# Licensed under a 3-clause BSD style license - see LICENSE.rst from __future__ import (absolute_import, division, print_function, unicode_literals) import warnings import numpy as np from .core import Kernel, Kernel1D, Kernel2D, MAX_NORMALIZATION from ..utils.exceptions import AstropyUserWarning from ..utils.console import human_file_size # Disabling all doctests in this module until a better way of handling warnings # in doctests can be determined __doctest_skip__ = ['*'] def convolve(array, kernel, boundary='fill', fill_value=0., normalize_kernel=False): ''' Convolve an array with a kernel. This routine differs from `scipy.ndimage.filters.convolve` because it includes a special treatment for ``NaN`` values. Rather than including ``NaN``s in the convolution calculation, which causes large ``NaN`` holes in the convolved image, ``NaN`` values are replaced with interpolated values using the kernel as an interpolation function. Parameters ---------- array : `numpy.ndarray` The array to convolve. This should be a 1, 2, or 3-dimensional array or a list or a set of nested lists representing a 1, 2, or 3-dimensional array. kernel : `numpy.ndarray` or `~astropy.convolution.Kernel` The convolution kernel. The number of dimensions should match those for the array, and the dimensions should be odd in all directions. boundary : str, optional A flag indicating how to handle boundaries: * `None` Set the ``result`` values to zero where the kernel extends beyond the edge of the array (default). * 'fill' Set values outside the array boundary to ``fill_value``. * 'wrap' Periodic boundary that wrap to the other side of ``array``. * 'extend' Set values outside the array to the nearest ``array`` value. fill_value : float, optional The value to use outside the array when using boundary='fill' normalize_kernel : bool, optional Whether to normalize the kernel prior to convolving Returns ------- result : `numpy.ndarray` An array with the same dimensions and as the input array, convolved with kernel. The data type depends on the input array type. If array is a floating point type, then the return array keeps the same data type, otherwise the type is ``numpy.float``. Notes ----- Masked arrays are not supported at this time. The convolution is always done at ``numpy.float`` precision. ''' from .boundary_none import (convolve1d_boundary_none, convolve2d_boundary_none, convolve3d_boundary_none) from .boundary_extend import (convolve1d_boundary_extend, convolve2d_boundary_extend, convolve3d_boundary_extend) from .boundary_fill import (convolve1d_boundary_fill, convolve2d_boundary_fill, convolve3d_boundary_fill) from .boundary_wrap import (convolve1d_boundary_wrap, convolve2d_boundary_wrap, convolve3d_boundary_wrap) # The cython routines all need float type inputs (so, a particular # bit size, endianness, etc.). So we have to convert, which also # has the effect of making copies so we don't modify the inputs. # After this, the variables we work with will be array_internal, and # kernel_internal. However -- we do want to keep track of what type # the input array was so we can cast the result to that at the end # if it's a floating point type. Don't bother with this for lists -- # just always push those as np.float. # It is always necessary to make a copy of kernel (since it is modified), # but, if we just so happen to be lucky enough to have the input array # have exactly the desired type, we just alias to array_internal # Check if kernel is kernel instance if isinstance(kernel, Kernel): # Check if array is also kernel instance, if so convolve and # return new kernel instance if isinstance(array, Kernel): if isinstance(array, Kernel1D) and isinstance(kernel, Kernel1D): new_array = convolve1d_boundary_fill(array.array, kernel.array, 0) new_kernel = Kernel1D(array=new_array) elif isinstance(array, Kernel2D) and isinstance(kernel, Kernel2D): new_array = convolve2d_boundary_fill(array.array, kernel.array, 