Actual source code: ex129.c

petsc-3.4.2 2013-07-02
  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 <petscdmda.h>

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

 23: int main(int argc,char **args)
 24: {
 26:   PetscMPIInt    size;
 27:   Vec            x,b,y,b1;
 28:   DM             da;
 29:   Mat            A,F,RHS,X,C1;
 30:   MatFactorInfo  info;
 31:   IS             perm,iperm;
 32:   PetscInt       dof =1,M=-8,m,n,nrhs;
 33:   PetscScalar    one = 1.0;
 34:   PetscReal      norm,tol=1.e-13;
 35:   PetscBool      InplaceLU=PETSC_FALSE;

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

 43:   DMDACreate(PETSC_COMM_WORLD,&da);
 44:   DMDASetDim(da,3);
 45:   DMDASetBoundaryType(da,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE);
 46:   DMDASetStencilType(da,DMDA_STENCIL_STAR);
 47:   DMDASetSizes(da,M,M,M);
 48:   DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);
 49:   DMDASetDof(da,dof);
 50:   DMDASetStencilWidth(da,1);
 51:   DMDASetOwnershipRanges(da,NULL,NULL,NULL);
 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,MATBAIJ,&A);
 61:   ComputeMatrix(da,A);
 62:   MatGetSize(A,&m,&n);
 63:   nrhs = 2;
 64:   PetscOptionsGetInt(NULL,"-nrhs",&nrhs,NULL);
 65:   ComputeRHSMatrix(m,nrhs,&RHS);
 66:   MatDuplicate(RHS,MAT_DO_NOT_COPY_VALUES,&X);

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


 71:   PetscOptionsGetBool(NULL,"-inplacelu",&InplaceLU,NULL);
 72:   MatFactorInfoInitialize(&info);
 73:   if (!InplaceLU) {
 74:     MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);
 75:     info.fill = 5.0;
 76:     MatLUFactorSymbolic(F,A,perm,iperm,&info);
 77:     MatLUFactorNumeric(F,A,&info);
 78:   } else { /* Test inplace factorization */
 79:     MatDuplicate(A,MAT_COPY_VALUES,&F);
 80:     /* or create F without DMDA
 81:     MatType     type;
 82:     PetscInt          i,ncols;
 83:     const PetscInt    *cols;
 84:     const PetscScalar *vals;
 85:     MatGetSize(A,&m,&n);
 86:     MatGetType(A,&type);
 87:     MatCreate(PetscObjectComm((PetscObject)A),&F);
 88:     MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,m,n);
 89:     MatSetType(F,type);
 90:     MatSetFromOptions(F);
 91:     for (i=0; i<m; i++) {
 92:       MatGetRow(A,i,&ncols,&cols,&vals);
 93:       MatSetValues(F,1,&i,ncols,cols,vals,INSERT_VALUES);
 94:     }
 95:     MatAssemblyBegin(F,MAT_FINAL_ASSEMBLY);
 96:     MatAssemblyEnd(F,MAT_FINAL_ASSEMBLY);
 97:     */
 98:     MatLUFactor(F,perm,iperm,&info);
 99:   }

101:   VecDuplicate(y,&b1);

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

112:   /* MatSolveTranspose */
113:   MatSolveTranspose(F,b,x);
114:   MatMultTranspose(A,x,b1);
115:   VecAXPY(b1,-1.0,b);
116:   VecNorm(b1,NORM_2,&norm);
117:   if (norm > tol) {
118:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveTranspose     : Error of norm %G\n",norm);
119:   }

121:   /* MatSolveAdd */
122:   MatSolveAdd(F,b,y,x);
123:   MatMult(A,y,b1);
124:   VecScale(b1,-1.0);
125:   MatMultAdd(A,x,b1,b1);
126:   VecAXPY(b1,-1.0,b);
127:   VecNorm(b1,NORM_2,&norm);
128:   if (norm > tol) {
129:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveAdd           : Error of norm %G\n",norm);
130:   }

132:   /* MatSolveTransposeAdd */
133:   MatSolveTransposeAdd(F,b,y,x);
134:   MatMultTranspose(A,y,b1);
135:   VecScale(b1,-1.0);
136:   MatMultTransposeAdd(A,x,b1,b1);
137:   VecAXPY(b1,-1.0,b);
138:   VecNorm(b1,NORM_2,&norm);
139:   if (norm > tol) {
140:     PetscPrintf(PETSC_COMM_WORLD,"MatSolveTransposeAdd  : Error of norm %G\n",norm);
141:   }

143:   /* MatMatSolve */
144:   MatMatSolve(F,RHS,X);
145:   MatMatMult(A,X,MAT_INITIAL_MATRIX,2.0,&C1);
146:   MatAXPY(C1,-1.0,RHS,SAME_NONZERO_PATTERN);
147:   MatNorm(C1,NORM_FROBENIUS,&norm);
148:   if (norm > tol) {
149:     PetscPrintf(PETSC_COMM_WORLD,"MatMatSolve           : Error of norm %G\n",norm);
150:   }

