Actual source code: ex145.c
petsc-3.6.4 2016-04-12
2: static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for an Elemental dense matrix.\n\n";
4: #include <petscmat.h>
8: int main(int argc,char **argv)
9: {
10: Mat A,F,B,X,C,Aher,G;
11: Vec b,x,c,d,e;
13: PetscInt m = 5,n,p,i,j,nrows,ncols;
14: PetscScalar *v,*barray,rval;
15: PetscReal norm,tol=1.e-12;
16: PetscMPIInt size,rank;
17: PetscRandom rand;
18: const PetscInt *rows,*cols;
19: IS isrows,iscols;
20: PetscBool mats_view=PETSC_FALSE;
21: MatFactorInfo finfo;
23: PetscInitialize(&argc,&argv,(char*) 0,help);
24: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
25: MPI_Comm_size(PETSC_COMM_WORLD,&size);
27: PetscRandomCreate(PETSC_COMM_WORLD,&rand);
28: PetscRandomSetFromOptions(rand);
30: /* Get local dimensions of matrices */
31: PetscOptionsGetInt(NULL,"-m",&m,NULL);
32: n = m;
33: PetscOptionsGetInt(NULL,"-n",&n,NULL);
34: p = m/2;
35: PetscOptionsGetInt(NULL,"-p",&p,NULL);
36: PetscOptionsHasName(NULL,"-mats_view",&mats_view);
38: /* Create matrix A */
39: PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix A\n");
40: MatCreate(PETSC_COMM_WORLD,&A);
41: MatSetSizes(A,m,n,PETSC_DECIDE,PETSC_DECIDE);
42: MatSetType(A,MATELEMENTAL);
43: MatSetFromOptions(A);
44: MatSetUp(A);
45: /* Set local matrix entries */
46: MatGetOwnershipIS(A,&isrows,&iscols);
47: ISGetLocalSize(isrows,&nrows);
48: ISGetIndices(isrows,&rows);
49: ISGetLocalSize(iscols,&ncols);
50: ISGetIndices(iscols,&cols);
51: PetscMalloc1(nrows*ncols,&v);
52: for (i=0; i<nrows; i++) {
53: for (j=0; j<ncols; j++) {
54: PetscRandomGetValue(rand,&rval);
55: v[i*ncols+j] = rval;
56: }
57: }
58: MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES);
59: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
60: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
61: ISRestoreIndices(isrows,&rows);
62: ISRestoreIndices(iscols,&cols);
63: ISDestroy(&isrows);
64: ISDestroy(&iscols);
65: PetscFree(v);
66: if (mats_view) {
67: PetscPrintf(PETSC_COMM_WORLD, "A: nrows %d, m %d; ncols %d, n %d\n",nrows,m,ncols,n);
68: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
69: }
71: /* Create rhs matrix B */
72: PetscPrintf(PETSC_COMM_WORLD," Create rhs matrix B\n");
73: MatCreate(PETSC_COMM_WORLD,&B);
74: MatSetSizes(B,m,p,PETSC_DECIDE,PETSC_DECIDE);
75: MatSetType(B,MATELEMENTAL);
76: MatSetFromOptions(B);
77: MatSetUp(B);
78: MatGetOwnershipIS(B,&isrows,&iscols);
79: ISGetLocalSize(isrows,&nrows);
80: ISGetIndices(isrows,&rows);
81: ISGetLocalSize(iscols,&ncols);
82: ISGetIndices(iscols,&cols);
83: PetscMalloc1(nrows*ncols,&v);
84: for (i=0; i<nrows; i++) {
85: for (j=0; j<ncols; j++) {
86: PetscRandomGetValue(rand,&rval);
87: v[i*ncols+j] = rval;
88: }
89: }
90: MatSetValues(B,nrows,rows,ncols,cols,v,INSERT_VALUES);
91: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
93: ISRestoreIndices(isrows,&rows);
94: ISRestoreIndices(iscols,&cols);
95: ISDestroy(&isrows);
