Actual source code: ex129.c


  2: /*
  3:   Laplacian in 3D. Use for testing MatSolve routines.
  4:   Modeled by the partial differential equation

  6:    - Laplacian u = 1,0 < x,y,z < 1,

  8:    with boundary conditions
  9:    u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
 10: */

 12: static char help[] = "This example is for testing different MatSolve routines :MatSolve(), MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd(), and MatMatSolve().\n\
 13: Example usage: ./ex129 -mat_type aij -dof 2\n\n";

 15: #include <petscdm.h>
 16: #include <petscdmda.h>

 18: extern PetscErrorCode ComputeMatrix(DM,Mat);
 19: extern PetscErrorCode ComputeRHS(DM,Vec);
 20: extern PetscErrorCode ComputeRHSMatrix(PetscInt,PetscInt,Mat*);

 22: int main(int argc,char **args)
 23: {
 25:   PetscMPIInt    size;
 26:   Vec            x,b,y,b1;
 27:   DM             da;
 28:   Mat            A,F,RHS,X,C1;
 29:   MatFactorInfo  info;
 30:   IS             perm,iperm;
 31:   PetscInt       dof =1,M=8,m,n,nrhs;
 32:   PetscScalar    one = 1.0;
 33:   PetscReal      norm,tol = 1000*PETSC_MACHINE_EPSILON;
 34:   PetscBool      InplaceLU=PETSC_FALSE;

 36:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 37:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 38:   if (size != 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only\n");
 39:   PetscOptionsGetInt(NULL,NULL,"-dof",&dof,NULL);
 40:   PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);

 42:   DMDACreate(PETSC_COMM_WORLD,&da);
 43:   DMSetDimension(da,3);
 44:   DMDASetBoundaryType(da,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE);
 45:   DMDASetStencilType(da,DMDA_STENCIL_STAR);
 46:   DMDASetSizes(da,M,M,M);
 47:   DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);
 48:   DMDASetDof(da,dof);
 49:   DMDASetStencilWidth(da,1);
 50:   DMDASetOwnershipRanges(da,NULL,NULL,NULL);
 51:   DMSetMatType(da,MATBAIJ);
 52:   DMSetFromOptions(da);
 53:   DMSetUp(da);

 55:   DMCreateGlobalVector(da,&x);
 56:   DMCreateGlobalVector(da,&b);
 57:   VecDuplicate(b,&y);
 58:   ComputeRHS(da,b);
 59:   VecSet(y,one);
 60:   DMCreateMatrix(da,&A);
 61:   ComputeMatrix(da,A);
 62:   MatGetSize(A,&m,&n);
 63:   nrhs = 2;
 64:   PetscOptionsGetInt(NULL,NULL,"-nrhs",&nrhs,NULL);
 65:   ComputeRHSMatrix(m,nrhs,&RHS);
 66:   MatDuplicate(RHS,MAT_DO_NOT_COPY_VALUES,&X);

 68:   MatGetOrdering(A,MATORDERINGND,&perm,&iperm);

 70:   PetscOptionsGetBool(NULL,NULL,"-inplacelu",&InplaceLU,NULL);
 71:   MatFactorInfoInitialize(&info);
 72:   if (!InplaceLU) {
 73:     MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);
 74:     info.fill = 5.0;
 75:     MatLUFactorSymbolic(F,A,perm,iperm,&info);
 76:     MatLUFactorNumeric(F,A,&info);
 77:   } else { /* Test inplace factorization */
 78:     MatDuplicate(A,MAT_COPY_VALUES,&F);
 79:     MatLUFactor(F,perm,iperm,&info);
 80:   }

 82:   VecDuplicate(y,&b1);

 84:   /* MatSolve */
 85:   MatSolve(F,b,x);
 86:   MatMult(A,x,b1);
 87:   VecAXPY(b1,-1.0,b);
 88:   VecNorm(b1,NORM_2,&norm);
 89:   if (norm > tol) {
 90:     PetscPrintf(PETSC_COMM_WORLD,"MatSolve              : Error of norm %g\n",(double)norm);
 91:   }

 93:   /* MatSolveTranspose */
 94:   MatSolveTranspose(F,b,x);
 95:   MatMultTranspose(A,x,b1);
 96:   VecAXPY(b1,-1.0,b);
 97:   VecNorm(b1,NORM_2,&norm);
 98:   if (norm > tol) {
 99:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveTranspose     : Error of norm %g\n",(double)norm);
100:   }

102:   /* MatSolveAdd */
103:   MatSolveAdd(F,b,y,x);
104:   MatMult(A,y,b1);
105:   VecScale(b1,-1.0);
106:   MatMultAdd(A,x,b1,b1);
107:   VecAXPY(b1,-1.0,b);
108:   VecNorm(b1,NORM_2,&norm);
109:   if (norm > tol) {
110:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveAdd           : Error of norm %g\n",(double)norm);
111:   }

113:   /* MatSolveTransposeAdd */
114:   MatSolveTransposeAdd(F,b,y,x);
115:   MatMultTranspose(A,y,b1);
116:   VecScale(b1,-1.0);
117:   MatMultTransposeAdd(A,x,b1,b1);
118:   VecAXPY(b1,-1.0,b);
119:   VecNorm(b1,NORM_2,&norm);
120:   if (norm > tol) {
121:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveTransposeAdd  : Error of norm %g\n",(double)norm);
122:   }

