1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
|
#!/usr/bin/env python
# Created by Pearu Peterson, June 2003
""" Test functions for interpolate.fitpack2 module
"""
__usage__ = """
Build interpolate:
python setup_interpolate.py build
Run tests if scipy is installed:
python -c 'import scipy;scipy.interpolate.test(<level>)'
Run tests if interpolate is not installed:
python tests/test_fitpack.py [<level>]
"""
#import libwadpy
from numpy.testing import assert_equal, assert_almost_equal, assert_array_equal, \
assert_array_almost_equal, assert_allclose, TestCase, run_module_suite
from numpy import array, diff, shape
from scipy.interpolate.fitpack2 import UnivariateSpline, LSQBivariateSpline, \
SmoothBivariateSpline, RectBivariateSpline
class TestUnivariateSpline(TestCase):
def test_linear_constant(self):
x = [1,2,3]
y = [3,3,3]
lut = UnivariateSpline(x,y,k=1)
assert_array_almost_equal(lut.get_knots(),[1,3])
assert_array_almost_equal(lut.get_coeffs(),[3,3])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2]),[3,3,3])
def test_preserve_shape(self):
x = [1, 2, 3]
y = [0, 2, 4]
lut = UnivariateSpline(x, y, k=1)
arg = 2
assert_equal(shape(arg), shape(lut(arg)))
assert_equal(shape(arg), shape(lut(arg, nu=1)))
arg = [1.5, 2, 2.5]
assert_equal(shape(arg), shape(lut(arg)))
assert_equal(shape(arg), shape(lut(arg, nu=1)))
def test_linear_1d(self):
x = [1,2,3]
y = [0,2,4]
lut = UnivariateSpline(x,y,k=1)
assert_array_almost_equal(lut.get_knots(),[1,3])
assert_array_almost_equal(lut.get_coeffs(),[0,4])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2]),[0,1,2])
def test_subclassing(self):
# See #731
class ZeroSpline(UnivariateSpline):
def __call__(self, x):
return 0*array(x)
sp = ZeroSpline([1,2,3,4,5], [3,2,3,2,3], k=2)
assert_array_equal(sp([1.5, 2.5]), [0., 0.])
def test_empty_input(self):
"""Test whether empty input returns an empty output. Ticket 1014"""
x = [1,3,5,7,9]
y = [0,4,9,12,21]
spl = UnivariateSpline(x, y, k=3)
assert_array_equal(spl([]), array([]))
def test_resize_regression(self):
"""Regression test for #1375."""
x = [-1., -0.65016502, -0.58856235, -0.26903553, -0.17370892,
-0.10011001, 0., 0.10011001, 0.17370892, 0.26903553, 0.58856235,
0.65016502, 1.]
y = [1.,0.62928599, 0.5797223, 0.39965815, 0.36322694, 0.3508061,
0.35214793, 0.3508061, 0.36322694, 0.39965815, 0.5797223,
0.62928599, 1.]
w = [1.00000000e+12, 6.88875973e+02, 4.89314737e+02, 4.26864807e+02,
6.07746770e+02, 4.51341444e+02, 3.17480210e+02, 4.51341444e+02,
6.07746770e+02, 4.26864807e+02, 4.89314737e+02, 6.88875973e+02,
1.00000000e+12]
spl = UnivariateSpline(x=x, y=y, w=w, s=None)
desired = array([ 0.35100374, 0.51715855, 0.87789547, 0.98719344])
assert_allclose(spl([0.1, 0.5, 0.9, 0.99]), desired, atol=5e-4)
class TestLSQBivariateSpline(TestCase):
def test_linear_constant(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [3,3,3,3,3,3,3,3,3]
s = 0.1
tx = [1+s,3-s]
ty = [1+s,3-s]
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
assert_almost_equal(lut(2,2), 3.)
