mirror of
https://github.com/apachecn/ailearning.git
synced 2026-05-04 14:23:27 +08:00
2020-10-19 21:08:55
This commit is contained in:
wizardforcel
@@ -4,7 +4,7 @@
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In [1]:
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```
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```py
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import numpy as np
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import matplotlib as mpl
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import matplotlib.pyplot as plt
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@@ -17,7 +17,7 @@ import matplotlib.pyplot as plt
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In [2]:
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```
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```py
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from numpy import polyfit, poly1d
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```
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@@ -26,7 +26,7 @@ from numpy import polyfit, poly1d
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In [3]:
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```
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```py
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x = np.linspace(-5, 5, 100)
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y = 4 * x + 1.5
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noise_y = y + np.random.randn(y.shape[-1]) * 2.5
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@@ -37,7 +37,7 @@ noise_y = y + np.random.randn(y.shape[-1]) * 2.5
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In [4]:
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```
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```py
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%matplotlib inline
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p = plt.plot(x, noise_y, 'rx')
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@@ -211,13 +211,13 @@ DpwbdZAmKImIJEytUzEiIlJhCuwiIgmjwC4ikjAK7CIiCaPALiKSMArsIiIJo8AuIpIwCuwiIgnz
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In [5]:
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```
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```py
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coeff = polyfit(x, noise_y, 1)
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print coeff
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```
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```
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```py
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[ 3.93921315 1.59379469]
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```
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@@ -228,7 +228,7 @@ print coeff
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In [6]:
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```
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```py
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p = plt.plot(x, noise_y, 'rx')
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p = plt.plot(x, coeff[0] * x + coeff[1], 'k-')
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p = plt.plot(x, y, 'b--')
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@@ -434,7 +434,7 @@ rkJggg==
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In [7]:
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```
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```py
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f = poly1d(coeff)
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p = plt.plot(x, noise_y, 'rx')
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p = plt.plot(x, f(x))
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@@ -623,14 +623,14 @@ TbkUxv9z1wIPRzoeHwCXxNtIA5REREIm36kYERHJMgV2EZGQUWAXEQkZBXYRkZBRYBcRCRkFdhGR
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kFFgFxEJGQV2EZGQ+X/DyfQNy7jRVwAAAABJRU5ErkJggg==
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)In [8]:
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```
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```py
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f
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```
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Out[8]:
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```
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```py
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poly1d([ 3.93921315, 1.59379469])
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```
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@@ -638,12 +638,12 @@ poly1d([ 3.93921315, 1.59379469])
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In [9]:
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```
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```py
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print f
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```
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```
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```py
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3.939 x + 1.594
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@@ -653,12 +653,12 @@ print f
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In [10]:
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```
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```py
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print f + 2 * f ** 2
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```
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```
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```py
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2
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31.03 x + 29.05 x + 6.674
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@@ -670,7 +670,7 @@ print f + 2 * f ** 2
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In [11]:
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```
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```py
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x = np.linspace(-np.pi,np.pi,100)
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y = np.sin(x)
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@@ -680,7 +680,7 @@ y = np.sin(x)
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In [12]:
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```
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```py
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y1 = poly1d(polyfit(x,y,1))
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y3 = poly1d(polyfit(x,y,3))
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y5 = poly1d(polyfit(x,y,5))
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@@ -691,7 +691,7 @@ y9 = poly1d(polyfit(x,y,9))
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```
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```py
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x = np.linspace(-3 * np.pi,3 * np.pi,100)
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p = plt.plot(x, np.sin(x), 'k')
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@@ -1137,7 +1137,7 @@ iBJ3hUKh0CFK3BUKhUKH/AdKQZTK2jwwogAAAABJRU5ErkJggg==
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In [14]:
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```
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```py
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from scipy.linalg import lstsq
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from scipy.stats import linregress
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@@ -1145,7 +1145,7 @@ from scipy.stats import linregress
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In [15]:
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```
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```py
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x = np.linspace(0,5,100)
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y = 0.5 * x + np.random.randn(x.shape[-1]) * 0.35
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@@ -1155,7 +1155,7 @@ plt.plot(x,y,'x')
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Out[15]:
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```
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```py
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[<matplotlib.lines.Line2D at 0xbc98518>]
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```
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@@ -1309,7 +1309,7 @@ $$\left[ \begin{matrix} x_0^{N-1} & \dots & x_0 & 1 \\\ x_1^{N-1} & \dots & x_1
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In [16]:
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```
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```py
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X = np.hstack((x[:,np.newaxis], np.ones((x.shape[-1],1))))
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X[1:5]
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@@ -1317,7 +1317,7 @@ X[1:5]
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Out[16]:
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```
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```py
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array([[ 0.05050505, 1\. ],
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[ 0.1010101 , 1\. ],
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[ 0.15151515, 1\. ],
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@@ -1328,7 +1328,7 @@ array([[ 0.05050505, 1\. ],
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In [17]:
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```
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```py
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C, resid, rank, s = lstsq(X, y)
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C, resid, rank, s
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@@ -1336,7 +1336,7 @@ C, resid, rank, s
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Out[17]:
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```
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```py
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(array([ 0.50432002, 0.0415695 ]),
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12.182942535066523,
