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 PetscErrorCode ierr; 20 PetscScalar *x; 21 PetscReal ftime; 22 PetscInt i,steps,nits,lits; 23 PetscBool view_final; 24 Ctx ctx; 25 26 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 27 ctx.n = 3; 28 CHKERRQ(PetscOptionsGetInt(NULL,NULL,"-n",&ctx.n,NULL)); 29 PetscCheck(ctx.n >= 2,PETSC_COMM_WORLD,PETSC_ERR_ARG_OUTOFRANGE,"The dimension specified with -n must be at least 2"); 30 31 view_final = PETSC_FALSE; 32 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-view_final",&view_final,NULL)); 33 34 ctx.monitor_short = PETSC_FALSE; 35 CHKERRQ(PetscOptionsGetBool(NULL,NULL,"-monitor_short",&ctx.monitor_short,NULL)); 36 37 /* 38 Create Jacobian matrix data structure and state vector 39 */ 40 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&J)); 41 CHKERRQ(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx.n,ctx.n)); 42 CHKERRQ(MatSetFromOptions(J)); 43 CHKERRQ(MatSetUp(J)); 44 CHKERRQ(MatCreateVecs(J,&X,NULL)); 45 46 /* Create time integration context */ 47 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 48 CHKERRQ(TSSetType(ts,TSPSEUDO)); 49 CHKERRQ(TSSetIFunction(ts,NULL,FormIFunction,&ctx)); 50 CHKERRQ(TSSetIJacobian(ts,J,J,FormIJacobian,&ctx)); 51 CHKERRQ(TSSetMaxSteps(ts,1000)); 52 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 53 CHKERRQ(TSSetTimeStep(ts,1e-3)); 54 CHKERRQ(TSMonitorSet(ts,MonitorObjective,&ctx,NULL)); 55 56 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 57 Customize time integrator; set runtime options 58 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 59 CHKERRQ(TSSetFromOptions(ts)); 60 61 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 62 Evaluate initial guess; then solve nonlinear system 63 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 64 CHKERRQ(VecSet(X,0.0)); 65 CHKERRQ(VecGetArray(X,&x)); 66 #if 1 67 x[0] = 5.; 68 x[1] = -5.; 69 for (i=2; i<ctx.n; i++) x[i] = 5.; 70 #else 71 x[0] = 1.0; 72 x[1] = 15.0; 73 for (i=2; i<ctx.n; i++) x[i] = 10.0; 74 #endif 75 CHKERRQ(VecRestoreArray(X,&x)); 76 77 CHKERRQ(TSSolve(ts,X)); 78 CHKERRQ(TSGetSolveTime(ts,&ftime)); 79 CHKERRQ(TSGetStepNumber(ts,&steps)); 80 CHKERRQ(TSGetSNESIterations(ts,&nits)); 81 CHKERRQ(TSGetKSPIterations(ts,&lits)); 82 CHKERRQ(PetscPrintf(PETSC_COMM_WORLD,"Time integrator took (%D,%D,%D) iterations to reach final time %g\n",steps,nits,lits,(double)ftime)); 83 if (view_final) { 84 CHKERRQ(VecView(X,PETSC_VIEWER_STDOUT_WORLD)); 85 } 86 87 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 88 Free work space. All PETSc objects should be destroyed when they 89 are no longer needed. 90 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 91 92 CHKERRQ(VecDestroy(&X)); 93 CHKERRQ(MatDestroy(&J)); 94 CHKERRQ(TSDestroy(&ts)); 95 ierr = PetscFinalize(); 96 return ierr; 97 } 98 99 static PetscErrorCode MonitorObjective(TS ts,PetscInt step,PetscReal t,Vec X,void *ictx) 100 { 101 Ctx *ctx = (Ctx*)ictx; 102 PetscErrorCode ierr; 103 const PetscScalar *x; 104 PetscScalar f; 105 PetscReal dt,gnorm; 106 PetscInt i,snesit,linit; 107 SNES snes; 108 Vec Xdot,F; 109 110 PetscFunctionBeginUser; 111 /* Compute objective functional */ 112 CHKERRQ(VecGetArrayRead(X,&x)); 113 f = 0; 114 for (i=0; i<ctx->n-1; i++) f += PetscSqr(1. - x[i]) + 100. * PetscSqr(x[i+1] - PetscSqr(x[i])); 115 CHKERRQ(VecRestoreArrayRead(X,&x)); 116 117 /* Compute norm of gradient */ 118 CHKERRQ(VecDuplicate(X,&Xdot)); 119 CHKERRQ(VecDuplicate(X,&F)); 120 CHKERRQ(VecZeroEntries(Xdot)); 121 CHKERRQ(FormIFunction(ts,t,X,Xdot,F,ictx)); 122 CHKERRQ(VecNorm(F,NORM_2,&gnorm)); 123 CHKERRQ(VecDestroy(&Xdot)); 124 CHKERRQ(VecDestroy(&F)); 125 126 CHKERRQ(TSGetTimeStep(ts,&dt)); 127 CHKERRQ(TSGetSNES(ts,&snes)); 128 CHKERRQ(SNESGetIterationNumber(snes,&snesit)); 129 