1 2 static char help[] = "Tests LU, Cholesky factorization and MatMatSolve() for an Elemental dense matrix.\n\n"; 3 4 #include <petscmat.h> 5 6 int main(int argc,char **argv) 7 { 8 Mat A,F,B,X,C,Aher,G; 9 Vec b,x,c,d,e; 10 PetscInt m = 5,n,p,i,j,nrows,ncols; 11 PetscScalar *v,*barray,rval; 12 PetscReal norm,tol=1.e-11; 13 PetscMPIInt size,rank; 14 PetscRandom rand; 15 const PetscInt *rows,*cols; 16 IS isrows,iscols; 17 PetscBool mats_view=PETSC_FALSE; 18 MatFactorInfo finfo; 19 20 PetscCall(PetscInitialize(&argc,&argv,(char*) 0,help)); 21 PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank)); 22 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 23 24 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&rand)); 25 PetscCall(PetscRandomSetFromOptions(rand)); 26 27 /* Get local dimensions of matrices */ 28 PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL)); 29 n = m; 30 PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); 31 p = m/2; 32 PetscCall(PetscOptionsGetInt(NULL,NULL,"-p",&p,NULL)); 33 PetscCall(PetscOptionsHasName(NULL,NULL,"-mats_view",&mats_view)); 34 35 /* Create matrix A */ 36 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix A\n")); 37 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 38 PetscCall(MatSetSizes(A,m,n,PETSC_DECIDE,PETSC_DECIDE)); 39 PetscCall(MatSetType(A,MATELEMENTAL)); 40 PetscCall(MatSetFromOptions(A)); 41 PetscCall(MatSetUp(A)); 42 /* Set local matrix entries */ 43 PetscCall(MatGetOwnershipIS(A,&isrows,&iscols)); 44 PetscCall(ISGetLocalSize(isrows,&nrows)); 45 PetscCall(ISGetIndices(isrows,&rows)); 46 PetscCall(ISGetLocalSize(iscols,&ncols)); 47 PetscCall(ISGetIndices(iscols,&cols)); 48 PetscCall(PetscMalloc1(nrows*ncols,&v)); 49 for (i=0; i<nrows; i++) { 50 for (j=0; j<ncols; j++) { 51 PetscCall(PetscRandomGetValue(rand,&rval)); 52 v[i*ncols+j] = rval; 53 } 54 } 55 PetscCall(MatSetValues(A,nrows,rows,ncols,cols,v,INSERT_VALUES)); 56 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 57 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 58 PetscCall(ISRestoreIndices(isrows,&rows)); 59 PetscCall(ISRestoreIndices(iscols,&cols)); 60 PetscCall(ISDestroy(&isrows)); 61 PetscCall(ISDestroy(&iscols)); 62 PetscCall(PetscFree(v)); 63 if (mats_view) { 64 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "A: nrows %" PetscInt_FMT ", m %" PetscInt_FMT "; ncols %" PetscInt_FMT ", n %" PetscInt_FMT "\n",nrows,m,ncols,n)); 65 PetscCall(MatView(A,PETSC_VIEWER_STDOUT_WORLD)); 66 } 67 68 /* Create rhs matrix B */ 69 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Create rhs matrix B\n")); 70 PetscCall(MatCreate(PETSC_COMM_WORLD,&B)); 71 PetscCall(MatSetSizes(B,m,p,PETSC_DECIDE,PETSC_DECIDE)); 72 PetscCall(MatSetType(B,MATELEMENTAL)); 73 PetscCall(MatSetFromOptions(B)); 74 PetscCall(MatSetUp(B)); 75 PetscCall(MatGetOwnershipIS(B,&isrows,&iscols)); 76 PetscCall(ISGetLocalSize(isrows,&nrows)); 77 PetscCall(ISGetIndices(isrows,&rows)); 78 PetscCall(ISGetLocalSize(iscols,&ncols)); 79 PetscCall(ISGetIndices(iscols,&cols)); 80 PetscCall(PetscMalloc1(nrows*ncols,&v)); 81 for (i=0; i<nrows; i++) { 82 for (j=0; j<ncols; j++) { 83 PetscCall(PetscRandomGetValue(rand,&rval)); 84 v[i*ncols+j] = rval; 85 } 86 } 87 PetscCall(MatSetValues(B,nrows,rows,ncols,cols,v,INSERT_VALUES)); 88 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 89 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 90 PetscCall(ISRestoreIndices(isrows,&rows)); 91 PetscCall(ISRestoreIndices(iscols,&cols)); 92 PetscCall(ISDestroy(&isrows)); 93 PetscCall(ISDestroy(&iscols)); 94 PetscCall(PetscFree(v)); 95 if (mats_view) { 96 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "B: nrows %" PetscInt_FMT ", m %" PetscInt_FMT "; ncols %" PetscInt_FMT ", p %" PetscInt_FMT "\n",nrows,m,ncols,p)); 97 PetscCall(MatView(B,PETSC_VIEWER_STDOUT_WORLD)); 98 } 99 100 /* Create rhs vector b and solution x (same size as b) */ 101 PetscCall(VecCreate(PETSC_COMM_WORLD,&b)); 102 PetscCall(VecSetSizes(b,m,PETSC_DECIDE)); 103 PetscCall(VecSetFromOptions(b)); 104 PetscCall(VecGetArray(b,&barray)); 105 for (j=0; j<m; j++) { 106 PetscCall(PetscRandomGetValue(rand,&rval)); 107 barray[j] = rval; 108 } 109 PetscCall(VecRestoreArray(b,&barray)); 110 PetscCall(VecAssemblyBegin(b)); 111 PetscCall(VecAssemblyEnd(b)); 112 if (mats_view) { 113 PetscCall(PetscSynchronizedPrintf(PETSC_COMM_WORLD, "[%d] b: m %" PetscInt_FMT "\n",rank,m)); 114 PetscCall(PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT)); 115 PetscCall(VecView(b,PETSC_VIEWER_STDOUT_WORLD)); 116 } 117 PetscCall(VecDuplicate(b,&x)); 118 119 /* Create matrix X - same size as B */ 120 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Create solution matrix X\n")); 121 PetscCall(MatCreate(PETSC_COMM_WORLD,&X)); 122 PetscCall(MatSetSizes(X,m,p,PETSC_DECIDE,PETSC_DECIDE)); 123 PetscCall(MatSetType(X,MATELEMENTAL)); 124 PetscCall(MatSetFromOptions(X)); 125 PetscCall(MatSetUp(X)); 126 PetscCall(MatAssemblyBegin(X,MAT_FINAL_ASSEMBLY)); 127 PetscCall(MatAssemblyEnd(X,MAT_FINAL_ASSEMBLY)); 128 129 /* Cholesky factorization */ 130 /*------------------------*/ 131 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Create Elemental matrix Aher\n")); 132 PetscCall(MatHermitianTranspose(A,MAT_INITIAL_MATRIX,&Aher)); 133 PetscCall(MatAXPY(Aher,1.0,A,SAME_NONZERO_PATTERN)); /* Aher = A + A^T */ 134 if (rank == 0) { /* add 100.0 to diagonals of Aher to make it spd */ 135 136 /* TODO: Replace this with a call to El::ShiftDiagonal( A, 100.), 137 or at least pre-allocate the right amount of space */ 138 PetscInt M,N; 139 PetscCall(MatGetSize(Aher,&M,&N)); 140 for (i=0; i<M; i++) { 141 rval = 100.0; 142 PetscCall(MatSetValues(Aher,1,&i,1,&i,&rval,ADD_VALUES)); 143 } 144 } 145 PetscCall(MatAssemblyBegin(Aher,MAT_FINAL_ASSEMBLY)); 146 PetscCall(MatAssemblyEnd(Aher,MAT_FINAL_ASSEMBLY)); 147 if (mats_view) { 148 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Aher:\n")); 149 PetscCall(MatView(Aher,PETSC_VIEWER_STDOUT_WORLD)); 150 } 151 152 /* Cholesky factorization */ 153 /*------------------------*/ 154 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Test Cholesky Solver \n")); 155 /* In-place Cholesky */ 156 /* Create matrix factor G, then copy Aher to G */ 157 PetscCall(MatCreate(PETSC_COMM_WORLD,&G)); 158 PetscCall(MatSetSizes(G,m,n,PETSC_DECIDE,PETSC_DECIDE)); 159 PetscCall(MatSetType(G,MATELEMENTAL)); 160 PetscCall(MatSetFromOptions(G)); 161 PetscCall(MatSetUp(G)); 162 PetscCall(MatAssemblyBegin(G,MAT_FINAL_ASSEMBLY)); 163 PetscCall(MatAssemblyEnd(G,MAT_FINAL_ASSEMBLY)); 164 PetscCall(MatCopy(Aher,G,SAME_NONZERO_PATTERN)); 165 166 /* Only G = U^T * U is implemented for now */ 167 PetscCall(MatCholeskyFactor(G,0,0)); 168 if (mats_view) { 169 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Cholesky Factor G:\n")); 170 PetscCall(MatView(G,PETSC_VIEWER_STDOUT_WORLD)); 171 } 172 173 /* Solve U^T * U x = b and U^T * U X = B */ 174 PetscCall(MatSolve(G,b,x)); 175 PetscCall(MatMatSolve(G,B,X)); 176 PetscCall(MatDestroy(&G)); 177 178 /* Out-place Cholesky */ 179 PetscCall(MatGetFactor(Aher,MATSOLVERELEMENTAL,MAT_FACTOR_CHOLESKY,&G)); 180 PetscCall(MatCholeskyFactorSymbolic(G,Aher,0,&finfo)); 181 PetscCall(MatCholeskyFactorNumeric(G,Aher,&finfo)); 182 if (mats_view) PetscCall(MatView(G,PETSC_VIEWER_STDOUT_WORLD)); 183 PetscCall(MatSolve(G,b,x)); 184 PetscCall(MatMatSolve(G,B,X)); 185 