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2,
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@@ -1347,7 +1347,7 @@ Out[17]:
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In [18]:
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```
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```py
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p = plt.plot(x, y, 'rx')
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p = plt.plot(x, C[0] * x + C[1], 'k--')
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print "sum squared residual = {:.3f}".format(resid)
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@@ -1356,7 +1356,7 @@ print "singular values of X = {}".format(s)
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```
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```
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```py
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sum squared residual = 12.183
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rank of the X matrix = 2
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singular values of X = [ 30.23732043 4.82146667]
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@@ -1545,7 +1545,7 @@ TkSuQmCC
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In [19]:
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```
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```py
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slope, intercept, r_value, p_value, stderr = linregress(x, y)
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slope, intercept
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@@ -1553,13 +1553,13 @@ slope, intercept
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Out[19]:
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```
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```py
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(0.50432001884393252, 0.041569499438028901)
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```
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In [20]:
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```
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```py
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p = plt.plot(x, y, 'rx')
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p = plt.plot(x, slope * x + intercept, 'k--')
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print "R-value = {:.3f}".format(r_value)
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@@ -1568,7 +1568,7 @@ print "Root mean squared error of the fit = {:.3f}".format(np.sqrt(stderr))
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```
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```
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```py
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R-value = 0.903
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p-value (probability there is no correlation) = 8.225e-38
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Root mean squared error of the fit = 0.156
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@@ -1756,7 +1756,7 @@ gzwRkY8xyBMR+RiDPBGRjzHIExH5GIM8EZGPMcgTEfnY/we7I5NFwW+W8wAAAABJRU5ErkJggg==
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In [21]:
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```
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```py
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from scipy.optimize import leastsq
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```
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@@ -1765,7 +1765,7 @@ from scipy.optimize import leastsq
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In [22]:
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```
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```py
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def function(x, a , b, f, phi):
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"""a function of x with four parameters"""
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result = a * np.exp(-b * np.sin(f * x + phi))
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@@ -1777,7 +1777,7 @@ def function(x, a , b, f, phi):
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In [23]:
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```
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```py
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x = np.linspace(0, 2 * np.pi, 50)
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actual_parameters = [3, 2, 1.25, np.pi / 4]
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y = function(x, *actual_parameters)
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@@ -1924,7 +1924,7 @@ LSKSMApuEZGEUXCLiCSMgltEJGH+Px9Ir5f410BLAAAAAElFTkSuQmCC
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In [24]:
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```
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```py
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from scipy.stats import norm
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y_noisy = y + 0.8 * norm.rvs(size=len(x))
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p = plt.plot(x, y, 'k-')
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@@ -2124,7 +2124,7 @@ AABJRU5ErkJggg==
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In [25]:
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```
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```py
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def f_err(p, y, x):
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return y - function(x, *p)
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@@ -2134,7 +2134,7 @@ def f_err(p, y, x):
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In [26]:
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```
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```py
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c, ret_val = leastsq(f_err, [1, 1, 1, 1], args=(y_noisy, x))
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c, ret_val
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@@ -2142,7 +2142,7 @@ c, ret_val
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Out[26]:
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```
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```py
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(array([ 3.03199715, 1.97689384, 1.30083191, 0.6393337 ]), 1)
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```
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@@ -2150,7 +2150,7 @@ Out[26]:
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In [27]:
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```
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```py
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p = plt.plot(x, y_noisy, 'rx')
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p = plt.plot(x, function(x, *c), 'k--')
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@@ -2317,7 +2317,7 @@ A5MAAAAASUVORK5CYII=
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In [28]:
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```
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```py
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from scipy.optimize import curve_fit
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```
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@@ -2326,21 +2326,21 @@ from scipy.optimize import curve_fit
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In [29]:
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```
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```py
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p_est, err_est = curve_fit(function, x, y_noisy)
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```
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In [30]:
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```
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```py
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print p_est
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p = plt.plot(x, y_noisy, "rx")
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p = plt.plot(x, function(x, *p_est), "k--")
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```
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```
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```py
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[ 3.03199711 1.97689385 1.3008319 0.63933373]
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```
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@@ -2504,12 +2504,12 @@ A5MAAAAASUVORK5CYII=
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In [31]:
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```
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```py
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print err_est
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```
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```
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```py
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[[ 0.08483704 -0.02782318 0.00967093 -0.03029038]
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[-0.02782318 0.00933216 -0.00305158 0.00955794]
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[ 0.00967093 -0.00305158 0.0014972 -0.00468919]
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@@ -2521,14 +2521,14 @@ print err_est
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In [32]:
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```
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```py
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print "normalized relative errors for each parameter"
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print " a\t b\t f\tphi"
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print np.sqrt(err_est.diagonal()) / p_est
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```
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```
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```py
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normalized relative errors for each parameter
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a b f phi
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[ 0.09606473 0.0488661 0.02974528 0.19056043]
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