diff --git a/benchmarks/cpp/main.cpp b/benchmarks/cpp/main.cpp new file mode 100644 index 0000000000..23d9ca1ffe --- /dev/null +++ b/benchmarks/cpp/main.cpp @@ -0,0 +1,195 @@ +#include +#include +#include +#include + +typedef double real; +using namespace std; + +// Class Star, contains the properties: +// mass (m) +// position (r) +// velocity (v) +// accelerations (a and a0) + +class Star { +public: + real m; + vector r; + vector v; + vector a, a0; + // Default constructor + Star() { + r.assign(3, 0); + v.assign(3, 0); + a.assign(3, 0); + a0.assign(3, 0); + } + // Detailed constructor + Star(real mass, vector pos, vector vel) { + m = mass; + r = pos; + v = vel; + } + // Print function (overloaded << operator) + friend ostream &operator<<(ostream &so, const Star &si) { + so << si.m << " " << si.r[0] << " " << si.r[1] << " " << si.r[2] << " " + << si.v[0] << " " << si.v[1] << " " << si.v[2] << endl; + return so; + } +}; +// Star cluster based on the Star class +// A star cluster contains a number of stars +// stored in the vector S +// +class Cluster : public Star { +protected: +public: + vector s; + Cluster() : Star() {} + // Computes the acceleration of each star in the cluster + void acceleration() { + for (vector::iterator si = s.begin(); si != s.end(); ++si) + si->a.assign(3, 0); + // For each star + for (vector::iterator si = s.begin(); si != s.end(); ++si) { + vector rij(3); + real init = 0.0; + // For each remaining star + for (vector::iterator sj = s.begin(); sj != s.end(); ++sj) { + if (si != sj) { + // Distance difference between the two stars + for (int i = 0; i != 3; ++i) + rij[i] = si->r[i] - sj->r[i]; + // Sum of the dot product + real RdotR = inner_product(rij.begin(), rij.end(), rij.begin(), init); + real apre = 1. / sqrt(RdotR * RdotR * RdotR); + // Update accelerations + for (int i = 0; i != 3; ++i) { + si->a[i] -= sj->m * apre * rij[i]; + } + } // end for + } // si != sj + } // end for + } // end acceleration + + // Update positions + void updatePositions(real dt) { + for (vector::iterator si = s.begin(); si != s.end(); ++si) { + // Update the positions, based on the calculated accelerations and + // velocities + si->a0 = si->a; + for (int i = 0; i != 3; ++i) // for each axis (x/y/z) + si->r[i] += dt * si->v[i] + 0.5 * dt * dt * si->a0[i]; + } + } + + // Update velocities based on previous and new accelerations + void updateVelocities(real dt) { + // Update the velocities based on the previous and old accelerations + for (vector::iterator si = s.begin(); si != s.end(); ++si) { + for (int i = 0; i != 3; ++i) + si->v[i] += 0.5 * dt * (si->a0[i] + si->a[i]); + si->a0 = si->a; + } + } + + // Compute the energy of the system, + // contains an expensive O(N^2) part which can be moved to the acceleration + // part where this is already calculated + vector energies() { + real init = 0; + vector E(3), rij(3); + E.assign(3, 0); + + // Kinetic energy + for (vector::iterator si = s.begin(); si != s.end(); ++si) + E[1] += 0.5 * si->m * + inner_product(si->v.begin(), si->v.end(), si->v.begin(), init); + + // Potential energy + for (vector::iterator si = s.begin(); si != s.end(); ++si) { + for (vector::iterator sj = si + 1; sj != s.end(); ++sj) { + for (int i = 0; i != 3; ++i) + rij[i] = si->r[i] - sj->r[i]; + E[2] -= si->m * sj->m / + sqrt(inner_product(rij.begin(), rij.end(), rij.begin(), init)); + } + } + E[0] = E[1] + E[2]; + return E; + } + + // Print function + friend ostream &operator<<(ostream &so, Cluster &cl) { + for (vector::iterator si = cl.s.begin(); si != cl.s.end(); ++si) + so << *si; + return so; + } +}; + +int main(int argc, char* argv[]) { + + Cluster cl; + real m; + int dummy; + vector r(3), v(3); + + // Read input data from the command line (makeplummer | dumbp) + do { + cin >> dummy; + cin >> m; + for (int i = 0; i != 3; ++i) + cin >> r[i]; + for (int i = 0; i != 3; ++i) + cin >> v[i]; + cl.s.push_back(Star(m, r, v)); + } while (!cin.eof()); + + // Remove the last one + cl.s.pop_back(); + + // Compute initial energu of the system + vector E(3), E0(3); + E0 = cl.energies(); + cerr << "Energies: " << E0[0] << " " << E0[1] << " " << E0[2] << endl; + + // Start time, end time and simulation step + real t = 0.0; + real tend; + + if (argc > 1) + tend = strtod(argv[1], NULL); + else + tend = 10.0; + + real dt = 1e-3; + int k = 0; + + // Initialize the accelerations + cl.acceleration(); + + // Start the main loop + while (t < tend) { + // Update positions based on velocities and accelerations + cl.updatePositions(dt); + + // Get new accelerations + cl.acceleration(); + + // Update velocities + cl.updateVelocities(dt); + + t += dt; + k += 1; + if (k % 100 == 0) { + E = cl.energies(); + cout << "t= " << t << " E= " << E[0] << " " << E[1] << " " << E[2] + << " dE/E = " << (E[0] - E0[0]) / E0[0] << endl; + } + } // end while + + cout << "number time steps: " << k << endl; + + return 0; +} // end program diff --git a/benchmarks/data/input128.txt b/benchmarks/data/input128.txt new file 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+ +import numpy as np +import pandas as pd + +from transonic import boost + +def load_input_data(path): + df = pd.read_csv( + path, names=["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter=r"\s+" + ) + + masses = np.ascontiguousarray(df["mass"].values) + positions = np.ascontiguousarray(df.loc[:, ["x", "y", "z"]].values) + velocities = np.ascontiguousarray(df.loc[:, ["vx", "vy", "vz"]].values) + + return