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‎NumPy/Code/ch10code/README‎

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NumPy Beginner's Guide
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Chapter 10 When Numpy is not enough: Scipy and beyond
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The example code requires SciPy and Matplotlib.
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Run the code examples with
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python <name of script>
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frequencies.py Demonstrates FFT transforms.
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gaussquad.py Demonstrates numerical integration.
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images.py Demonstrates image manipulation.
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optfit.py Demonstrates optimization.
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pair.py Demonstrates two samples statistical tests.
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scipyio.py Demonstrates Matlab/Octave interoperability.
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sincinterp.py Demonstrates interpolation.
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statistics.py Demonstrates statistical functionality.
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trend.py Demonstrates the detrend function.

‎NumPy/Code/ch10code/a.mat‎

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‎NumPy/Code/ch10code/algebra.py‎

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from matplotlib.finance import quotes_historical_yahoo
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from datetime import date
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import fftpack
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from scipy import signal
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from matplotlib.dates import DateFormatter, DayLocator, MonthLocator
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from scipy import optimize
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today = date.today()
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start = (today.year - 1, today.month, today.day)
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quotes = quotes_historical_yahoo("QQQ", start, today)
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quotes = np.array(quotes)
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dates = quotes.T[0]
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qqq = quotes.T[4]
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y = signal.detrend(qqq)
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alldays = DayLocator()
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months = MonthLocator()
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month_formatter = DateFormatter("%b %Y")
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fig = plt.figure()
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ax = fig.add_subplot(211)
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ax.xaxis.set_minor_locator(alldays)
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ax.xaxis.set_major_locator(months)
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ax.xaxis.set_major_formatter(month_formatter)
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amps = np.abs(fftpack.fftshift(fftpack.rfft(y)))
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amps[amps < amps.max()] = 0
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def residuals(p, y, x):
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A,k,theta = p
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err = y-A * np.sin(2* np.pi* k * x + theta)
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return err
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filtered = -fftpack.irfft(fftpack.ifftshift(amps))
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N = len(qqq)
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f = np.linspace(-N/2, N/2, N)
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p0 = [filtered.max(), f[amps.argmax()]/N, np.pi/3]
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plsq = optimize.leastsq(residuals, p0, args=(filtered, dates))
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p = plsq[0]
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print p
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plt.plot(dates, y, 'o', label="detrended")
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plt.plot(dates, filtered, label="filtered")
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plt.plot(dates, p[0] * np.sin(2 * np.pi * dates * p[1] + p[2]), '^', label="fit")
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fig.autofmt_xdate()
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plt.legend()
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ax2 = fig.add_subplot(212)
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plt.plot(f, amps, label="transformed")
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plt.legend()
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plt.show()

‎NumPy/Code/ch10code/frequencies.py‎

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from matplotlib.finance import quotes_historical_yahoo
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from datetime import date
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import numpy as np
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from scipy import signal
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import matplotlib.pyplot as plt
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from scipy import fftpack
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from matplotlib.dates import DateFormatter
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from matplotlib.dates import DayLocator
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from matplotlib.dates import MonthLocator
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today = date.today()
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start = (today.year - 1, today.month, today.day)
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quotes = quotes_historical_yahoo("QQQ", start, today)
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quotes = np.array(quotes)
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dates = quotes.T[0]
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qqq = quotes.T[4]
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y = signal.detrend(qqq)
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alldays = DayLocator()
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months = MonthLocator()
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month_formatter = DateFormatter("%b %Y")
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fig = plt.figure()
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fig.subplots_adjust(hspace=.3)
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ax = fig.add_subplot(211)
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ax.xaxis.set_minor_locator(alldays)
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ax.xaxis.set_major_locator(months)
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ax.xaxis.set_major_formatter(month_formatter)
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# make font size bigger
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ax.tick_params(axis='both', which='major', labelsize='x-large')
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amps = np.abs(fftpack.fftshift(fftpack.rfft(y)))
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amps[amps < 0.1 * amps.max()] = 0
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plt.plot(dates, y, 'o', label="detrended")
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plt.plot(dates, -fftpack.irfft(fftpack.ifftshift(amps)), label="filtered")
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fig.autofmt_xdate()
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plt.legend(prop={'size':'x-large'})
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ax2 = fig.add_subplot(212)
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ax2.tick_params(axis='both', which='major', labelsize='x-large')
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N = len(qqq)
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plt.plot(np.linspace(-N/2, N/2, N), amps, label="transformed")
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plt.legend(prop={'size':'x-large'})
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plt.show()

‎NumPy/Code/ch10code/gaussquad.py‎

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from scipy import integrate
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import numpy as np
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print "Gaussian integral", np.sqrt(np.pi), integrate.quad(lambda x: np.exp(-x**2), -np.inf, np.inf)