PetscCall(MatDestroy(&G)); 186 187 /* Check norm(Aher*x - b) */ 188 PetscCall(VecCreate(PETSC_COMM_WORLD,&c)); 189 PetscCall(VecSetSizes(c,m,PETSC_DECIDE)); 190 PetscCall(VecSetFromOptions(c)); 191 PetscCall(MatMult(Aher,x,c)); 192 PetscCall(VecAXPY(c,-1.0,b)); 193 PetscCall(VecNorm(c,NORM_1,&norm)); 194 if (norm > tol) { 195 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*x - b| for Cholesky %g\n",(double)norm)); 196 } 197 198 /* Check norm(Aher*X - B) */ 199 PetscCall(MatMatMult(Aher,X,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&C)); 200 PetscCall(MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN)); 201 PetscCall(MatNorm(C,NORM_1,&norm)); 202 if (norm > tol) { 203 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: |Aher*X - B| for Cholesky %g\n",(double)norm)); 204 } 205 206 /* LU factorization */ 207 /*------------------*/ 208 PetscCall(PetscPrintf(PETSC_COMM_WORLD," Test LU Solver \n")); 209 /* In-place LU */ 210 /* Create matrix factor F, then copy A to F */ 211 PetscCall(MatCreate(PETSC_COMM_WORLD,&F)); 212 PetscCall(MatSetSizes(F,m,n,PETSC_DECIDE,PETSC_DECIDE)); 213 PetscCall(MatSetType(F,MATELEMENTAL)); 214 PetscCall(MatSetFromOptions(F)); 215 PetscCall(MatSetUp(F)); 216 PetscCall(MatAssemblyBegin(F,MAT_FINAL_ASSEMBLY)); 217 PetscCall(MatAssemblyEnd(F,MAT_FINAL_ASSEMBLY)); 218 PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN)); 219 /* Create vector d to test MatSolveAdd() */ 220 PetscCall(VecDuplicate(x,&d)); 221 PetscCall(VecCopy(x,d)); 222 223 /* PF=LU or F=LU factorization - perms is ignored by Elemental; 224 set finfo.dtcol !0 or 0 to enable/disable partial pivoting */ 225 finfo.dtcol = 0.1; 226 PetscCall(MatLUFactor(F,0,0,&finfo)); 227 228 /* Solve LUX = PB or LUX = B */ 229 PetscCall(MatSolveAdd(F,b,d,x)); 230 PetscCall(MatMatSolve(F,B,X)); 231 PetscCall(MatDestroy(&F)); 232 233 /* Check norm(A*X - B) */ 234 PetscCall(VecCreate(PETSC_COMM_WORLD,&e)); 235 PetscCall(VecSetSizes(e,m,PETSC_DECIDE)); 236 PetscCall(VecSetFromOptions(e)); 237 PetscCall(MatMult(A,x,c)); 238 PetscCall(MatMult(A,d,e)); 239 PetscCall(VecAXPY(c,-1.0,e)); 240 PetscCall(VecAXPY(c,-1.0,b)); 241 PetscCall(VecNorm(c,NORM_1,&norm)); 242 if (norm > tol) { 243 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*x - b| for LU %g\n",(double)norm)); 244 } 245 /* Reuse product C; replace Aher with A */ 246 PetscCall(MatProductReplaceMats(A,NULL,NULL,C)); 247 PetscCall(MatMatMult(A,X,MAT_REUSE_MATRIX,PETSC_DEFAULT,&C)); 248 PetscCall(MatAXPY(C,-1.0,B,SAME_NONZERO_PATTERN)); 249 PetscCall(MatNorm(C,NORM_1,&norm)); 250 if (norm > tol) { 251 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: |A*X - B| for LU %g\n",(double)norm)); 252 } 253 254 /* Out-place LU */ 255 PetscCall(MatGetFactor(A,MATSOLVERELEMENTAL,MAT_FACTOR_LU,&F)); 256 PetscCall(MatLUFactorSymbolic(F,A,0,0,&finfo)); 257 PetscCall(MatLUFactorNumeric(F,A,&finfo)); 258 if (mats_view) PetscCall(MatView(F,PETSC_VIEWER_STDOUT_WORLD)); 259 PetscCall(MatSolve(F,b,x)); 260 PetscCall(MatMatSolve(F,B,X)); 261 PetscCall(MatDestroy(&F)); 262 263 /* Free space */ 264 PetscCall(MatDestroy(&A)); 265 PetscCall(MatDestroy(&Aher)); 266 PetscCall(MatDestroy(&B)); 267 PetscCall(MatDestroy(&C)); 268 PetscCall(MatDestroy(&X)); 269 PetscCall(VecDestroy(&b)); 270 PetscCall(VecDestroy(&c)); 271 PetscCall(VecDestroy(&d)); 272 PetscCall(VecDestroy(&e)); 273 PetscCall(VecDestroy(&x)); 274 PetscCall(PetscRandomDestroy(&rand)); 275 PetscCall(PetscFinalize()); 276 return 0; 277 } 278 279 /*TEST 280 281 build: 282 requires: elemental 283 284 test: 285 nsize: 2 286 output_file: output/ex145.out 287 288 test: 289 suffix: 2 290 nsize: 6 291 output_file: output/ex145.out 292 293 TEST*/ 294