masses, positions, velocities + + +def advance_positions(positions, velocities, accelerations, time_step): + positions += time_step * velocities + 0.5 * accelerations * time_step ** 2 + + +def advance_velocities(velocities, accelerations, accelerations1, time_step): + velocities += 0.5 * time_step * (accelerations + accelerations1) + + +def compute_distance(vec): + return math.sqrt(sum(vec ** 2)) + +def compute_accelerations(accelerations, masses, positions): + number_of_particles = masses.size + for index_p0 in range(number_of_particles - 1): + position0 = positions[index_p0] + masses0 = masses[index_p0] + vector = np.empty(3) + for index_p1 in range(index_p0 + 1, number_of_particles): + masses1 = masses[index_p1] + position1 = positions[index_p1] + for i in range(3): + vector[i] = position0[i] - position1[i] + + distance = sum(vector ** 2) * math.sqrt(sum(vector ** 2)) + coef_m1 = masses0 / distance + coef_m2 = masses1 / distance + for i in range(3): + accelerations[index_p0][i] -= coef_m1 * vector[i] + accelerations[index_p1][i] += coef_m2 * vector[i] + return accelerations + + +@boost +def pythran_loop( + time_step: float, + nb_steps: int, + masses: "float[]", + positions: "float[:,:]", + velocities: "float[:,:]", +): + + accelerations = np.zeros_like(positions) + accelerations1 = np.zeros_like(positions) + + accelerations = compute_accelerations(accelerations, masses, positions) + + time = 0.0 + energy0, _, _ = compute_energies(masses, positions, velocities) + energy_previous = energy0 + + for step in range(nb_steps): + advance_positions(positions, velocities, accelerations, time_step) + # swap acceleration arrays + accelerations, accelerations1 = accelerations1, accelerations + accelerations.fill(0) + compute_accelerations(accelerations, masses, positions) + advance_velocities(velocities, accelerations, accelerations1, time_step) + time += time_step + + if not step % 100: + energy, _, _ = compute_energies(masses, positions, velocities) + # f-strings supported by Pythran>=0.9.8 + #print( + # f"t = {time_step * step:5.2f}, E = {energy:.7f}, " + # f"dE/E = {(energy - energy_previous) / energy_previous:+.7f}" + #) + energy_previous = energy + + return math.floor((10000000*energy)/10000000), math.floor((10000000*energy0)/10000000) + #return energy, energy0 + +def compute_kinetic_energy(masses, velocities): + return 0.5 * np.sum(masses * np.sum(velocities ** 2, 1)) + + +def compute_potential_energy(masses, positions): + nb_particules = masses.size + pe = 0.0 + for index_p0 in range(nb_particules - 1): + mass0 = masses[index_p0] + for index_p1 in range(index_p0 + 1, nb_particules): + mass1 = masses[index_p1] + vector = positions[index_p0] - positions[index_p1] + distance = compute_distance(vector) + pe -= (mass0 * mass1) / distance + return pe + + +def compute_energies(masses, positions, velocities): + energy_kin = compute_kinetic_energy(masses, velocities) + energy_pot = compute_potential_energy(masses, positions) + return energy_kin + energy_pot, energy_kin, energy_pot + + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10.0 + + time_step = 0.001 + nb_steps = int(time_end / time_step) + 1 + + path_input = sys.argv[1] + masses, positions, velocities = load_input_data(path_input) + + start = time.time() + for i in range(5): + energy, energy0 = pythran_loop(time_step, nb_steps, masses, positions, velocities) + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print( + f"{nb_steps} time steps run in {timedelta(seconds=end-start)}" + ) diff --git a/benchmarks/python/bench_numba.py b/benchmarks/python/bench_numba.py new file mode 100644 index 0000000000..db08dd2216 --- /dev/null +++ b/benchmarks/python/bench_numba.py @@ -0,0 +1,165 @@ +import sys +import math +import time +from datetime import timedelta + +import numpy as np +import pandas as pd + +from numba import njit + +jit = njit(cache = True, fastmath = True) + + +def load_input_data(path): + df = pd.read_csv( + path, names = ["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter = r"\s+" + ) + + # warning: copy() is for Pythran... + masses = df["mass"].values.copy() + positions = df.loc[:, ["x", "y", "z"]].values.copy() + velocities = df.loc[:, ["vx", "vy", "vz"]].values.copy() + + return masses, positions, velocities + + +@jit +def advance_positions(positions, velocities, accelerations, time_step): + positions += time_step * velocities + 0.5 * accelerations * time_step ** 2 + + +@jit +def advance_velocities(velocities, accelerations, accelerations1, time_step): + velocities += 0.5 * time_step * (accelerations + accelerations1) + + +@jit +def compute_distance(vec): + d2 = vec[0] ** 2 + vec[1] ** 2 + vec[2] ** 2 + return math.sqrt(d2) + + +@jit +def compute_distance_cube(vec): + d2 = vec[0] ** 2 + vec[1] ** 2 + vec[2] ** 2 + return d2 * math.sqrt(d2) + + +@jit +def compute_accelerations(accelerations, masses, positions): + nb_particules = masses.size + vector = np.empty(3) + for index_p0 in range(nb_particules - 1): + position0 = positions[index_p0] + mass0 = masses[index_p0] + for index_p1 in range(index_p0 + 1, nb_particules): + mass1 = masses[index_p1] + position1 = positions[index_p1] + + for i in range(3): + vector[i] = position0[i] - position1[i] + + distance_cube = compute_distance_cube(vector) + coef_m1 = mass1 / distance_cube + coef_m0 = mass0 / distance_cube + + acceleration0 = accelerations[index_p0] + acceleration1 = accelerations[index_p1] + + for i in range(3): + acceleration0[i] -= coef_m1 * vector[i] + acceleration1[i] += coef_m0 * vector[i] + + return accelerations + + +@jit +def numba( + time_step: float, + nb_steps: int, + masses: "float[:]", + positions: "float[:,:]", + velocities: "float[:,:]", +): + accelerations = np.zeros_like(positions) + accelerations1 = np.zeros_like(positions) + + accelerations = compute_accelerations(accelerations, masses, positions) + + time = 0.0 + energy0, _, _ = compute_energies(masses, positions, velocities) + energy_previous = energy0 + + for step in range(nb_steps): + advance_positions(positions, velocities, accelerations, time_step) + # swap acceleration arrays + accelerations, accelerations1 = accelerations1, accelerations + accelerations.fill(0) + compute_accelerations(accelerations, masses, positions) + advance_velocities(velocities, accelerations, accelerations1, time_step) + time += time_step + + if not step % 100: + energy, _, _ = compute_energies(masses, positions, velocities) + # Numba doesn't support string formatting! + #print( + # "t = ", time_step * step, "E = ", energy, + # "dE/E = ", (energy - energy_previous) / energy_previous, + #) + + energy_previous = energy + + #return math.floor((100*energy)/100), math.floor((100*energy0)/100) + return math.floor((10000000*energy)/10000000), math.floor((10000000*energy0)/10000000) + +@jit +def compute_kinetic_energy(masses, velocities): + return 0.5 * np.sum(masses * np.sum(velocities ** 2, 1)) + + +@jit +def compute_potential_energy(masses, positions): + nb_particules = masses.size + pe = 0.0 + for index_p0 in range(nb_particules - 1): + mass0 = masses[index_p0] + for index_p1 in range(index_p0 + 1, nb_particules): + mass1 = masses[index_p1] + vector = positions[index_p0] - positions[index_p1] + distance = compute_distance(vector) + pe -= (mass0 * mass1) / distance + return pe + + +@jit +def compute_energies(masses, positions, velocities): + energy_kin = compute_kinetic_energy(masses, velocities) + energy_pot = compute_potential_energy(masses, positions) + return energy_kin + energy_pot, energy_kin, energy_pot + + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10.0 + + time_step = 0.001 + + nb_steps = int(time_end / time_step) + 1 + + path_input = sys.argv[1] + masses, positions, velocities = load_input_data(path_input) + + start = time.time() + for i in range(5): + energy, energy0 = numba(time_step, nb_steps, masses, positions, velocities) + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print( + f"{nb_steps} time steps run in {timedelta(seconds=end-start)}" + ) + diff --git a/benchmarks/python/bench_numpy_highlevel.py b/benchmarks/python/bench_numpy_highlevel.py new file mode 100644 index 0000000000..4453656c53 --- /dev/null +++ b/benchmarks/python/bench_numpy_highlevel.py @@ -0,0 +1,128 @@ +import sys +import math +import time +from datetime import timedelta + +import numpy as np +import pandas as pd + +def load_input_data(path): + df = pd.read_csv( + path, names = ["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter=r"\s+" + ) + masses = df["mass"].values.copy() + positions = df.loc[:, ["x", "y", "z"]].values.copy() + velocities = df.loc[:, ["vx", "vy", "vz"]].values.copy() + return masses, positions, velocities + +def advance_positions(positions, velocities, accelerations, time_step): + positions += velocities * time_step + 0.5 * accelerations * time_step ** 2 + +def advance_velocities(velocities, accelerations, accelerations1, time_step): + velocities += 0.5 * time_step * (accelerations + accelerations1) + + +def compute_accelerations(accelerations, masses, positions): + nb_particles = masses.size + for index_p0 in range(nb_particles - 1): + position0 = positions[index_p0] + mass0 = masses[index_p0] + vector = np.empty(3) + for index_p1 in range(index_p0 + 1, nb_particles): + mass1 = masses[index_p1] + position1 = positions[index_p1] + for i in range(3): + vector[i] = position0[i] - position1[i] + + distance = sum(vector ** 2) * math.sqrt(sum(vector ** 2)) + + coef_m1 = mass0 / distance + coef_m2 = mass1 / distance + + for i in range(3): + accelerations[index_p0][i] -= coef_m1 * vector[i] + accelerations[index_p1][i] += coef_m2 * vector[i] + + return accelerations + +def numpy_highlevel( + time_step: float, + number_of_steps: int, + masses: "float[]", + positions: "float[:,:]", + velocities: "float[:,:]", + ): + accelerations = np.zeros_like(positions) + accelerations1 = np.zeros_like(positions) + + # Initial Acceleration + accelerations = compute_accelerations(accelerations, masses, positions) + + time = 0.0 + energy0, _, _ = compute_energies(masses, positions, velocities) + energy_previous = energy0 + + for step in range(number_of_steps): + advance_positions(positions, velocities, accelerations, time_step) + accelerations, accelerations1 = accelerations1, accelerations + accelerations.fill(0) + compute_accelerations(accelerations, masses, positions) + advance_velocities(velocities, accelerations, accelerations1, time_step) + time += time_step + + if not step % 100: + energy, _, _ = compute_energies(masses, positions, velocities) + #print( + # f"t = {time_step * step:5.2f}, E = {energy:.7f}, " + # f"dE/E = {(energy - energy_previous) / energy_previous:+.7f}" + #) + energy_previous = energy + + return math.floor((10000000*energy)/10000000), math.floor((10000000*energy0)/10000000) + #return energy, energy0 + +def