152:   VecDestroy(&x);
153:   VecDestroy(&b);
154:   VecDestroy(&b1);
155:   VecDestroy(&y);
156:   MatDestroy(&A);
157:   MatDestroy(&F);
158:   MatDestroy(&RHS);
159:   MatDestroy(&C1);
160:   MatDestroy(&X);
161:   ISDestroy(&perm);
162:   ISDestroy(&iperm);
163:   DMDestroy(&da);
164:   PetscFinalize();
165:   return 0;
166: }

170: PetscErrorCode ComputeRHS(DM da,Vec b)
171: {
173:   PetscInt       mx,my,mz;
174:   PetscScalar    h;

177:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
178:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
179:   VecSet(b,h);
180:   return(0);
181: }

185: PetscErrorCode ComputeRHSMatrix(PetscInt m,PetscInt nrhs,Mat *C)
186: {
188:   PetscRandom    rand;
189:   Mat            RHS;
190:   PetscScalar    *array,rval;
191:   PetscInt       i,k;

194:   MatCreate(PETSC_COMM_WORLD,&RHS);
195:   MatSetSizes(RHS,m,PETSC_DECIDE,PETSC_DECIDE,nrhs);
196:   MatSetType(RHS,MATSEQDENSE);
197:   MatSetUp(RHS);

199:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
200:   PetscRandomSetFromOptions(rand);
201:   MatDenseGetArray(RHS,&array);
202:   for (i=0; i<m; i++) {
203:     PetscRandomGetValue(rand,&rval);
204:     array[i] = rval;
205:   }
206:   if (nrhs > 1) {
207:     for (k=1; k<nrhs; k++) {
208:       for (i=0; i<m; i++) {
209:         array[m*k+i] = array[i];
210:       }
211:     }
212:   }
213:   MatDenseRestoreArray(RHS,&array);
214:   MatAssemblyBegin(RHS,MAT_FINAL_ASSEMBLY);
215:   MatAssemblyEnd(RHS,MAT_FINAL_ASSEMBLY);
216:   *C   = RHS;
217:   PetscRandomDestroy(&rand);
218:   return(0);
219: }


224: PetscErrorCode ComputeMatrix(DM da,Mat B)
225: {
227:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,dof,k1,k2,k3;
228:   PetscScalar    *v,*v_neighbor,Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy,r1,r2;
229:   MatStencil     row,col;
230:   PetscRandom    rand;

233:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
234:   PetscRandomSetType(rand,PETSCRAND);
235:   PetscRandomSetSeed(rand,1);
236:   PetscRandomSetInterval(rand,-.001,.001);
237:   PetscRandomSetFromOptions(rand);

239:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
240:   /* For simplicity, this example only works on mx=my=mz */
241:   if (mx != my || mx != mz) SETERRQ3(PETSC_COMM_SELF,1,"This example only works with mx %d = my %d = mz %d\n",mx,my,mz);

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

246:   PetscMalloc((2*dof*dof+1)*sizeof(PetscScalar),&v);
247:   v_neighbor = v + dof*dof;
248:   PetscMemzero(v,(2*dof*dof+1)*sizeof(PetscScalar));
249:   k3         = 0;
250:   for (k1=0; k1<dof; k1++) {
251:     for (k2=0; k2<dof; k2++) {
252:       if (k1 == k2) {
253:         v[k3]          = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
254:         v_neighbor[k3] = -HxHydHz;
255:       } else {
256:         PetscRandomGetValue(rand,&r1);
257:         PetscRandomGetValue(rand,&r2);

259:         v[k3]          = r1;
260:         v_neighbor[k3] = r2;
261:       }
262:       k3++;
263:     }
264:   }
265:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

267:   for (k=zs; k<zs+zm; k++) {
268:     for (j=ys; j<ys+ym; j++) {
269:       for (i=xs; i<xs+xm; i++) {
270:         row.i = i; row.j = j; row.k = k;
271:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) { /* boudary points */
272:           MatSetValuesBlockedStencil(B,1,&row,1,&row,v,INSERT_VALUES);
273:         } else { /* interior points */
274:           /* center */
275:           col.i = i; col.j = j; col.k = k;
276:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v,INSERT_VALUES);

278:           /* x neighbors */
279:           col.i = i-1; col.j = j; col.k = k;
280:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
281:           col.i = i+1; col.j = j; col.k = k;
282:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

284:           /* y neighbors */
285:           col.i = i; col.j = j-1; col.k = k;
286:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
287:           col.i = i; col.j = j+1; col.k = k;
288:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

290:           /* z neighbors */
291:           col.i = i; col.j = j; col.k = k-1;
292:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
293:           col.i = i; col.j = j; col.k = k+1;
294:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
295:         }
296:       }
297:     }
298:   }
299:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
300:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
301:   PetscFree(v);
302:   PetscRandomDestroy(&rand);
303:   return(0);
304: }