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add scipy learning
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‎scipy/001_special.py‎

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#!/usr/bin/env python
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#-*- coding:utf-8 -*-
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# FileName: 001_special.py
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#
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# Description:
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#
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# Version: 1.0
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# Created: 2018-06-13 09:13:12
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# Last Modified: 2018-06-13 09:26:10
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# Revision: none
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# Compiler: gcc
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#
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# Author: zt ()
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# Organization:
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import matplotlib.pyplot as plt
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from numpy import *
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from scipy.special import jn, yn, jn_zeros, yn_zeros
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n = 0
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x = 0.0
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print("J_%d(%f)=%f" % (n, x, jn(n, x)))
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x = 1.0
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print("Y_%d(%f)=%f" % (n, x, yn(n, x)))
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x = linspace(0, 10, 100)
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fig, ax = plt.subplots()
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for n in xrange(4):
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ax.plot(x, jn(n, x), label=r"$J_%d(x)$" % n)
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ax.legend()
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plt.show()
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n = 0
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m = 4
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jn_zeros(n, m)

‎scipy/002_integrate.py‎

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#!/usr/bin/env python
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#-*- coding:utf-8 -*-
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# FileName: 002_integrate.py
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#
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# Description:
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#
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# Version: 1.0
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# Created: 2018-06-13 09:26:33
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# Last Modified: 2018-06-13 10:22:12
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# Revision: none
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# Compiler: gcc
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#
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# Author: zt ()
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# Organization:
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from numpy import *
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from scipy.integrate import quad, dblquad, tplquad
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from scipy.special import jn, yn, jn_zeros, yn_zeros
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def f(x):
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return x
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x_lower = 0
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x_upper = 1
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val, abserr = quad(f, x_lower, x_upper)
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print("integral value=", val, ",absolute error=", abserr)
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def integrand(x, n):
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return jn(n, x)
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x_lower = 0
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x_upper = 10
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val, abserr = quad(integrand, x_lower, x_upper, args=(3, ))
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print("integral value=", val, ",absolute error=", abserr)
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val, abserr = quad(lambda x: exp(-x**2), -Inf, Inf)
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print("integral value=", val, ",absolute error=", abserr)
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analytical = sqrt(pi)
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print("analytical=", analytical)
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def integrand(x, y):
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return exp(-x**2 - y**2)
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x_lower = 0
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x_upper = 10
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y_lower = 0
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y_upper = 10
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val, abserr = dblquad(integrand, x_lower, x_upper, lambda x: y_lower,
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lambda x: y_upper)
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print("integral value=", val, ",absolute error=", abserr)

‎scipy/003_02_ode.py‎

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#!/usr/bin/env python
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#-*- coding:utf-8 -*-
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# FileName: 003_02_ode.py
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#
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# Description:
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#
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# Version: 1.0
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# Created: 2018-06-13 10:22:44
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# Last Modified: 2018-06-13 10:30:22
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# Revision: none
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# Compiler: gcc
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#
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# Author: zt ()
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# Organization:
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import matplotlib.pyplot as plt
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from numpy import *
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from scipy.integrate import quad, dblquad, tplquad
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from scipy.integrate import odeint, ode
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from scipy.special import jn, yn, jn_zeros, yn_zeros
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def dy(y, t, zeta, w0):
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x, p = y[0], y[1]
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dx = p
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dp = -2 * zeta * w0 * p - w0**2 * x
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return [dx, dp]
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y0 = [1.0, 0.0]
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t = linspace(0, 10, 1000)
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w0 = 2 * pi * 1.0
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y1 = odeint(dy, y0, t, args=(0.0, w0))
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y2 = odeint(dy, y0, t, args=(0.2, w0))
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y3 = odeint(dy, y0, t, args=(1.0, w0))
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y4 = odeint(dy, y0, t, args=(5.0, w0))
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fig, ax = plt.subplots()
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ax.plot(t, y1[:, 0], 'k', label="undamped", linewidth=0.25)
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ax.plot(t, y2[:, 0], 'r', label="under damped")
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ax.plot(t, y3[:, 0], 'g', label=r"critical damping")
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ax.plot(t, y4[:, 0], 'b', label="over undamped")
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ax.legend()
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plt.show()

‎scipy/004_fftpack.py‎

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#!/usr/bin/env python
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#-*- coding:utf-8 -*-
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# FileName: 004_fftpack.py
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#
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# Description:
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#
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# Version: 1.0
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# Created: 2018-06-13 10:31:32
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# Last Modified: 2018-06-13 10:44:29
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# Revision: none
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# Compiler: gcc
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#
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# Author: zt ()
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# Organization:
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import matplotlib.pyplot as plt
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from numpy import *
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from scipy.integrate import quad, dblquad, tplquad
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from scipy.integrate import odeint, ode
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from scipy.special import jn, yn, jn_zeros, yn_zeros
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from numpy.fft import fftfreq
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from scipy.fftpack import *
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def dy(y, t, zeta, w0):
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x, p = y[0], y[1]
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dx = p
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dp = -2 * zeta * w0 * p - w0**2 * x
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return [dx, dp]
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y0 = [1.0, 0.0]
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t = linspace(0, 10, 1000)
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w0 = 2 * pi * 1.0
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y1 = odeint(dy, y0, t, args=(0.0, w0))
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y2 = odeint(dy, y0, t, args=(0.2, w0))
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y3 = odeint(dy, y0, t, args=(1.0, w0))
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y4 = odeint(dy, y0, t, args=(5.0, w0))
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# fig, ax = plt.subplots()
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# ax.plot(t, y1[:, 0], 'k', label="undamped", linewidth=0.25)
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# ax.plot(t, y2[:, 0], 'r', label="under damped")
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# ax.plot(t, y3[:, 0], 'g', label=r"critical damping")
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# ax.plot(t, y4[:, 0], 'b', label="over undamped")
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# ax.legend()
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# plt.show()
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N = len(t)
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dt = t[1] - t[0]
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# print(y2)
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F = fft(y2[:, 0])
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W = fftfreq(N, dt)
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fig, ax = plt.subplots(figsize=(9, 3))
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ax.plot(W, abs(F))
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indices = where(W > 0)
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W_pos = W[indices]
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F_pos = F[indices]
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fig, ax = plt.subplots(figsize=(9, 3))
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ax.plot(W_pos, abs(F_pos))
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ax.set_xlim(0, 5)
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plt.show()

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