1 static char help[] = "Pseudotransient continuation to solve a many-variable system that comes from the 2 variable Rosenbrock function + trivial.\n\n"; 2 3 #include <petscts.h> 4 5 static PetscErrorCode FormIJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *); 6 static PetscErrorCode FormIFunction(TS, PetscReal, Vec, Vec, Vec, void *); 7 static PetscErrorCode MonitorObjective(TS, PetscInt, PetscReal, Vec, void *); 8 9 typedef struct { 10 PetscInt n; 11 PetscBool monitor_short; 12 } Ctx; 13 14 int main(int argc, char **argv) { 15 TS ts; /* time integration context */ 16 Vec X; /* solution, residual vectors */ 17 Mat J; /* Jacobian matrix */ 18 PetscScalar *x; 19 PetscReal ftime; 20 PetscInt i, steps, nits, lits; 21 PetscBool view_final; 22 Ctx ctx; 23 24 PetscFunctionBeginUser; 25 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 26 ctx.n = 3; 27 PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &ctx.n, NULL)); 28 PetscCheck(ctx.n >= 2, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, "The dimension specified with -n must be at least 2"); 29 30 view_final = PETSC_FALSE; 31 PetscCall(PetscOptionsGetBool(NULL, NULL, "-view_final", &view_final, NULL)); 32 33 ctx.monitor_short = PETSC_FALSE; 34 PetscCall(PetscOptionsGetBool(NULL, NULL, "-monitor_short", &ctx.monitor_short, NULL)); 35 36 /* 37 Create Jacobian matrix data structure and state vector 38 */ 39 PetscCall(MatCreate(PETSC_COMM_WORLD, &J)); 40 PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, ctx.n, ctx.n)); 41 PetscCall(MatSetFromOptions(J)); 42 PetscCall(MatSetUp(J)); 43 PetscCall(MatCreateVecs(J, &X, NULL)); 44 45 /* Create time integration context */ 46 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 47 PetscCall(TSSetType(ts, TSPSEUDO)); 48 PetscCall(TSSetIFunction(ts, NULL, FormIFunction, &ctx)); 49 PetscCall(TSSetIJacobian(ts, J, J, FormIJacobian, &ctx)); 50 PetscCall(TSSetMaxSteps(ts, 1000)); 51 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 52 PetscCall(TSSetTimeStep(ts, 1e-3)); 53 PetscCall(TSMonitorSet(ts, MonitorObjective, &ctx, NULL)); 54 55 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 56 Customize time integrator; set runtime options 57 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 58 PetscCall(TSSetFromOptions(ts)); 59 60 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 61 Evaluate initial guess; then solve nonlinear system 62 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 63 PetscCall(VecSet(X, 0.0)); 64 PetscCall(VecGetArray(X, &x)); 65 #if 1 66 x[0] = 5.; 67 x[1] = -5.; 68 for (i = 2; i < ctx.n; i++) x[i] = 5.; 69 #else 70 x[0] = 1.0; 71 x[1] = 15.0; 72 for (i = 2; i < ctx.n; i++) x[i] = 10.0; 73 #endif 74 PetscCall(VecRestoreArray(X, &x)); 75 76 PetscCall(TSSolve(ts, X)); 77 PetscCall(TSGetSolveTime(ts, &ftime)); 78 PetscCall(TSGetStepNumber(ts, &steps)); 79 PetscCall(TSGetSNESIterations(ts, &nits)); 80 PetscCall(TSGetKSPIterations(ts, &lits)); 81 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Time integrator took (%" PetscInt_FMT ",%" PetscInt_FMT ",%" PetscInt_FMT ") iterations to reach final time %g\n", steps, nits, lits, (double)ftime)); 82 if (view_final) PetscCall(VecView(X, PETSC_VIEWER_STDOUT_WORLD)); 83 84 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 85 Free work space. All PETSc objects should be destroyed when they 86 are no longer needed. 87 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 88 89 PetscCall(VecDestroy(&X)); 90 PetscCall(MatDestroy(&J)); 91 PetscCall(TSDestroy(&ts)); 92 PetscCall(PetscFinalize()); 93 return 0; 94 } 95 96 static PetscErrorCode MonitorObjective(TS ts, PetscInt step, PetscReal t, Vec X, void *ictx) { 97 Ctx *ctx = (Ctx *)ictx; 98 const PetscScalar *x; 99 PetscScalar f; 100 PetscReal dt, gnorm; 101 PetscInt i, snesit, linit; 102 SNES snes; 103 Vec Xdot, F; 104 105 PetscFunctionBeginUser; 106 /* Compute objective functional */ 107 PetscCall(VecGetArrayRead(X, &x)); 108 f = 0; 109 for (i = 0; i < ctx->n - 1; i++) f += PetscSqr(1. - x[i]) + 100. * PetscSqr(x[i + 1] - PetscSqr(x[i])); 110 PetscCall(VecRestoreArrayRead(X, &x)); 111 112 /* Compute norm of gradient */ 113 PetscCall(VecDuplicate(X, &Xdot)); 114 PetscCall(VecDuplicate(X, &F)); 115 PetscCall(VecZeroEntries(Xdot)); 116 PetscCall(FormIFunction(ts, t, X, Xdot, F, ictx)); 117 