Source code for astropy.convolution.utils

# Licensed under a 3-clause BSD style license - see LICENSE.rst
import ctypes
import numpy as np

from astropy.modeling.core import FittableModel, custom_model

__all__ = ['discretize_model']


class DiscretizationError(Exception):
    """
    Called when discretization of models goes wrong.
    """


class KernelSizeError(Exception):
    """
    Called when size of kernels is even.
    """


def has_even_axis(array):
    if isinstance(array, (list, tuple)):
        return not len(array) % 2
    else:
        return any(not axes_size % 2 for axes_size in array.shape)


def raise_even_kernel_exception():
    raise KernelSizeError("Kernel size must be odd in all axes.")


def add_kernel_arrays_1D(array_1, array_2):
    """
    Add two 1D kernel arrays of different size.

    The arrays are added with the centers lying upon each other.
    """
    if array_1.size > array_2.size:
        new_array = array_1.copy()
        center = array_1.size // 2
        slice_ = slice(center - array_2.size // 2,
                       center + array_2.size // 2 + 1)
        new_array[slice_] += array_2
        return new_array
    elif array_2.size > array_1.size:
        new_array = array_2.copy()
        center = array_2.size // 2
        slice_ = slice(center - array_1.size // 2,
                       center + array_1.size // 2 + 1)
        new_array[slice_] += array_1
        return new_array
    return array_2 + array_1


def add_kernel_arrays_2D(array_1, array_2):
    """
    Add two 2D kernel arrays of different size.

    The arrays are added with the centers lying upon each other.
    """
    if array_1.size > array_2.size:
        new_array = array_1.copy()
        center = [axes_size // 2 for axes_size in array_1.shape]
        slice_x = slice(center[1] - array_2.shape[1] // 2,
                        center[1] + array_2.shape[1] // 2 + 1)
        slice_y = slice(center[0] - array_2.shape[0] // 2,
                        center[0] + array_2.shape[0] // 2 + 1)
        new_array[slice_y, slice_x] += array_2
        return new_array
    elif array_2.size > array_1.size:
        new_array = array_2.copy()
        center = [axes_size // 2 for axes_size in array_2.shape]
        slice_x = slice(center[1] - array_1.shape[1] // 2,
                        center[1] + array_1.shape[1] // 2 + 1)
        slice_y = slice(center[0] - array_1.shape[0] // 2,
                        center[0] + array_1.shape[0] // 2 + 1)
        new_array[slice_y, slice_x] += array_1
        return new_array
    return array_2 + array_1


