def test_is_consistency_with_astropy_convolution(self, mode):
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode)
x = np.arange(-5, 6)
ans = eval("{}(model(x), kernel(x))".format(mode))
assert_allclose(ans, model_conv(x), atol=1e-5)
def test_convolve_box_models(self, mode):
kernel = models.Box1D()
model = models.Box1D()
model_conv = convolve_models(model, kernel, mode=mode)
x = np.linspace(-1, 1, 99)
ans = (x + 1) * (x < 0) + (-x + 1) * (x >= 0)
assert_allclose(ans, model_conv(x), atol=1e-3)
def test_is_consistency_with_astropy_convolution(self, mode):
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode)
x = np.arange(-5, 6)
ans = eval("{}(model(x), kernel(x))".format(mode))
assert_allclose(ans, model_conv(x), atol=1e-5)
def test_convolve_box_models(self, mode):
kernel = models.Box1D()
model = models.Box1D()
model_conv = convolve_models(model, kernel, mode=mode)
x = np.linspace(-1, 1, 99)
ans = (x + 1) * (x < 0) + (-x + 1) * (x >= 0)
assert_allclose(ans, model_conv(x), atol=1e-3)
def test_against_scipy(self, mode):
from scipy.signal import fftconvolve
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode)
x = np.arange(-5, 6)
ans = fftconvolve(kernel(x), model(x), mode='same')
assert_allclose(ans, model_conv(x) * kernel(x).sum(), atol=1e-5)
def test_against_scipy(self, mode):
from scipy.signal import fftconvolve
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode)
x = np.arange(-5, 6)
ans = fftconvolve(kernel(x), model(x), mode='same')
assert_allclose(ans, model_conv(x) * kernel(x).sum(), atol=1e-5)
def test_against_scipy_with_additional_keywords(self, mode):
from scipy.signal import fftconvolve
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode,
normalize_kernel=False)
x = np.arange(-5, 6)
ans = fftconvolve(kernel(x), model(x), mode='same')
assert_allclose(ans, model_conv(x), atol=1e-5)
def test_against_scipy_with_additional_keywords(self, mode):
from scipy.signal import fftconvolve
kernel = models.Gaussian1D(1, 0, 1)
model = models.Gaussian1D(1, 0, 1)
model_conv = convolve_models(model, kernel, mode=mode,
normalize_kernel=False)
x = np.arange(-5, 6)
ans = fftconvolve(kernel(x), model(x), mode='same')
assert_allclose(ans, model_conv(x), atol=1e-5)
def test_sum_of_gaussians(self, mode):
"""
Test that convolving N(a, b) with N(c, d) gives N(a + c, b + d),
where N(., .) stands for Gaussian probability density function,
in which a and c are their means and b and d are their variances.
"""
kernel = models.Gaussian1D(1 / math.sqrt(2 * np.pi), 1, 1)
model = models.Gaussian1D(1 / math.sqrt(2 * np.pi), 3, 1)
model_conv = convolve_models(model, kernel, mode=mode,
normalize_kernel=False)
ans = models.Gaussian1D(1 / (2 * math.sqrt(np.pi)), 4, np.sqrt(2))
x = np.arange(-5, 6)
assert_allclose(ans(x), model_conv(x), atol=1e-3)
def test_sum_of_gaussians(self, mode):
"""
Test that convolving N(a, b) with N(c, d) gives N(a + c, b + d),
where N(., .) stands for Gaussian probability density function,
in which a and c are their means and b and d are their variances.
"""
kernel = models.Gaussian1D(1 / math.sqrt(2 * np.pi), 1, 1)
model = models.Gaussian1D(1 / math.sqrt(2 * np.pi), 3, 1)
model_conv = convolve_models(model, kernel, mode=mode,
normalize_kernel=False)
ans = models.Gaussian1D(1 / (2 * math.sqrt(np.pi)), 4, np.sqrt(2))
x = np.arange(-5, 6)
assert_allclose(ans(x), model_conv(x), atol=1e-3)
def test_fitting_convolve_models(self, mode):
"""
test that a convolve model can be fitted
"""
b1 = models.Box1D()
g1 = models.Gaussian1D()
x = np.linspace(-5, 5, 99)
fake_model = models.Gaussian1D(amplitude=10)
with NumpyRNGContext(123):
fake_data = fake_model(x) + np.random.normal(size=len(x))
init_model = convolve_models(b1, g1, mode=mode, normalize_kernel=False)
fitter = fitting.LevMarLSQFitter()
fitted_model = fitter(init_model, x, fake_data)
me = np.mean(fitted_model(x) - fake_data)
assert_almost_equal(me, 0.0, decimal=2)
def test_fitting_convolve_models(self, mode):
"""
test that a convolve model can be fitted
"""
b1 = models.Box1D()
g1 = models.Gaussian1D()
x = np.linspace(-5, 5, 99)
fake_model = models.Gaussian1D(amplitude=10)
with NumpyRNGContext(123):
fake_data = fake_model(x) + np.random.normal(size=len(x))
init_model = convolve_models(b1, g1, mode=mode, normalize_kernel=False)
fitter = fitting.LevMarLSQFitter()
fitted_model = fitter(init_model, x, fake_data)
me = np.mean(fitted_model(x) - fake_data)
assert_almost_equal(me, 0.0, decimal=2)
