, NULL); |
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| 72 | * to *optionally* set the diagonal of the scaling matrix |
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| 73 | * (for PCG, only the first of the two scaling vectors is used) |
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| 74 | * flag = SUNLinSolInitialize(LS); |
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| 75 | * to perform internal solver memory allocations, |
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| 76 | * flag = SUNLinSolSetup(LS, NULL); |
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| 77 | * to call the psetup routine (if non-NULL); |
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| 78 | * flag = SUNLinSolSolve(LS, NULL, x, b, w, tol); |
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| 79 | * to solve the linear system to the tolerance 'tol' |
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| 80 | * long int nli = SUNLinSolNumIters(LS); |
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| 81 | * to *optionally* retrieve the number of linear iterations |
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| 82 | * performed by the solver, |
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| 83 | * long int lastflag = SUNLinSolLastFlag(LS); |
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| 84 | * to *optionally* retrieve the last internal solver error flag, |
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| 85 | * realtype resnorm = SUNLinSolResNorm(LS); |
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| 86 | * to *optionally* retrieve the final linear residual norm, |
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| 87 | * flag = SUNLinSolFree(LS); |
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| 88 | * to free the solver memory. |
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| 89 | * Complete details for specifying atimes, psetup and psolve |
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| 90 | * and for the usage calls are given below. |
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| 91 | * |
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| 92 | * ----------------------------------------------------------------- |
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| 93 | * |
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| 94 | * Part I contains declarations specific to the PCG implementation |
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| 95 | * of the supplied SUNLINSOL module. |
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| 96 | * |
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| 97 | * Part II contains the prototype for the constructor SUNPCG as well |
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| 98 | * as implementation-specific prototypes for various useful solver |
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| 99 | * operations. |
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| 100 | * |
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| 101 | * Notes: |
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| 102 | * |
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| 103 | * - The definition of the generic SUNLinearSolver structure can |
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| 104 | * be found in the header file sundials_linearsolver.h. |
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| 105 | * |
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| 106 | * ----------------------------------------------------------------- |
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| 107 | */ |
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| 108 | |
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| 109 | #ifndef _SUNLINSOL_PCG_H |
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| 110 | #define _SUNLINSOL_PCG_H |
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| 111 | |
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| 112 | #include <sundials/sundials_linearsolver.h> |
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| 113 | #include <sundials/sundials_matrix.h> |
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| 114 | #include <sundials/sundials_nvector.h> |
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| 115 | #include <sundials/sundials_pcg.h> |
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| 116 | |
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| 117 | #ifdef __cplusplus /* wrapper to enable C++ usage */ |
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| 118 | extern "C" { |
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| 119 | #endif |
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| 120 | |
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| 121 | /* Default PCG solver parameters */ |
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| 122 | #define SUNPCG_MAXL_DEFAULT 5 |
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| 123 | |
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| 124 | /* |
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| 125 | * ----------------------------------------------------------------- |
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| 126 | * PART I: PCG implementation of SUNLinearSolver |
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| 127 | * |
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| 128 | * The PCG implementation of the SUNLinearSolver 'content' |
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| 129 | * structure contains: |
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| 130 | * maxl -- number of PCG iterations to use |
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| 131 | * pretype -- flag for use of preconditioning |
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| 132 | * numiters -- number of iterations from most-recent solve |
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| 133 | * resnorm -- final linear residual norm from most-recent solve |
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| 134 | * last_flag -- last error return flag from internal setup/solve |
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| 135 | * ATimes -- function pointer to ATimes routine |
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| 136 | * ATData -- pointer to structure for ATimes |
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| 137 | * Psetup -- function pointer to preconditioner setup routine |
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| 138 | * Psolve -- function pointer to preconditioner solve routine |
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| 139 | * PData -- pointer to structure for Psetup/Psolve |
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| 140 | * s -- vector (type N_Vector) which holds the diagonal of the |
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| 141 | * scaling matrix S |
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| 142 | * r -- vector (type N_Vector) which holds the preconditioned |