96: ISDestroy(&iscols);
97: PetscFree(v);
98: if (mats_view) {
99: PetscPrintf(PETSC_COMM_WORLD, "B: nrows %d, m %d; ncols %d, p %d\n",nrows,m,ncols,p);
100: MatView(B,PETSC_VIEWER_STDOUT_WORLD);
101: }
103: /* Create rhs vector b and solution x (same size as b) */
104: VecCreate(PETSC_COMM_WORLD,&b);
105: VecSetSizes(b,m,PETSC_DECIDE);
106: VecSetFromOptions(b);
107: VecGetArray(b,&barray);
108: for (j=0; j<m; j++) {
109: PetscRandomGetValue(rand,&rval);
110: barray[j] = rval;
111: }
112: VecRestoreArray(b,&barray);
113: VecAssemblyBegin(b);
114: VecAssemblyEnd(b);
115: if (mats_view) {
116: PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] b: m %d\n",rank,m);
117: PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);
118: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
119: }
120: VecDuplicate(b,&x);
122: /* Create matrix X - same size as B */
123: PetscPrintf(PETSC_COMM_WORLD," Create solution matrix X\n");
124: MatCreate(PETSC_COMM_WORLD,&X);
125: MatSetSizes(X,m,p,PETSC_DECIDE,PETSC_DECIDE);
126: MatSetType(X,MATELEMENTAL);
127: MatSetFromOptions(X);
128: MatSetUp(X);
129: MatAssemblyBegin(X,MAT_FINAL_ASSEMBLY);
130: MatAssemblyEnd(X,MAT_FINAL_ASSEMBLY);
132: /* Cholesky factorization */
133: /*------------------------*/
134: PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix Aher\n");
135: MatHermitianTranspose(A,MAT_INITIAL_MATRIX,&Aher);
136: MatAXPY(Aher,1.0,A,SAME_NONZERO_PATTERN); /* Aher = A + A^T */
137: if (!rank) { /* add 100.0 to diagonals of Aher to make it spd */
138: PetscInt M,N;
139: MatGetSize(Aher,&M,&N);
140: for (i=0; i<M; i++) {
141: rval = 100.0;
142: MatSetValues(Aher,1,&i,1,&i,&rval,ADD_VALUES);
143: }
144: }
145: MatAssemblyBegin(Aher,MAT_FINAL_ASSEMBLY);
146: MatAssemblyEnd(Aher,MAT_FINAL_ASSEMBLY);
147: if (mats_view) {
148: PetscPrintf(PETSC_COMM_WORLD, "Aher:\n");
149: MatView(Aher,PETSC_VIEWER_STDOUT_WORLD);
150: }
152: /* Cholesky factorization */
153: /*------------------------*/
154: PetscPrintf(PETSC_COMM_WORLD," Test Cholesky Solver \n");
155: /* In-place Cholesky */
156: /* Create matrix factor G, then copy Aher to G */
157: MatCreate(PETSC_COMM_WORLD,&G);
158: MatSetSizes(G,m,n,PETSC_DECIDE,PETSC_DECIDE);
159: MatSetType(G,MATELEMENTAL);
160: MatSetFromOptions(G);
161: MatSetUp(G);
162: MatAssemblyBegin(G,MAT_FINAL_ASSEMBLY);
163: MatAssemblyEnd(G,MAT_FINAL_ASSEMBLY);
164: MatCopy(Aher,G,SAME_NONZERO_PATTERN);
166: /* Only G = U^T * U is implemented for now */
167: MatCholeskyFactor(G,0,0);
168: if (mats_view) {
169: PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n");
170: MatView(G,PETSC_VIEWER_STDOUT_WORLD);
171: }
173: /* Solve U^T * U x = b and U^T * U X = B */
174: MatSolve(G,b,x);
175: MatMatSolve(G,B,X);
176: MatDestroy(&G);
178: /* Out-place Cholesky */
179: MatGetFactor(Aher,MATSOLVERELEMENTAL,MAT_FACTOR_CHOLESKY,&G);
180: MatCholeskyFactorSymbolic(G,Aher,0,&finfo);
181: MatCholeskyFactorNumeric(G,Aher,&finfo);
182: if (mats_view) {
