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 MPI_Comm comm; 25 Mat A; 26 Vec x, y; 27 ISLocalToGlobalMapping map; 28 PetscScalar elemMat[4] = {1.0, -1.0, -1.0, 1.0}; 29 PetscReal error; 30 PetscInt overlapSize = 2, globalIdx[2]; 31 PetscMPIInt rank, size; 32 33 CHKERRQ(PetscInitialize(&argc, &argv, NULL, help)); 34 comm = PETSC_COMM_WORLD; 35 CHKERRMPI(MPI_Comm_rank(comm, &rank)); 36 CHKERRMPI(MPI_Comm_size(comm, &size)); 37 /* Create local-to-global map */ 38 globalIdx[0] = rank; 39 globalIdx[1] = rank+1; 40 CHKERRQ(ISLocalToGlobalMappingCreate(comm, 1, overlapSize, globalIdx, PETSC_COPY_VALUES, &map)); 41 /* Create matrix */ 42 CHKERRQ(MatCreateIS(comm, 1, PETSC_DECIDE, PETSC_DECIDE, size+1, size+1, map, map, &A)); 43 CHKERRQ(PetscObjectSetName((PetscObject) A, "A")); 44 CHKERRQ(ISLocalToGlobalMappingDestroy(&map)); 45 CHKERRQ(MatISSetPreallocation(A, overlapSize, NULL, overlapSize, NULL)); 46 CHKERRQ(MatSetValues(A, 2, globalIdx, 2, globalIdx, elemMat, ADD_VALUES)); 47 CHKERRQ(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 48 CHKERRQ(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 49 /* Check that the constant vector is in the nullspace */ 50 CHKERRQ(MatCreateVecs(A, &x, &y)); 51 CHKERRQ(VecSet(x, 1.0)); 52 CHKERRQ(PetscObjectSetName((PetscObject) x, "x")); 53 CHKERRQ(VecViewFromOptions(x, NULL, "-x_view")); 54 CHKERRQ(MatMult(A, x, y)); 55 CHKERRQ(PetscObjectSetName((PetscObject) y, "y")); 56 CHKERRQ(VecViewFromOptions(y, NULL, "-y_view")); 57 CHKERRQ(VecNorm(y, NORM_2, &error)); 58 PetscCheckFalse(error > PETSC_SMALL,comm, PETSC_ERR_ARG_WRONG, "Invalid output, x should be in the nullspace of A"); 59 /* Check that an interior unit vector gets mapped to something of 1-norm 4 */ 60 if (size > 1) { 61 CHKERRQ(VecSet(x, 0.0)); 62 CHKERRQ(VecSetValue(x, 1, 1.0, INSERT_VALUES)); 63 CHKERRQ(VecAssemblyBegin(x)); 64 CHKERRQ(VecAssemblyEnd(x)); 65 CHKERRQ(MatMult(A, x, y)); 66 CHKERRQ(VecNorm(y, NORM_1, &error)); 67 PetscCheckFalse(PetscAbsReal(error - 4) > PETSC_SMALL,comm, PETSC_ERR_ARG_WRONG, "Invalid output for matrix multiply"); 68 } 69 /* Cleanup */ 70 CHKERRQ(MatDestroy(&A)); 71 CHKERRQ(VecDestroy(&x)); 72 CHKERRQ(VecDestroy(&y)); 73 CHKERRQ(PetscFinalize()); 74 return 0; 75 } 76 77 /*TEST 78 79 test: 80 suffix: 0 81 requires: 82 args: 83 84 test: 85 suffix: 1 86 nsize: 3 87 args: 88 89 test: 90 suffix: 2 91 nsize: 7 92 args: 93 94 TEST*/ 95