From e62c42bb2c440b52fb01aa626f65ef75cc96e134 Mon Sep 17 00:00:00 2001 From: Lars Bogner Date: Thu, 4 Sep 2025 08:56:55 +0200 Subject: [PATCH] Fix issues with limited numerical precision and artifacts with big N. --- projects/project1/main.pdf | Bin 316731 -> 535303 bytes projects/project1/main.tex | 5 +- src/project1/poisson_solver.cpp | 8 +-- src/project1/python/poisson_plotter.py | 83 +++++++++++++++++-------- src/project1/python/timing_plotter.py | 30 +++++++++ 5 files changed, 94 insertions(+), 32 deletions(-) diff --git a/projects/project1/main.pdf b/projects/project1/main.pdf index 58de6bb224a44a9b11f0a0986c33183775526045..1267e389e423dbffd15245388887379ece62996f 100644 GIT binary patch delta 343365 zcmZs?V{~P~+BMp-lTOFBZQC8&c6V&A*fu&&$F^;!W81cqn{&SR9rqh|+<$Y;n)S@5 z*4|_9v1+brD@6%eAdDpkWoAt1S)c?4G*)d^#lL$ms$azkkIio|P{E>F?h*>6AMB(M zPXrLpG-{=(h?d%XbecCyrzK+jg}_FI9G`dK(pFMtrblUh(-=La?g?K$3NWZ!|3LPLC`>(cpY3e2@q%YE%9SDw~w 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zZ54aE!alM03$c$asVfot3*c38pimr~Zga6oat=Z>?~YVhj+POuWl%lAe;NhtA+*sY zH+1jORpJCFcd?7< z?ZLVLeJIdrLVxcrZnjV9f69S&9R_-LX@I72nIgWDDgNmqt{xTFcs$pSiyL>v%_4DY zg1Eg&{97&V>=gg?fCJ+0W#_&7Rrp&XwnfCXR3GgU32TJvMEog|7K`LWs1fx$iWKdT zPn`qWHJ`S@rc0v;G>Sl@2%}*PjD>M9o~81h33Q)O1=crcBY`#&f2P1xmJs)fL ziA9M%R{EPoNj^6BJ&TfkY(sO4>igK)e2Y?i?Dn%3rTVxkhA7R)`#fq1jnTt0beXOT{)dsAz}Y8qr(1LbLKw-KXN9 zULDc9>TA*ayTym9 \num{1e-10}$ are considered. +Plotting the relative error for different values of $N$ reveals a constant value for the relative error accross the entire domain of $x$. The relative error decreases by two orders of magnitude for every order of magnitude increase in $N$. The results are summarized in \autoref{fig:rel_error_plot}. To avoiud issues with divisions by zero, the points where $u(x) \leq \num{e-10}$ were omitted from the plot. \begin{figure} \centering @@ -253,7 +253,7 @@ Plotting the relative error for different values of $N$ reveals the increase of \end{figure} \subsection*{Subproblem (c)} -The maximum relative errors are calculated directly using C++ as the output size scales linearly with $N$ and gets overwhelmingly large for bigger $N$. The results are output using the \texttt{std::cout} command and retrieved using GNU/Linux command line utilities. The code for calculating the maximum relative error $\max_i \frac{\delta v_i}{u_i}$ (see \eqref{eq:relerror}) is included in the C++ implementation. The results are summarized in \autoref{tab:rel_errors}. We see a steady decrease of the relative error up to $N = \num{100000}$, after which the relative error increases again. This will most likely be due to the artifacts seen in \autoref{fig:rel_error_plot} starting at $N = \num{10000}$. The source of these artifacts is not entirely clear. +The maximum relative errors are calculated directly using C++ as the output size scales linearly with $N$ and gets overwhelmingly large for bigger $N$. The results are output using the \texttt{std::cout} command and retrieved using GNU/Linux command line utilities. The code for calculating the maximum relative error $\max_i \frac{\delta v_i}{u_i}$ (see \eqref{eq:relerror}) is included in the C++ implementation. The results are summarized in \autoref{tab:rel_errors}. We see a steady decrease of the relative error up to $N = \num{100000}$, after which the relative error increases again. This will most likely be due to the limited numerical precision of floating point numbers in C++ and associated numerical errors. \begin{table}[H] \centering @@ -332,3 +332,4 @@ To evaluate the performance of the different algorithms, the algorithms were exe \bibliography{include/citations} \end{document} + \ No newline at end of file diff --git a/src/project1/poisson_solver.cpp b/src/project1/poisson_solver.cpp index 27c23e8..a752bc4 100644 --- a/src/project1/poisson_solver.cpp +++ b/src/project1/poisson_solver.cpp @@ -43,11 +43,11 @@ int main(int argc, char* argv[]){ // Output the solution string filename = "numerical_solution_" + to_string(N) + ".csv"; ofstream ofs(filename); - ofs << "x,u(x)" << endl; + ofs << "x,v(x),u(x)" << endl; for (int i = 0; i <= N; i++) { - ofs << fixed << setprecision(decimal_places) << scientific << x[i] << "," << solution[i] << endl; - } - ofs.close(); + ofs << fixed << setprecision(decimal_places) << scientific << x[i] << "," << solution[i] << "," << u[i] << endl; + } + ofs.close(); } diff --git a/src/project1/python/poisson_plotter.py b/src/project1/python/poisson_plotter.py index 287dd9d..2660edc 100644 --- a/src/project1/python/poisson_plotter.py +++ b/src/project1/python/poisson_plotter.py @@ -13,12 +13,43 @@ args = parser.parse_args() FILENAME = args.filename REFERENCE = args.reference +def get_rc_params(): + colors = ["FF220C", "70D6FF", "8AAA79", "666370", "1C1F33"] + rcParams = plt.rcParams + # Use LaTeX for rendering + # Setup fonts + rcParams["text.usetex"] = True + rcParams["font.family"] = "serif" + rcParams["font.size"] = 12 + rcParams["axes.labelsize"] = 12 + rcParams["axes.titlesize"] = 12 + rcParams["legend.fontsize"] = 10 + rcParams["xtick.labelsize"] = 10 + rcParams["ytick.labelsize"] = 10 + # Figure size and resolution + rcParams["figure.figsize"] = (6, 4) + rcParams["figure.dpi"] = 300 + # Use colors from the palette + rcParams["axes.prop_cycle"] = plt.cycler(color=[f"#{color}" for color in colors]) + # Grid + rcParams["axes.grid"] = True + rcParams["grid.alpha"] = 0.5 + rcParams["grid.linestyle"] = "--" + # Point ticks to the inside of the axes + rcParams["xtick.direction"] = "in" + rcParams["ytick.direction"] = "in" + rcParams["xtick.top"] = True + rcParams["ytick.right"] = True + return rcParams + + def singular_plot(): + plt.rcParams.update(get_rc_params()) df = pd.read_csv(FILENAME) fig, ax = plt.subplots(figsize=(6,3)) - ax.plot(df["x"], df["u(x)"]) + ax.plot(df["x"], df[df.columns[1]]) ax.set_xlabel(r"$x$") - ax.set_ylabel(r"$u(x)$") + ax.set_ylabel(rf"${df.columns[1]}$") fig.tight_layout() @@ -27,22 +58,21 @@ def singular_plot(): fig.savefig(os.path.join(output_directory, output_file)) def reference_plot(): + plt.rcParams.update(get_rc_params()) df = pd.read_csv(FILENAME).sort_values("x") - df_ref = pd.read_csv(REFERENCE).sort_values("x") fig, (ax1, ax2) = plt.subplots(nrows=2, sharex=True, height_ratios=[3, 1], figsize=(4, 8)) - ax1.plot(df["x"], df["u(x)"], label="Numerical Solution") - ax1.plot(df_ref["x"], df_ref["u(x)"], label="Reference Solution", linestyle="--") + ax1.plot(df["x"], df["v(x)"], label="Numerical Solution") + ax1.plot(df["x"], df["u(x)"], label="Reference Solution", linestyle="--") ax1.set_xlabel(r"$x$") ax1.set_ylabel(r"$u(x)$") ax1.legend() - combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) - ratio = (combined_df["u(x)_num"] - combined_df["u(x)_ref"]) / combined_df["u(x)_ref"] + ratio = (df["v(x)"] - df["u(x)"]) / df["u(x)"] - ax2.plot(combined_df["x"], ratio.abs()) + ax2.plot(df["x"], ratio.abs()) ax2.set_xlabel(r"$x$") - ax2.set_ylabel(r"$|\frac{u(x)_{num} - u(x)_{ref}}{u(x)_{ref}}|$") + ax2.set_ylabel(r"$|\frac{v(x) - u(x)}{u(x)}|$") ax2.axhline(y=1, color="gray", linestyle="--") ax2.set_yscale("log") @@ -53,30 +83,29 @@ def reference_plot(): fig.savefig(os.path.join(output_directory, output_file)) def multiple_reference_plot(): + plt.rcParams.update(get_rc_params()) # Filename is wildcard -> Find files import glob files = glob.glob(FILENAME) files.sort() fig, (ax1, ax2) = plt.subplots(nrows=2, sharex=True, height_ratios=[3, 1], figsize=(6,5)) - df_ref = pd.read_csv(REFERENCE).sort_values("x") for file in files: df = pd.read_csv(file).sort_values("x") label = f"Num. (N = {os.path.basename(file).replace(".csv", "").split("_")[-1]})" - ax1.plot(df["x"], df["u(x)"], label=label) + ax1.plot(df["x"], df["v(x)"], label=label) - combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) - ratio = (combined_df["u(x)_num"] - combined_df["u(x)_ref"]) / combined_df["u(x)_ref"] - ax2.plot(combined_df["x"], ratio.abs(), label=label) - - ax1.plot(df_ref["x"], df_ref["u(x)"], label="Reference Solution", linestyle="--", color="gray") + ratio = (df["v(x)"] - df["u(x)"]) / df["u(x)"] + ax2.plot(df["x"], ratio.abs(), label=label) + + ax1.plot(df["x"], df["u(x)"], label="Reference