Actual source code: ex214.c

petsc-3.12.5 2020-03-29
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  2: static char help[] = "Tests MatMatSolve() and MatMatTransposeSolve() for computing inv(A) with MUMPS.\n\
  3: Example: mpiexec -n <np> ./ex214 -displ \n\n";

  5:  #include <petscmat.h>

  7: int main(int argc,char **args)
  8: {
 10:   PetscMPIInt    size,rank;
 11: #if defined(PETSC_HAVE_MUMPS)
 12:   Mat            A,RHS,C,F,X,AX,spRHST;
 13:   PetscInt       m,n,nrhs,M,N,i,Istart,Iend,Ii,j,J,test;
 14:   PetscScalar    v;
 15:   PetscReal      norm,tol=PETSC_SQRT_MACHINE_EPSILON;
 16:   PetscRandom    rand;
 17:   PetscBool      displ=PETSC_FALSE;
 18:   char           solver[256];
 19: #endif

 21:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 22:   MPI_Comm_size(PETSC_COMM_WORLD,&size);
 23:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);

 25: #if !defined(PETSC_HAVE_MUMPS)
 26:   if (!rank) {PetscPrintf(PETSC_COMM_SELF,"This example requires MUMPS, exit...\n");}
 27:   PetscFinalize();
 28:   return ierr;
 29: #else

 31:   PetscOptionsGetBool(NULL,NULL,"-displ",&displ,NULL);

 33:   /* Create matrix A */
 34:   m = 4; n = 4;
 35:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 36:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);

 38:   MatCreate(PETSC_COMM_WORLD,&A);
 39:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 40:   MatSetFromOptions(A);
 41:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 42:   MatSeqAIJSetPreallocation(A,5,NULL);

 44:   MatGetOwnershipRange(A,&Istart,&Iend);
 45:   for (Ii=Istart; Ii<Iend; Ii++) {
 46:     v = -1.0; i = Ii/n; j = Ii - i*n;
 47:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 48:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 49:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 50:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 51:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 52:   }
 53:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 54:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 56:   MatGetLocalSize(A,&m,&n);
 57:   MatGetSize(A,&M,&N);
 58:   if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);

 60:   /* Create dense matrix C and X; C holds true solution with identical colums */
 61:   nrhs = N;
 62:   PetscOptionsGetInt(NULL,NULL,"-nrhs",&nrhs,NULL);
 63:   MatCreate(PETSC_COMM_WORLD,&C);
 64:   MatSetSizes(C,m,PETSC_DECIDE,PETSC_DECIDE,nrhs);
 65:   MatSetType(C,MATDENSE);
 66:   MatSetFromOptions(C);
 67:   MatSetUp(C);

 69:   PetscRandomCreate(PETSC_COMM_WORLD,&rand);
 70:   PetscRandomSetFromOptions(rand);
 71:   MatSetRandom(C,rand);
 72:   MatDuplicate(C,MAT_DO_NOT_COPY_VALUES,&X);

 74:   PetscStrcpy(solver,MATSOLVERMUMPS);
 75:   if (!rank && displ) {PetscPrintf(PETSC_COMM_SELF,"Solving with %s: nrhs %D, size mat %D x %D\n",solver,nrhs,M,N);}

 77:   for (test=0; test<2; test++) {
 78:     if (test == 0) {
 79:       /* Test LU Factorization */
 80:       PetscPrintf(PETSC_COMM_WORLD,"test LU factorization\n");
 81:       MatGetFactor(A,solver,MAT_FACTOR_LU,&F);
 82:       MatLUFactorSymbolic(F,A,NULL,NULL,NULL);
 83:       MatLUFactorNumeric(F,A,NULL);
 84:     } else {
 85:       /* Test Cholesky Factorization */
 86:       PetscBool flg;
 87:       MatIsSymmetric(A,0.0,&flg);
 88:       if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A must be symmetric for Cholesky factorization");

 90:       PetscPrintf(PETSC_COMM_WORLD,"test Cholesky factorization\n");
 91:       MatGetFactor(A,solver,MAT_FACTOR_CHOLESKY,&F);
 92:       MatCholeskyFactorSymbolic(F,A,NULL,NULL);
 93:       MatCholeskyFactorNumeric(F,A,NULL);
 94:     }

 96:     /* (1) Test MatMatSolve(): dense RHS = A*C, C: true solutions */
 97:     /* ---------------------------------------------------------- */
 98:     MatMatMult(A,C,MAT_INITIAL_MATRIX,2.0,&RHS);
 99:     MatMatSolve(F,RHS,X);

101:     /* Check the error */
102:     MatAXPY(X,-1.0,C,SAME_NONZERO_PATTERN);
103:     MatNorm(X,NORM_FROBENIUS,&norm);
104:     if (norm > tol) {
105:       PetscPrintf(PETSC_COMM_SELF,"(1) MatMatSolve: Norm of error %g\n",norm);
106:     }