compute_kinetic_energy(masses, velocities): + return 0.5 * np.sum(masses * np.sum(velocities ** 2, 1)) + + +def compute_potential_energy(masses, positions): + number_of_particles = masses.size + pe = 0.0 + for index_p0 in range(number_of_particles - 1): + mass = masses[index_p0] + for index_p1 in range(index_p0 + 1, number_of_particles): + mass1 = masses[index_p1] + vector = positions[index_p0] - positions[index_p1] + distance = math.sqrt(sum(vector ** 2)) + pe -= (mass * mass1) / distance + return pe + +def compute_energies(masses, positions, velocities): + ke = compute_kinetic_energy(masses, velocities) + pe = compute_potential_energy(masses, positions) + return ke+pe, ke, pe + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10.0 + + time_step = 0.001 + number_of_steps = int(time_end/time_step) + 1 + + path_input = sys.argv[1] + + masses, positions, velocities = load_input_data(path_input) + + start = time.time() + for i in range(5): + energy, energy0 = numpy_highlevel(time_step, number_of_steps, masses, positions, velocities) + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print( + f"{number_of_steps} time steps run in {timedelta(seconds=end-start)}" + ) + diff --git a/benchmarks/python/bench_numpy_highlevel_jit.py b/benchmarks/python/bench_numpy_highlevel_jit.py new file mode 100644 index 0000000000..0fe9009d14 --- /dev/null +++ b/benchmarks/python/bench_numpy_highlevel_jit.py @@ -0,0 +1,122 @@ +import sys +import math +import time +from datetime import timedelta + +import numpy as np +import pandas as pd + +from transonic import jit + +def load_input_data(path): + df = pd.read_csv( + path, names = ["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter = r"\s+" + ) + masses = df["mass"].values.copy() + positions = df.loc[:, ["x", "y", "z"]].values.copy() + velocities = df.loc[:, ["vx", "vy", "vz"]].values.copy() + return masses, positions, velocities + +def advance_positions(positions, velocities, accelerations, time_step): + positions += velocities * time_step + 0.5 * accelerations * time_step ** 2 + +def advance_velocities(velocities, accelerations, accelerations1, time_step): + velocities += 0.5 * time_step * (accelerations + accelerations1) + +def compute_accelerations(accelerations, masses, positions): + nb_particles = masses.size + for index_p0 in range(nb_particles - 1): + position0 = positions[index_p0] + masses0 = masses[index_p0] + vector = np.empty(3) + for index_p1 in range(index_p0 + 1, nb_particles): + masses1 = masses[index_p1] + position1 = positions[index_p1] + for i in range(3): + vector[i] = position0[i] - position1[i] + + distance = sum(vector ** 2) * math.sqrt(sum(vector ** 2)) + coef_m1 = masses0 / distance + coef_m2 = masses1 / distance + for i in range(3): + accelerations[index_p0][i] -= coef_m1 * vector[i] + accelerations[index_p1][i] += coef_m2 * vector[i] + return accelerations + + +@jit +def pythran_naive(time_step, number_of_steps, masses, positions, velocities): + + accelerations = np.zeros_like(positions) + accelerations1 = np.zeros_like(positions) + + # Initial Acceleration + accelerations = compute_accelerations(accelerations, masses, positions) + + time = 0.0 + energy0, _, _ = compute_energies(masses, positions, velocities) + energy_previous = energy0 + + for step in range(number_of_steps): + advance_positions(positions, velocities, accelerations, time_step) + accelerations, accelerations1 = accelerations1, accelerations + accelerations.fill(0) + compute_accelerations(accelerations, masses, positions) + advance_velocities(velocities, accelerations, accelerations1, time_step) + time += time_step + + if not step % 100: + energy, _, _ = compute_energies(masses, positions, velocities) + #print( + # f"t = {time_step * step:5.2f}, E = {energy:.7f}, " + # f"dE/E = {(energy - energy_previous) / energy_previous:+.7f}" + #) + energy_previous = energy + + return math.floor((10000000*energy)/10000000), math.floor((10000000*energy0)/10000000) + + +def compute_kinetic_energy(masses, velocities): + return 0.5 * np.sum(masses * np.sum(velocities ** 2, 1)) + +def compute_potential_energy(masses, positions): + number_of_particles = masses.size + pe = 0.0 + for index_p0 in range(number_of_particles - 1): + mass = masses[index_p0] + for index_p1 in range(index_p0 + 1, number_of_particles): + mass1 = masses[index_p1] + vector = positions[index_p0] - positions[index_p1] + distance = math.sqrt(sum(vector ** 2)) + pe -= (mass * mass1) / distance + return pe + +def compute_energies(masses, positions, velocities): + ke = compute_kinetic_energy(masses, velocities) + pe = compute_potential_energy(masses, positions) + return ke+pe, ke, pe + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10.0 + + time_step = 0.001 + number_of_steps = int(time_end/time_step) + 1 + + path_input = sys.argv[1] + masses, positions, velocities = load_input_data(path_input) + + start = time.time() + for i in range(5): + energy, energy0 = pythran_naive(time_step, number_of_steps, masses, positions, velocities) + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print( + f"{number_of_steps} time steps run in {timedelta(seconds = end - start)}" + ) + + diff --git a/benchmarks/python/bench_pure_numpy_highlevel.py b/benchmarks/python/bench_pure_numpy_highlevel.py new file mode 100644 index 0000000000..ae7500ed70 --- /dev/null +++ b/benchmarks/python/bench_pure_numpy_highlevel.py @@ -0,0 +1,122 @@ +import sys +import time +import math +from datetime