diff --git a/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork new file mode 100644 index 0000000..e956077 Binary files /dev/null and b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork differ diff --git a/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.cpp b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.cpp new file mode 100644 index 0000000..a4c7278 --- /dev/null +++ b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.cpp @@ -0,0 +1,217 @@ +/** + * + * Schritt 1 + * ------------- + * |T0|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * + * Schritt 2 + * ------------- + * |xx|T0|--|--| + * ------------- + * |T1|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * + * Schritt 3 + * ------------- + * |xx|xx|T0|--| + * ------------- + * |xx|T1|--|--| + * ------------- + * |T2|--|--|--| + * ------------- + * |--|--|--|--| + * ------------- + * + * Schritt 4 + * ------------- + * |xx|xx|xx|T0| + * ------------- + * |xx|xx|T1|--| + * ------------- + * |xx|T2|--|--| + * ------------- + * |T3|--|--|--| + * ------------- + */ + +#include +#include "matrix.h" +#include +#include +#include + +void gauss_seidel(Matrix &phi, int maxNumIter) +{ + const int m = phi.dim1(); + const int n = phi.dim2(); + const double osth = 1. / 4; + for (int iIter = 0; iIter < maxNumIter; ++iIter) + { + // Shared data per iteration + std::vector> column(m); + for (int i = 0; i < m; ++i) + { + column[i].store(1); + } + std::atomic threadsCount(0); + +#pragma omp parallel for schedule(static) + for (int rowToCalculate = 1; rowToCalculate < (n - 1); rowToCalculate++) + { + int row = rowToCalculate; + while (column[row] < n - 1) + { + // All threads beneath T_row1 have to check specific circumstances, where + // T_row1 has no condition to wait for + if (row != 1) + { + // T_rowx has to wait at least until T_row(x-1) has calculated values from + // its last row + // T_rowx will calculate value x at row,column if T_row(x-1) has calculated + // its value at row-1, column-1 + while (column[row] == column[row - 1]) + { + // Wait for wave (thread) above + } + } + + // Central jacobi calculation + phi(row, column[row]) = osth * (phi(row + 1, column[row]) + phi(row - 1, column[row]) + phi(row, column[row] + 1) + + phi(row, column[row] - 1)); + + // Increment column index + column[row]++; + } + } + } +} + +void gauss_seidel_lin(Matrix &phi, int maxNumIter) +{ + const int m = phi.dim1(); + const int n = phi.dim2(); + + const double osth = 1. / 4; + + for (int iter = 0; iter < maxNumIter; ++iter) + { + for (int i = 1; i < m - 1; ++i) + { + for (int j = 1; j < n - 1; ++j) + { + phi(i, j) = osth * (phi(i + 1, j) + phi(i - 1, j) + phi(i, j + 1) + + phi(i, j - 1)); + } + } + } +} + +void fill_matrix(Matrix &matrix, const int filler) +{ + const int m = matrix.dim1(); + const int n = matrix.dim2(); + + for (int i = 0; i < m; ++i) + { + for (int j = 0; j < n; ++j) + { + if (i == 0 || i == m - 1 || j == 0 || j == n - 1) + { + matrix(i, j) = filler; + } + else + matrix(i, j) = 0; + } + } +} + +void check(const Matrix &a, const Matrix &b) +{ + const int m = a.dim1(); + const int n = a.dim2(); + + for (int i = 0; i < m; ++i) + { + for (int j = 0; j < n; ++j) + { + if (a(i, j) != b(i, j)) + { + std::cout << "Not equal at (" << i << ", " << j << "), a: " << a(i, j) + << " != " << b(i, j) << " :b" << std::endl; + } + } + } +} + +void print_matrix(const Matrix &matrix) +{ + const int m = matrix.dim1(); + const int n = matrix.dim2(); + + for (int i = 0; i < m; ++i) + { + for (int j = 0; j < n; ++j) + { + std::cout << matrix(i, j) << " "; + } + std::cout << std::endl; + } +} + +void