//----------------------------------------------------------------------------- // TestMatrixRowSum //----------------------------------------------------------------------------- bool TestMatrixRowSum() { Matrix A("1,2,3;4,5,6;7,8,9"); Matrix x; RowSum( A, x ); Matrix row_sum("6;15;24"); return ApproxEqual(x,row_sum,TOLERANCE); }
int maxKilledEnemies(vector<vector<char>>& grid) { if (grid.empty() || grid[0].empty()) return 0; unsigned long m = grid.size(), n = grid[0].size(); vector<vector<short>> left(m, vector<short>(n)), right(m, vector<short>(n)), up(m, vector<short>(n)) ,down(m, vector<short>(n)); rowSum.resize(m, vector<short>(n)); colSum.resize(m, vector<short>(n)); for (int i=0;i<m;++i) for (int j=0;j<n;++j) { if (j==0) rowSum[i][j] = (short)(grid[i][j] == 'E'); else rowSum[i][j] = rowSum[i][j-1] + (short)(grid[i][j] == 'E'); if (i==0) colSum[i][j] = (short)(grid[i][j] == 'E'); else colSum[i][j] = colSum[i-1][j] + (short)(grid[i][j] == 'E'); } for (int i=0; i<m; ++i) for (int j=0; j<n; ++j) { if (j==0 || grid[i][j-1] == 'W') left[i][j] = j; else left[i][j] = left[i][j-1]; if (i==0 || grid[i-1][j] == 'W') up[i][j] = i; else up[i][j] = up[i-1][j]; } for (int i=m-1; i>=0; --i) for (int j=n-1; j>=0; --j) { if (j==n-1 || grid[i][j+1] == 'W') right[i][j] = j; else right[i][j] = right[i][j+1]; if (i==m-1 || grid[i+1][j] == 'W') down[i][j] = i; else down[i][j] = down[i+1][j]; } int ans = 0; for (int i=0;i<m;++i) for (int j=0;j<n;++j) if (grid[i][j] == '0') { ans = max(ans, RowSum(i, left[i][j], j) + RowSum(i, j, right[i][j]) + ColSum(j, up[i][j], i) + ColSum(j, i, down[i][j]) ); } return ans; }
int Ifpack_Analyze(const Epetra_RowMatrix& A, const bool Cheap, const int NumPDEEqns) { int NumMyRows = A.NumMyRows(); long long NumGlobalRows = A.NumGlobalRows64(); long long NumGlobalCols = A.NumGlobalCols64(); long long MyBandwidth = 0, GlobalBandwidth; long long MyLowerNonzeros = 0, MyUpperNonzeros = 0; long long GlobalLowerNonzeros, GlobalUpperNonzeros; long long MyDiagonallyDominant = 0, GlobalDiagonallyDominant; long long MyWeaklyDiagonallyDominant = 0, GlobalWeaklyDiagonallyDominant; double MyMin, MyAvg, MyMax; double GlobalMin, GlobalAvg, GlobalMax; long long GlobalStorage; bool verbose = (A.Comm().MyPID() == 0); GlobalStorage = sizeof(int*) * NumGlobalRows + sizeof(int) * A.NumGlobalNonzeros64() + sizeof(double) * A.NumGlobalNonzeros64(); if (verbose) { print(); Ifpack_PrintLine(); print<const char*>("Label", A.Label()); print<long long>("Global rows", NumGlobalRows); print<long long>("Global columns", NumGlobalCols); print<long long>("Stored nonzeros", A.NumGlobalNonzeros64()); print<long long>("Nonzeros / row", A.NumGlobalNonzeros64() / NumGlobalRows); print<double>("Estimated storage (Mbytes)", 1.0e-6 * GlobalStorage); } long long NumMyActualNonzeros = 0, NumGlobalActualNonzeros; long long NumMyEmptyRows = 0, NumGlobalEmptyRows; long long NumMyDirichletRows = 0, NumGlobalDirichletRows; std::vector<int> colInd(A.MaxNumEntries()); std::vector<double> colVal(A.MaxNumEntries()); Epetra_Vector Diag(A.RowMatrixRowMap()); Epetra_Vector RowSum(A.RowMatrixRowMap()); Diag.PutScalar(0.0); RowSum.PutScalar(0.0); for (int i = 0 ; i < NumMyRows ; ++i) { long long GRID = A.RowMatrixRowMap().GID64(i); int Nnz; IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz, &colVal[0],&colInd[0])); if (Nnz == 0) NumMyEmptyRows++; if (Nnz == 1) NumMyDirichletRows++; for (int j = 0 ; j < Nnz ; ++j) { double v = colVal[j]; if (v < 0) v = -v; if (colVal[j] != 0.0) NumMyActualNonzeros++; long long GCID = A.RowMatrixColMap().GID64(colInd[j]); if (GCID != GRID) RowSum[i] += v; else Diag[i] = v; if (GCID < GRID) MyLowerNonzeros++; else if (GCID > GRID) MyUpperNonzeros++; long long b = GCID - GRID; if (b < 0) b = -b; if (b > MyBandwidth) MyBandwidth = b; } if (Diag[i] > RowSum[i]) MyDiagonallyDominant++; if (Diag[i] >= RowSum[i]) MyWeaklyDiagonallyDominant++; RowSum[i] += Diag[i]; } // ======================== // // summing up global values // // ======================== // A.Comm().SumAll(&MyDiagonallyDominant,&GlobalDiagonallyDominant,1); A.Comm().SumAll(&MyWeaklyDiagonallyDominant,&GlobalWeaklyDiagonallyDominant,1); A.Comm().SumAll(&NumMyActualNonzeros, &NumGlobalActualNonzeros, 1); A.Comm().SumAll(&NumMyEmptyRows, &NumGlobalEmptyRows, 1); A.Comm().SumAll(&NumMyDirichletRows, &NumGlobalDirichletRows, 1); A.Comm().SumAll(&MyBandwidth, &GlobalBandwidth, 1); A.Comm().SumAll(&MyLowerNonzeros, &GlobalLowerNonzeros, 1); A.Comm().SumAll(&MyUpperNonzeros, &GlobalUpperNonzeros, 1); A.Comm().SumAll(&MyDiagonallyDominant, &GlobalDiagonallyDominant, 1); A.Comm().SumAll(&MyWeaklyDiagonallyDominant, &GlobalWeaklyDiagonallyDominant, 1); double NormOne = A.NormOne(); double NormInf = A.NormInf(); double NormF = Ifpack_FrobeniusNorm(A); if (verbose) { print(); print<long long>("Actual nonzeros", NumGlobalActualNonzeros); print<long long>("Nonzeros in strict lower part", GlobalLowerNonzeros); print<long long>("Nonzeros in strict upper part", GlobalUpperNonzeros); print(); print<long long>("Empty rows", NumGlobalEmptyRows, 100.0 * NumGlobalEmptyRows / NumGlobalRows); print<long long>("Dirichlet rows", NumGlobalDirichletRows, 100.0 * NumGlobalDirichletRows / NumGlobalRows); print<long long>("Diagonally dominant rows", GlobalDiagonallyDominant, 100.0 * GlobalDiagonallyDominant / NumGlobalRows); print<long long>("Weakly diag. dominant rows", GlobalWeaklyDiagonallyDominant, 100.0 * GlobalWeaklyDiagonallyDominant / NumGlobalRows); print(); print<long long>("Maximum bandwidth", GlobalBandwidth); print(); print("", "one-norm", "inf-norm", "Frobenius", false); print("", "========", "========", "=========", false); print(); print<double>("A", NormOne, NormInf, NormF); } if (Cheap == false) { // create A + A^T and A - A^T Epetra_FECrsMatrix AplusAT(Copy, A.RowMatrixRowMap(), 0); Epetra_FECrsMatrix AminusAT(Copy, A.RowMatrixRowMap(), 0); #ifndef EPETRA_NO_32BIT_GLOBAL_INDICES if(A.RowMatrixRowMap().GlobalIndicesInt()) { for (int i = 0 ; i < NumMyRows ; ++i) { int GRID = A.RowMatrixRowMap().GID(i); assert (GRID != -1); int Nnz; IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz, &colVal[0],&colInd[0])); for (int j = 0 ; j < Nnz ; ++j) { int GCID = A.RowMatrixColMap().GID(colInd[j]); assert (GCID != -1); double plus_val = colVal[j]; double minus_val = -colVal[j]; if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) { IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val)); } if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) { IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val)); } if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) { IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val)); } if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) { IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val)); } } } } else #endif #ifndef EPETRA_NO_64BIT_GLOBAL_INDICES if(A.RowMatrixRowMap().GlobalIndicesLongLong()) { for (int i = 0 ; i < NumMyRows ; ++i) { long long GRID = A.RowMatrixRowMap().GID64(i); assert (GRID != -1); int Nnz; IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz, &colVal[0],&colInd[0])); for (int j = 0 ; j < Nnz ; ++j) { long long GCID = A.RowMatrixColMap().GID64(colInd[j]); assert (GCID != -1); double plus_val = colVal[j]; double minus_val = -colVal[j]; if (AplusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) { IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val)); } if (AplusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&plus_val) != 0) { IFPACK_CHK_ERR(AplusAT.InsertGlobalValues(1,&GCID,1,&GRID,&plus_val)); } if (AminusAT.SumIntoGlobalValues(1,&GRID,1,&GCID,&plus_val) != 0) { IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GRID,1,&GCID,&plus_val)); } if (AminusAT.SumIntoGlobalValues(1,&GCID,1,&GRID,&minus_val) != 0) { IFPACK_CHK_ERR(AminusAT.InsertGlobalValues(1,&GCID,1,&GRID,&minus_val)); } } } } else #endif throw "Ifpack_Analyze: GlobalIndices type