183: MatView(G,PETSC_VIEWER_STDOUT_WORLD);
184: }
185: MatSolve(G,b,x);
186: MatMatSolve(G,B,X);
187: MatDestroy(&G);
189: /* Check norm(Aher*x - b) */
190: VecCreate(PETSC_COMM_WORLD,&c);
191: VecSetSizes(c,m,PETSC_DECIDE);
192: VecSetFromOptions(c);
193: MatMult(Aher,x,c);
194: VecAXPY(c,-1.0,b);
195: VecNorm(c,NORM_1,&norm);
196: if (norm > tol) {
197: PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*x - b| for Cholesky %g\n",(double)norm);
198: }
200: /* Check norm(Aher*X - B) */
201: MatMatMult(Aher,X,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&C);
202: MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);
203: MatNorm(C,NORM_1,&norm);
204: if (norm > tol) {
205: PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*X - B| for Cholesky %g\n",(double)norm);
206: }
208: /* LU factorization */
209: /*------------------*/
210: PetscPrintf(PETSC_COMM_WORLD," Test LU Solver \n");
211: /* In-place LU */
212: /* Create matrix factor F, then copy A to F */
213: MatCreate(PETSC_COMM_WORLD,&F);
214: MatSetSizes(F,m,n,PETSC_DECIDE,PETSC_DECIDE);
215: MatSetType(F,MATELEMENTAL);
216: MatSetFromOptions(F);
217: MatSetUp(F);
218: MatAssemblyBegin(F,MAT_FINAL_ASSEMBLY);
219: MatAssemblyEnd(F,MAT_FINAL_ASSEMBLY);
220: MatCopy(A,F,SAME_NONZERO_PATTERN);
221: /* Create vector d to test MatSolveAdd() */
222: VecDuplicate(x,&d);
223: VecCopy(x,d);
225: /* PF=LU or F=LU factorization - perms is ignored by Elemental;
226: set finfo.dtcol !0 or 0 to enable/disable partial pivoting */
227: finfo.dtcol = 0.1;
228: MatLUFactor(F,0,0,&finfo);
230: /* Solve LUX = PB or LUX = B */
231: MatSolveAdd(F,b,d,x);
232: MatMatSolve(F,B,X);
233: MatDestroy(&F);
235: /* Check norm(A*X - B) */
236: VecCreate(PETSC_COMM_WORLD,&e);
237: VecSetSizes(e,m,PETSC_DECIDE);
238: VecSetFromOptions(e);
239: MatMult(A,x,c);
240: MatMult(A,d,e);
241: VecAXPY(c,-1.0,e);
242: VecAXPY(c,-1.0,b);
243: VecNorm(c,NORM_1,&norm);
244: if (norm > tol) {
245: PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*x - b| for LU %g\n",(double)norm);
246: }
247: MatMatMult(A,X,MAT_REUSE_MATRIX,PETSC_DEFAULT,&C);
248: MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN);
249: MatNorm(C,NORM_1,&norm);
250: if (norm > tol) {
251: PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*X - B| for LU %g\n",(double)norm);
252: }
254: /* Out-place LU */
255: MatGetFactor(A,MATSOLVERELEMENTAL,MAT_FACTOR_LU,&F);
256: MatLUFactorSymbolic(F,A,0,0,&finfo);
257: MatLUFactorNumeric(F,A,&finfo);
258: if (mats_view) {
259: MatView(F,PETSC_VIEWER_STDOUT_WORLD);
260: }
261: MatSolve(F,b,x);
262: MatMatSolve(F,B,X);
263: MatDestroy(&F);
265: /* Free space */
266: MatDestroy(&A);
267: MatDestroy(&Aher);
268: MatDestroy(&B);
269: MatDestroy(&C);
270: MatDestroy(&X);
271: VecDestroy(&b);
272: VecDestroy(&c);
273: VecDestroy(&d);
274: VecDestroy(&e);
275: VecDestroy(&x);
276: PetscRandomDestroy(&rand);
277: PetscFinalize();
278: return 0;
279: }