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diff_int.py
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diff_int.py
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"""This file contains code used in "Think DSP",
by Allen B. Downey, available from greenteapress.com
Copyright 2014 Allen B. Downey
License: GNU GPLv3 http://www.gnu.org/licenses/gpl.html
"""
from __future__ import print_function, division
import numpy as np
import pandas as pd
import thinkdsp
import thinkplot
PI2 = np.pi * 2
GRAY = '0.7'
def plot_wave_and_spectrum(wave, root):
"""Makes a plot showing a wave and its spectrum.
wave: Wave object
root: string used to generate filenames
"""
thinkplot.preplot(cols=2)
wave.plot()
thinkplot.config(xlabel='Time (days)',
ylabel='Price ($)')
thinkplot.subplot(2)
spectrum = wave.make_spectrum()
print(spectrum.estimate_slope())
spectrum.plot()
thinkplot.config(xlabel='Frequency (1/days)',
ylabel='Amplitude',
xlim=[0, spectrum.fs[-1]],
xscale='log',
yscale='log')
thinkplot.save(root=root)
def plot_sawtooth_and_spectrum(wave, root):
"""Makes a plot showing a sawtoothwave and its spectrum.
"""
thinkplot.preplot(cols=2)
wave.plot()
thinkplot.config(xlabel='Time (s)')
thinkplot.subplot(2)
spectrum = wave.make_spectrum()
spectrum.plot()
thinkplot.config(xlabel='Frequency (Hz)',
#ylabel='Amplitude',
xlim=[0, spectrum.fs[-1]])
thinkplot.save(root)
def make_filter(window, wave):
"""Computes the filter that corresponds to a window.
window: NumPy array
wave: wave used to choose the length and framerate
returns: new Spectrum
"""
padded = thinkdsp.zero_pad(window, len(wave))
window_wave = thinkdsp.Wave(padded, framerate=wave.framerate)
window_spectrum = window_wave.make_spectrum()
return window_spectrum
def plot_filters(close):
"""Plots the filter that corresponds to diff, deriv, and integral.
"""
thinkplot.preplot(3, cols=2)
diff_window = np.array([1.0, -1.0])
diff_filter = make_filter(diff_window, close)
diff_filter.plot(label='diff')
deriv_filter = close.make_spectrum()
deriv_filter.hs = PI2 * 1j * deriv_filter.fs
deriv_filter.plot(label='derivative')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
loc='upper left')
thinkplot.subplot(2)
integ_filter = deriv_filter.copy()
integ_filter.hs = 1 / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral')
thinkplot.config(xlabel='Frequency (1/day)',
ylabel='Amplitude ratio',
yscale='log')
thinkplot.save('diff_int3')
def plot_diff_deriv(close):
change = thinkdsp.Wave(np.diff(close.ys), framerate=1)
deriv_spectrum = close.make_spectrum().differentiate()
deriv = deriv_spectrum.make_wave()
low, high = 0, 50
thinkplot.preplot(2)
thinkplot.plot(change.ys[low:high], label='diff')
thinkplot.plot(deriv.ys[low:high], label='derivative')
thinkplot.config(xlabel='Time (day)', ylabel='Price change ($)')
thinkplot.save('diff_int4')
def plot_integral(close):
deriv_spectrum = close.make_spectrum().differentiate()
integ_spectrum = deriv_spectrum.integrate()
print(integ_spectrum.hs[0])
integ_spectrum.hs[0] = 0
thinkplot.preplot(2)
integ_wave = integ_spectrum.make_wave()
close.plot(label='closing prices')
integ_wave.plot(label='integrated derivative')
thinkplot.config(xlabel='Time (day)', ylabel='Price ($)',
legend=True, loc='upper left')
thinkplot.save('diff_int5')
def plot_ratios(in_wave, out_wave):
# compare filters for cumsum and integration
diff_window = np.array([1.0, -1.0])
padded = thinkdsp.zero_pad(diff_window, len(in_wave))
diff_wave = thinkdsp.Wave(padded, framerate=in_wave.framerate)
diff_filter = diff_wave.make_spectrum()
cumsum_filter = diff_filter.copy()
cumsum_filter.hs = 1 / cumsum_filter.hs
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
integ_filter = cumsum_filter.copy()
integ_filter.hs = integ_filter.framerate / (PI2 * 1j * integ_filter.fs)
integ_filter.plot(label='integral filter')
thinkplot.config(xlim=[0, integ_filter.max_freq],
yscale='log', legend=True)
thinkplot.save('diff_int8')
# compare cumsum filter to actual ratios
cumsum_filter.plot(label='cumsum filter', color=GRAY, linewidth=7)
in_spectrum = in_wave.make_spectrum()
out_spectrum = out_wave.make_spectrum()
ratio_spectrum = out_spectrum.ratio(in_spectrum, thresh=1)
ratio_spectrum.plot(label='ratio', style='.', markersize=4)
thinkplot.config(xlabel='Frequency (Hz)',
ylabel='Amplitude ratio',
xlim=[0, integ_filter.max_freq],
yscale='log', legend=True)
thinkplot.save('diff_int9')
def plot_diff_filters(wave):
window1 = np.array([1, -1])
window2 = np.array([-1, 4, -3]) / 2.0
window3 = np.array([2, -9, 18, -11]) / 6.0
window4 = np.array([-3, 16, -36, 48, -25]) / 12.0
window5 = np.array([12, -75, 200, -300, 300, -137]) / 60.0
thinkplot.preplot(5)
for i, window in enumerate([window1, window2, window3, window4, window5]):
padded = thinkdsp.zero_pad(window, len(wave))
fft_window = np.fft.rfft(padded)
n = len(fft_window)
thinkplot.plot(abs(fft_window)[:], label=i+1)
thinkplot.show()
def main():
names = ['date', 'open', 'high', 'low', 'close', 'volume']
df = pd.read_csv('fb_1.csv', header=0, names=names, parse_dates=[0])
ys = df.close.values[::-1]
close = thinkdsp.Wave(ys, framerate=1)
plot_wave_and_spectrum(close, root='diff_int1')
change = thinkdsp.Wave(np.diff(ys), framerate=1)
plot_wave_and_spectrum(change, root='diff_int2')
plot_filters(close)
plot_diff_deriv(close)
signal = thinkdsp.SawtoothSignal(freq=50)
in_wave = signal.make_wave(duration=0.1, framerate=44100)
plot_sawtooth_and_spectrum(in_wave, 'diff_int6')
out_wave = in_wave.cumsum()
out_wave.unbias()
plot_sawtooth_and_spectrum(out_wave, 'diff_int7')
plot_integral(close)
plot_ratios(in_wave, out_wave)
if __name__ == '__main__':
main()