124:   /* MatMatSolve */
125:   MatMatSolve(F,RHS,X);
126:   MatMatMult(A,X,MAT_INITIAL_MATRIX,2.0,&C1);
127:   MatAXPY(C1,-1.0,RHS,SAME_NONZERO_PATTERN);
128:   MatNorm(C1,NORM_FROBENIUS,&norm);
129:   if (norm > tol) {
130:     PetscPrintf(PETSC_COMM_WORLD,"MatMatSolve           : Error of norm %g\n",(double)norm);
131:   }

133:   VecDestroy(&x);
134:   VecDestroy(&b);
135:   VecDestroy(&b1);
136:   VecDestroy(&y);
137:   MatDestroy(&A);
138:   MatDestroy(&F);
139:   MatDestroy(&RHS);
140:   MatDestroy(&C1);
141:   MatDestroy(&X);
142:   ISDestroy(&perm);
143:   ISDestroy(&iperm);
144:   DMDestroy(&da);
145:   PetscFinalize();
146:   return ierr;
147: }

149: PetscErrorCode ComputeRHS(DM da,Vec b)
150: {
152:   PetscInt       mx,my,mz;
153:   PetscScalar    h;

156:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
157:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
158:   VecSet(b,h);
159:   return(0);
160: }

162: PetscErrorCode ComputeRHSMatrix(PetscInt m,PetscInt nrhs,Mat *C)
163: {
165:   PetscRandom    rand;
166:   Mat            RHS;
167:   PetscScalar    *array,rval;
168:   PetscInt       i,k;

171:   MatCreate(PETSC_COMM_WORLD,&RHS);
172:   MatSetSizes(RHS,m,PETSC_DECIDE,PETSC_DECIDE,nrhs);
173:   MatSetType(RHS,MATSEQDENSE);
174:   MatSetUp(RHS);

176:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
177:   PetscRandomSetFromOptions(rand);
178:   MatDenseGetArray(RHS,&array);
179:   for (i=0; i<m; i++) {
180:     PetscRandomGetValue(rand,&rval);
181:     array[i] = rval;
182:   }
183:   if (nrhs > 1) {
184:     for (k=1; k<nrhs; k++) {
185:       for (i=0; i<m; i++) {
186:         array[m*k+i] = array[i];
187:       }
188:     }
189:   }
190:   MatDenseRestoreArray(RHS,&array);
191:   MatAssemblyBegin(RHS,MAT_FINAL_ASSEMBLY);
192:   MatAssemblyEnd(RHS,MAT_FINAL_ASSEMBLY);
193:   *C   = RHS;
194:   PetscRandomDestroy(&rand);
195:   return(0);
196: }

198: PetscErrorCode ComputeMatrix(DM da,Mat B)
199: {
201:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,dof,k1,k2,k3;
202:   PetscScalar    *v,*v_neighbor,Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy,r1,r2;
203:   MatStencil     row,col;
204:   PetscRandom    rand;

207:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
208:   PetscRandomSetSeed(rand,1);
209:   PetscRandomSetInterval(rand,-.001,.001);
210:   PetscRandomSetFromOptions(rand);

212:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
213:   /* For simplicity, this example only works on mx=my=mz */
214:   if (mx != my || mx != mz) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_SUP,"This example only works with mx %d = my %d = mz %d\n",mx,my,mz);

216:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
217:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;

219:   PetscMalloc1(2*dof*dof+1,&v);
220:   v_neighbor = v + dof*dof;
221:   PetscArrayzero(v,2*dof*dof+1);
222:   k3         = 0;
223:   for (k1=0; k1<dof; k1++) {
224:     for (k2=0; k2<dof; k2++) {
225:       if (k1 == k2) {
226:         v[k3]          = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
227:         v_neighbor[k3] = -HxHydHz;
228:       } else {
229:         PetscRandomGetValue(rand,&r1);
230:         PetscRandomGetValue(rand,&r2);

232:         v[k3]          = r1;
233:         v_neighbor[k3] = r2;
234:       }
235:       k3++;
236:     }
237:   }
238:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

240:   for (k=zs; k<zs+zm; k++) {
241:     for (j=ys; j<ys+ym; j++) {
242:       for (i=xs; i<xs+xm; i++) {
243:         row.i = i; row.j = j; row.k = k;
244:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) { /* boundary points */
245:           MatSetValuesBlockedStencil(B,1,&row,1,&row,v,INSERT_VALUES);
246:         } else { /* interior points */
247:           /* center */
248:           col.i = i; col.j = j; col.k = k;
249:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v,INSERT_VALUES);

251:           /* x neighbors */
252:           col.i = i-1; col.j = j; col.k = k;
253:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
254:           col.i = i+1; col.j = j; col.k = k;
255:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

257:           /* y neighbors */
258:           col.i = i; col.j = j-1; col.k = k;
259:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
260:           col.i = i; col.j = j+1; col.k = k;
261:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

263:           /* z neighbors */
264:           col.i = i; col.j = j; col.k = k-1;
265:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
266:           col.i = i; col.j = j; col.k = k+1;
267:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
268:         }
269:       }
270:     }
271:   }
272:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
273:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
274:   PetscFree(v);
275:   PetscRandomDestroy(&rand);
276:   return(0);
277: }

279: /*TEST

281:    test:
282:       args: -dm_mat_type aij -dof 1
283:       output_file: output/ex129.out

285:    test:
286:       suffix: 2
287:       args: -dm_mat_type aij -dof 1 -inplacelu
288:       output_file: output/ex129.out

290: TEST*/