0) new_kernel = Kernel2D(array=new_array) else: raise Exception("Can't convolve 1D and 2D kernel.") new_kernel._separable = kernel._separable and array._separable new_kernel._is_bool = False return new_kernel kernel = kernel.array # Check that the arguments are lists or Numpy arrays if isinstance(array, list): array_internal = np.array(array, dtype=np.float) array_dtype = array_internal.dtype elif isinstance(array, np.ndarray): # Note this won't copy if it doesn't have to -- which is okay # because none of what follows modifies array_internal. However, # only numpy > 1.7 has support for no-copy astype, so we use # a try/except because astropy supports 1.5 and 1.6 array_dtype = array.dtype try: array_internal = array.astype(float, copy=False) except TypeError: array_internal = array.astype(float) else: raise TypeError("array should be a list or a Numpy array") if isinstance(kernel, list): kernel_internal = np.array(kernel, dtype=float) elif isinstance(kernel, np.ndarray): # Note this always makes a copy, since we will be modifying it kernel_internal = kernel.astype(float) else: raise TypeError("kernel should be a list or a Numpy array") # Check that the number of dimensions is compatible if array_internal.ndim != kernel_internal.ndim: raise Exception('array and kernel have differing number of ' 'dimensions.') # Because the Cython routines have to normalize the kernel on the fly, we # explicitly normalize the kernel here, and then scale the image at the # end if normalization was not requested. kernel_sum = kernel_internal.sum() if kernel_sum < 1. / MAX_NORMALIZATION and normalize_kernel: raise Exception("The kernel can't be normalized, because its sum is " "close to zero. The sum of the given kernel is < {0}" .format(1. / MAX_NORMALIZATION)) kernel_internal /= kernel_sum if array_internal.ndim == 0: raise Exception("cannot convolve 0-dimensional arrays") elif array_internal.ndim == 1: if boundary == 'extend': result = convolve1d_boundary_extend(array_internal, kernel_internal) elif boundary == 'fill': result = convolve1d_boundary_fill(array_internal, kernel_internal, float(fill_value)) elif boundary == 'wrap': result = convolve1d_boundary_wrap(array_internal, kernel_internal) else: result = convolve1d_boundary_none(array_internal, kernel_internal) elif array_internal.ndim == 2: if boundary == 'extend': result = convolve2d_boundary_extend(array_internal, kernel_internal) elif boundary == 'fill': result = convolve2d_boundary_fill(array_internal, kernel_internal, float(fill_value)) elif boundary == 'wrap': result = convolve2d_boundary_wrap(array_internal, kernel_internal) else: result = convolve2d_boundary_none(array_internal, kernel_internal) elif array_internal.ndim == 3: if boundary == 'extend': result = convolve3d_boundary_extend(array_internal, kernel_internal) elif boundary == 'fill': result = convolve3d_boundary_fill(array_internal, kernel_internal, float(fill_value)) elif boundary == 'wrap': result = convolve3d_boundary_wrap(array_internal, kernel_internal) else: result = convolve3d_boundary_none(array_internal, kernel_internal) else: raise NotImplemented('convolve only supports 1, 2, and 3-dimensional ' 'arrays at this time') # If normalization was not requested, we need to scale the array (since # the kernel was normalized prior to convolution) if not normalize_kernel: result *= kernel_sum # Try to preserve the input type if it's a floating point type if array_dtype.kind == 'f': # Avoid making another copy if possible try: return result.astype(array_dtype, copy=False) except TypeError: return result.astype(array_dtype) else: return result def convolve_fft(array, kernel, boundary='fill', fill_value=0, crop=True, return_fft=False, fft_pad=True, psf_pad=False, interpolate_nan=False, quiet=False, ignore_edge_zeros=False, min_wt=0.0, normalize_kernel=False, allow_huge=False, fftn=np.fft.fftn, ifftn=np.fft.ifftn, complex_dtype=np.complex): """ Convolve an ndarray with an nd-kernel. Returns a convolved image with shape = array.shape. Assumes kernel is centered. `convolve_fft` differs from `scipy.signal.fftconvolve` in a few ways: * It can treat ``NaN`` values as zeros or interpolate over them. * ``inf`` values are treated as ``NaN`` * (optionally) It pads to the nearest 2^n size to improve FFT speed. * Its only valid ``mode`` is 'same' (i.e., the same shape array is returned) * It lets you use your own fft, e.g., `pyFFTW `_ or `pyFFTW3 `_ , which can lead to performance improvements, depending on your system configuration. pyFFTW3 is threaded, and therefore may yield significant performance benefits on multi-core machines at the cost of greater memory requirements. Specify the ``fftn`` and ``ifftn`` keywords to override the default, which is `numpy.fft.fft` and `numpy.fft.ifft`. Parameters ---------- array : `numpy.ndarray` Array to be convolved with ``kernel`` kernel : `numpy.ndarray` Will be normalized if ``normalize_kernel`` is set. Assumed to be centered (i.e., shifts may result if your kernel is asymmetric) boundary : {'fill', 'wrap'}, optional A flag indicating how to handle boundaries: * 'fill': set values outside the array boundary to fill_value (default) * 'wrap': periodic boundary interpolate_nan : bool, optional The convolution will be re-weighted assuming ``NaN`` values are meant to be ignored, not treated as zero. If this is off, all ``NaN`` values will be treated as zero. ignore_edge_zeros : bool, optional Ignore the zero-pad-created zeros. This will effectively decrease the kernel area on the edges but will not re-normalize the kernel. This parameter may result in 'edge-brightening' effects if you're using a normalized kernel min_wt : float, optional If ignoring ``NaN`` / zeros, force all grid points with a weight less than this value to ``NaN`` (the weight of a grid point with *no* ignored neighbors is 1.0). If ``min_wt`` is zero, then all zero-weight points will be set to zero instead of ``NaN`` (which they would be otherwise, because 1/0 = nan). See the examples below normalize_kernel : function or boolean, optional If specified, this is the function to divide kernel by to normalize it. e.g., ``normalize_kernel=np.sum`` means that kernel will be modified to be: ``kernel = kernel / np.sum(kernel)``. If True, defaults to ``normalize_kernel = np.sum``. Other Parameters ---------------- fft_pad : bool, optional Default on. Zero-pad image to the nearest 2^n psf_pad : bool, optional Default off. Zero-pad image to be at least the sum of the image sizes (in order to avoid edge-wrapping when smoothing) crop : bool, optional Default on. Return an image of the size of the largest input image. If the images are asymmetric in opposite directions, will return the largest image in both directions. For example, if an input image has shape [100,3] but a kernel with shape [6,6] is used, the output will be [100,6]. return_fft : bool, optional Return the fft(image)*fft(kernel) instead of the convolution (which is ifft(fft(image)*fft(kernel))). Useful for making PSDs. fftn, ifftn : functions, optional The fft and inverse fft functions. Can be overridden to use your own ffts, e.g. an fftw3 wrapper or scipy's fftn, e.g. ``fftn=scipy.fftpack.fftn`` complex_dtype : np.complex, optional Which complex dtype to use. `numpy` has a range of options, from 64 to 256. quiet : bool, optional Silence warning message about NaN interpolation allow_huge : bool, optional Allow huge arrays in the FFT? If False, will raise an exception if the array or kernel size is >1 GB Raises ------ ValueError: If the array is bigger than 1 GB after padding, will raise this exception unless allow_huge is True See Also -------- convolve : Convolve is a non-fft version of this code. It is more memory efficient and for small kernels can be faster. Returns ------- default : ndarray **array** convolved with ``kernel``. If ``return_fft`` is