""" The arraypad module contains a group of functions to pad values onto the edges of an n-dimensional array. """ from __future__ import division, absolute_import, print_function import numpy as np __all__ = ['pad'] ############################################################################### # Private utility functions. def _arange_ndarray(arr, shape, axis, reverse=False): """ Create an ndarray of `shape` with increments along specified `axis` Parameters ---------- arr : ndarray Input array of arbitrary shape. shape : tuple of ints Shape of desired array. Should be equivalent to `arr.shape` except `shape[axis]` which may have any positive value. axis : int Axis to increment along. reverse : bool If False, increment in a positive fashion from 1 to `shape[axis]`, inclusive. If True, the bounds are the same but the order reversed. Returns ------- padarr : ndarray Output array sized to pad `arr` along `axis`, with linear range from 1 to `shape[axis]` along specified `axis`. Notes ----- The range is deliberately 1-indexed for this specific use case. Think of this algorithm as broadcasting `np.arange` to a single `axis` of an arbitrarily shaped ndarray. """ initshape = tuple(1 if i != axis else shape[axis] for (i, x) in enumerate(arr.shape)) if not reverse: padarr = np.arange(1, shape[axis] + 1) else: padarr = np.arange(shape[axis], 0, -1) padarr = padarr.reshape(initshape) for i, dim in enumerate(shape): if padarr.shape[i] != dim: padarr = padarr.repeat(dim, axis=i) return padarr def _round_ifneeded(arr, dtype): """ Rounds arr inplace if destination dtype is integer. Parameters ---------- arr : ndarray Input array. dtype : dtype The dtype of the destination array. """ if np.issubdtype(dtype, np.integer): arr.round(out=arr) def _prepend_const(arr, pad_amt, val, axis=-1): """ Prepend constant `val` along `axis` of `arr`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. val : scalar Constant value to use. For best results should be of type `arr.dtype`; if not `arr.dtype` will be cast to `arr.dtype`. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` constant `val` prepended along `axis`. """ if pad_amt == 0: return arr padshape = tuple(x if i != axis else pad_amt for (i, x) in enumerate(arr.shape)) if val == 0: return np.concatenate((np.zeros(padshape, dtype=arr.dtype), arr), axis=axis) else: return np.concatenate(((np.zeros(padshape) + val).astype(arr.dtype), arr), axis=axis) def _append_const(arr, pad_amt, val, axis=-1): """ Append constant `val` along `axis` of `arr`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. val : scalar Constant value to use. For best results should be of type `arr.dtype`; if not `arr.dtype` will be cast to `arr.dtype`. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` constant `val` appended along `axis`. """ if pad_amt == 0: return arr padshape = tuple(x if i != axis else pad_amt for (i, x) in enumerate(arr.shape)) if val == 0: return np.concatenate((arr, np.zeros(padshape, dtype=arr.dtype)), axis=axis) else: return np.concatenate( (arr, (np.zeros(padshape) + val).astype(arr.dtype)), axis=axis) def _prepend_edge(arr, pad_amt, axis=-1): """ Prepend `pad_amt` to `arr` along `axis` by extending edge values. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, extended by `pad_amt` edge values appended along `axis`. """ if pad_amt == 0: return arr edge_slice = tuple(slice(None) if i != axis else 0 for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) edge_arr = arr[edge_slice].reshape(pad_singleton) return np.concatenate((edge_arr.repeat(pad_amt, axis=axis), arr), axis=axis) def _append_edge(arr, pad_amt, axis=-1): """ Append `pad_amt` to `arr` along `axis` by extending edge values. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, extended by `pad_amt` edge values prepended along `axis`. """ if pad_amt == 0: return arr edge_slice = tuple(slice(None) if i != axis else arr.shape[axis] - 1 for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) edge_arr = arr[edge_slice].reshape(pad_singleton) return np.concatenate((arr, edge_arr.repeat(pad_amt, axis=axis)), axis=axis) def _prepend_ramp(arr, pad_amt, end, axis=-1): """ Prepend linear ramp along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. end : scalar Constal value to use. For best results should be of type `arr.dtype`; if not `arr.dtype` will be cast to `arr.dtype`. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values prepended along `axis`. The prepended region ramps linearly from the edge value to `end`. """ if pad_amt == 0: return arr # Generate shape for final concatenated array padshape = tuple(x if i != axis else pad_amt for (i, x) in enumerate(arr.shape)) # Generate an n-dimensional array incrementing along `axis` ramp_arr = _arange_ndarray(arr, padshape, axis, reverse=True).astype(np.float64) # Appropriate slicing to extract n-dimensional edge along `axis` edge_slice = tuple(slice(None) if i != axis else 0 for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract edge, reshape to original rank, and extend along `axis` edge_pad = arr[edge_slice].reshape(pad_singleton).repeat(pad_amt, axis) # Linear ramp slope = (end - edge_pad) / float(pad_amt) ramp_arr = ramp_arr * slope ramp_arr += edge_pad _round_ifneeded(ramp_arr, arr.dtype) # Ramp values will most likely be float, cast them to the same type as arr return np.concatenate((ramp_arr.astype(arr.dtype), arr), axis=axis) def _append_ramp(arr, pad_amt, end, axis=-1): """ Append linear ramp along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. end : scalar Constal value to use. For best results should be of type `arr.dtype`; if not `arr.dtype` will be cast to `arr.dtype`. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The appended region ramps linearly from the edge value to `end`. """ if pad_amt == 0: return arr # Generate shape for final concatenated array padshape = tuple(x if i != axis else pad_amt for (i, x) in enumerate(arr.shape)) # Generate an n-dimensional array incrementing along `axis` ramp_arr = _arange_ndarray(arr, padshape, axis, reverse=False).astype(np.float64) # Slice a chunk from the edge to calculate stats on edge_slice = tuple(slice(None) if i != axis else -1 for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract edge, reshape to original rank, and extend along `axis` edge_pad = arr[edge_slice].reshape(pad_singleton).repeat(pad_amt, axis) # Linear ramp slope = (end - edge_pad) / float(pad_amt) ramp_arr = ramp_arr * slope ramp_arr += edge_pad _round_ifneeded(ramp_arr, arr.dtype) # Ramp values will most likely be float, cast them to the same type as arr return np.concatenate((arr, ramp_arr.astype(arr.dtype)), axis=axis) def _prepend_max(arr, pad_amt, num, axis=-1): """ Prepend `pad_amt` maximum values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. num : int Depth into `arr` along `axis` to calculate maximum. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The prepended region is the maximum of the first `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _prepend_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on max_slice = tuple(slice(None) if i != axis else slice(num) for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate max, reshape to add singleton dimension back max_chunk = arr[max_slice].max(axis=axis).reshape(pad_singleton) # Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt` return np.concatenate((max_chunk.repeat(pad_amt, axis=axis), arr), axis=axis) def _append_max(arr, pad_amt, num, axis=-1): """ Pad one `axis` of `arr` with the maximum of the last `num` elements. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. num : int Depth into `arr` along `axis` to calculate maximum. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The appended region is the maximum of the final `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _append_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on end = arr.shape[axis] - 1 if num is not None: max_slice = tuple( slice(None) if i != axis else slice(end, end - num, -1) for (i, x) in enumerate(arr.shape)) else: max_slice = tuple(slice(None) for x in arr.shape) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate max, reshape to add singleton dimension back max_chunk = arr[max_slice].max(axis=axis).reshape(pad_singleton) # Concatenate `arr` with `max_chunk`, extended along `axis` by `pad_amt` return np.concatenate((arr, max_chunk.repeat(pad_amt, axis=axis)), axis=axis) def _prepend_mean(arr, pad_amt, num, axis=-1): """ Prepend `pad_amt` mean values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. num : int Depth into `arr` along `axis` to calculate mean. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values prepended along `axis`. The prepended region is the mean of the first `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _prepend_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on mean_slice = tuple(slice(None) if i != axis else slice(num) for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate mean, reshape to add singleton dimension back mean_chunk = arr[mean_slice].mean(axis).reshape(pad_singleton) _round_ifneeded(mean_chunk, arr.dtype) # Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt` return np.concatenate((mean_chunk.repeat(pad_amt, axis).astype(arr.dtype), arr), axis=axis) def _append_mean(arr, pad_amt, num, axis=-1): """ Append `pad_amt` mean values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. num : int Depth into `arr` along `axis` to calculate mean. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The appended region is the maximum of the final `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _append_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on end = arr.shape[axis] - 1 if num is not None: mean_slice = tuple( slice(None) if i != axis else slice(end, end - num, -1) for (i, x) in enumerate(arr.shape)) else: mean_slice = tuple(slice(None) for x in arr.shape) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate mean, reshape to add singleton dimension back mean_chunk = arr[mean_slice].mean(axis=axis).reshape(pad_singleton) _round_ifneeded(mean_chunk, arr.dtype) # Concatenate `arr` with `mean_chunk`, extended along `axis` by `pad_amt` return np.concatenate( (arr, mean_chunk.repeat(pad_amt, axis).astype(arr.dtype)), axis=axis) def _prepend_med(arr, pad_amt, num, axis=-1): """ Prepend `pad_amt` median values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. num : int Depth into `arr` along `axis` to calculate median. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values prepended along `axis`. The prepended region is the median of the first `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _prepend_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on med_slice = tuple(slice(None) if i != axis else slice(num) for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate median, reshape to add singleton dimension back med_chunk = np.median(arr[med_slice], axis=axis).reshape(pad_singleton) _round_ifneeded(med_chunk, arr.dtype) # Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt` return np.concatenate( (med_chunk.repeat(pad_amt, axis).astype(arr.dtype), arr), axis=axis) def _append_med(arr, pad_amt, num, axis=-1): """ Append `pad_amt` median values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. num : int Depth into `arr` along `axis` to calculate median. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The appended region is the median of the final `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _append_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on end = arr.shape[axis] - 1 if num is not None: med_slice = tuple( slice(None) if i != axis else slice(end, end - num, -1) for (i, x) in enumerate(arr.shape)) else: med_slice = tuple(slice(None) for x in arr.shape) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate median, reshape to add singleton dimension back med_chunk = np.median(arr[med_slice], axis=axis).reshape(pad_singleton) _round_ifneeded(med_chunk, arr.dtype) # Concatenate `arr` with `med_chunk`, extended along `axis` by `pad_amt` return np.concatenate( (arr, med_chunk.repeat(pad_amt, axis).astype(arr.dtype)), axis=axis) def _prepend_min(arr, pad_amt, num, axis=-1): """ Prepend `pad_amt` minimum values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to prepend. num : int Depth into `arr` along `axis` to calculate minimum. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values prepended along `axis`. The prepended region is the minimum of the first `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _prepend_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on min_slice = tuple(slice(None) if i != axis else slice(num) for (i, x) in enumerate(arr.shape)) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate min, reshape to add singleton dimension back min_chunk = arr[min_slice].min(axis=axis).reshape(pad_singleton) # Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt` return np.concatenate((min_chunk.repeat(pad_amt, axis=axis), arr), axis=axis) def _append_min(arr, pad_amt, num, axis=-1): """ Append `pad_amt` median values along `axis`. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : int Amount of padding to append. num : int Depth into `arr` along `axis` to calculate minimum. Range: [1, `arr.shape[axis]`] or None (entire axis) axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt` values appended along `axis`. The appended region is the minimum of the final `num` values along `axis`. """ if pad_amt == 0: return arr # Equivalent to edge padding for single value, so do that instead if num == 1: return _append_edge(arr, pad_amt, axis) # Use entire array if `num` is too large if num is not None: if num >= arr.shape[axis]: num = None # Slice a chunk from the edge to calculate stats on end = arr.shape[axis] - 1 if num is not None: min_slice = tuple( slice(None) if i != axis else slice(end, end - num, -1) for (i, x) in enumerate(arr.shape)) else: min_slice = tuple(slice(None) for x in arr.shape) # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) # Extract slice, calculate min, reshape to add singleton dimension back min_chunk = arr[min_slice].min(axis=axis).reshape(pad_singleton) # Concatenate `arr` with `min_chunk`, extended along `axis` by `pad_amt` return np.concatenate((arr, min_chunk.repeat(pad_amt, axis=axis)), axis=axis) def _pad_ref(arr, pad_amt, method, axis=-1): """ Pad `axis` of `arr` by reflection. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : tuple of ints, length 2 Padding to (prepend, append) along `axis`. method : str Controls method of reflection; options are 'even' or 'odd'. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt[0]` values prepended and `pad_amt[1]` values appended along `axis`. Both regions are padded with reflected values from the original array. Notes ----- This algorithm does not pad with repetition, i.e. the edges are not repeated in the reflection. For that behavior, use `mode='symmetric'`. The modes 'reflect', 'symmetric', and 'wrap' must be padded with a single function, lest the indexing tricks in non-integer multiples of the original shape would violate repetition in the final iteration. """ # Implicit booleanness to test for zero (or None) in any scalar type if pad_amt[0] == 0 and pad_amt[1] == 0: return arr ########################################################################## # Prepended region # Slice off a reverse indexed chunk from near edge to pad `arr` before ref_slice = tuple(slice(None) if i != axis else slice(pad_amt[0], 0, -1) for (i, x) in enumerate(arr.shape)) ref_chunk1 = arr[ref_slice] # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) if pad_amt[0] == 1: ref_chunk1 = ref_chunk1.reshape(pad_singleton) # Memory/computationally more expensive, only do this if `method='odd'` if 'odd' in method and pad_amt[0] > 0: edge_slice1 = tuple(slice(None) if i != axis else 0 for (i, x) in enumerate(arr.shape)) edge_chunk = arr[edge_slice1].reshape(pad_singleton) ref_chunk1 = 2 * edge_chunk - ref_chunk1 del edge_chunk ########################################################################## # Appended region # Slice off a reverse indexed chunk from far edge to pad `arr` after start = arr.shape[axis] - pad_amt[1] - 1 end = arr.shape[axis] - 1 ref_slice = tuple(slice(None) if i != axis else slice(start, end) for (i, x) in enumerate(arr.shape)) rev_idx = tuple(slice(None) if i != axis else slice(None, None, -1) for (i, x) in enumerate(arr.shape)) ref_chunk2 = arr[ref_slice][rev_idx] if pad_amt[1] == 1: ref_chunk2 = ref_chunk2.reshape(pad_singleton) if 'odd' in method: edge_slice2 = tuple(slice(None) if i != axis else -1 for (i, x) in enumerate(arr.shape)) edge_chunk = arr[edge_slice2].reshape(pad_singleton) ref_chunk2 = 2 * edge_chunk - ref_chunk2 del edge_chunk # Concatenate `arr` with both chunks, extending along `axis` return np.concatenate((ref_chunk1, arr, ref_chunk2), axis=axis) def _pad_sym(arr, pad_amt, method, axis=-1): """ Pad `axis` of `arr` by symmetry. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : tuple of ints, length 2 Padding to (prepend, append) along `axis`. method : str Controls method of symmetry; options are 'even' or 'odd'. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt[0]` values prepended and `pad_amt[1]` values appended along `axis`. Both regions are padded with symmetric values from the original array. Notes ----- This algorithm DOES pad with repetition, i.e. the edges are repeated. For padding without repeated edges, use `mode='reflect'`. The modes 'reflect', 'symmetric', and 'wrap' must be padded with a single function, lest the indexing tricks in non-integer multiples of the original shape would violate repetition in the final iteration. """ # Implicit booleanness to test for zero (or None) in any scalar type if pad_amt[0] == 0 and pad_amt[1] == 0: return arr ########################################################################## # Prepended region # Slice off a reverse indexed chunk from near edge to pad `arr` before sym_slice = tuple(slice(None) if i != axis else slice(0, pad_amt[0]) for (i, x) in enumerate(arr.shape)) rev_idx = tuple(slice(None) if i != axis else slice(None, None, -1) for (i, x) in enumerate(arr.shape)) sym_chunk1 = arr[sym_slice][rev_idx] # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) if pad_amt[0] == 1: sym_chunk1 = sym_chunk1.reshape(pad_singleton) # Memory/computationally more expensive, only do this if `method='odd'` if 'odd' in method and pad_amt[0] > 0: edge_slice1 = tuple(slice(None) if i != axis else 0 for (i, x) in enumerate(arr.shape)) edge_chunk = arr[edge_slice1].reshape(pad_singleton) sym_chunk1 = 2 * edge_chunk - sym_chunk1 del edge_chunk ########################################################################## # Appended region # Slice off a reverse indexed chunk from far edge to pad `arr` after start = arr.shape[axis] - pad_amt[1] end = arr.shape[axis] sym_slice = tuple(slice(None) if i != axis else slice(start, end) for (i, x) in enumerate(arr.shape)) sym_chunk2 = arr[sym_slice][rev_idx] if pad_amt[1] == 1: sym_chunk2 = sym_chunk2.reshape(pad_singleton) if 'odd' in method: edge_slice2 = tuple(slice(None) if i != axis else -1 for (i, x) in enumerate(arr.shape)) edge_chunk = arr[edge_slice2].reshape(pad_singleton) sym_chunk2 = 2 * edge_chunk - sym_chunk2 del edge_chunk # Concatenate `arr` with both chunks, extending along `axis` return np.concatenate((sym_chunk1, arr, sym_chunk2), axis=axis) def _pad_wrap(arr, pad_amt, axis=-1): """ Pad `axis` of `arr` via wrapping. Parameters ---------- arr : ndarray Input array of arbitrary shape. pad_amt : tuple of ints, length 2 Padding to (prepend, append) along `axis`. axis : int Axis along which to pad `arr`. Returns ------- padarr : ndarray Output array, with `pad_amt[0]` values prepended and `pad_amt[1]` values appended along `axis`. Both regions are padded wrapped values from the opposite end of `axis`. Notes ----- This method of padding is also known as 'tile' or 'tiling'. The modes 'reflect', 'symmetric', and 'wrap' must be padded with a single function, lest the indexing tricks in non-integer multiples of the original shape would violate repetition in the final iteration. """ # Implicit booleanness to test for zero (or None) in any scalar type if pad_amt[0] == 0 and pad_amt[1] == 0: return arr ########################################################################## # Prepended region # Slice off a reverse indexed chunk from near edge to pad `arr` before start = arr.shape[axis] - pad_amt[0] end = arr.shape[axis] wrap_slice = tuple(slice(None) if i != axis else slice(start, end) for (i, x) in enumerate(arr.shape)) wrap_chunk1 = arr[wrap_slice] # Shape to restore singleton dimension after slicing pad_singleton = tuple(x if i != axis else 1 for (i, x) in enumerate(arr.shape)) if pad_amt[0] == 1: wrap_chunk1 = wrap_chunk1.reshape(pad_singleton) ########################################################################## # Appended region # Slice off a reverse indexed chunk from far edge to pad `arr` after wrap_slice = tuple(slice(None) if