benchmarkComputeResult(benchmark::State& state) { + int iterations = state.range(0); + Matrix sec = Matrix(1000, 1000); + fill_matrix(sec, 10); + + for (auto _ : state) { + gauss_seidel(sec, iterations); + benchmark::DoNotOptimize(sec); + } +} + +int main(int argc, char** argv) { + ::benchmark::Initialize(&argc, argv); + + for (int iterations = 0; iterations < 10000; iterations++) { + benchmark::RegisterBenchmark("idk", benchmarkComputeResult) + ->Arg(iterations) + ->Unit(benchmark::kMillisecond); + } + + ::benchmark::RunSpecifiedBenchmarks(); + + return 0; +} + +// int main() +// { +// Matrix first = Matrix(8, 8); +// Matrix sec = Matrix(8, 8); + +// fill_matrix(first, 10); +// fill_matrix(sec, 10); + +// print_matrix(first); +// print_matrix(sec); + +// gauss_seidel_lin(first, 1000); +// gauss_seidel(sec, 1000); + +// check(first, sec); + +// print_matrix(first); +// print_matrix(sec); + +// return 0; +// } diff --git a/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.sh b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.sh new file mode 100644 index 0000000..4f2eb77 --- /dev/null +++ b/lab07/results/aaron_benchmark_failed/jacobiWaveSplitWork.sh @@ -0,0 +1,11 @@ +#!/bin/bash +#SBATCH --job-name=jacobiWaveSplitWorkTest +#SBATCH --output=benchmark_jacobiWaveSplitWork.out +#SBATCH --ntasks=1 +#SBATCH --cpus-per-task=12 + +# Load modules or activate environment if needed +# module load gcc cmake ... + +# Run the benchmark binary +./jacobiWaveSplitWork --benchmark_out=results.json --benchmark_out_format=json diff --git a/lab07/results/aaron_benchmark_failed/matrix.h b/lab07/results/aaron_benchmark_failed/matrix.h new file mode 100644 index 0000000..7dcf1cf --- /dev/null +++ b/lab07/results/aaron_benchmark_failed/matrix.h @@ -0,0 +1,343 @@ +/** + * matrix.h a very simplistic class for m times n matrices. + */ + +#ifndef MATRIX_H +#define MATRIX_H + +#include +#include +#include +#include + +// A very simplistic vector class for vectors of size n +class Vector { + public: + // constructors + Vector(int n) : n_(n), data_(n_, 0) {} + Vector(const Vector& other) = default; + Vector(Vector&& other) = default; + ~Vector() = default; + + // assignment operators + Vector& operator=(const Vector& other) = default; + Vector& operator=(Vector&& other) = default; + + // element access + double& operator()(int i) { return data_[i]; } + const double& operator()(int i) const { return data_[i]; } + + // getter functions for the dimensions + int dim() const { return n_; } + + // comparison operators + bool operator==(const Vector& b) { return (data_ == b.data_); } + bool operator!=(const Vector& b) { return (data_ != b.data_); } + + // addition + Vector& operator+=(const Vector& b) { + for (int i = 0; i < n_; ++i) { + operator()(i) += b(i); + } + return *this; + } + + // subtraction + Vector& operator-=(const Vector& b) { + for (int i = 0; i < n_; ++i) { + operator()(i) -= b(i); + } + return *this; + } + + // scalar multiplication + Vector& operator*=(double x) { + for (int i = 0; i < n_; ++i) { + operator()(i) *= x; + } + return *this; + } + + // dot product between two vectors + double dot(const Vector& other) const { + double sum = 0; + for (int i = 0; i < n_; ++i) { + sum += operator()(i) * other(i); + } + return sum; + } + + private: + int n_; // vector dimension + std::vector data_; // the vectors entries +}; + +inline double dot(const Vector& v1, const Vector& v2) { + return v1.dot(v2); +} + +// Print the vector as a table +inline std::ostream& operator<<(std::ostream& os, const Vector& a) { + const int width = 10; + const int precision = 4; + + const auto originalPrecision = os.precision(); + os << std::setprecision(precision); + + for (int i = 0; i < a.dim(); ++i) { + os << std::setw(width) << a(i) << " "; + } + + os << "\n"; + + os << std::setprecision(originalPrecision); + return os; +} + +// A very simple class for m times n matrices +class Matrix { + public: + // constructors + Matrix() : Matrix(0, 0) {} + Matrix(int m, int n) : m_(m), n_(n), data_(m_ * n_, 0) {} + Matrix(std::pair dim) : Matrix(dim.first, dim.second) {} + Matrix(int n) : Matrix(n, n) {} + Matrix(const Matrix& other) = default; + Matrix(Matrix&& other) = default; + ~Matrix() = default; + + // assignment operators + Matrix& operator=(const Matrix& other) = default; + Matrix& operator=(Matrix&& other) = default; + + // element access + double& operator()(int i, int j) { return data_[i * n_ + j]; } + const double& operator()(int i, int j) const { return data_[i * n_ + j]; } + + // getter functions for the dimensions + std::pair dim() const { return std::pair(m_, n_); } + int dim1() const { return m_; } + int dim2() const { return n_; } + int numEntries() const { return data_.size(); } + + // comparison operators + bool operator==(const Matrix& b) { return (data_ == b.data_); } + bool operator!=(const Matrix& b) { return (data_ != b.data_); } + + // addition + Matrix& operator+=(const Matrix& b) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) += b(i, j); + } + } + return *this; + } + + // subtraction + Matrix& operator-=(const Matrix& b) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) -= b(i, j); + } + } + return *this; + } + + // scalar multiplication + Matrix& operator*=(double x) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) *= x; + } + } + return *this; + } + + // scalar division + Matrix& operator/=(double x) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) /= x; + } + } + return *this; + } + + // matrix product (only for square matrices of equal dimension) + Matrix& operator*=(const Matrix& b) { + if (dim1() != dim2()) { + std::cout << "Error in matrix multiplication: no square matrix\n"; + } else if (dim1() != b.dim1() || dim2() != b.dim2()) { + std::cout << "Error in matrix multiplication: dimensions do not match\n"; + } else { + Matrix a = *this; + Matrix& c = *this; + const int m = dim1(); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < m; ++j) { + for (int k = 0; k < m; ++k) { + c(i, j) += a(i, k) * b(k, j); + } + } + } + } + + return *this; + } + + public: + int m_; // first dimension + int n_; // second dimension + std::vector data_; // the matrix' entries +}; + +// Print the matrix as a table +inline std::ostream& operator<<(std::ostream& os, const Matrix& a) { + const int width = 10; + const int precision = 4; + + const auto originalPrecision = os.precision(); + os << std::setprecision(precision); + + for (int i = 0; i < a.dim1(); ++i) { + for (int j = 0; j < a.dim2(); ++j) { + os << std::setw(width) << a(i, j) << " "; + } + if (i != a.dim1() - 1) + os << "\n"; + } + + os << std::setprecision(originalPrecision); + return os; +} + +// matrix product +inline Matrix operator*(const Matrix& a, const Matrix& b) { + if (a.dim2() == b.dim1()) { + int m = a.dim1(); + int n = a.dim2(); + int p = b.dim2(); + Matrix c(m, p); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < p; ++j) { + for (int k = 0; k < n; ++k) { + c(i, j) += a(i, k) * b(k, j); + } + } + } + return c; + } else { + return Matrix(0, 0); + } +} + +inline bool equalWithinRange(const Matrix& a, + const Matrix& b, + double eps = 1e-12) { + if (a.dim1() != b.dim1() || a.dim2() != b.dim2()) + return false; + + int m = a.dim1(); + int n = a.dim2(); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < n; ++j) { + if (fabs(a(i, j) - b(i, j)) > eps) { + return false; + } + } + } + + return true; +} + +// A very simple class for "3D-Matrices" (tensors) with dimension l x m x n +class Matrix3D { + public: + // constructors + Matrix3D(int l, int m, int n) : l_(l), m_(m), n_(n), data_(l) { + for (int i = 0; i < l_; ++i) { + data_[i] = std::vector>(m_); + for (int j = 0; j < m_; ++j) { + data_[i][j] = std::vector(n_, 0); + } + } + } + Matrix3D(int n) : Matrix3D(n, n, n) {} + Matrix3D(const Matrix3D& other) = default; + Matrix3D(Matrix3D&& other) = default; + ~Matrix3D() = default; + + // assignment operators + Matrix3D& operator=(const Matrix3D& other) = default; + Matrix3D& operator=(Matrix3D&& other) = default; + + // element access + double& operator()(int i, int j, int k) { return data_[i][j][k]; } + const double& operator()(int i, int j, int k) const { return data_[i][j][k]; } + + // getter functions for the dimensions + int dim1() const { return l_; } + int dim2() const { return m_; } + int dim3() const { return n_; } + + // comparison operators + bool operator==(const Matrix3D& b) { return (data_ == b.data_); } + bool operator!=(const Matrix3D& b) { return (data_ != b.data_); } + + // addition + Matrix3D& operator+=(const Matrix3D& b) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) += b(i, j, k); + } + } + } + return *this; + } + + // substraction + Matrix3D& operator-=(const Matrix3D& b) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) -= b(i, j, k); + } + } + } + return *this; + } + + // scalar multiplication + Matrix3D& operator*=(double x) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) *= x; + } + } + } + return *this; + } + + // scalar division + Matrix3D& operator/=(double x) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) /= x; + } + } + } + return *this; + } + + private: + int l_; // first dimension + int m_; // second dimension + int n_; // third dimension + std::vector>> data_; // the tensors' entries +}; + +#endif // MATRIX_H diff --git a/lab07/results/aaron_benchmark_failed/results.json b/lab07/results/aaron_benchmark_failed/results.json new file mode 100644 index 0000000..0578bb8 --- /dev/null +++ b/lab07/results/aaron_benchmark_failed/results.json @@ -0,0 +1,52130 @@ +{ + "context": { + "date": "2025-05-06T13:35:22+02:00", + "host_name": "hpcvl2", + "executable": "./jacobiWaveSplitWork", + "num_cpus": 12, + 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b/lab07/results/kai_benchmark/kaiJacobiWave new file mode 100644 index 0000000..b5e05b8 Binary files /dev/null and b/lab07/results/kai_benchmark/kaiJacobiWave differ diff --git a/lab07/results/kai_benchmark/kaiJacobiWave.cpp b/lab07/results/kai_benchmark/kaiJacobiWave.cpp new file mode 100644 index 0000000..ebfc817 --- /dev/null +++ b/lab07/results/kai_benchmark/kaiJacobiWave.cpp @@ -0,0 +1,123 @@ +#include "matrix.h" +#include +#include +#include + +void gauss_seidel(Matrix &phi, int maxNumIter) { + const int m = phi.dim1(); + const int n = phi.dim2(); + + const double osth = 1. / 4; + + for (int iter = 0; iter < maxNumIter; ++iter) { + for (int i = 1; i < m - 1; ++i) { + for (int j = 1; j < n - 1; ++j) { + phi(i, j) = osth * (phi(i + 1, j) + phi(i - 1, j) + phi(i, j + 1) + + phi(i, j - 1)); + } + } + } +} + +void gauss_seidel_par(Matrix &phi, int maxNumIter) { + const int m = phi.dim1(); + const int n = phi.dim2(); + + const double osth = 1. / 4; + + for (int iter = 0; iter < maxNumIter; ++iter) { +#pragma omp parallel num_threads(10) + { + int num_theads = omp_get_num_threads(); + int chunk = (m - 2) / num_theads; + int start = 1 + chunk * omp_get_thread_num(); + int end = chunk * (omp_get_thread_num() + 1); + + // printf("thread %d, start: %d, end: %d\n", omp_get_thread_num(), start, + // end); + + for (int j = 1; j < n + omp_get_num_threads() - 1; ++j) { + for (int i = start; i <= end; ++i) { + + int k = j - omp_get_thread_num(); + + // printf("thread %d, i: %d, j: %d, k: %d\n", omp_get_thread_num(), i, + // j, + // k); + + if (k > 0 && k < n - 1) { + phi(i, k) = osth * (phi(i + 1, k) + phi(i - 1, k) + phi(i, k + 1) + + phi(i, k - 1)); + } +#pragma omp barrier + } + } + } + } +} + +void fill_matrix(Matrix &matrix, const int filler) { + const int m = matrix.dim1(); + const int n = matrix.dim2(); + + for (int i = 0; i < m; ++i) { + for (int j = 0; j < n; ++j) { + if (i == 0 || i == m - 1 || j == 0 || j == n - 1) { + matrix(i, j) = filler; + } else + matrix(i, j) = 0; + } + } +} + +void check(const Matrix &a, const Matrix &b) { + const int m = a.dim1(); + const int n = a.dim2(); + + for (int i = 0; i < m; ++i) { + for (int j = 0; j < n; ++j) { + if (a(i, j) != b(i, j)) { + std::cout << "Not equal at (" << i << ", " << j << "), a: " << a(i, j) + << " != " << b(i, j) << " :b" << std::endl; + } + } + } +} + +void print_matrix(const Matrix &matrix) { + const int m = matrix.dim1(); + const int n = matrix.dim2(); + + for (int i = 0; i < m; ++i) { + for (int j = 0; j < n; ++j) { + std::cout << matrix(i, j) << " "; + } + std::cout << std::endl; + } +} + +void benchmarkComputeResult(benchmark::State &state) { + int iterations = state.range(0); + Matrix matrix = Matrix(1000, 1000); + + fill_matrix(matrix, 10); + + for (auto _ : state) { + gauss_seidel(matrix, iterations); + benchmark::DoNotOptimize(matrix); + } +} + +int main(int argc, char **argv) { + ::benchmark::Initialize(&argc, argv); + + for (int iterations = 0; iterations < 10000; iterations++) { + benchmark::RegisterBenchmark("bench_gaus_seidel", benchmarkComputeResult) + ->Arg(iterations) + ->Unit(benchmark::kMillisecond); + } + + ::benchmark::RunSpecifiedBenchmarks(); + + return 0; +} diff --git a/lab07/results/kai_benchmark/kai_results.json b/lab07/results/kai_benchmark/kai_results.json new file mode 100644 index 0000000..9225c67 --- /dev/null +++ b/lab07/results/kai_benchmark/kai_results.json @@ -0,0 +1,120040 @@ +{ + "context": { + "date": "2025-05-06T13:33:16+02:00", + "host_name": "hpcvl1", + "executable": "./kaiJacobiWave", + "num_cpus": 12, + "mhz_per_cpu": 3100, + "cpu_scaling_enabled": true, + "caches": [ + { + "type": "Data", + "level": 1, + "size": 32768, + "num_sharing": 1 + }, + { + "type": "Instruction", + "level": 1, + "size": 32768, + "num_sharing": 1 + }, + { + "type": "Unified", + "level": 2, + "size": 262144, + "num_sharing": 1 + }, + { + "type": "Unified", + "level": 3, + "size": 15728640, + "num_sharing": 6 + } + ], + "load_avg": 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--output=kaiJacobiWaveSplitWork.out +#SBATCH --ntasks=1 +#SBATCH --cpus-per-task=12 + +# Load modules or activate environment if needed +# module load gcc cmake ... + +# Run the benchmark binary +./kaiJacobiWave --benchmark_out=kai_results.json --benchmark_out_format=json diff --git a/lab07/results/kai_benchmark/matrix.h b/lab07/results/kai_benchmark/matrix.h new file mode 100644 index 0000000..7dcf1cf --- /dev/null +++ b/lab07/results/kai_benchmark/matrix.h @@ -0,0 +1,343 @@ +/** + * matrix.h a very simplistic class for m times n matrices. + */ + +#ifndef MATRIX_H +#define MATRIX_H + +#include +#include +#include +#include + +// A very simplistic vector class for vectors of size n +class Vector { + public: + // constructors + Vector(int n) : n_(n), data_(n_, 0) {} + Vector(const Vector& other) = default; + Vector(Vector&& other) = default; + ~Vector() = default; + + // assignment operators + Vector& operator=(const Vector& other) = default; + Vector& operator=(Vector&& other) = default; + + // element access + double& operator()(int i) { return data_[i]; } + const double& operator()(int i) const { return data_[i]; } + + // getter functions for the dimensions + int dim() const { return n_; } + + // comparison operators + bool operator==(const Vector& b) { return (data_ == b.data_); } + bool operator!