set, returns fft(**array**) * fft(``kernel``). If crop is not set, returns the image, but with the fft-padded size instead of the input size Examples -------- >>> convolve_fft([1, 0, 3], [1, 1, 1]) array([ 1., 4., 3.]) >>> convolve_fft([1, np.nan, 3], [1, 1, 1]) array([ 1., 4., 3.]) >>> convolve_fft([1, 0, 3], [0, 1, 0]) array([ 1., 0., 3.]) >>> convolve_fft([1, 2, 3], [1]) array([ 1., 2., 3.]) >>> convolve_fft([1, np.nan, 3], [0, 1, 0], interpolate_nan=True) ... array([ 1., 0., 3.]) >>> convolve_fft([1, np.nan, 3], [0, 1, 0], interpolate_nan=True, ... min_wt=1e-8) array([ 1., nan, 3.]) >>> convolve_fft([1, np.nan, 3], [1, 1, 1], interpolate_nan=True) array([ 1., 4., 3.]) >>> convolve_fft([1, np.nan, 3], [1, 1, 1], interpolate_nan=True, ... normalize_kernel=True, ignore_edge_zeros=True) array([ 1., 2., 3.]) >>> import scipy.fftpack # optional - requires scipy >>> convolve_fft([1, np.nan, 3], [1, 1, 1], interpolate_nan=True, ... normalize_kernel=True, ignore_edge_zeros=True, ... fftn=scipy.fftpack.fft, ifftn=scipy.fftpack.ifft) array([ 1., 2., 3.]) """ # Checking copied from convolve.py - however, since FFTs have real & # complex components, we change the types. Only the real part will be # returned! Note that this always makes a copy. # Check kernel is kernel instance if isinstance(kernel, Kernel): kernel = kernel.array if isinstance(array, Kernel): raise TypeError("Can't convolve two kernels. Use convolve() instead.") # Convert array dtype to complex # and ensure that list inputs become arrays array = np.asarray(array, dtype=np.complex) kernel = np.asarray(kernel, dtype=np.complex) # Check that the number of dimensions is compatible if array.ndim != kernel.ndim: raise ValueError("Image and kernel must have same number of " "dimensions") arrayshape = array.shape kernshape = kernel.shape array_size_B = (np.product(arrayshape, dtype=np.int64) * np.dtype(complex_dtype).itemsize) if array_size_B > 1024**3 and not allow_huge: raise ValueError("Size Error: Arrays will be %s. Use " "allow_huge=True to override this exception." % human_file_size(array_size_B)) # mask catching - masks must be turned into NaNs for use later if np.ma.is_masked(array): mask = array.mask array = np.array(array) array[mask] = np.nan if np.ma.is_masked(kernel): mask = kernel.mask kernel = np.array(kernel) kernel[mask] = np.nan # NaN and inf catching nanmaskarray = np.isnan(array) + np.isinf(array) array[nanmaskarray] = 0 nanmaskkernel = np.isnan(kernel) + np.isinf(kernel) kernel[nanmaskkernel] = 0 if ((nanmaskarray.sum() > 0 or nanmaskkernel.sum() > 0) and not interpolate_nan and not quiet): warnings.warn("NOT ignoring NaN values even though they are present " " (they are treated as 0)", AstropyUserWarning) if normalize_kernel is True: if kernel.sum() < 1. / MAX_NORMALIZATION: raise Exception("The kernel can't be normalized, because its sum is " "close to zero. The sum of the given kernel is < {0}" .format(1. / MAX_NORMALIZATION)) kernel = kernel / kernel.sum() kernel_is_normalized = True elif normalize_kernel: # try this. If a function is not passed, the code will just crash... I # think type checking would be better but PEPs say otherwise... kernel = kernel / normalize_kernel(kernel) kernel_is_normalized = True else: if np.abs(kernel.sum() - 1) < 1e-8: kernel_is_normalized = True else: kernel_is_normalized = False if (interpolate_nan or ignore_edge_zeros): warnings.warn("Kernel is not normalized, therefore " "ignore_edge_zeros and interpolate_nan will be " "ignored.", AstropyUserWarning) if boundary is None: warnings.warn("The convolve_fft version of boundary=None is " "equivalent to the convolve boundary='fill'. There is " "no FFT equivalent to convolve's " "zero-if-kernel-leaves-boundary", AstropyUserWarning) psf_pad = True elif boundary == 'fill': # create a boundary region at least as large as the kernel psf_pad = True elif boundary == 'wrap': psf_pad = False fft_pad = False fill_value = 0 # force zero; it should not be used elif boundary == 'extend': raise NotImplementedError("The 'extend' option is not implemented " "for fft-based convolution") # find ideal size (power of 2) for fft. # Can add shapes because they are tuples if fft_pad: # default=True if psf_pad: # default=False # add the dimensions and then take the max (bigger) fsize = 2 ** np.ceil(np.log2( np.max(np.array(arrayshape) + np.array(kernshape)))) else: # add the shape lists (max of a list of length 4) (smaller) # also makes the shapes square fsize = 2 ** np.ceil(np.log2(np.max(arrayshape + kernshape))) newshape = np.array([fsize for ii in range(array.ndim)], dtype=int) else: if psf_pad: # just add the biggest dimensions newshape = np.array(arrayshape) + np.array(kernshape) else: newshape = np.array([np.max([imsh, kernsh]) for imsh, kernsh in zip(arrayshape, kernshape)]) # For future reference, this can be used to predict "almost exactly" # how much *additional* memory will be used. # size * (array + kernel + kernelfft + arrayfft + # (kernel*array)fft + # optional(weight image + weight_fft + weight_ifft) + # optional(returned_fft)) #total_memory_used_GB = (np.product(newshape)*np.dtype(complex_dtype).itemsize # * (5 + 3*((interpolate_nan or ignore_edge_zeros) and kernel_is_normalized)) # + (1 + (not return_fft)) * # np.product(arrayshape)*np.dtype(complex_dtype).itemsize # + np.product(arrayshape)*np.dtype(bool).itemsize # + np.product(kernshape)*np.dtype(bool).itemsize) # ) / 1024.**3 # separate each dimension by the padding size... this is to determine the # appropriate slice size to get back to the input dimensions arrayslices = [] kernslices = [] for ii, (newdimsize, arraydimsize, kerndimsize) in enumerate(zip(newshape, arrayshape, kernshape)): center = newdimsize - (newdimsize + 1) // 2 arrayslices += [slice(center - arraydimsize // 2, center + (arraydimsize + 1) // 2)] kernslices += [slice(center - kerndimsize // 2, center + (kerndimsize + 1) // 2)] if not np.all(newshape == arrayshape): bigarray = np.ones(newshape, dtype=complex_dtype) * fill_value bigarray[arrayslices] = array else: bigarray = array if not np.all(newshape == kernshape): bigkernel = np.zeros(newshape, dtype=complex_dtype) bigkernel[kernslices] = kernel else: bigkernel = kernel arrayfft = fftn(bigarray) # need to shift the kernel so that, e.g., [0,0,1,0] -> [1,0,0,0] = unity kernfft = fftn(np.fft.ifftshift(bigkernel)) fftmult = arrayfft * kernfft if (interpolate_nan or ignore_edge_zeros) and kernel_is_normalized: if ignore_edge_zeros: bigimwt = np.zeros(newshape, dtype=complex_dtype) else: bigimwt = np.ones(newshape, dtype=complex_dtype) bigimwt[arrayslices] = 1.0 - nanmaskarray * interpolate_nan wtfft = fftn(bigimwt) # I think this one HAS to be normalized (i.e., the weights can't be # computed with a non-normalized kernel) wtfftmult = wtfft * kernfft / kernel.sum() wtsm = ifftn(wtfftmult) # need to re-zero weights outside of the image (if it is padded, we # still don't weight those regions) bigimwt[arrayslices] = wtsm.real[arrayslices] # curiously, at the floating-point limit, can get slightly negative numbers # they break the min_wt=0 "flag" and must therefore be removed bigimwt[bigimwt < 0] = 0 else: bigimwt = 1 if np.isnan(fftmult).any(): # this check should be unnecessary; call it an insanity check raise ValueError("Encountered NaNs in convolve. This is disallowed.") # restore NaNs in original image (they were modified inplace earlier) # We don't have to worry about masked arrays - if input was masked, it was # copied array[nanmaskarray] = np.nan kernel[nanmaskkernel] = np.nan if return_fft: return fftmult if interpolate_nan or ignore_edge_zeros: rifft = (ifftn(fftmult)) / bigimwt if not np.isscalar(bigimwt): rifft[bigimwt < min_wt] = np.nan if min_wt == 0.0: rifft[bigimwt == 0.0] = 0.0 else: rifft = (ifftn(fftmult)) if crop: result = rifft[arrayslices].real return result else: return rifft.real