i != axis else slice(0, pad_amt[1]) for (i, x) in enumerate(arr.shape)) wrap_chunk2 = arr[wrap_slice] if pad_amt[1] == 1: wrap_chunk2 = wrap_chunk2.reshape(pad_singleton) # Concatenate `arr` with both chunks, extending along `axis` return np.concatenate((wrap_chunk1, arr, wrap_chunk2), axis=axis) def _normalize_shape(ndarray, shape, cast_to_int=True): """ Private function which does some checks and normalizes the possibly much simpler representations of 'pad_width', 'stat_length', 'constant_values', 'end_values'. Parameters ---------- narray : ndarray Input ndarray shape : {sequence, array_like, float, int}, optional The width of padding (pad_width), the number of elements on the edge of the narray used for statistics (stat_length), the constant value(s) to use when filling padded regions (constant_values), or the endpoint target(s) for linear ramps (end_values). ((before_1, after_1), ... (before_N, after_N)) unique number of elements for each axis where `N` is rank of `narray`. ((before, after),) yields same before and after constants for each axis. (constant,) or val is a shortcut for before = after = constant for all axes. cast_to_int : bool, optional Controls if values in ``shape`` will be rounded and cast to int before being returned. Returns ------- normalized_shape : tuple of tuples val => ((val, val), (val, val), ...) [[val1, val2], [val3, val4], ...] => ((val1, val2), (val3, val4), ...) ((val1, val2), (val3, val4), ...) => no change [[val1, val2], ] => ((val1, val2), (val1, val2), ...) ((val1, val2), ) => ((val1, val2), (val1, val2), ...) [[val , ], ] => ((val, val), (val, val), ...) ((val , ), ) => ((val, val), (val, val), ...) """ ndims = ndarray.ndim # Shortcut shape=None if shape is None: return ((None, None), ) * ndims # Convert any input `info` to a NumPy array shape_arr = np.asarray(shape) try: shape_arr = np.broadcast_to(shape_arr, (ndims, 2)) except ValueError: fmt = "Unable to create correctly shaped tuple from %s" raise ValueError(fmt % (shape,)) # Cast if necessary if cast_to_int is True: shape_arr = np.round(shape_arr).astype(int) # Convert list of lists to tuple of tuples return tuple(tuple(axis) for axis in shape_arr.tolist()) def _validate_lengths(narray, number_elements): """ Private function which does some checks and reformats pad_width and stat_length using _normalize_shape. Parameters ---------- narray : ndarray Input ndarray number_elements : {sequence, int}, optional The width of padding (pad_width) or the number of elements on the edge of the narray used for statistics (stat_length). ((before_1, after_1), ... (before_N, after_N)) unique number of elements for each axis. ((before, after),) yields same before and after constants for each axis. (constant,) or int is a shortcut for before = after = constant for all axes. Returns ------- _validate_lengths : tuple of tuples int => ((int, int), (int, int), ...) [[int1, int2], [int3, int4], ...] => ((int1, int2), (int3, int4), ...) ((int1, int2), (int3, int4), ...) => no change [[int1, int2], ] => ((int1, int2), (int1, int2), ...) ((int1, int2), ) => ((int1, int2), (int1, int2), ...) [[int , ], ] => ((int, int), (int, int), ...) ((int , ), ) => ((int, int), (int, int), ...) """ normshp = _normalize_shape(narray, number_elements) for i in normshp: chk = [1 if x is None else x for x in i] chk = [1 if x >= 0 else -1 for x in chk] if (chk[0] < 0) or (chk[1] < 0): fmt = "%s cannot contain negative values." raise ValueError(fmt % (number_elements,)) return normshp ############################################################################### # Public functions def pad(array, pad_width, mode, **kwargs): """ Pads an array. Parameters ---------- array : array_like of rank N Input array pad_width : {sequence, array_like, int} Number of values padded to the edges of each axis. ((before_1, after_1), ... (before_N, after_N)) unique pad widths for each axis. ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes. mode : str or function One of the following string values or a user supplied function. 'constant' Pads with a constant value. 'edge' Pads with the edge values of array. 'linear_ramp' Pads with the linear ramp between end_value and the array edge value. 