=(const Vector& b) { return (data_ != b.data_); } + + // addition + Vector& operator+=(const Vector& b) { + for (int i = 0; i < n_; ++i) { + operator()(i) += b(i); + } + return *this; + } + + // subtraction + Vector& operator-=(const Vector& b) { + for (int i = 0; i < n_; ++i) { + operator()(i) -= b(i); + } + return *this; + } + + // scalar multiplication + Vector& operator*=(double x) { + for (int i = 0; i < n_; ++i) { + operator()(i) *= x; + } + return *this; + } + + // dot product between two vectors + double dot(const Vector& other) const { + double sum = 0; + for (int i = 0; i < n_; ++i) { + sum += operator()(i) * other(i); + } + return sum; + } + + private: + int n_; // vector dimension + std::vector data_; // the vectors entries +}; + +inline double dot(const Vector& v1, const Vector& v2) { + return v1.dot(v2); +} + +// Print the vector as a table +inline std::ostream& operator<<(std::ostream& os, const Vector& a) { + const int width = 10; + const int precision = 4; + + const auto originalPrecision = os.precision(); + os << std::setprecision(precision); + + for (int i = 0; i < a.dim(); ++i) { + os << std::setw(width) << a(i) << " "; + } + + os << "\n"; + + os << std::setprecision(originalPrecision); + return os; +} + +// A very simple class for m times n matrices +class Matrix { + public: + // constructors + Matrix() : Matrix(0, 0) {} + Matrix(int m, int n) : m_(m), n_(n), data_(m_ * n_, 0) {} + Matrix(std::pair dim) : Matrix(dim.first, dim.second) {} + Matrix(int n) : Matrix(n, n) {} + Matrix(const Matrix& other) = default; + Matrix(Matrix&& other) = default; + ~Matrix() = default; + + // assignment operators + Matrix& operator=(const Matrix& other) = default; + Matrix& operator=(Matrix&& other) = default; + + // element access + double& operator()(int i, int j) { return data_[i * n_ + j]; } + const double& operator()(int i, int j) const { return data_[i * n_ + j]; } + + // getter functions for the dimensions + std::pair dim() const { return std::pair(m_, n_); } + int dim1() const { return m_; } + int dim2() const { return n_; } + int numEntries() const { return data_.size(); } + + // comparison operators + bool operator==(const Matrix& b) { return (data_ == b.data_); } + bool operator!=(const Matrix& b) { return (data_ != b.data_); } + + // addition + Matrix& operator+=(const Matrix& b) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) += b(i, j); + } + } + return *this; + } + + // subtraction + Matrix& operator-=(const Matrix& b) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) -= b(i, j); + } + } + return *this; + } + + // scalar multiplication + Matrix& operator*=(double x) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) *= x; + } + } + return *this; + } + + // scalar division + Matrix& operator/=(double x) { + for (int i = 0; i < m_; ++i) { + for (int j = 0; j < n_; ++j) { + operator()(i, j) /= x; + } + } + return *this; + } + + // matrix product (only for square matrices of equal dimension) + Matrix& operator*=(const Matrix& b) { + if (dim1() != dim2()) { + std::cout << "Error in matrix multiplication: no square matrix\n"; + } else if (dim1() != b.dim1() || dim2() != b.dim2()) { + std::cout << "Error in matrix multiplication: dimensions do not match\n"; + } else { + Matrix a = *this; + Matrix& c = *this; + const int m = dim1(); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < m; ++j) { + for (int k = 0; k < m; ++k) { + c(i, j) += a(i, k) * b(k, j); + } + } + } + } + + return *this; + } + + public: + int m_; // first dimension + int n_; // second dimension + std::vector data_; // the matrix' entries +}; + +// Print the matrix as a table +inline std::ostream& operator<<(std::ostream& os, const Matrix& a) { + const int width = 10; + const int precision = 4; + + const auto originalPrecision = os.precision(); + os << std::setprecision(precision); + + for (int i = 0; i < a.dim1(); ++i) { + for (int j = 0; j < a.dim2(); ++j) { + os << std::setw(width) << a(i, j) << " "; + } + if (i != a.dim1() - 1) + os << "\n"; + } + + os << std::setprecision(originalPrecision); + return os; +} + +// matrix product +inline Matrix operator*(const Matrix& a, const Matrix& b) { + if (a.dim2() == b.dim1()) { + int m = a.dim1(); + int n = a.dim2(); + int p = b.dim2(); + Matrix c(m, p); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < p; ++j) { + for (int k = 0; k < n; ++k) { + c(i, j) += a(i, k) * b(k, j); + } + } + } + return c; + } else { + return Matrix(0, 0); + } +} + +inline bool equalWithinRange(const Matrix& a, + const Matrix& b, + double eps = 1e-12) { + if (a.dim1() != b.dim1() || a.dim2() != b.dim2()) + return false; + + int m = a.dim1(); + int n = a.dim2(); + for (int i = 0; i < m; ++i) { + for (int j = 0; j < n; ++j) { + if (fabs(a(i, j) - b(i, j)) > eps) { + return false; + } + } + } + + return true; +} + +// A very simple class for "3D-Matrices" (tensors) with dimension l x m x n +class Matrix3D { + public: + // constructors + Matrix3D(int l, int m, int n) : l_(l), m_(m), n_(n), data_(l) { + for (int i = 0; i < l_; ++i) { + data_[i] = std::vector>(m_); + for (int j = 0; j < m_; ++j) { + data_[i][j] = std::vector(n_, 0); + } + } + } + Matrix3D(int n) : Matrix3D(n, n, n) {} + Matrix3D(const Matrix3D& other) = default; + Matrix3D(Matrix3D&& other) = default; + ~Matrix3D() = default; + + // assignment operators + Matrix3D& operator=(const Matrix3D& other) = default; + Matrix3D& operator=(Matrix3D&& other) = default; + + // element access + double& operator()(int i, int j, int k) { return data_[i][j][k]; } + const double& operator()(int i, int j, int k) const { return data_[i][j][k]; } + + // getter functions for the dimensions + int dim1() const { return l_; } + int dim2() const { return m_; } + int dim3() const { return n_; } + + // comparison operators + bool operator==(const Matrix3D& b) { return (data_ == b.data_); } + bool operator!=(const Matrix3D& b) { return (data_ != b.data_); } + + // addition + Matrix3D& operator+=(const Matrix3D& b) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) += b(i, j, k); + } + } + } + return *this; + } + + // substraction + Matrix3D& operator-=(const Matrix3D& b) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) -= b(i, j, k); + } + } + } + return *this; + } + + // scalar multiplication + Matrix3D& operator*=(double x) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) *= x; + } + } + } + return *this; + } + + // scalar division + Matrix3D& operator/=(double x) { + for (int i = 0; i < l_; ++i) { + for (int j = 0; j < m_; ++j) { + for (int k = 0; k < n_; ++k) { + operator()(i, j, k) /= x; + } + } + } + return *this; + } + + private: + int l_; // first dimension + int m_; // second dimension + int n_; // third dimension + std::vector>> data_; // the tensors' entries +}; + +#endif // MATRIX_H