/usr/lib/python3/dist-packages/photutils/isophote/tests/test_harmonics.py is in python3-photutils 0.4-1.
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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 | # Licensed under a 3-clause BSD style license - see LICENSE.rst
from __future__ import (absolute_import, division, print_function,
unicode_literals)
import numpy as np
import pytest
from .make_test_data import make_test_image
from ..harmonics import (fit_first_and_second_harmonics, fit_upper_harmonic,
first_and_second_harmonic_function)
from ..sample import EllipseSample
try:
from scipy.optimize import leastsq # noqa
HAS_SCIPY = True
except ImportError:
HAS_SCIPY = False
@pytest.mark.skipif('not HAS_SCIPY')
def test_harmonics_1():
# this is an almost as-is example taken from stackoverflow
N = 100 # number of data points
t = np.linspace(0, 4*np.pi, N)
# create artificial data with noise:
# mean = 0.5, amplitude = 3., phase = 0.1, noise-std = 0.01
data = 3.0 * np.sin(t + 0.1) + 0.5 + 0.01 * np.random.randn(N)
# first guesses for harmonic parameters
guess_mean = np.mean(data)
guess_std = 3 * np.std(data) / 2**0.5
guess_phase = 0
# Minimize the difference between the actual data and our "guessed"
# parameters
# optimize_func = lambda x: x[0] * np.sin(t + x[1]) + x[2] - data
def optimize_func(x):
return x[0] * np.sin(t + x[1]) + x[2] - data
est_std, est_phase, est_mean = leastsq(
optimize_func, [guess_std, guess_phase, guess_mean])[0]
# recreate the fitted curve using the optimized parameters
data_fit = est_std * np.sin(t + est_phase) + est_mean
residual = data - data_fit
assert np.mean(residual) == pytest.approx(0.00, abs=0.001)
assert np.std(residual) == pytest.approx(0.01, abs=0.01)
@pytest.mark.skipif('not HAS_SCIPY')
def test_harmonics_2():
# this uses the actual functional form used for fitting ellipses
N = 100
E = np.linspace(0, 4*np.pi, N)
y0_0 = 100.
a1_0 = 10.
b1_0 = 5.
a2_0 = 8.
b2_0 = 2.
data = (y0_0 + a1_0*np.sin(E) + b1_0*np.cos(E) + a2_0*np.sin(2*E) +
b2_0*np.cos(2*E) + 0.01*np.random.randn(N))
harmonics = fit_first_and_second_harmonics(E, data)
y0, a1, b1, a2, b2 = harmonics[0]
data_fit = (y0 + a1*np.sin(E) + b1*np.cos(E) + a2*np.sin(2*E) +
b2*np.cos(2*E) + 0.01*np.random.randn(N))
residual = data - data_fit
assert np.mean(residual) == pytest.approx(0.00, abs=0.01)
assert np.std(residual) == pytest.approx(0.015, abs=0.01)
@pytest.mark.skipif('not HAS_SCIPY')
def test_harmonics_3():
"""Tests an upper harmonic fit."""
N = 100
E = np.linspace(0, 4*np.pi, N)
y0_0 = 100.
a1_0 = 10.
b1_0 = 5.
order = 3
data = (y0_0 + a1_0*np.sin(order*E) + b1_0*np.cos(order*E) +
0.01*np.random.randn(N))
harmonic = fit_upper_harmonic(E, data, order)
y0, a1, b1 = harmonic[0]
data_fit = (y0 + a1*np.sin(order*E) + b1*np.cos(order*E) +
0.01*np.random.randn(N))
residual = data - data_fit
assert np.mean(residual) == pytest.approx(0.00, abs=0.01)
assert np.std(residual) == pytest.approx(0.015, abs=0.01)
@pytest.mark.skipif('not HAS_SCIPY')
class TestFitEllipseSamples(object):
def setup_class(self):
# major axis parallel to X image axis
self.data1 = make_test_image(random_state=123)
# major axis tilted 45 deg wrt X image axis
self.data2 = make_test_image(pa=np.pi/4, random_state=123)
def test_fit_ellipsesample_1(self):
sample = EllipseSample(self.data1, 40.)
s = sample.extract()
harmonics = fit_first_and_second_harmonics(s[0], s[2])
y0, a1, b1, a2, b2 = harmonics[0]
assert np.mean(y0) == pytest.approx(200.019, abs=0.001)
assert np.mean(a1) == pytest.approx(-0.000138, abs=0.001)
assert np.mean(b1) == pytest.approx(0.000254, abs=0.001)
assert np.mean(a2) == pytest.approx(-5.658e-05, abs=0.001)
assert np.mean(b2) == pytest.approx(-0.00911, abs=0.001)
# check that harmonics subtract nicely
model = first_and_second_harmonic_function(
s[0], np.array([y0, a1, b1, a2, b2]))
residual = s[2] - model
assert np.mean(residual) == pytest.approx(0.00, abs=0.001)
assert np.std(residual) == pytest.approx(0.015, abs=0.01)
def test_fit_ellipsesample_2(self):
# initial guess is rounder than actual image
sample = EllipseSample(self.data1, 40., eps=0.1)
s = sample.extract()
harmonics = fit_first_and_second_harmonics(s[0], s[2])
y0, a1, b1, a2, b2 = harmonics[0]
assert np.mean(y0) == pytest.approx(188.686, abs=0.001)
assert np.mean(a1) == pytest.approx(0.000283, abs=0.001)
assert np.mean(b1) == pytest.approx(0.00692, abs=0.001)
assert np.mean(a2) == pytest.approx(-0.000215, abs=0.001)
assert np.mean(b2) == pytest.approx(10.153, abs=0.001)
def test_fit_ellipsesample_3(self):
# initial guess for center is offset
sample = EllipseSample(self.data1, x0=220., y0=210., sma=40.)
s = sample.extract()
harmonics = fit_first_and_second_harmonics(s[0], s[2])
y0, a1, b1, a2, b2 = harmonics[0]
assert np.mean(y0) == pytest.approx(152.660, abs=0.001)
assert np.mean(a1) == pytest.approx(55.338, abs=0.001)
assert np.mean(b1) == pytest.approx(33.091, abs=0.001)
assert np.mean(a2) == pytest.approx(33.036, abs=0.001)
assert np.mean(b2) == pytest.approx(-14.306, abs=0.001)
def test_fit_ellipsesample_4(self):
sample = EllipseSample(self.data2, 40., eps=0.4)
s = sample.extract()
harmonics = fit_first_and_second_harmonics(s[0], s[2])
y0, a1, b1, a2, b2 = harmonics[0]
assert np.mean(y0) == pytest.approx(245.102, abs=0.001)
assert np.mean(a1) == pytest.approx(-0.003108, abs=0.001)
assert np.mean(b1) == pytest.approx(-0.0578, abs=0.001)
assert np.mean(a2) == pytest.approx(28.781, abs=0.001)
assert np.mean(b2) == pytest.approx(-63.184, abs=0.001)
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