108:     /* (2) Test MatMatSolve() for inv(A) with dense RHS:
109:      RHS = [e[0],...,e[nrhs-1]], dense X holds first nrhs columns of inv(A) */
110:     /* -------------------------------------------------------------------- */
111:     MatZeroEntries(RHS);
112:     for (i=0; i<nrhs; i++) {
113:       v = 1.0;
114:       MatSetValues(RHS,1,&i,1,&i,&v,INSERT_VALUES);
115:     }
116:     MatAssemblyBegin(RHS,MAT_FINAL_ASSEMBLY);
117:     MatAssemblyEnd(RHS,MAT_FINAL_ASSEMBLY);

119:     MatMatSolve(F,RHS,X);
120:     if (displ) {
121:       if (!rank) {PetscPrintf(PETSC_COMM_SELF," \n(2) first %D columns of inv(A) with dense RHS:\n",nrhs);}
122:       MatView(X,PETSC_VIEWER_STDOUT_WORLD);
123:     }

125:     /* Check the residual */
126:     MatMatMult(A,X,MAT_INITIAL_MATRIX,2.0,&AX);
127:     MatAXPY(AX,-1.0,RHS,SAME_NONZERO_PATTERN);
128:     MatNorm(AX,NORM_INFINITY,&norm);
129:     if (norm > tol) {
130:       PetscPrintf(PETSC_COMM_SELF,"(2) MatMatSolve: Norm of residual %g\n",norm);
131:     }
132:     MatZeroEntries(X);

134:     /* (3) Test MatMatTransposeSolve() for inv(A) with sparse RHS stored in the host:
135:      spRHST = [e[0],...,e[nrhs-1]]^T, dense X holds first nrhs columns of inv(A) */
136:     /* --------------------------------------------------------------------------- */
137:     /* Create spRHST: PETSc does not support compressed column format which is required by MUMPS for sparse RHS matrix,
138:      thus user must create spRHST=spRHS^T and call MatMatTransposeSolve() */
139:     MatCreate(PETSC_COMM_WORLD,&spRHST);
140:     if (!rank) {
141:       /* MUMPS requirs RHS be centralized on the host! */
142:       MatSetSizes(spRHST,nrhs,M,PETSC_DECIDE,PETSC_DECIDE);
143:     } else {
144:       MatSetSizes(spRHST,0,0,PETSC_DECIDE,PETSC_DECIDE);
145:     }
146:     MatSetType(spRHST,MATAIJ);
147:     MatSetFromOptions(spRHST);
148:     MatSetUp(spRHST);
149:     if (!rank) {
150:       v = 1.0;
151:       for (i=0; i<nrhs; i++) {
152:         MatSetValues(spRHST,1,&i,1,&i,&v,INSERT_VALUES);
153:       }
154:     }
155:     MatAssemblyBegin(spRHST,MAT_FINAL_ASSEMBLY);
156:     MatAssemblyEnd(spRHST,MAT_FINAL_ASSEMBLY);

158:     MatMatTransposeSolve(F,spRHST,X);

160:     if (displ) {
161:       if (!rank) {PetscPrintf(PETSC_COMM_SELF," \n(3) first %D columns of inv(A) with sparse RHS:\n",nrhs);}
162:       MatView(X,PETSC_VIEWER_STDOUT_WORLD);
163:     }

165:     /* Check the residual: R = A*X - RHS */
166:     MatMatMult(A,X,MAT_REUSE_MATRIX,2.0,&AX);

168:     MatAXPY(AX,-1.0,RHS,SAME_NONZERO_PATTERN);
169:     MatNorm(AX,NORM_INFINITY,&norm);
170:     if (norm > tol) {
171:       PetscPrintf(PETSC_COMM_SELF,"(3) MatMatSolve: Norm of residual %g\n",norm);
172:     }

174:     /* (4) Test MatMatSolve() for inv(A) with selected entries:
175:      input: spRHS gives selected indices; output: spRHS holds selected entries of inv(A) */
176:     /* --------------------------------------------------------------------------------- */
177:     if (nrhs == N) { /* mumps requires nrhs = n */
178:       /* Create spRHS on proc[0] */
179:       Mat spRHS = NULL;

181:       /* Create spRHS = spRHST^T. Two matrices share internal matrix data structure */
182:       MatCreateTranspose(spRHST,&spRHS);
183:       MatMumpsGetInverse(F,spRHS);
184:       MatDestroy(&spRHS);

186:       MatMumpsGetInverseTranspose(F,spRHST);
187:       if (displ) {
188:         PetscPrintf(PETSC_COMM_WORLD,"\nSelected entries of inv(A^T):\n");
189:         MatView(spRHST,PETSC_VIEWER_STDOUT_WORLD);
190:       }
191:       MatDestroy(&spRHS);
192:     }
193:     MatDestroy(&AX);
194:     MatDestroy(&F);
195:     MatDestroy(&RHS);
196:     MatDestroy(&spRHST);
197:   }

199:   /* Free data structures */
200:   MatDestroy(&A);
201:   MatDestroy(&C);
202:   MatDestroy(&X);
203:   PetscRandomDestroy(&rand);
204:   PetscFinalize();
205:   return ierr;
206: #endif
207: }

209: /*TEST


212:    test:
213:      requires: mumps double !complex !define(PETSC_USE_64BIT_INDICES)

215:    test:
216:      suffix: 2
217:      requires: mumps double !complex !define(PETSC_USE_64BIT_INDICES)
218:      nsize: 2

220: TEST*/