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 { 16 TS ts; /* time integration context */ 17 Vec X; /* solution, residual vectors */ 18 Mat J; /* Jacobian matrix */ 19 PetscScalar *x; 20 PetscReal ftime; 21 PetscInt i,steps,nits,lits; 22 PetscBool view_final; 23 Ctx ctx; 24 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 { 98 Ctx *ctx = (Ctx*)ictx; 99 const PetscScalar *x; 100 PetscScalar f; 101 PetscReal dt,gnorm; 102 PetscInt i,snesit,linit; 103 SNES snes; 104 Vec Xdot,F; 105 106 PetscFunctionBeginUser; 107 /* Compute objective functional */ 108 PetscCall(VecGetArrayRead(X,&x)); 109 f = 0; 110 for (i=0; i<ctx->n-1; i++) f += PetscSqr(1. - x[i]) + 100. * PetscSqr(x[i+1] - PetscSqr(x[i])); 111 PetscCall(VecRestoreArrayRead(X,&x)); 112 113 /* Compute norm of gradient */ 114 PetscCall(VecDuplicate(X,&Xdot)); 115 PetscCall(VecDuplicate(X,&F)); 116 PetscCall(VecZeroEntries(Xdot)); 117 PetscCall(FormIFunction(ts,t,X,Xdot,F,ictx)); 118 PetscCall(VecNorm(F,NORM_2,&gnorm)); 119 PetscCall(VecDestroy(&Xdot)); 120 PetscCall(VecDestroy(&F)); 121 122 PetscCall(TSGetTimeStep(ts,&dt)); 123 PetscCall(TSGetSNES(ts,&snes)); 124 PetscCall(SNESGetIterationNumber(snes,&snesit)); 125 PetscCall(SNESGetLinearSolveIterations(snes,&linit)); 126 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" 127 : "%3" PetscInt_FMT " t=%10.4e dt=%10.4e f=%10.4e df=%10.4e it=(%2" PetscInt_FMT ",%3" PetscInt_FMT ")\n"), 128 step,(double)t,(double)dt,(double)PetscRealPart(f),(double)gnorm,snesit,linit)); 129 PetscFunctionReturn(0); 130 } 131 132 /* ------------------------------------------------------------------- */ 133 /* 134 FormIFunction - Evaluates nonlinear function, F(X,Xdot) = Xdot + grad(objective(X)) 135 136 Input Parameters: 137 + ts - the TS context 138 . t - time 139 . X - input vector 140 . Xdot - time derivative 141 - ctx - optional user-defined context 142 143 Output Parameter: 144 . F - function vector 145 */ 146 static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ictx) 147 { 148 const PetscScalar *x; 149 PetscScalar *f; 150 PetscInt i; 151 Ctx *ctx = (Ctx*)ictx; 152 153 PetscFunctionBeginUser; 154 /* 155 Get pointers to vector data. 156 - For default PETSc vectors, VecGetArray() returns a pointer to 157 the data array. Otherwise, the routine is implementation dependent. 158 - You MUST call VecRestoreArray() when you no longer need access to 159 the array. 160 */ 161 PetscCall(VecGetArrayRead(X,&x)); 162 PetscCall(VecZeroEntries(F)); 163 PetscCall(VecGetArray(F,&f)); 164 165 /* Compute gradient of objective */ 166 for (i=0; i<ctx->n-1; i++) { 167 PetscScalar a,a0,a1; 168 a = x[i+1] - PetscSqr(x[i]); 169 a0 = -2.*x[i]; 170 a1 = 1.; 171 f[i] += -2.*(1. - x[i]) + 200.*a*a0; 172 f[i+1] += 200.*a*a1; 173 } 174 /* Restore vectors */ 175 PetscCall(VecRestoreArrayRead(X,&x)); 176 PetscCall(VecRestoreArray(F,&f)); 177 PetscCall(VecAXPY(F,1.0,Xdot)); 178 PetscFunctionReturn(0); 179 } 180 /* ------------------------------------------------------------------- */ 181 /* 182 FormIJacobian - Evaluates Jacobian matrix. 183 184 Input Parameters: 185 + ts - the TS context 186 . t - pseudo-time 187 . X - input vector 188 . Xdot - time derivative 189 . shift - multiplier for mass matrix 190 . dummy - user-defined context 191 192 Output Parameters: 193 . J - Jacobian matrix 194 . B - optionally different preconditioning matrix 195 . flag - flag indicating matrix structure 196 */ 197 static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat J,Mat B,void *ictx) 198 { 199 const PetscScalar *x; 200 PetscInt i; 201 Ctx *ctx = (Ctx*)ictx; 202 203 PetscFunctionBeginUser; 204 PetscCall(MatZeroEntries(B)); 205 /* 206 Get pointer to vector data 207 */ 208 PetscCall(VecGetArrayRead(X,&x)); 209 210 /* 211 Compute Jacobian entries and insert into matrix. 212 */ 213 for (i=0; i<ctx->n-1; i++) { 214 PetscInt rowcol[2]; 215 PetscScalar v[2][2],a,a0,a1,a00,a01,a10,a11; 216 rowcol[0] = i; 217 rowcol[1] = i+1; 218 a = x[i+1] - PetscSqr(x[i]); 219 a0 = -2.*x[i]; 220 a00 = -2.; 221 a01 = 0.; 222 a1 = 1.; 223 a10 = 0.; 224 a11 = 0.; 225 v[0][0] = 2. + 200.*(a*a00 + a0*a0); 226 v[0][1] = 200.*(a*a01 + a1*a0); 227 v[1][0] = 200.*(a*a10 + a0*a1); 228 v[1][1] = 200.*(a*a11 + a1*a1); 229 PetscCall(MatSetValues(B,2,rowcol,2,rowcol,&v[0][0],ADD_VALUES)); 230 } 231 for (i=0; i<ctx->n; i++) { 232 PetscCall(MatSetValue(B,i,i,(PetscScalar)shift,ADD_VALUES)); 233 } 234 235 PetscCall(VecRestoreArrayRead(X,&x)); 236 237 /* 238 Assemble matrix 239 */ 240 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 241 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 242 if (J != B) { 243 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 244 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 245 } 246 PetscFunctionReturn(0); 247 } 248 249 /*TEST 250 251 test: 252 requires: !single 253 254 test: 255 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 -1 256 requires: !single 257 suffix: 2 258 259 TEST*/ 260