Make small changes
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@@ -7,7 +7,7 @@
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#include <iomanip>
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#include <iomanip>
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#define RANGE 1000
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#define RANGE 1000
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#define FILENAME "analytical_solution.txt"
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#define FILENAME "output/analytical_solution.txt"
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double u(double x);
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double u(double x);
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void generate_range(std::vector<double> &vec, double start, double stop, int n);
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void generate_range(std::vector<double> &vec, double start, double stop, int n);
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@@ -4,7 +4,9 @@
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#include <armadillo>
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#include <armadillo>
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#include <cmath>
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#include <cmath>
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#define PRECISION 20
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#define PRECISION 8
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#define N_STEPS_EXP 7
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double f(double x);
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double f(double x);
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@@ -33,7 +33,7 @@ void general_algorithm_main()
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int steps;
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int steps;
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double step_size;
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double step_size;
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for (int i = 0; i < 6; i++) {
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for (int i = 0; i < N_STEPS_EXP; i++) {
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steps = std::pow(10, i+1);
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steps = std::pow(10, i+1);
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step_size = 1./(double) steps;
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step_size = 1./(double) steps;
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@@ -58,7 +58,7 @@ void general_algorithm_error()
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int steps;
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int steps;
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double step_size, abs_err, rel_err, u_i, v_i;
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double step_size, abs_err, rel_err, u_i, v_i;
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for (int i=0; i < 7; i++) {
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for (int i=0; i < N_STEPS_EXP; i++) {
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steps = std::pow(10, i+1);
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steps = std::pow(10, i+1);
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step_size = 1./(double) steps;
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step_size = 1./(double) steps;
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@@ -20,7 +20,7 @@ void timing() {
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ofile.open("output/timing.txt");
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ofile.open("output/timing.txt");
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// Timing
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// Timing
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for (int i=1; i <= 6; i++) {
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for (int i=1; i < N_STEPS_EXP; i++) {
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n_steps = std::pow(10, i);
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n_steps = std::pow(10, i);
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clock_t g_1, g_2, s_1, s_2;
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clock_t g_1, g_2, s_1, s_2;
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double g_res = 0, s_res = 0;
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double g_res = 0, s_res = 0;
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@@ -6,7 +6,7 @@ def main():
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x = []
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x = []
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v = []
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v = []
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with open('analytical_solution.txt') as f:
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with open('output/analytical_solution.txt') as f:
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for line in f:
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for line in f:
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a, b = line.strip().split()
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a, b = line.strip().split()
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x.append(float(a))
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x.append(float(a))
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@@ -4,8 +4,7 @@ import numpy as np
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analytical_func = lambda x: 1 - (1 - np.exp(-10))*x - np.exp(-10*x)
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analytical_func = lambda x: 1 - (1 - np.exp(-10))*x - np.exp(-10*x)
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def main():
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def main():
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fig, ax = plt.subplots()
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for i in range(7):
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for i in range(6):
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x = []
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x = []
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y = []
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y = []
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x.append(0.)
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x.append(0.)
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@@ -20,12 +19,12 @@ def main():
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x.append(1.)
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x.append(1.)
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y.append(0.)
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y.append(0.)
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ax.plot(x, y, label=f"n$_{{steps}} = 10^{i+1}$")
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plt.plot(x, y, label=f"n$_{{steps}} = 10^{i+1}$")
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x = np.linspace(0, 1, 1001)
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x = np.linspace(0, 1, 1001)
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ax.plot(x, analytical_func(x), label=f"u$_{{exact}}$")
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plt.plot(x, analytical_func(x), label=f"u$_{{exact}}$")
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ax.legend()
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plt.legend()
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fig.savefig("../latex/images/problem7.pdf")
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plt.savefig("../latex/images/problem7.pdf")
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if __name__ == "__main__":
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if __name__ == "__main__":
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main()
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main()
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@@ -4,10 +4,7 @@ import matplotlib.pyplot as plt
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# plt.rc('font', family='serif')
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# plt.rc('font', family='serif')
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def main():
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def main():
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fig_a, ax_a = plt.subplots()
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for i in range(7):
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fig_b, ax_b = plt.subplots()
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fig_c, ax_c = plt.subplots()
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for i in range(6):
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x = []
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x = []
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abs_err = []
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abs_err = []
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rel_err = []
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rel_err = []
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@@ -19,16 +16,25 @@ def main():
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abs_err.append(float(abs_err_i))
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abs_err.append(float(abs_err_i))
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rel_err.append(float(rel_err_i))
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rel_err.append(float(rel_err_i))
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ax_a.plot(x, abs_err, label=f"n$_{{steps}} = 10^{i+1}$")
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plt.figure(1)
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ax_b.plot(x, rel_err, label=f"n$_{{steps}} = 10^{i+1}$")
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plt.plot(x, abs_err, label=f"n$_{{steps}} = 10^{i+1}$")
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plt.figure(2)
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plt.plot(x, rel_err, label=f"n$_{{steps}} = 10^{i+1}$")
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ax_c.plot(i+1, max(rel_err), marker="o", markersize=10)
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plt.figure(3)
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plt.plot(i+1, max(rel_err), marker="o", markersize=10)
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ax_a.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
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plt.figure(1)
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ax_b.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
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plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
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fig_a.savefig("../latex/images/problem8_a.pdf", bbox_inches="tight")
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plt.figure(2)
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fig_b.savefig("../latex/images/problem8_b.pdf", bbox_inches="tight")
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plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
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fig_c.savefig("../latex/images/problem8_c.pdf", bbox_inches="tight")
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plt.figure(1)
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plt.savefig("../latex/images/problem8_a.pdf", bbox_inches="tight")
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plt.figure(2)
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plt.savefig("../latex/images/problem8_b.pdf", bbox_inches="tight")
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plt.figure(3)
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plt.savefig("../latex/images/problem8_c.pdf", bbox_inches="tight")
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if __name__ == "__main__":
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if __name__ == "__main__":
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main()
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main()
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@@ -33,7 +33,7 @@ void special_algorithm_main()
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int steps;
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int steps;
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double sub_sig, main_sig, sup_sig, step_size;
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double sub_sig, main_sig, sup_sig, step_size;
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for (int i = 0; i < 6; i++) {
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for (int i = 0; i < N_STEPS_EXP; i++) {
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steps = std::pow(10, i+1);
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steps = std::pow(10, i+1);
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step_size = 1./(double) steps;
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step_size = 1./(double) steps;
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build_g_vec(steps, g_vec);
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build_g_vec(steps, g_vec);
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@@ -1,5 +1,4 @@
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import matplotlib.pyplot as plt
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import matplotlib.pyplot as plt
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import numpy as np
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def main():
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def main():
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fig, ax = plt.subplots()
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fig, ax = plt.subplots()
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@@ -14,11 +13,11 @@ def main():
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gen_alg.append(float(gen_i))
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gen_alg.append(float(gen_i))
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spec_alg.append(float(spec_i))
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spec_alg.append(float(spec_i))
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ax.plot(x, gen_alg, label=f"General algorithm")
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plt.plot(x, gen_alg, label=f"General algorithm")
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ax.plot(x, spec_alg, label=f"Special algorithm")
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plt.plot(x, spec_alg, label=f"Special algorithm")
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ax.legend()
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plt.legend()
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fig.savefig("../latex/images/problem10.pdf")
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plt.savefig("../latex/images/problem10.pdf")
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if __name__ == "__main__":
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if __name__ == "__main__":
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main()
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main()
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