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| 143 | * linear system residual |
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| 144 | * p, z and Ap -- vectors (type N_Vector) used for workspace by |
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| 145 | * the PCG algorithm |
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| 146 | * ----------------------------------------------------------------- |
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| 147 | */ |
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| 148 | |
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| 149 | struct _SUNLinearSolverContent_PCG { |
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| 150 | int maxl; |
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| 151 | int pretype; |
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| 152 | int numiters; |
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| 153 | realtype resnorm; |
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| 154 | long int last_flag; |
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| 155 | |
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| 156 | ATimesFn ATimes; |
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| 157 | void* ATData; |
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| 158 | PSetupFn Psetup; |
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| 159 | PSolveFn Psolve; |
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| 160 | void* PData; |
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| 161 | |
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| 162 | N_Vector s; |
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| 163 | N_Vector r; |
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| 164 | N_Vector p; |
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| 165 | N_Vector z; |
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| 166 | N_Vector Ap; |
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| 167 | }; |
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| 168 | |
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| 169 | typedef struct _SUNLinearSolverContent_PCG *SUNLinearSolverContent_PCG; |
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| 170 | |
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| 171 | |
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| 172 | /* |
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| 173 | * ----------------------------------------------------------------- |
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| 174 | * PART III: functions exported by sunlinsol_pcg |
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| 175 | * |
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| 176 | * CONSTRUCTOR: |
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| 177 | * SUNPCG creates and allocates memory for a PCG solver |
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| 178 | * ----------------------------------------------------------------- |
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| 179 | */ |
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| 180 | |
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| 181 | SUNDIALS_EXPORT SUNLinearSolver SUNPCG(N_Vector y, int pretype, int maxl); |
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| 182 | SUNDIALS_EXPORT int SUNPCGSetPrecType(SUNLinearSolver S, int pretype); |
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| 183 | SUNDIALS_EXPORT int SUNPCGSetMaxl(SUNLinearSolver S, int maxl); |
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| 184 | |
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| 185 | /* |
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| 186 | * ----------------------------------------------------------------- |
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| 187 | * PCG implementations of various useful linear solver operations |
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| 188 | * ----------------------------------------------------------------- |
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| 189 | */ |
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| 190 | |
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| 191 | SUNDIALS_EXPORT SUNLinearSolver_Type SUNLinSolGetType_PCG(SUNLinearSolver S); |
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| 192 | SUNDIALS_EXPORT int SUNLinSolInitialize_PCG(SUNLinearSolver S); |
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| 193 | SUNDIALS_EXPORT int SUNLinSolSetATimes_PCG(SUNLinearSolver S, void* A_data, |
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| 194 | ATimesFn ATimes); |
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| 195 | SUNDIALS_EXPORT int SUNLinSolSetPreconditioner_PCG(SUNLinearSolver S, |
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| 196 | void* P_data, |
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| 197 | PSetupFn Pset, |
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| 198 | PSolveFn Psol); |
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| 199 | SUNDIALS_EXPORT int SUNLinSolSetScalingVectors_PCG(SUNLinearSolver S, |
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| 200 | N_Vector s, |
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| 201 | N_Vector nul); |
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| 202 | SUNDIALS_EXPORT int SUNLinSolSetup_PCG(SUNLinearSolver S, SUNMatrix nul); |
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| 203 | SUNDIALS_EXPORT int SUNLinSolSolve_PCG(SUNLinearSolver S, SUNMatrix nul, |
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| 204 | N_Vector x, N_Vector b, realtype tol); |
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| 205 | SUNDIALS_EXPORT int SUNLinSolNumIters_PCG(SUNLinearSolver S); |
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| 206 | SUNDIALS_EXPORT realtype SUNLinSolResNorm_PCG(SUNLinearSolver S); |
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| 207 | SUNDIALS_EXPORT N_Vector SUNLinSolResid_PCG(SUNLinearSolver S); |
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| 208 | SUNDIALS_EXPORT long int SUNLinSolLastFlag_PCG(SUNLinearSolver S); |
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| 209 | SUNDIALS_EXPORT int SUNLinSolSpace_PCG(SUNLinearSolver S, |
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| 210 | long int *lenrwLS, |
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| 211 | long int *leniwLS); |
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| 212 | SUNDIALS_EXPORT int SUNLinSolFree_PCG(SUNLinearSolver S); |
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| 213 | |
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| 214 | #ifdef __cplusplus |
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| 215 | } |
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| 216 | #endif |
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| 217 | |
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| 218 | #endif |
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