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163 lines
5.3 KiB
Python
163 lines
5.3 KiB
Python
import numpy
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import scipy
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import matplotlib.pyplot as pyplot
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import time
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numpy.random.seed(int(time.time()))
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PART_1_COEFFICIENTS = numpy.array([-0.1, 4.0, -0.1, 10.0], float)
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PART_1_X_LIMITS = [-10.0, 25.0]
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def plot_form(axis_handle, x_limit=None, title="", x_label="x", y_label="f(x)"):
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if x_limit is not None:
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axis_handle.set_xlim(x_limit)
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axis_handle.set_title(title)
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axis_handle.set_xlabel(x_label)
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axis_handle.set_ylabel(y_label)
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def part_1_polynomial(x_input):
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return numpy.polyval(PART_1_COEFFICIENTS, x_input)
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def part_2_plot():
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x_limit_min = PART_1_X_LIMITS[0]
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x_limit_max = PART_1_X_LIMITS[1]
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temp = numpy.linspace(x_limit_min, x_limit_max, 351, dtype=float)
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function_handle_1, axis_handle_1 = pyplot.subplots()
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axis_handle_1.plot(temp, part_1_polynomial(temp), "b-")
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plot_form(axis_handle_1, PART_1_X_LIMITS, "Original Polynomial")
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function_handle_1.savefig("figures/hw0_original_polynomial.pdf", bbox_inches="tight")
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def part_3():
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x_limit_min = PART_1_X_LIMITS[0]
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x_limit_max = PART_1_X_LIMITS[1]
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bin_width = (x_limit_max-x_limit_min) / 14.0
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x_bin = numpy.arange(x_limit_min, x_limit_max, bin_width, float)
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y_bin = part_1_polynomial(x_bin)
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function_handle, axis_handle = pyplot.subplots()
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axis_handle.bar(x_bin + bin_width/2.0, y_bin, width=bin_width, edgecolor="k")
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plot_form(axis_handle, PART_1_X_LIMITS, "Discretized Bins")
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function_handle.savefig("figures/hw0_discretized_bins.pdf", bbox_inches="tight")
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def part_4():
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x_limit_min = PART_1_X_LIMITS[0]
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x_limit_max = PART_1_X_LIMITS[1]
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bin_width = (x_limit_max - x_limit_min) / 14.0
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x_bin = numpy.arange(x_limit_min, x_limit_max, bin_width, float)
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y_bin = part_1_polynomial(x_bin)
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y_bin_normalized = y_bin / y_bin.sum()
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function_handle, axis_handle = pyplot.subplots()
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axis_handle.bar(x_bin + bin_width / 2.0, y_bin_normalized, width=bin_width, edgecolor="k")
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plot_form(axis_handle, PART_1_X_LIMITS, "Discretized Bins (Normalized) sum=%s" % y_bin_normalized.sum(), y_label="p(k)")
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function_handle.savefig("figures/hw0_discretized_bins_normalized.pdf", bbox_inches="tight")
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def part_5_1():
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num_samples = 500
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x_rand_values = numpy.arange(1, num_samples+1, 1, int)
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y_rand_values = numpy.random.random(num_samples)
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function_handle, axis_handle = pyplot.subplots()
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pyplot.plot(x_rand_values, y_rand_values, "k+")
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plot_form(axis_handle, x_limit=[1, num_samples], title="%s Samples, Uniformly Distributed" % num_samples)
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function_handle.savefig("figures/hw0_%s_random_samples.pdf" % num_samples, bbox_inches="tight")
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return (x_rand_values, y_rand_values)
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def part_5_2(vals):
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num_samples = 500
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x_limit_min = PART_1_X_LIMITS[0]
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x_limit_max = PART_1_X_LIMITS[1]
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bin_width = (x_limit_max - x_limit_min) / 14.0
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x_bin = numpy.arange(x_limit_min, x_limit_max, bin_width, float)
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x_rand_values = vals[0]
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y_rand_values = vals[1]
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y_random_scaled = y_rand_values * ((x_limit_max - x_limit_min) + x_limit_min)
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function_handle, axis_handle = pyplot.subplots()
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pyplot.plot(x_rand_values, y_random_scaled, "k+")
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for i in range(0, len(x_bin)):
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axis_handle.plot([1, num_samples], [x_bin[0], x_bin[1]])
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plot_form(axis_handle, [1, num_samples], "Random Samples Mapped to X Ranges Of Bins")
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function_handle.savefig("figures/hw0_random_bins_to_ranges.pdf", bbox_inches="tight")
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def part_5_3():
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y_count_incorrect = numpy.zeros(x_bin.shape)
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for i in range(0, len(y_rand_scaled)):
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for j in range(len(x_bin), 0, -1):
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if y_rand_scaled[i] > x_bin[j-1]:
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y_count_incorrect[j-1] += 1
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break
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function_handle, axis_handle = pyplot.subplots()
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pyplot.plot(x_bin+b_width/2.0, y_random_incorrect, "k+")
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plot_form(axis_handle, PART_1_X_LIMITS, "Samples per bin (incorrect)", bbox_inches="tight")
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#savefig "hw0_samples_per_bin_incorrect.pdf"
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def part_5_4():
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y_bin_cdf = y_bin_normalized.copy()
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i = 0
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while i < len(y_bin_cdf) - 1:
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i += 1
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y_bin_cdf[i] += y_bin_cdf[i-1]
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function_handle, axis_handle = pyplot.subplots()
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axis_handle.plot(x_rand, y_rand, "k+")
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for i in range(0, len(y_bin_cdf)):
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axis_handle.plot([1, num_samples], [y_bin_cdf[0], y_bin_cdf[1]])
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axis_handle.set_title("Dividing up the samples according to bin height")
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function_handle.savefig("hw0_correct_sample_division.pdf", bbox_inches="tight")
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y_count_correct = numpy.zeros(x_bin.shape)
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for i in range(0, len(y_rand)):
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for j in range(len_bin_cdf):
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if y_rand[i] < y_bin_cdf[j]:
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y_count_correct[j] += 1
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break
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function_handle_1, axis_handle_1 = pyplot.subplots()
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axis_handle_1.bar(x_bin + b_width/2.0, y_count_correct, width=b_width, edgecolor="k")
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plot_form(axis_handle_1, x_limit=PART_1_X_LIMITS, "Samples per bin (correct)", y_label="samples")
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function_handle.savefig("hw0_samples_per_bin_correct.pdf", bbox_inches="tight")
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def real_part_2():
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pass
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if __name__ == '__main__':
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# part_2_plot()
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# part_3()
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# part_4()
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# vals = part_5_1()
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# part_5_2(vals)
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real_part_2()
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pyplot.show()
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