'maximum' Pads with the maximum value of all or part of the vector along each axis. 'mean' Pads with the mean value of all or part of the vector along each axis. 'median' Pads with the median value of all or part of the vector along each axis. 'minimum' Pads with the minimum value of all or part of the vector along each axis. 'reflect' Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis. 'symmetric' Pads with the reflection of the vector mirrored along the edge of the array. 'wrap' Pads with the wrap of the vector along the axis. The first values are used to pad the end and the end values are used to pad the beginning. <function> Padding function, see Notes. stat_length : sequence or int, optional Used in 'maximum', 'mean', 'median', and 'minimum'. Number of values at edge of each axis used to calculate the statistic value. ((before_1, after_1), ... (before_N, after_N)) unique statistic lengths for each axis. ((before, after),) yields same before and after statistic lengths for each axis. (stat_length,) or int is a shortcut for before = after = statistic length for all axes. Default is ``None``, to use the entire axis. constant_values : sequence or int, optional Used in 'constant'. The values to set the padded values for each axis. ((before_1, after_1), ... (before_N, after_N)) unique pad constants for each axis. ((before, after),) yields same before and after constants for each axis. (constant,) or int is a shortcut for before = after = constant for all axes. Default is 0. end_values : sequence or int, optional Used in 'linear_ramp'. The values used for the ending value of the linear_ramp and that will form the edge of the padded array. ((before_1, after_1), ... (before_N, after_N)) unique end values for each axis. ((before, after),) yields same before and after end values for each axis. (constant,) or int is a shortcut for before = after = end value for all axes. Default is 0. reflect_type : {'even', 'odd'}, optional Used in 'reflect', and 'symmetric'. The 'even' style is the default with an unaltered reflection around the edge value. For the 'odd' style, the extented part of the array is created by subtracting the reflected values from two times the edge value. Returns ------- pad : ndarray Padded array of rank equal to `array` with shape increased according to `pad_width`. Notes ----- .. versionadded:: 1.7.0 For an array with rank greater than 1, some of the padding of later axes is calculated from padding of previous axes. This is easiest to think about with a rank 2 array where the corners of the padded array are calculated by using padded values from the first axis. The padding function, if used, should return a rank 1 array equal in length to the vector argument with padded values replaced. It has the following signature:: padding_func(vector, iaxis_pad_width, iaxis, **kwargs) where vector : ndarray A rank 1 array already padded with zeros. Padded values are vector[:pad_tuple[0]] and vector[-pad_tuple[1]:]. iaxis_pad_width : tuple A 2-tuple of ints, iaxis_pad_width[0] represents the number of values padded at the beginning of vector where iaxis_pad_width[1] represents the number of values padded at the end of vector. iaxis : int The axis currently being calculated. kwargs : misc Any keyword arguments the function requires. Examples -------- >>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2,3), 'constant', constant_values=(4, 6)) array([4, 4, 1, 2, 3, 4, 5, 6, 6, 6]) >>> np.lib.pad(a, (2, 3), 'edge') array([1, 1, 1, 2, 3, 4, 5, 5, 5, 5]) >>> np.lib.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4)) array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4]) >>> np.lib.pad(a, (2,), 'maximum') array([5, 5, 1, 2, 3, 4, 5, 5, 5]) >>> np.lib.pad(a, (2,), 'mean') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> np.lib.pad(a, (2,), 'median') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> a = [[1, 2], [3, 4]] >>> np.lib.pad(a, ((3, 2), (2, 3)), 'minimum') array([[1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [3, 3, 3, 4, 3, 3, 3], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1]]) >>> a = [1, 2, 3, 4, 5] >>> np.lib.pad(a, (2, 3), 'reflect') array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2]) >>> np.lib.pad(a, (2, 