def test_bilinearity(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [0,7,8,3,4,7,1,3,4]
s = 0.1
tx = [1+s,3-s]
ty = [1+s,3-s]
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
tx, ty = lut.get_knots()
for xa, xb in zip(tx[:-1], tx[1:]):
for ya, yb in zip(ty[:-1], ty[1:]):
for t in [0.1, 0.5, 0.9]:
for s in [0.3, 0.4, 0.7]:
xp = xa*(1-t) + xb*t
yp = ya*(1-s) + yb*s
zp = (+ lut(xa, ya)*(1-t)*(1-s)
+ lut(xb, ya)*t*(1-s)
+ lut(xa, yb)*(1-t)*s
+ lut(xb, yb)*t*s)
assert_almost_equal(lut(xp,yp), zp)
def test_integral(self):
x = [1,1,1,2,2,2,8,8,8]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
s = 0.1
tx = [1+s,3-s]
ty = [1+s,3-s]
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
tx, ty = lut.get_knots()
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
*(tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
def test_empty_input(self):
"""Test whether empty inputs returns an empty output. Ticket 1014"""
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [3,3,3,3,3,3,3,3,3]
s = 0.1
tx = [1+s,3-s]
ty = [1+s,3-s]
lut = LSQBivariateSpline(x,y,z,tx,ty,kx=1,ky=1)
assert_array_equal(lut([], []), array([]))
class TestSmoothBivariateSpline(TestCase):
def test_linear_constant(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [3,3,3,3,3,3,3,3,3]
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
assert_array_almost_equal(lut.get_coeffs(),[3,3,3,3])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[3,3],[3,3],[3,3]])
def test_linear_1d(self):
x = [1,1,1,2,2,2,3,3,3]
y = [1,2,3,1,2,3,1,2,3]
z = [0,0,0,2,2,2,4,4,4]
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1)
assert_array_almost_equal(lut.get_knots(),([1,1,3,3],[1,1,3,3]))
assert_array_almost_equal(lut.get_coeffs(),[0,0,4,4])
assert_almost_equal(lut.get_residual(),0.0)
assert_array_almost_equal(lut([1,1.5,2],[1,1.5]),[[0,0],[1,1],[2,2]])
def test_integral(self):
x = [1,1,1,2,2,2,4,4,4]
y = [1,2,3,1,2,3,1,2,3]
z = array([0,7,8,3,4,7,1,3,4])
lut = SmoothBivariateSpline(x,y,z,kx=1,ky=1,s=0)
tx = [1,2,4]
ty = [1,2,3]
tz = lut(tx, ty)
trpz = .25*(diff(tx)[:,None]*diff(ty)[None,:]
*(tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz)
lut2 = SmoothBivariateSpline(x,y,z,kx=2,ky=2,s=0)
assert_almost_equal(lut2.integral(tx[0], tx[-1], ty[0], ty[-1]), trpz,
decimal=0) # the quadratures give 23.75 and 23.85
tz = lut(tx[:-1], ty[:-1])
trpz = .25*(diff(tx[:-1])[:,None]*diff(ty[:-1])[None,:]
*(tz[:-1,:-1]+tz[1:,:-1]+tz[:-1,1:]+tz[1:,1:])).sum()
assert_almost_equal(lut.integral(tx[0], tx[-2], ty[0], ty[-2]), trpz)
class TestRectBivariateSpline(TestCase):
def test_defaults(self):
x = array([1,2,3,4,5])
y = array([1,2,3,4,5])
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
lut = RectBivariateSpline(x,y,z)
assert_array_almost_equal(lut(x,y),z)
def test_evaluate(self):
x = array([1,2,3,4,5])
y = array([1,2,3,4,5])
z = array([[1,2,1,2,1],[1,2,1,2,1],[1,2,3,2,1],[1,2,2,2,1],[1,2,1,2,1]])
lut = RectBivariateSpline(x,y,z)
xi = [1, 2.3, 5.3, 0.5, 3.3, 1.2, 3]
yi = [1, 3.3, 1.2, 4.0, 5.0, 1.0, 3]
zi = lut.ev(xi, yi)
zi2 = array([lut(xp, yp)[0,0] for xp, yp in zip(xi, yi)])
assert_almost_equal(zi, zi2)
if __name__ == "__main__":
run_module_suite()
|
