Skip to content

Commit e48d0a3

Browse files
pvpv
authored
Merge pull request #40 from cassiasamp/edit-RadialBasisFunctions
Fix up notebook RadialBasisFunctions.ipynb
2 parents edfa8f3 + 6aa0788 commit e48d0a3

File tree

1 file changed

+130
-118
lines changed

1 file changed

+130
-118
lines changed

‎ipython/RadialBasisFunctions.ipynb‎

Lines changed: 130 additions & 118 deletions
Original file line numberDiff line numberDiff line change
@@ -1,121 +1,133 @@
11
{
2-
"metadata": {},
3-
"nbformat": 3,
4-
"nbformat_minor": 0,
5-
"worksheets": [
2+
"cells": [
63
{
7-
"cells": [
8-
{
9-
"cell_type": "markdown",
10-
"metadata": {},
11-
"source": [
12-
"Using radial basis functions for smoothing/interpolation\n",
13-
"========================================================\n",
14-
"\n",
15-
"Radial basis functions can be used for smoothing/interpolating scattered\n",
16-
"data in n-dimensions, but should be used with caution for extrapolation\n",
17-
"outside of the observed data range.\n",
18-
"\n",
19-
"1d example\n",
20-
"----------\n",
21-
"\n",
22-
"This example compares the usage of the Rbf and UnivariateSpline classes\n",
23-
"from the scipy.interpolate module."
24-
]
25-
},
26-
{
27-
"cell_type": "code",
28-
"collapsed": false,
29-
"input": [
30-
"import numpy as np\n",
31-
"from scipy.interpolate import Rbf, InterpolatedUnivariateSpline\n",
32-
"\n",
33-
"import matplotlib\n",
34-
"matplotlib.use('Agg')\n",
35-
"import matplotlib.pyplot as plt\n",
36-
"\n",
37-
"# setup data\n",
38-
"x = np.linspace(0, 10, 9)\n",
39-
"y = np.sin(x)\n",
40-
"xi = np.linspace(0, 10, 101)\n",
41-
"\n",
42-
"# use fitpack2 method\n",
43-
"ius = InterpolatedUnivariateSpline(x, y)\n",
44-
"yi = ius(xi)\n",
45-
"\n",
46-
"plt.subplot(2, 1, 1)\n",
47-
"plt.plot(x, y, 'bo')\n",
48-
"plt.plot(xi, yi, 'g')\n",
49-
"plt.plot(xi, np.sin(xi), 'r')\n",
50-
"plt.title('Interpolation using univariate spline')\n",
51-
"\n",
52-
"# use RBF method\n",
53-
"rbf = Rbf(x, y)\n",
54-
"fi = rbf(xi)\n",
55-
"\n",
56-
"plt.subplot(2, 1, 2)\n",
57-
"plt.plot(x, y, 'bo')\n",
58-
"plt.plot(xi, yi, 'g')\n",
59-
"plt.plot(xi, np.sin(xi), 'r')\n",
60-
"plt.title('Interpolation using RBF - multiquadrics')\n",
61-
"plt.savefig('rbf1d.png')"
62-
],
63-
"language": "python",
64-
"metadata": {},
65-
"outputs": []
66-
},
67-
{
68-
"cell_type": "markdown",
69-
"metadata": {},
70-
"source": [
71-
"![](files/attachments/RadialBasisFunctions/rbf1dnew.png)\n",
72-
"\n",
73-
"2d example\n",
74-
"==========\n",
75-
"\n",
76-
"This example shows how to interpolate scattered 2d data."
77-
]
78-
},
79-
{
80-
"cell_type": "code",
81-
"collapsed": false,
82-
"input": [
83-
"import numpy as np\n",
84-
"from scipy.interpolate import Rbf\n",
85-
"\n",
86-
"import matplotlib\n",
87-
"matplotlib.use('Agg')\n",
88-
"import matplotlib.pyplot as plt\n",
89-
"from matplotlib import cm\n",
90-
"\n",
91-
"# 2-d tests - setup scattered data\n",
92-
"x = np.random.rand(100)*4.0-2.0\n",
93-
"y = np.random.rand(100)*4.0-2.0\n",
94-
"z = x*np.exp(-x**2-y**2)\n",
95-
"ti = np.linspace(-2.0, 2.0, 100)\n",
96-
"XI, YI = np.meshgrid(ti, ti)\n",
97-
"\n",
98-
"# use RBF\n",
99-
"rbf = Rbf(x, y, z, epsilon=2)\n",
100-
"ZI = rbf(XI, YI)\n",
101-
"\n",
102-
"# plot the result\n",
103-
"n = plt.normalize(-2., 2.)\n",
104-
"plt.subplot(1, 1, 1)\n",
105-
"plt.pcolor(XI, YI, ZI, cmap=cm.jet)\n",
106-
"plt.scatter(x, y, 100, z, cmap=cm.jet)\n",
107-
"plt.title('RBF interpolation - multiquadrics')\n",
108-
"plt.xlim(-2, 2)\n",
109-
"plt.ylim(-2, 2)\n",
110-
"plt.colorbar()\n",
111-
"plt.savefig('rbf2d.png')"
112-
],
113-
"language": "python",
114-
"metadata": {},
115-
