1 static char help[] = "Scalable algorithm for Connected Components problem.\n\ 2 Entails changing the MatMult() for this matrix.\n\n\n"; 3 4 #include <petscmat.h> 5 6 PETSC_EXTERN PetscErrorCode MatMultMax_SeqAIJ(Mat, Vec, Vec); 7 PETSC_EXTERN PetscErrorCode MatMultAddMax_SeqAIJ(Mat, Vec, Vec, Vec); 8 #include <../src/mat/impls/aij/mpi/mpiaij.h> 9 10 /* 11 Paper with Ananth: Frbenius norm of band was good proxy, but really want to know the rank outside 12 13 LU for diagonal blocks must do shifting instead of pivoting, preferably shifting individual rows (like Pardiso) 14 15 Draw picture of flow of reordering 16 17 Measure Forbenius norm of the blocks being dropped by Truncated SPIKE (might be contaminated by pivoting in LU) 18 19 Report on using Florida matrices (Maxim, Murat) 20 */ 21 22 /* 23 I have thought about how to do this. Here is a prototype algorithm. Let A be 24 the adjacency matrix (0 or 1), and let each component be identified by the 25 lowest numbered vertex in it. We initialize a vector c so that each vertex is 26 a component, c_i = i. Now we act on c with A, using a special product 27 28 c = A * c 29 30 where we replace addition with min. The fixed point of this operation is a vector 31 c which is the component for each vertex. The number of iterates is 32 33 max_{components} depth of BFS tree for component 34 35 We can accelerate this algorithm by preprocessing all locals domains using the 36 same algorithm. Then the number of iterations is bounded the depth of the BFS 37 tree for the graph on supervertices defined over local components, which is 38 bounded by p. In practice, this should be very fast. 39 */ 40 41 /* Only isolated vertices get a 1 on the diagonal */ 42 PetscErrorCode CreateGraph(MPI_Comm comm, PetscInt testnum, Mat *A) 43 { 44 Mat G; 45 46 PetscFunctionBegin; 47 PetscCall(MatCreate(comm, &G)); 48 /* The identity matrix */ 49 switch (testnum) { 50 case 0: { 51 Vec D; 52 53 PetscCall(MatSetSizes(G, PETSC_DETERMINE, PETSC_DETERMINE, 5, 5)); 54 PetscCall(MatSetUp(G)); 55 PetscCall(MatCreateVecs(G, &D, NULL)); 56 PetscCall(VecSet(D, 1.0)); 57 PetscCall(MatDiagonalSet(G, D, INSERT_VALUES)); 58 PetscCall(VecDestroy(&D)); 59 } break; 60 case 1: { 61 PetscScalar vals[3] = {1.0, 1.0, 1.0}; 62 PetscInt cols[3]; 63 PetscInt rStart, rEnd, row; 64 65 PetscCall(MatSetSizes(G, PETSC_DETERMINE, PETSC_DETERMINE, 5, 5)); 66 PetscCall(MatSetFromOptions(G)); 67 PetscCall(MatSeqAIJSetPreallocation(G, 2, NULL)); 68 PetscCall(MatSetUp(G)); 69 PetscCall(MatGetOwnershipRange(G, &rStart, &rEnd)); 70 row = 0; 71 cols[0] = 0; 72 cols[1] = 1; 73 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 74 row = 1; 75 cols[0] = 0; 76 cols[1] = 1; 77 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 78 row = 2; 79 cols[0] = 2; 80 cols[1] = 3; 81 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 82 row = 3; 83 cols[0] = 3; 84 cols[1] = 4; 85 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 86 row = 4; 87 cols[0] = 4; 88 cols[1] = 2; 89 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 90 PetscCall(MatAssemblyBegin(G, MAT_FINAL_ASSEMBLY)); 91 PetscCall(MatAssemblyEnd(G, MAT_FINAL_ASSEMBLY)); 92 } break; 93 case 2: { 94 PetscScalar vals[3] = {1.0, 1.0, 1.0}; 95 PetscInt cols[3]; 96 PetscInt rStart, rEnd, row; 97 98 