import timedelta + +import numpy as np +import pandas as pd + +def load_input_data(path): + df = pd.read_csv( + path, names = ["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter = r"\s+" + ) + masses = df["mass"].values.copy() + positions = df.loc[:, ["x", "y", "z"]].values.copy() + velocities = df.loc[:, ["vx", "vy", "vz"]].values.copy() + return masses, positions, velocities + +def advance_positions(positions, velocities, accelerations, time_step): + positions += np.add(np.multiply(velocities, time_step), np.multiply(0.5, np.multiply(accelerations, np.power(time_step, 2)))) + +def advance_velocities(velocities, accelerations, accelerations1, time_step): + velocities += np.multiply(0.5, np.multiply(time_step, np.add(accelerations, accelerations1))) + +def compute_accelerations(accelerations, masses, positions): + number_of_particles = masses.size + for index_p0 in range(number_of_particles - 1): + position0 = positions[index_p0] + masses0 = masses[index_p0] + vector = np.empty(3) + for index_p1 in range(index_p0 +1, number_of_particles): + masses1 = masses[index_p1] + position1 = positions[index_p1] + for i in range(3): + vector[i] = position0[i] - position1[i] + + distance = sum(vector ** 2) * math.sqrt(sum(vector ** 2)) + coef_m1 = masses0 / distance + coef_m2 = masses1 / distance + for i in range(3): + accelerations[index_p0][i] -= coef_m1 * vector[i] + accelerations[index_p1][i] += coef_m2 * vector[i] + return accelerations + +def pure_numpy_highlevel(time_step: float, + number_of_steps: int, + masses: "float[]", + positions: "float[:,:]", + velocities: "float[:,:]", + ): + + accelerations0 = np.zeros_like(positions) + accelerations1 = np.zeros_like(positions) + + accelerations0 = compute_accelerations(accelerations0, masses, positions) + + time = 0.0 + energy0, _, _ = compute_energies(masses, positions, velocities) + energy_previous = energy0 + + for step in range(number_of_steps): + advance_positions(positions, velocities, accelerations0, time_step) + accelerations0, accelerations1 = accelerations1, accelerations0 + accelerations0.fill(0) + compute_accelerations(accelerations0, masses, positions) + advance_velocities(velocities, accelerations0, accelerations1, time_step) + time += time_step + + if not step % 100: + energy, _, _ = compute_energies(masses, positions, velocities) + #print( + # f"t = {time_step * step:5.2f}, E = {energy:.7f}, " + # f"dE/E = {(energy - energy_previous) / energy_previous:+.7f}" + #) + energy_previous = energy + + return math.floor((10000000*energy)/10000000), math.floor((10000000*energy0)/10000000) + + +def compute_kinetic_energy(masses, velocities): + return np.multiply(0.5, np.sum(np.multiply(masses, np.sum(np.power(velocities, 2), 1)))) + +def compute_potential_energy(masses, positions): + number_of_particles = masses.size + pe = 0.0 + for index_p0 in range(number_of_particles -1): + masses0 = masses[index_p0] + for index_p1 in range(index_p0 + 1, number_of_particles): + masses1 = masses[index_p1] + vector = np.subtract(positions[index_p0], positions[index_p1]) + distance = math.sqrt(sum(np.power(vector,2))) + pe -= np.multiply(masses0, masses1) / distance + return pe + +def compute_energies(masses, positions, velocities): + ke = compute_kinetic_energy(masses, velocities) + pe = compute_potential_energy(masses, positions) + return ke+pe, ke, pe + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10.0 + + time_step = 0.001 + number_of_steps = int(time_end/time_step) +1 + + path_input = sys.argv[1] + masses, positions, velocities = load_input_data(path_input) + + start = time.time() + for i in range(5): + energy, energy0 = pure_numpy_highlevel(time_step, number_of_steps, masses, positions, velocities) + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print( + f"{number_of_steps} time steps run in {timedelta(seconds=end-start)}" + ) + + diff --git a/benchmarks/python/bench_purepy_particle.py b/benchmarks/python/bench_purepy_particle.py new file mode 100644 index 0000000000..cd54802a6f --- /dev/null +++ b/benchmarks/python/bench_purepy_particle.py @@ -0,0 +1,172 @@ +import sys +import math +import time +from itertools import combinations +from datetime import timedelta + + +class Point3D: + def __init__(self, x, y, z): + self.x = x + self.y = y + self.z = z + + @classmethod + def _zero(cls): + return cls(0.0, 0.0, 0.0) + + def norm(self): + return math.sqrt(self.norm2()) + + def norm_cube(self): + norm2 = self.norm2() + return norm2 * math.sqrt(norm2) + + def norm2(self): + return self.x ** 2 + self.y ** 2 + self.z ** 2 + + def __repr__(self): + return f"[{self.x:.10f}, {self.y:.10f}, {self.z:.10f}]" + + def __add__(self, other): + return Point3D(self.x + other.x, self.y + other.y, self.z + other.z) + + def __sub__(self, other): + return Point3D(self.x - other.x, self.y - other.y, self.z - other.z) + + def __mul__(self, other): + return Point3D(other * self.x, other * self.y, other * self.z) + + __rmul__ = __mul__ + + def reset_to_0(self): + self.x = 0.0 + self.y = 0.0 + self.z = 0.0 + + +def make_inlined_point(name): + x = f"_{name}_x" + y = f"_{name}_y" + z = f"_{name}_z" + + def get(self): + return Point3D(getattr(self, x), getattr(self, y), getattr(self, z)) + + def set(self, value): + setattr(self, x, value.x) + setattr(self, y, value.y) + setattr(self, z, value.z) + + return property(get, set) + + +class Particle: + """ + A Particle has mass, position, velocity and acceleration. + """ + + position = make_inlined_point("position") + velocity = make_inlined_point("velocity") + acceleration = make_inlined_point("acceleration") + acceleration1 = make_inlined_point("acceleration1") + + def __init__(self, mass, x, y, z, vx, vy, vz): + self.mass = mass + self.position = Point3D(x, y, z) + self.velocity = Point3D(vx, vy, vz) + self.acceleration = Point3D(0.0, 0.0, 0.0) + self.acceleration1 = Point3D(0.0, 0.0, 0.0) + + @property + def ke(self): + return 0.5 * self.mass * self.velocity.norm2() + + +class Cluster(list): + """ + A Cluster is just a list of particles with methods to accelerate and + advance them. + """ + + @property + def ke(self): + return sum(particle.ke for particle in self) + + @property + def pe(self): + pe = 0.0 + for p1, p2 in combinations(self, 2): + vector = p1.position - p2.position + distance = math.sqrt(vector.norm2()) + pe -= (p1.mass * p2.mass) / distance + return pe + + @property + def energy(self): + return self.ke + self.pe + + def step(self, dt): + self.__advance_positions(dt) + self.accelerate() + self.__advance_velocities(dt) + + def accelerate(self): + for particle in self: + particle.acceleration1 = particle.acceleration + particle.acceleration = Point3D(0.0, 0.0, 0.0) + + nb_particules = len(self) + for i0 in range(nb_particules - 1): + p0 = self[i0] + for i1 in range(i0 + 1, nb_particules): + p1 = self[i1] + delta = p0.position - p1.position + distance_cube = delta.norm_cube() + p0.acceleration -= p1.mass / distance_cube * delta + p1.acceleration += p0.mass / distance_cube * delta + + def __advance_positions(self, dt): + for p in self: + p.position += dt * p.velocity + 0.5 * dt ** 2 * p.acceleration + + def __advance_velocities(self, dt): + for p in self: + p.velocity += 0.5 * dt * (p.acceleration + p.acceleration1) + + +if __name__ == "__main__": + + try: + time_end = float(sys.argv[2]) + except IndexError: + time_end = 10. + + time_step = 0.001 + + start = time.time() + for i in range(5): + cluster = Cluster() + with open(sys.argv[1]) as input_file: + for line in input_file: + try: + cluster.append(Particle(*[float(x) for x in line.split()[1:]])) + except TypeError: + pass + + old_energy = energy0 = energy = -0.25 + cluster.accelerate() + for step in range(1, int(time_end / time_step + 1)): + cluster.step(time_step) + if not step % 100: + energy = cluster.energy + #print( + # f"t = {time_step * step:.2f}, E = {energy:.10f}, " + # f"dE/E = {(energy - old_energy) / old_energy:.10f}" + #) + old_energy = energy + + end = time.time() + + print(f"Final dE/E = {(energy - energy0) / energy0:.7e}") + print(f"run in {timedelta(seconds=end - start)}") diff --git a/benchmarks/python/benchmark-2.py b/benchmarks/python/benchmark-2.py new file mode 100644 index 0000000000..abcd8dabf3 --- /dev/null +++ b/benchmarks/python/benchmark-2.py @@ -0,0 +1,70 @@ +import time +import math +from typing import List, Dict + +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +from data_loader import load_input_data +from bench import pythran +from bench_numba import numba +from bench_numpy_highlevel_jit import pythran_naive +from bench_numpy_highlevel import numpy_highlevel +from bench_pure_numpy_highlevel import pure_numpy_highlevel + + +# TODO: Name this function something else +def calculate_time(time_step: int, number_of_steps: int, iterations: int, masses: List, positions: List, velocities: List) -> Dict[str, float]: + """ + This function is used to calculate time for following implementations: NumPy, XYZ, ... + + Parameters + ========== + time_step: Interval after which energy of each particle is calculated. + number_of_steps: Total number of steps taken by particle in the given time. + masses: mass of each article. + position: position of particle after each interaction + velocities: velocites of particle after each interaction + + Returns + ========= + _time: List[int], Time taken for all types of implementations listed above. + """ + times = {} + + for loop_function in (pythran, numba, pythran_naive, numpy_highlevel, pure_numpy_highlevel): + start = time.time() + for iters in range(iterations): + energy, energy0 = loop_function(time_step, number_of_steps, masses, positions, velocities) + end = time.time() + times[loop_function.__name__] = round((end-start)/iterations, 2) + + return times + + +if __name__ == "__main__": + masses = [] + positions = [] + velocities = [] + + datasets_time = {} + iterations = 5 + time_end = 10.0 + time_step = 0.001 + number_of_steps = int(time_end/time_step) + 1 + + # Iterating over different datasets + for dataset_name in ["16.txt", "32.txt", "64.txt"]: + file_path = "input" + dataset_name + masses, positions, velocities = load_input_data(file_path) + times_list = calculate_time(time_step, number_of_steps, iterations, masses, positions, velocities) + datasets_time[file_path.strip(".txt")] = times_list + + # Conver tthe output dictionary from datasets_time to a CSV file + df = pd.DataFrame() + df = df.append((datasets_time.values()).tolist()) + df.columns = ["Pythran", "Numba", "Pythran Naive", "NumPy", "Pure NumPy"] + df = df.T + df.columns = datasets_time.keys() + df.to_csv("iter_6-b.csv") diff --git a/benchmarks/python/data_loader.py b/benchmarks/python/data_loader.py new file mode 100644 index 0000000000..4f0d61150e --- /dev/null +++ b/benchmarks/python/data_loader.py @@ -0,0 +1,13 @@ +import pandas as pd + +def load_input_data(path): + df = pd.read_csv( + path, names=["mass", "x", "y", "z", "vx", "vy", "vz"], delimiter=r"\s+" + ) + + # warning: copy() is for Pythran... + masses = df["mass"].values.copy() + positions = df.loc[:, ["x", "y", "z"]].values.copy() + velocities = df.loc[:, ["vx", "vy", "vz"]].values.copy() + + return masses, positions, velocities diff --git a/benchmarks/python/plot-modified-1.py b/benchmarks/python/plot-modified-1.py new file mode 100644 index 0000000000..e21c9ffe7b --- /dev/null +++ b/benchmarks/python/plot-modified-1.py @@ -0,0 +1,54 @@ +import pandas as pd +import numpy as np +import matplotlib.pyplot as plt +from matplotlib.pyplot import figure + +def main(x, labels): + + fig, ax = plt.subplots() + + #figure(figsize=(20, 5), dpi=80) + width = 0.17 + j = 0 + rect = [0, 0, 0, 0, 0]#, 0] + + for i in _list_df: + rect[j] = plt.bar(x - width*j, i, width, align='center', label = labels[j]) + ax.bar_label(rect[j], padding=3) + j += 1 + + plt.title('Performance Comparision') + plt.xlabel('Datasets') + plt.ylabel('Time (s)') + + ax.set_xticks(x) + ax.set_xticklabels(df.columns) + + plt.grid(True) + plt.legend() + + fig.tight_layout() + plt.savefig("output-modify-2-new.jpg") + + +if __name__ == "__main__": + + df = pd.read_csv("iter_6-b.csv") + + df = df.drop(['Unnamed: 0'], axis = 1) + + df = df.T + + df.columns = ["Pythran", "Numba", "Pythran Naive", "NumPy", "Pure NumPy"]#, "Pythran Opti"] + + labels = [] + for i in range(len(df.columns)): + labels.append(df.columns[i]) + #print(labels) + + df = df.T + x = np.arange(len(df.columns)) + _list_df = df[0:].to_numpy().tolist() + + main(x, labels) + diff --git a/content/en/benchmark.md b/content/en/benchmark.md new file mode 100644 index 0000000000..208cdd3edd --- /dev/null +++ b/content/en/benchmark.md @@ -0,0 +1,252 @@ +--- +title: NumPy Benchmarks +sidebar: false +--- + +Visualization + + +## Overview + +This blog post aims to benchmark NumPy's performance on the widely accepted N-body problem[1]. This work also compares NumPy with other popular libraries and compilers like Numba, Pythran, Transonic and pure Python and C++ implementations. + +The objective of benchmarking NumPy revolves around the efficiency of the library in quasi real-life situations, and the N-body problem suits the purpose well. Benchmarking is performed over several iterations for different datasets to ensure the accuracy of the results. + + + + + + + + + + + + + + + +## About N-Body Problem + + + + + +> In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. + +Source: [Wikipedia](https://en.wikipedia.org/wiki/N-body_problem). + +From the definition above, the N-body problem involves computations related to energies, acceleration, velocity, the distance of several particles in the space, which has also allowed it to be one of the widely accepted algorithms in the community. A brief description of computations involved in solving the N-body problem is given below, along with the pseudo-code in the next section: + +Consider $n$ bodies of masses $m_1, m_2, m_3, ... , m_n$, moving under the mutual [gravitational force](https://en.wikipedia.org/wiki/Gravity) of attraction between them in an [inertial frame of reference](https://en.wikipedia.org/wiki/Inertial_frame_of_reference) of three dimensions, such that consecutive positions and velocities of an ${ith}$ body are denoted by ($s_{i-1}$, $s_i$) and ($v_{i-1}$, $v_i$) respectively. The gravitational force felt on the $ith$ body of mass $m_i$ by a single body of mass $m_j$ is denoted as $F$ and the acceleration of the $ith$ body is represented as $a_i$. Consider the position vectors of these two bodies as $r_i$ and $r_j$. + +The final aim is to find the total energy of each particle in the celestial space and the equations involved in solving the problem are listed below: + +\begin{equation} {s_i} = {s_{i-1}} + {u\times t} + \frac{a\times t^2}{2} \tag{i} \end{equation} + +\begin{equation}{v_i} = {v_{i-1}} + {a\times t} \tag{ii} \end{equation} + +\begin{equation} {F} = \frac{{G\times {m_i}\times {m_j}}\times \mid {r_i}-{r_j} \mid}{{\mid {r_i}-{r_j} \mid}^3} \tag{iii} \end{equation} + +\begin{equation} {F} = {m\times a} \tag{iv} \end{equation} + +\begin{equation} {a} = \frac{F}{m} \tag{v} \end{equation} + +\begin{equation} \textrm{Self Potential Energy} = \textrm{U} = -\frac{{m_i}\times {m_j}}{r^2} \tag{vi} \end{equation} + +\begin{equation} \textrm{Kinetic Energy} = \textrm{K.E} = \frac{\sum m\times v^2}{2} \tag{vii} \end{equation} + +\begin{equation} \textrm{Total Energy} = \textrm{Kinetic Energy} + \textrm{Self Potential Energy} \tag{viii} \end{equation} + +### Pseudo Code of Solving N-body Problem + +```bash +Set time to 0, time_step to 0.001 and time_end to 10s +THEN number_of_step is 10/0.001 +FOR time is less than or equal to time_end + Calculate accelerations (a[i], for given position r[i]) + Calculate total initial energies: + Calculate kinetic energy + Calculate potential energy + FOR i less than number_of_step + Calculate positions (r[i+1]) + Swap accelerations + Calculate accelerations + Calculate velocities (v[i+1]) + Increment time + IF number_of_step % 100 is not 0 THEN + Calculate total energy + Print energy + ENDIF + END FOR +END FOR +``` + +## Dataset Description + +* Nine different text files, named as `InputX.txt`, where $X$ is number of particles in the celestial space (for this problem, number of particles are: $16, 32, 64, 128, 256, 512, 1000, 2000$ and $16000$). +* Dataset[2] consists