"outputs": []
116-
}
117-
],
118-
"metadata": {}
4+
"cell_type": "markdown",
5+
"metadata": {},
6+
"source": [
7+
"Using radial basis functions for smoothing/interpolation\n",
8+
"========================================================\n",
9+
"\n",
10+
"Radial basis functions can be used for smoothing/interpolating scattered\n",
11+
"data in n-dimensions, but should be used with caution for extrapolation\n",
12+
"outside of the observed data range.\n",
13+
"\n",
14+
"1d example\n",
15+
"----------\n",
16+
"\n",
17+
"This example compares the usage of the Rbf and UnivariateSpline classes\n",
18+
"from the scipy.interpolate module."
19+
]
20+
},
21+
{
22+
"cell_type": "code",
23+
"execution_count": null,
24+
"metadata": {},
25+
"outputs": [],
26+
"source": [
27+
"import numpy as np\n",
28+
"from scipy.interpolate import Rbf, InterpolatedUnivariateSpline\n",
29+
"\n",
30+
"import matplotlib\n",
31+
"matplotlib.use('Agg')\n",
32+
"import matplotlib.pyplot as plt\n",
33+
"\n",
34+
"# setup data\n",
35+
"x = np.linspace(0, 10, 9)\n",
36+
"y = np.sin(x)\n",
37+
"xi = np.linspace(0, 10, 101)\n",
38+
"\n",
39+
"# use fitpack2 method\n",
40+
"ius = InterpolatedUnivariateSpline(x, y)\n",
41+
"yi = ius(xi)\n",
42+
"\n",
43+
"plt.subplot(2, 1, 1)\n",
44+
"plt.plot(x, y, 'bo')\n",
45+
"plt.plot(xi, yi, 'g')\n",
46+
"plt.plot(xi, np.sin(xi), 'r')\n",
47+
"plt.title('Interpolation using univariate spline')\n",
48+
"\n",
49+
"# use RBF method\n",
50+
"rbf = Rbf(x, y)\n",
51+
"fi = rbf(xi)\n",
52+
"\n",
53+
"plt.subplot(2, 1, 2)\n",
54+
"plt.plot(x, y, 'bo')\n",
55+
"plt.plot(xi, fi, 'g')\n",
56+
"plt.plot(xi, np.sin(xi), 'r')\n",
57+
"plt.title('Interpolation using RBF - multiquadrics')\n",
58+
"plt.tight_layout()\n",
59+
"plt.savefig('rbf1d.png')"
60+
]
61+
},
62+
{
63+
"cell_type": "markdown",
64+
"metadata": {},
65+
"source": [
66+
"![](files/attachments/RadialBasisFunctions/rbf1dnew.png)\n",
67+
"\n",
68+
"2d example\n",
69+
"==========\n",
70+
"\n",
71+
"This example shows how to interpolate scattered 2d data."
72+
]
73+
},
74+
{
75+
"cell_type": "code",
76+
"execution_count": null,
77+
"metadata": {},
78+
"outputs": [],
79+
"source": [
80+
"import numpy as np\n",
81+
"from scipy.interpolate import Rbf\n",
82+
"\n",
83+
"import matplotlib\n",
84+
"matplotlib.use('Agg')\n",
85+
"import matplotlib.pyplot as plt\n",
86+
"from matplotlib import cm\n",
87+
"\n",
88+
"# 2-d tests - setup scattered data\n",
89+
"x = np.random.rand(100)*4.0-2.0\n",
90+
"y = np.random.rand(100)*4.0-2.0\n",
91+
"z = x*np.exp(-x**2-y**2)\n",
92+
"ti = np.linspace(-2.0, 2.0, 100)\n",
93+
"XI, YI = np.meshgrid(ti, ti)\n",
94+
"\n",
95+
"# use RBF\n",
96+
"rbf = Rbf(x, y, z, epsilon=2)\n",
97+
"ZI = rbf(XI, YI)\n",
98+
"\n",
99+
"# plot the result\n",
100+
"n = plt.normalize(-2., 2.)\n",
101+
"plt.subplot(1, 1, 1)\n",
102+
"plt.pcolor(XI, YI, ZI, cmap=cm.jet)\n",
103+
"plt.scatter(x, y, 100, z, cmap=cm.jet)\n",
104+
"plt.title('RBF interpolation - multiquadrics')\n",
105+
"plt.xlim(-2, 2)\n",
106+
"plt.ylim(-2, 2)\n",
107+
"plt.colorbar()\n",
108+
"plt.savefig('rbf2d.png')"
109+
]
110+
}
111+
],
112+
"metadata": {
113+
"kernelspec": {
114+
"display_name": "Python 3",
115+
"language": "python",
116+
"name": "python3"
117+
},
118+
"language_info": {
119+
"codemirror_mode": {
120+
"name": "ipython",
121+
"version": 3
122+
},
123+
"file_extension": ".py",
124+
"mimetype": "text/x-python",
125+
"name": "python",
126+
"nbconvert_exporter": "python",
127+
"pygments_lexer": "ipython3",
128+
"version": "3.8.2"
119129
}
120-
]
121-
}
130+
},
131+
"nbformat": 4,
132+
"nbformat_minor": 1
133+
}

0 commit comments

Comments
 (0)