PetscCall(MatSetSizes(G, PETSC_DETERMINE, PETSC_DETERMINE, 5, 5)); 99 PetscCall(MatSetFromOptions(G)); 100 PetscCall(MatSeqAIJSetPreallocation(G, 2, NULL)); 101 PetscCall(MatSetUp(G)); 102 PetscCall(MatGetOwnershipRange(G, &rStart, &rEnd)); 103 row = 0; 104 cols[0] = 0; 105 cols[1] = 4; 106 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 107 row = 1; 108 cols[0] = 1; 109 cols[1] = 2; 110 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 111 row = 2; 112 cols[0] = 2; 113 cols[1] = 3; 114 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 115 row = 3; 116 cols[0] = 3; 117 cols[1] = 1; 118 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 119 row = 4; 120 cols[0] = 0; 121 cols[1] = 4; 122 if ((row >= rStart) && (row < rEnd)) PetscCall(MatSetValues(G, 1, &row, 2, cols, vals, INSERT_VALUES)); 123 PetscCall(MatAssemblyBegin(G, MAT_FINAL_ASSEMBLY)); 124 PetscCall(MatAssemblyEnd(G, MAT_FINAL_ASSEMBLY)); 125 } break; 126 default: 127 SETERRQ(comm, PETSC_ERR_PLIB, "Unknown test %d", testnum); 128 } 129 *A = G; 130 PetscFunctionReturn(PETSC_SUCCESS); 131 } 132 133 int main(int argc, char **argv) 134 { 135 MPI_Comm comm; 136 Mat A; /* A graph */ 137 Vec c; /* A vector giving the component of each vertex */ 138 Vec cold; /* The vector c from the last iteration */ 139 PetscScalar *carray; 140 PetscInt testnum = 0; 141 PetscInt V, vStart, vEnd, v, n; 142 PetscMPIInt size; 143 144 PetscFunctionBeginUser; 145 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 146 comm = PETSC_COMM_WORLD; 147 PetscCallMPI(MPI_Comm_size(comm, &size)); 148 /* Use matrix to encode a graph */ 149 PetscCall(PetscOptionsGetInt(NULL, NULL, "-testnum", &testnum, NULL)); 150 PetscCall(CreateGraph(comm, testnum, &A)); 151 PetscCall(MatGetSize(A, &V, NULL)); 152 /* Replace matrix-vector multiplication with one that calculates the minimum rather than the sum */ 153 if (size == 1) { 154 PetscCall(MatShellSetOperation(A, MATOP_MULT, (void(*))MatMultMax_SeqAIJ)); 155 } else { 156 Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data; 157 158 PetscCall(MatShellSetOperation(a->A, MATOP_MULT, (void(*))MatMultMax_SeqAIJ)); 159 PetscCall(MatShellSetOperation(a->B, MATOP_MULT, (void(*))MatMultMax_SeqAIJ)); 160 PetscCall(MatShellSetOperation(a->B, MATOP_MULT_ADD, (void(*))MatMultAddMax_SeqAIJ)); 161 } 162 /* Initialize each vertex as a separate component */ 163 PetscCall(MatCreateVecs(A, &c, NULL)); 164 PetscCall(MatGetOwnershipRange(A, &vStart, &vEnd)); 165 PetscCall(VecGetArray(c, &carray)); 166 for (v = vStart; v < vEnd; ++v) carray[v - vStart] = v; 167 PetscCall(VecRestoreArray(c, &carray)); 168 /* Preprocess in parallel to find local components */ 169 /* Multiply until c does not change */ 170 PetscCall(VecDuplicate(c, &cold)); 171 for (v = 0; v < V; ++v) { 172 Vec cnew = cold; 173 PetscBool stop; 174 175 PetscCall(MatMult(A, c, cnew)); 176 PetscCall(VecEqual(c, cnew, &stop)); 177 if (stop) break; 178 cold = c; 179 c = cnew; 180 } 181 /* Report */ 182 PetscCall(VecUniqueEntries(c, &n, NULL)); 183 PetscCall(PetscPrintf(comm, "Components: %d Iterations: %d\n", n, v)); 184 PetscCall(VecView(c, PETSC_VIEWER_STDOUT_WORLD)); 185 /* Cleanup */ 186 PetscCall(VecDestroy(&c)); 187 PetscCall(VecDestroy(&cold)); 188 PetscCall(PetscFinalize()); 189 return 0; 190 } 191