of the masses of each particle and information about their initial positions and velocities along the three-dimensional axis. + +An example from the dataset[2] used is given below: (for a single particle) + +``` +# Ordered as: label, mass (grams), position_x, position_y, position_z, velocity_x, velocity_y, velocity_z +-1 0.0625 0.214835865608654947 -0.120469325327368135 -0.2661811268232539 0.757849421156586822 0.157644506165220161 -0.0715602005208729741 +``` + +## Implemented Accelerators + +Accelerators like [Numba](http://numba.pydata.org/), [Pythran](https://transonic.readthedocs.io/), and [Transonic](https://transonic.readthedocs.io/) are considered for also considered for benchmarking. This decision is inspired from [Ralf Gommer's Presentation on SciPy 1.0](https://www.slideshare.net/RalfGommers/scipy-10-and-beyond-a-story-of-community-and-code) (conference [video](https://www.youtube.com/watch?v=oHmm3mPxg6Y)). We give brief details on few of the accelerators below: + +### Numba + +From official [Numba's website](http://numba.pydata.org/): + +> Numba is an open source JIT compiler that translates a subset of Python and NumPy code into fast machine code. + +Since Numba is a compiler focused on accelerating Python codes, the user API of the library comes with decorators like: `@jit, @vectorize, @guvectorize, @stencil, @jitclass, @cfunc, @overload` to support ease-of-use of the library. Along with the decorators, it has a `nopython` mode to generate fully compiled results without the need of intermediate Python interpreter calls. Numba supporting NumPy arrays and functions also makes it a good candidate for comparison. + + + +Implementation details for benchmarking: + +* `jit` decorator from Numba was used to compile the Python functions just-in-time. +* `cache = True`: To avoid repetitive compile time. +* Uses NumPy arrays and loops. +* Implemented `jit` decorated functions to call another `jit` decorated functions to increase the performance of our model. + +### Pythran + +Pythran is a Python-specific Ahead Of Time compiler. Its primary focus was on scientific computing. It uses the same C++ API as NumPy, which was designed specifically for scientific computing. Pythran converts annotated Python modules into native Python modules. These modules have the same interface but (hopefully) are faster to load. Pythran's main advantage is that it uses [Expression Templating](https://en.wikipedia.org/wiki/Expression_templates) and [SIMD](https://en.wikipedia.org/wiki/SIMD) instructions. + +NumPy arrays in Cython should be stored in contiguous memory like C-style or Fortran to use Pythran in the backend. Here, the Pythran lacks behind. Another limitation is that the sequence of bytes of words must be the same as the targeted architecture to make Pythran work. + +Pythran GitHub repository is available [here](https://github.com/serge-sans-paille/pythran) + +## Results + +Table values represent the time taken by each algorithm to run on the given datasets for $5$ number of iterations. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Input $\rightarrow$163264128
Python-NumPy47.14179.67263399.8
Pure-NumPy42.7167.87583198.2
Pure-Python65.1202.3
C++0.371.585.4622.06
Numba0.751.111.92 4.27
Pythran-Naive: Transonic1.391.161.663.62
+ + + +**Note** on machine configuration used for benchmarking: + +* **Machine:** Intel(R) Core(TM) i7-10870H CPU @ 2.20GHz, 16GB RAM +* **Operating System:** Ubuntu 20.04.2 LTS +* **Library Versions:** + * Python: 3.8.10 + * NumPy: 1.21.1 + * Numba: 0.53.1 + * Transonic: 0.4.10 + +## Source Code + +* These codes are highly inspired from Pierre Augier's work on N-Body Problem. +* Benchmarking Code: here. +* Visualization Code: here. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
AlgorithmsSource CodesImplementation Details
Python-NumPybench_numpy_highlevel.pyOptimized NumPy
Pure-NumPybench_pure_numpy_highlevel.pyOnly NumPy Functions
Pure-Pythonbench_pure_particle.pyOnly NumPy Functions
C++main.cppOptimized C++
Numbabench_pure_numba.pyStandart puntions of Python Functions
Pythran-Naive: Transonic Jitbench_numpy_highlevel_jit.pyJust-In-Time Compilation
+ + + +## References + +* [Wikipedia's Article on N-Body Problem](https://en.wikipedia.org/wiki/N-body_problem) +* [Dataset used from Pierre Augier's repository](https://github.com/paugier/nbabel/tree/master/data) diff --git a/content/en/config.yaml b/content/en/config.yaml index 874ff08e89..3db6622092 100644 --- a/content/en/config.yaml +++ b/content/en/config.yaml @@ -44,6 +44,9 @@ params: casestudies: title: CASE STUDIES features: + - title: NumPy Benchmarks + text: demo + url: /benchmark - title: First Image of a Black Hole text: How NumPy, together with libraries like SciPy and Matplotlib that depend on NumPy, enabled the Event Horizon Telescope to produce the first ever image of a black hole img: /images/content_images/case_studies/blackhole.png diff --git a/static/images/content_images/benchmark-plot.jpg b/static/images/content_images/benchmark-plot.jpg new file mode 100644 index 0000000000..2a87cac71f Binary files /dev/null and b/static/images/content_images/benchmark-plot.jpg differ diff --git a/static/images/content_images/output-modify-2b-new.jpg b/static/images/content_images/output-modify-2b-new.jpg new file mode 100644 index 0000000000..6def45564a Binary files /dev/null and b/static/images/content_images/output-modify-2b-new.jpg differ