unknown"; AplusAT.FillComplete(); AminusAT.FillComplete(); AplusAT.Scale(0.5); AminusAT.Scale(0.5); NormOne = AplusAT.NormOne(); NormInf = AplusAT.NormInf(); NormF = Ifpack_FrobeniusNorm(AplusAT); if (verbose) { print<double>("A + A^T", NormOne, NormInf, NormF); } NormOne = AminusAT.NormOne(); NormInf = AminusAT.NormInf(); NormF = Ifpack_FrobeniusNorm(AminusAT); if (verbose) { print<double>("A - A^T", NormOne, NormInf, NormF); } } if (verbose) { print(); print<const char*>("", "min", "avg", "max", false); print<const char*>("", "===", "===", "===", false); } MyMax = -DBL_MAX; MyMin = DBL_MAX; MyAvg = 0.0; for (int i = 0 ; i < NumMyRows ; ++i) { int Nnz; IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz, &colVal[0],&colInd[0])); for (int j = 0 ; j < Nnz ; ++j) { MyAvg += colVal[j]; if (colVal[j] > MyMax) MyMax = colVal[j]; if (colVal[j] < MyMin) MyMin = colVal[j]; } } A.Comm().MaxAll(&MyMax, &GlobalMax, 1); A.Comm().MinAll(&MyMin, &GlobalMin, 1); A.Comm().SumAll(&MyAvg, &GlobalAvg, 1); GlobalAvg /= A.NumGlobalNonzeros64(); if (verbose) { print(); print<double>(" A(i,j)", GlobalMin, GlobalAvg, GlobalMax); } MyMax = 0.0; MyMin = DBL_MAX; MyAvg = 0.0; for (int i = 0 ; i < NumMyRows ; ++i) { int Nnz; IFPACK_CHK_ERR(A.ExtractMyRowCopy(i,A.MaxNumEntries(),Nnz, &colVal[0],&colInd[0])); for (int j = 0 ; j < Nnz ; ++j) { double v = colVal[j]; if (v < 0) v = -v; MyAvg += v; if (colVal[j] > MyMax) MyMax = v; if (colVal[j] < MyMin) MyMin = v; } } A.Comm().MaxAll(&MyMax, &GlobalMax, 1); A.Comm().MinAll(&MyMin, &GlobalMin, 1); A.Comm().SumAll(&MyAvg, &GlobalAvg, 1); GlobalAvg /= A.NumGlobalNonzeros64(); if (verbose) { print<double>("|A(i,j)|", GlobalMin, GlobalAvg, GlobalMax); } // ================= // // diagonal elements // // ================= // Diag.MinValue(&GlobalMin); Diag.MaxValue(&GlobalMax); Diag.MeanValue(&GlobalAvg); if (verbose) { print(); print<double>(" A(k,k)", GlobalMin, GlobalAvg, GlobalMax); } Diag.Abs(Diag); Diag.MinValue(&GlobalMin); Diag.MaxValue(&GlobalMax); Diag.MeanValue(&GlobalAvg); if (verbose) { print<double>("|A(k,k)|", GlobalMin, GlobalAvg, GlobalMax); } // ============================================== // // cycle over all equations for diagonal elements // // ============================================== // if (NumPDEEqns > 1 ) { if (verbose) print(); for (int ie = 0 ; ie < NumPDEEqns ; ie++) { MyMin = DBL_MAX; MyMax = -DBL_MAX; MyAvg = 0.0; for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) { double d = Diag[i]; MyAvg += d; if (d < MyMin) MyMin = d; if (d > MyMax) MyMax = d; } A.Comm().MinAll(&MyMin, &GlobalMin, 1); A.Comm().MaxAll(&MyMax, &GlobalMax, 1); A.Comm().SumAll(&MyAvg, &GlobalAvg, 1); // does not really work fine if the number of global // elements is not a multiple of NumPDEEqns GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns); if (verbose) { char str[80]; sprintf(str, " A(k,k), eq %d", ie); print<double>(str, GlobalMin, GlobalAvg, GlobalMax); } } } // ======== // // row sums // // ======== // RowSum.MinValue(&GlobalMin); RowSum.MaxValue(&GlobalMax); RowSum.MeanValue(&GlobalAvg); if (verbose) { print(); print<double>(" sum_j A(k,j)", GlobalMin, GlobalAvg, GlobalMax); } // ===================================== // // cycle over all equations for row sums // // ===================================== // if (NumPDEEqns > 1 ) { if (verbose) print(); for (int ie = 0 ; ie < NumPDEEqns ; ie++) { MyMin = DBL_MAX; MyMax = -DBL_MAX; MyAvg = 0.0; for (int i = ie ; i < Diag.MyLength() ; i += NumPDEEqns) { double d = RowSum[i]; MyAvg += d; if (d < MyMin) MyMin = d; if (d > MyMax) MyMax = d; } A.Comm().MinAll(&MyMin, &GlobalMin, 1); A.Comm().MaxAll(&MyMax, &GlobalMax, 1); A.Comm().SumAll(&MyAvg, &GlobalAvg, 1); // does not really work fine if the number of global // elements is not a multiple of NumPDEEqns GlobalAvg /= (Diag.GlobalLength64() / NumPDEEqns); if (verbose) { char str[80]; sprintf(str, " sum_j A(k,j), eq %d", ie); print<double>(str, GlobalMin, GlobalAvg, GlobalMax); } } } if (verbose) Ifpack_PrintLine(); return(0); }