CHKERRQ(SNESGetLinearSolveIterations(snes,&linit)); 130 ierr = PetscPrintf(PETSC_COMM_WORLD, 131 (ctx->monitor_short 132 ? "%3D t=%10.1e dt=%10.1e f=%10.1e df=%10.1e it=(%2D,%3D)\n" 133 : "%3D t=%10.4e dt=%10.4e f=%10.4e df=%10.4e it=(%2D,%3D)\n"), 134 step,(double)t,(double)dt,(double)PetscRealPart(f),(double)gnorm,snesit,linit);CHKERRQ(ierr); 135 PetscFunctionReturn(0); 136 } 137 138 /* ------------------------------------------------------------------- */ 139 /* 140 FormIFunction - Evaluates nonlinear function, F(X,Xdot) = Xdot + grad(objective(X)) 141 142 Input Parameters: 143 + ts - the TS context 144 . t - time 145 . X - input vector 146 . Xdot - time derivative 147 - ctx - optional user-defined context 148 149 Output Parameter: 150 . F - function vector 151 */ 152 static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ictx) 153 { 154 const PetscScalar *x; 155 PetscScalar *f; 156 PetscInt i; 157 Ctx *ctx = (Ctx*)ictx; 158 159 PetscFunctionBeginUser; 160 /* 161 Get pointers to vector data. 162 - For default PETSc vectors, VecGetArray() returns a pointer to 163 the data array. Otherwise, the routine is implementation dependent. 164 - You MUST call VecRestoreArray() when you no longer need access to 165 the array. 166 */ 167 CHKERRQ(VecGetArrayRead(X,&x)); 168 CHKERRQ(VecZeroEntries(F)); 169 CHKERRQ(VecGetArray(F,&f)); 170 171 /* Compute gradient of objective */ 172 for (i=0; i<ctx->n-1; i++) { 173 PetscScalar a,a0,a1; 174 a = x[i+1] - PetscSqr(x[i]); 175 a0 = -2.*x[i]; 176 a1 = 1.; 177 f[i] += -2.*(1. - x[i]) + 200.*a*a0; 178 f[i+1] += 200.*a*a1; 179 } 180 /* Restore vectors */ 181 CHKERRQ(VecRestoreArrayRead(X,&x)); 182 CHKERRQ(VecRestoreArray(F,&f)); 183 CHKERRQ(VecAXPY(F,1.0,Xdot)); 184 PetscFunctionReturn(0); 185 } 186 /* ------------------------------------------------------------------- */ 187 /* 188 FormIJacobian - Evaluates Jacobian matrix. 189 190 Input Parameters: 191 + ts - the TS context 192 . t - pseudo-time 193 . X - input vector 194 . Xdot - time derivative 195 . shift - multiplier for mass matrix 196 . dummy - user-defined context 197 198 Output Parameters: 199 . J - Jacobian matrix 200 . B - optionally different preconditioning matrix 201 . flag - flag indicating matrix structure 202 */ 203 static PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal shift,Mat J,Mat B,void *ictx) 204 { 205 const PetscScalar *x; 206 PetscInt i; 207 Ctx *ctx = (Ctx*)ictx; 208 209 PetscFunctionBeginUser; 210 CHKERRQ(MatZeroEntries(B)); 211 /* 212 Get pointer to vector data 213 */ 214 CHKERRQ(VecGetArrayRead(X,&x)); 215 216 /* 217 Compute Jacobian entries and insert into matrix. 218 */ 219 for (i=0; i<ctx->n-1; i++) { 220 PetscInt rowcol[2]; 221 PetscScalar v[2][2],a,a0,a1,a00,a01,a10,a11; 222 rowcol[0] = i; 223 rowcol[1] = i+1; 224 a = x[i+1] - PetscSqr(x[i]); 225 a0 = -2.*x[i]; 226 a00 = -2.; 227 a01 = 0.; 228 a1 = 1.; 229 a10 = 0.; 230 a11 = 0.; 231 v[0][0] = 2. + 200.*(a*a00 + a0*a0); 232 v[0][1] = 200.*(a*a01 + a1*a0); 233 v[1][0] = 200.*(a*a10 + a0*a1); 234 v[1][1] = 200.*(a*a11 + a1*a1); 235 CHKERRQ(MatSetValues(B,2,rowcol,2,rowcol,&v[0][0],ADD_VALUES)); 236 } 237 for (i=0; i<ctx->n; i++) { 238 CHKERRQ(MatSetValue(B,i,i,(PetscScalar)shift,ADD_VALUES)); 239 } 240 241 CHKERRQ(VecRestoreArrayRead(X,&x)); 242 243 /* 244 Assemble matrix 245 */ 246 CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 247 CHKERRQ(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 248 if (J != B) { 249 CHKERRQ(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 250 CHKERRQ(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 251 } 252 PetscFunctionReturn(0); 253 } 254 255 /*TEST 256 257 test: 258 requires: !single 259 260 test: 261 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 -1 262 requires: !single 263 suffix: 2 264 265 TEST*/ 266