Solution", linestyle="--", color="gray") ax1.set_xlabel(r"$x$") ax1.set_ylabel(r"$u(x)$") ax1.legend() ax2.axhline(y=1, color="gray", linestyle="--") ax2.set_xlabel(r"$x$") - ax2.set_ylabel(r"$|\frac{u(x)_{num} - u(x)_{ref}}{u(x)_{ref}}|$") + ax2.set_ylabel(r"$|\frac{v(x) - u(x)}{u(x)}|$") ax2.set_yscale("log") fig.tight_layout() @@ -92,6 +121,7 @@ def error_plots(): def abs_error_plot(): + plt.rcParams.update(get_rc_params()) import glob files = glob.glob(FILENAME) files.sort() @@ -101,12 +131,12 @@ def abs_error_plot(): fig, ax = plt.subplots(figsize=(6,3)) for file in files: df = pd.read_csv(file).sort_values("x") - combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) - log_abs_err = np.log10((combined_df["u(x)_num"] - combined_df["u(x)_ref"]).abs()) - ax.plot(combined_df["x"], log_abs_err, label=f"N={os.path.basename(file).replace('.csv','').split('_')[-1]}") + # combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) + log_abs_err = np.log10((df["u(x)"] - df["v(x)"]).abs()) + ax.plot(df["x"], log_abs_err, label=f"N={os.path.basename(file).replace('.csv','').split('_')[-1]}") ax.set_xlabel(r"$x$") - ax.set_ylabel(r"$\log_{10}(|u(x)_{num} - u(x)_{ref}|)$") + ax.set_ylabel(r"$\log_{10}(|u(x) - v(x)|)$") ax.legend() fig.tight_layout() @@ -117,6 +147,7 @@ def abs_error_plot(): def rel_error_plot(): + plt.rcParams.update(get_rc_params()) import glob files = glob.glob(FILENAME) files.sort() @@ -126,14 +157,14 @@ def rel_error_plot(): fig, ax = plt.subplots(figsize=(6,3)) for file in files: df = pd.read_csv(file).sort_values("x") - combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) + # combined_df = pd.merge_asof(df, df_ref, on="x", suffixes=("_num", "_ref")) # Drop rows where u(x)_ref is zero - combined_df = combined_df[combined_df["u(x)_ref"].abs() > 1e-10] - log_rel_err = np.log10((combined_df["u(x)_num"] - combined_df["u(x)_ref"]).abs() / combined_df["u(x)_ref"].abs()) - ax.plot(combined_df["x"], log_rel_err, label=f"N={os.path.basename(file).replace('.csv','').split('_')[-1]}") + df = df[df["u(x)"] > 1e-10] + log_rel_err = np.log10((df["u(x)"] - df["v(x)"]).abs() / df["u(x)"].abs()) + ax.plot(df["x"], log_rel_err, label=f"N={os.path.basename(file).replace('.csv','').split('_')[-1]}") ax.set_xlabel(r"$x$") - ax.set_ylabel(r"$\log_{10}(|\frac{u(x)_{num} - u(x)_{ref}}{u(x)_{ref}}|)$") + ax.set_ylabel(r"$\log_{10}(|\frac{u(x) - v(x)}{u(x)}|)$") ax.legend() fig.tight_layout() diff --git a/src/project1/python/timing_plotter.py b/src/project1/python/timing_plotter.py index f7dcf35..6082f46 100644 --- a/src/project1/python/timing_plotter.py +++ b/src/project1/python/timing_plotter.py @@ -4,10 +4,40 @@ import matplotlib.pyplot as plt import argparse import os +def get_rc_params(): + colors = ["FF220C", "70D6FF", "8AAA79", "666370", "1C1F33"] + rcParams = plt.rcParams + # Use LaTeX for rendering + # Setup fonts + rcParams["text.usetex"] = True + rcParams["font.family"] = "serif" + rcParams["font.size"] = 12 + rcParams["axes.labelsize"] = 12 + rcParams["axes.titlesize"] = 12 + rcParams["legend.fontsize"] = 10 + rcParams["xtick.labelsize"] = 10 + rcParams["ytick.labelsize"] = 10 + # Figure size and resolution + rcParams["figure.figsize"] = (6, 4) + rcParams["figure.dpi"] = 300 + # Use colors from the palette + rcParams["axes.prop_cycle"] = plt.cycler(color=[f"#{color}" for color in colors]) + # Grid + rcParams["axes.grid"] = True + rcParams["grid.alpha"] = 0.5 + rcParams["grid.linestyle"] = "--" + # Point ticks to the inside of the axes + rcParams["xtick.direction"] = "in" + rcParams["ytick.direction"] = "in" + rcParams["xtick.top"] = True + rcParams["ytick.right"] = True + return rcParams + parser = argparse.ArgumentParser(description="Plot timing results from CSV file.") parser.add_argument("csv_file", help="Path to the CSV file containing timing results.") args = parser.parse_args() +plt.rcParams.update(get_rc_params()) df = pd.read_csv(args.csv_file) for column in df.columns[1:]: df[column] = df[column] / df["N"] # Normalize by N