1 static char help[] = "Illustration of MatIS using a 1D Laplacian assembly\n\n"; 2 3 /* 4 MatIS means that the matrix is not assembled. The easiest way to think of this (for me) is that processes do not have 5 to hold full matrix rows. One process can hold part of row i, and another processes can hold another part. However, there 6 are still the same number of global rows. The local size here is not the size of the local IS block, which we call the 7 overlap size, since that is a property only of MatIS. It is the size of the local piece of the vector you multiply in 8 MatMult(). This allows PETSc to understand the parallel layout of the Vec, and how it matches the Mat. If you only know 9 the overlap size when assembling, it is best to use PETSC_DECIDE for the local size in the creation routine, so that PETSc 10 automatically partitions the unknowns. 11 12 Each P_1 element matrix for a cell will be 13 14 / 1 -1 \ 15 \ -1 1 / 16 17 so that the assembled matrix has a tridiagonal [-1, 2, -1] pattern. We will use 1 cell per process for illustration, 18 and allow PETSc to decide the ownership. 19 */ 20 21 #include <petscmat.h> 22 23 int main(int argc, char **argv) 24 { 25 MPI_Comm comm; 26 Mat A; 27 Vec x, y; 28 ISLocalToGlobalMapping map; 29 PetscScalar elemMat[4] = {1.0, -1.0, -1.0, 1.0}; 30 PetscReal error; 31 PetscInt overlapSize = 2, globalIdx[2]; 32 PetscMPIInt rank, size; 33 34 PetscFunctionBeginUser; 35 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 36 comm = PETSC_COMM_WORLD; 37 PetscCallMPI(MPI_Comm_rank(comm, &rank)); 38 PetscCallMPI(MPI_Comm_size(comm, &size)); 39 /* Create local-to-global map */ 40 globalIdx[0] = rank; 41 globalIdx[1] = rank + 1; 42 PetscCall(ISLocalToGlobalMappingCreate(comm, 1, overlapSize, globalIdx, PETSC_COPY_VALUES, &map)); 43 /* Create matrix */ 44 PetscCall(MatCreateIS(comm, 1, PETSC_DECIDE, PETSC_DECIDE, size + 1, size + 1, map, map, &A)); 45 PetscCall(PetscObjectSetName((PetscObject)A, "A")); 46 PetscCall(ISLocalToGlobalMappingDestroy(&map)); 47 PetscCall(MatISSetPreallocation(A, overlapSize, NULL, overlapSize, NULL)); 48 PetscCall(MatSetValues(A, 2, globalIdx, 2, globalIdx, elemMat, ADD_VALUES)); 49 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 50 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 51 /* Check that the constant vector is in the nullspace */ 52 PetscCall(MatCreateVecs(A, &x, &y)); 53 PetscCall(VecSet(x, 1.0)); 54 PetscCall(PetscObjectSetName((PetscObject)x, "x")); 55 PetscCall(VecViewFromOptions(x, NULL, "-x_view")); 56 PetscCall(MatMult(A, x, y)); 57 PetscCall(PetscObjectSetName((PetscObject)y, "y")); 58 PetscCall(VecViewFromOptions(y, NULL, "-y_view")); 59 PetscCall(VecNorm(y, NORM_2, &error)); 60 PetscCheck(error <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Invalid output, x should be in the nullspace of A"); 61 /* Check that an interior unit vector gets mapped to something of 1-norm 4 */ 62 if (size > 1) { 63 PetscCall(VecSet(x, 0.0)); 64 PetscCall(VecSetValue(x, 1, 1.0, INSERT_VALUES)); 65 PetscCall(VecAssemblyBegin(x)); 66 PetscCall(VecAssemblyEnd(x)); 67 PetscCall(MatMult(A, x, y)); 68 PetscCall(VecNorm(y, NORM_1, &error)); 69 PetscCheck(PetscAbsReal(error - 4) <= PETSC_SMALL, comm, PETSC_ERR_ARG_WRONG, "Invalid output for matrix multiply"); 70 } 71 /* Cleanup */ 72 PetscCall(MatDestroy(&A)); 73 PetscCall(VecDestroy(&x)); 74 PetscCall(VecDestroy(&y)); 75 PetscCall(PetscFinalize()); 76 return 0; 77 } 78 79 /*TEST 80 81 test: 82 suffix: 0 83 requires: 84 args: 85 output_file: output/empty.out 86 87 test: 88 suffix: 1 89 nsize: 3 90 args: 91 output_file: output/empty.out 92 93 test: 94 suffix: 2 95 nsize: 7 96 args: 97 output_file: output/empty.out 98 99 TEST*/ 100