PetscCall(VecNorm(F, NORM_2, &gnorm)); 118 PetscCall(VecDestroy(&Xdot)); 119 PetscCall(VecDestroy(&F)); 120 121 PetscCall(TSGetTimeStep(ts, &dt)); 122 PetscCall(TSGetSNES(ts, &snes)); 123 PetscCall(SNESGetIterationNumber(snes, &snesit)); 124 PetscCall(SNESGetLinearSolveIterations(snes, &linit)); 125 PetscCall(PetscPrintf(PETSC_COMM_WORLD, (ctx->monitor_short ? "%3" PetscInt_FMT " t=%10.1e dt=%10.1e f=%10.1e df=%10.1e it=(%2" PetscInt_FMT ",%3" PetscInt_FMT ")\n" : "%3" PetscInt_FMT " t=%10.4e dt=%10.4e f=%10.4e df=%10.4e it=(%2" PetscInt_FMT ",%3" PetscInt_FMT ")\n"), step, (double)t, (double)dt, (double)PetscRealPart(f), (double)gnorm, snesit, linit)); 126 PetscFunctionReturn(0); 127 } 128 129 /* ------------------------------------------------------------------- */ 130 /* 131 FormIFunction - Evaluates nonlinear function, F(X,Xdot) = Xdot + grad(objective(X)) 132 133 Input Parameters: 134 + ts - the TS context 135 . t - time 136 . X - input vector 137 . Xdot - time derivative 138 - ctx - optional user-defined context 139 140 Output Parameter: 141 . F - function vector 142 */ 143 static PetscErrorCode FormIFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ictx) { 144 const PetscScalar *x; 145 PetscScalar *f; 146 PetscInt i; 147 Ctx *ctx = (Ctx *)ictx; 148 149 PetscFunctionBeginUser; 150 /* 151 Get pointers to vector data. 152 - For default PETSc vectors, VecGetArray() returns a pointer to 153 the data array. Otherwise, the routine is implementation dependent. 154 - You MUST call VecRestoreArray() when you no longer need access to 155 the array. 156 */ 157 PetscCall(VecGetArrayRead(X, &x)); 158 PetscCall(VecZeroEntries(F)); 159 PetscCall(VecGetArray(F, &f)); 160 161 /* Compute gradient of objective */ 162 for (i = 0; i < ctx->n - 1; i++) { 163 PetscScalar a, a0, a1; 164 a = x[i + 1] - PetscSqr(x[i]); 165 a0 = -2. * x[i]; 166 a1 = 1.; 167 f[i] += -2. * (1. - x[i]) + 200. * a * a0; 168 f[i + 1] += 200. * a * a1; 169 } 170 /* Restore vectors */ 171 PetscCall(VecRestoreArrayRead(X, &x)); 172 PetscCall(VecRestoreArray(F, &f)); 173 PetscCall(VecAXPY(F, 1.0, Xdot)); 174 PetscFunctionReturn(0); 175 } 176 /* ------------------------------------------------------------------- */ 177 /* 178 FormIJacobian - Evaluates Jacobian matrix. 179 180 Input Parameters: 181 + ts - the TS context 182 . t - pseudo-time 183 . X - input vector 184 . Xdot - time derivative 185 . shift - multiplier for mass matrix 186 . dummy - user-defined context 187 188 Output Parameters: 189 . J - Jacobian matrix 190 . B - optionally different preconditioning matrix 191 . flag - flag indicating matrix structure 192 */ 193 static PetscErrorCode FormIJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal shift, Mat J, Mat B, void *ictx) { 194 const PetscScalar *x; 195 PetscInt i; 196 Ctx *ctx = (Ctx *)ictx; 197 198 PetscFunctionBeginUser; 199 PetscCall(MatZeroEntries(B)); 200 /* 201 Get pointer to vector data 202 */ 203 PetscCall(VecGetArrayRead(X, &x)); 204 205 /* 206 Compute Jacobian entries and insert into matrix. 207 */ 208 for (i = 0; i < ctx->n - 1; i++) { 209 PetscInt rowcol[2]; 210 PetscScalar v[2][2], a, a0, a1, a00, a01, a10, a11; 211 rowcol[0] = i; 212 rowcol[1] = i + 1; 213 a = x[i + 1] - PetscSqr(x[i]); 214 a0 = -2. * x[i]; 215 a00 = -2.; 216 a01 = 0.; 217 a1 = 1.; 218 a10 = 0.; 219 a11 = 0.; 220 v[0][0] = 2. + 200. * (a * a00 + a0 * a0); 221 v[0][1] = 200. * (a * a01 + a1 * a0); 222 v[1][0] = 200. * (a * a10 + a0 * a1); 223 v[1][1] = 200. * (a * a11 + a1 * a1); 224 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &v[0][0], ADD_VALUES)); 225 } 226 for (i = 0; i < ctx->n; i++) { PetscCall(MatSetValue(B, i, i, (PetscScalar)shift, ADD_VALUES)); } 227 228 PetscCall(VecRestoreArrayRead(X, &x)); 229 230 /* 231 Assemble matrix 232 */ 233 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 234 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 235 if (J != B) { 236 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 237 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 238 } 239 PetscFunctionReturn(0); 240 } 241 242 /*TEST 243 244 test: 245 requires: !single 246 247 test: 248 args: -pc_type lu -ts_dt 1e-5 -ts_max_time 1e5 -n 50 -monitor_short -snes_max_it 5 -snes_type newtonls -ts_max_snes_failures -1 249 requires: !single 250 suffix: 2 251 252 TEST*/ 253