‎NumPy/Code/ch10code/images.py‎

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from scipy import misc
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import ndimage
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image = misc.lena().astype(np.float32)
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plt.subplot(221)
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plt.title("Original Image")
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img = plt.imshow(image, cmap=plt.cm.gray)
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plt.axis("off")
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plt.subplot(222)
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plt.title("Median Filter")
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filtered = ndimage.median_filter(image, size=(42,42))
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plt.imshow(filtered, cmap=plt.cm.gray)
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plt.axis("off")
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plt.subplot(223)
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plt.title("Rotated")
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rotated = ndimage.rotate(image, 90)
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plt.imshow(rotated, cmap=plt.cm.gray)
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plt.axis("off")
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plt.subplot(224)
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plt.title("Prewitt Filter")
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filtered = ndimage.prewitt(image)
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plt.imshow(filtered, cmap=plt.cm.gray)
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plt.axis("off")
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plt.show()

‎NumPy/Code/ch10code/optfit.py‎

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from matplotlib.finance import quotes_historical_yahoo
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy import fftpack
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from scipy import signal
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from matplotlib.dates import DateFormatter
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from matplotlib.dates import DayLocator
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from matplotlib.dates import MonthLocator
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from scipy import optimize
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start = (2010, 7, 25)
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end = (2011, 7, 25)
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quotes = quotes_historical_yahoo("QQQ", start, end)
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quotes = np.array(quotes)
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dates = quotes.T[0]
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qqq = quotes.T[4]
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y = signal.detrend(qqq)
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alldays = DayLocator()
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months = MonthLocator()
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month_formatter = DateFormatter("%b %Y")
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fig = plt.figure()
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fig.subplots_adjust(hspace=.3)
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ax = fig.add_subplot(211)
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ax.xaxis.set_minor_locator(alldays)
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ax.xaxis.set_major_locator(months)
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ax.xaxis.set_major_formatter(month_formatter)
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ax.tick_params(axis='both', which='major', labelsize='x-large')
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amps = np.abs(fftpack.fftshift(fftpack.rfft(y)))
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amps[amps < amps.max()] = 0
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def residuals(p, y, x):
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A,k,theta,b = p
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err = y-A * np.sin(2* np.pi* k * x + theta) + b
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return err
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filtered = -fftpack.irfft(fftpack.ifftshift(amps))
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N = len(qqq)
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f = np.linspace(-N/2, N/2, N)
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p0 = [filtered.max(), f[amps.argmax()]/(2*N), 0, 0]
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print "P0", p0
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plsq = optimize.leastsq(residuals, p0, args=(filtered, dates))
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p = plsq[0]
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print "P", p
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plt.plot(dates, y, 'o', label="detrended")
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plt.plot(dates, filtered, label="filtered")
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plt.plot(dates, p[0] * np.sin(2 * np.pi * dates * p[1] + p[2]) + p[3], '^', label="fit")
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fig.autofmt_xdate()
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plt.legend(prop={'size':'x-large'})
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ax2 = fig.add_subplot(212)
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ax2.tick_params(axis='both', which='major', labelsize='x-large')
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plt.plot(f, amps, label="transformed")
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plt.legend(prop={'size':'x-large'})
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plt.show()

‎NumPy/Code/ch10code/pair.py‎

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from matplotlib.finance import quotes_historical_yahoo
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from datetime import date
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import numpy as np
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from scipy import stats
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from statsmodels.stats.stattools import jarque_bera
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import matplotlib.pyplot as plt
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def get_close(symbol):
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today = date.today()
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start = (today.year - 1, today.month, today.day)
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quotes = quotes_historical_yahoo(symbol, start, today)
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quotes = np.array(quotes)
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return quotes.T[4]
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spy = np.diff(np.log(get_close("SPY")))
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dia = np.diff(np.log(get_close("DIA")))
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print "Means comparison", stats.ttest_ind(spy, dia)
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print "Kolmogorov smirnov test", stats.ks_2samp(spy, dia)
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print "Jarque Bera test", jarque_bera(spy - dia)[1]
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plt.hist(spy, histtype="step", lw=1, label="SPY")
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plt.hist(dia, histtype="step", lw=2, label="DIA")
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plt.hist(spy - dia, histtype="step", lw=3, label="Delta")
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plt.legend()
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plt.show()

‎NumPy/Code/ch10code/repeat_audio.py‎

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from scipy.io import wavfile
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import matplotlib.pyplot as plt
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import urllib2
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import numpy as np
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import sys
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response = urllib2.urlopen('http://www.thesoundarchive.com/austinpowers/smashingbaby.wav')
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print response.info()
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WAV_FILE = 'smashingbaby.wav'
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filehandle = open(WAV_FILE, 'w')
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filehandle.write(response.read())
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filehandle.close()
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sample_rate, data = wavfile.read(WAV_FILE)
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print "Data type", data.dtype, "Shape", data.shape
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plt.subplot(2, 1, 1)
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plt.title("Original")
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plt.plot(data)
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plt.subplot(2, 1, 2)
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# Repeat the audio fragment
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repeated = np.tile(data, int(sys.argv[1]))
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# Plot the audio data
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plt.title("Repeated")
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plt.plot(repeated)
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wavfile.write("repeated_yababy.wav",
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sample_rate, repeated)
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plt.show()

‎NumPy/Code/ch10code/scipyio.py‎

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import numpy as np
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from scipy import io
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a = np.arange(7)
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io.savemat("a.mat", {"array": a})

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