[docs]def discretize_model(model, x_range, y_range=None, mode='center', factor=10): """ Function to evaluate analytical model functions on a grid. So far the function can only deal with pixel coordinates. Parameters ---------- model : `~astropy.modeling.FittableModel` or callable. Analytic model function to be discretized. Callables, which are not an instances of `~astropy.modeling.FittableModel` are passed to `~astropy.modeling.custom_model` and then evaluated. x_range : tuple x range in which the model is evaluated. The difference between the upper an lower limit must be a whole number, so that the output array size is well defined. y_range : tuple, optional y range in which the model is evaluated. The difference between the upper an lower limit must be a whole number, so that the output array size is well defined. Necessary only for 2D models. mode : str, optional One of the following modes: * ``'center'`` (default) Discretize model by taking the value at the center of the bin. * ``'linear_interp'`` Discretize model by linearly interpolating between the values at the corners of the bin. For 2D models interpolation is bilinear. * ``'oversample'`` Discretize model by taking the average on an oversampled grid. * ``'integrate'`` Discretize model by integrating the model over the bin using `scipy.integrate.quad`. Very slow. factor : float or int Factor of oversampling. Default = 10. Returns ------- array : `numpy.array` Model value array Notes ----- The ``oversample`` mode allows to conserve the integral on a subpixel scale. Here is the example of a normalized Gaussian1D: .. plot:: :include-source: import matplotlib.pyplot as plt import numpy as np from astropy.modeling.models import Gaussian1D from astropy.convolution.utils import discretize_model gauss_1D = Gaussian1D(1 / (0.5 * np.sqrt(2 * np.pi)), 0, 0.5) y_center = discretize_model(gauss_1D, (-2, 3), mode='center') y_corner = discretize_model(gauss_1D, (-2, 3), mode='linear_interp') y_oversample = discretize_model(gauss_1D, (-2, 3), mode='oversample') plt.plot(y_center, label='center sum = {0:3f}'.format(y_center.sum())) plt.plot(y_corner, label='linear_interp sum = {0:3f}'.format(y_corner.sum())) plt.plot(y_oversample, label='oversample sum = {0:3f}'.format(y_oversample.sum())) plt.xlabel('pixels') plt.ylabel('value') plt.legend() plt.show() """ if not callable(model): raise TypeError('Model must be callable.') if not isinstance(model, FittableModel): model = custom_model(model)() ndim = model.n_inputs if ndim > 2: raise ValueError('discretize_model only supports 1-d and 2-d models.') if not float(np.diff(x_range)).is_integer(): raise ValueError("The difference between the upper an lower limit of" " 'x_range' must be a whole number.") if y_range: if not float(np.diff(y_range)).is_integer(): raise ValueError("The difference between the upper an lower limit of" " 'y_range' must be a whole number.") if ndim == 2 and y_range is None: raise ValueError("y range not specified, but model is 2-d") if ndim == 1 and y_range is not None: raise ValueError("y range specified, but model is only 1-d.") if mode == "center": if ndim == 1: return discretize_center_1D(model, x_range) elif ndim == 2: return discretize_center_2D(model, x_range, y_range) elif mode == "linear_interp": if ndim == 1: return discretize_linear_1D(model, x_range) if ndim == 2: return discretize_bilinear_2D(model, x_range, y_range) elif mode == "oversample": if ndim == 1: return discretize_oversample_1D(model, x_range, factor) if ndim == 2: return discretize_oversample_2D(model, x_range, y_range, factor) elif mode == "integrate": if ndim == 1: return discretize_integrate_1D(model, x_range) if ndim == 2: return discretize_integrate_2D(model, x_range, y_range) else: raise DiscretizationError('Invalid mode.')
def discretize_center_1D(model, x_range): """ Discretize model by taking the value at the center of the bin. """ x = np.arange(*x_range) return model(x) def discretize_center_2D(model, x_range, y_range): """ Discretize model by taking the value at the center of the pixel. """ x = np.arange(*x_range) y = np.arange(*y_range) x, y = np.meshgrid(x, y) return model(x, y) def discretize_linear_1D(model, x_range): """ Discretize model by performing a linear interpolation. """ # Evaluate model 0.5 pixel outside the boundaries x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5) values_intermediate_grid = model(x) return 0.5 * (values_intermediate_grid[1:] + values_intermediate_grid[:-1]) def discretize_bilinear_2D(model, x_range, y_range): """ Discretize model by performing a bilinear interpolation. """ # Evaluate model 0.5 pixel outside the boundaries x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5) y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5) x, y = np.meshgrid(x, y) values_intermediate_grid = model(x, y) # Mean in y direction values = 0.5 * (values_intermediate_grid[1:, :] + values_intermediate_grid[:-1, :]) # Mean in x direction values = 0.5 * (values[:, 1:] + values[:, :-1]) return values def discretize_oversample_1D(model, x_range, factor=10): """ Discretize model by taking the average on an oversampled grid. """ # Evaluate model on oversampled grid x = np.linspace(x_range[0] - 0.5 * (1 - 1 / factor), x_range[1] - 0.5 * (1 + 1 / factor), num = (x_range[1] - x_range[0]) * factor) values = model(x) # Reshape and compute mean values = np.reshape(values, (x.size // factor, factor)) return values.mean(axis=1) def discretize_oversample_2D(model, x_range, y_range, factor=10): """ Discretize model by taking the average on an oversampled grid. """ # Evaluate model on oversampled grid x = np.linspace(x_range[0] - 0.5 * (1 - 1 / factor), x_range[1] - 0.5 * (1 + 1 / factor), num = (x_range[1] - x_range[0]) * factor) y = np.linspace(y_range[0] - 0.5 * (1 - 1 / factor), y_range[1] - 0.5 * (1 + 1 / factor), num = (y_range[1] - y_range[0]) * factor) x_grid, y_grid = np.meshgrid(x, y) values = model(x_grid, y_grid) # Reshape and compute mean shape = (y.size // factor, factor, x.size // factor, factor) values = np.reshape(values, shape) return values.mean(axis=3).mean(axis=1) def discretize_integrate_1D(model, x_range): """ Discretize model by integrating numerically the model over the bin. """ from scipy.integrate import quad # Set up grid x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5) values = np.array([]) # Integrate over all bins for i in range(x.size - 1): values = np.append(values, quad(model, x[i], x[i + 1])[0]) return values def discretize_integrate_2D(model, x_range, y_range): """ Discretize model by integrating the model over the pixel. """ from scipy.integrate import dblquad # Set up grid x = np.arange(x_range[0] - 0.5, x_range[1] + 0.5) y = np.arange(y_range[0] - 0.5, y_range[1] + 0.5) values = np.empty((y.size - 1, x.size - 1)) # Integrate over all pixels for i in range(x.size - 1): for j in range(y.size - 1): values[j, i] = dblquad(lambda y, x: model(x, y), x[i], x[i + 1], lambda x: y[j], lambda x: y[j + 1])[0] return values