3), 'reflect', reflect_type='odd') array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) >>> np.lib.pad(a, (2, 3), 'symmetric') array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3]) >>> np.lib.pad(a, (2, 3), 'symmetric', reflect_type='odd') array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7]) >>> np.lib.pad(a, (2, 3), 'wrap') array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3]) >>> def padwithtens(vector, pad_width, iaxis, kwargs): ... vector[:pad_width[0]] = 10 ... vector[-pad_width[1]:] = 10 ... return vector >>> a = np.arange(6) >>> a = a.reshape((2, 3)) >>> np.lib.pad(a, 2, padwithtens) array([[10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 0, 1, 2, 10, 10], [10, 10, 3, 4, 5, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10]]) """ if not np.asarray(pad_width).dtype.kind == 'i': raise TypeError('`pad_width` must be of integral type.') narray = np.array(array) pad_width = _validate_lengths(narray, pad_width) allowedkwargs = { 'constant': ['constant_values'], 'edge': [], 'linear_ramp': ['end_values'], 'maximum': ['stat_length'], 'mean': ['stat_length'], 'median': ['stat_length'], 'minimum': ['stat_length'], 'reflect': ['reflect_type'], 'symmetric': ['reflect_type'], 'wrap': [], } kwdefaults = { 'stat_length': None, 'constant_values': 0, 'end_values': 0, 'reflect_type': 'even', } if isinstance(mode, np.compat.basestring): # Make sure have allowed kwargs appropriate for mode for key in kwargs: if key not in allowedkwargs[mode]: raise ValueError('%s keyword not in allowed keywords %s' % (key, allowedkwargs[mode])) # Set kwarg defaults for kw in allowedkwargs[mode]: kwargs.setdefault(kw, kwdefaults[kw]) # Need to only normalize particular keywords. for i in kwargs: if i == 'stat_length': kwargs[i] = _validate_lengths(narray, kwargs[i]) if i in ['end_values', 'constant_values']: kwargs[i] = _normalize_shape(narray, kwargs[i], cast_to_int=False) else: # Drop back to old, slower np.apply_along_axis mode for user-supplied # vector function function = mode # Create a new padded array rank = list(range(narray.ndim)) total_dim_increase = [np.sum(pad_width[i]) for i in rank] offset_slices = [slice(pad_width[i][0], pad_width[i][0] + narray.shape[i]) for i in rank] new_shape = np.array(narray.shape) + total_dim_increase newmat = np.zeros(new_shape, narray.dtype) # Insert the original array into the padded array newmat[offset_slices] = narray # This is the core of pad ... for iaxis in rank: np.apply_along_axis(function, iaxis, newmat, pad_width[iaxis], iaxis, kwargs) return newmat # If we get here, use new padding method newmat = narray.copy() # API preserved, but completely new algorithm which pads by building the # entire block to pad before/after `arr` with in one step, for each axis. if mode == 'constant': for axis, ((pad_before, pad_after), (before_val, after_val)) \ in enumerate(zip(pad_width, kwargs['constant_values'])): newmat = _prepend_const(newmat, pad_before, before_val, axis) newmat = _append_const(newmat, pad_after, after_val, axis) elif mode == 'edge': for axis, (pad_before, pad_after) in enumerate(pad_width): newmat = _prepend_edge(newmat, pad_before, axis) newmat = _append_edge(newmat, pad_after, axis) elif mode == 'linear_ramp': for axis, ((pad_before, pad_after), (before_val, after_val)) \ in enumerate(zip(pad_width, kwargs['end_values'])): newmat = _prepend_ramp(newmat, pad_before, before_val, axis) newmat = _append_ramp(newmat, pad_after, after_val, axis) elif mode == 'maximum': for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \ in enumerate(zip(pad_width, kwargs['stat_length'])): newmat = _prepend_max(newmat, pad_before, chunk_before, axis) newmat = _append_max(newmat, pad_after, chunk_after, axis) elif mode == 'mean': for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \ in enumerate(zip(pad_width, kwargs['stat_length'])): newmat = _prepend_mean(newmat, pad_before, chunk_before, axis) newmat = _append_mean(newmat, pad_after, chunk_after, axis) elif mode == 'median': for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \ in enumerate(zip(pad_width, kwargs['stat_length'])): newmat = _prepend_med(newmat, pad_before, chunk_before, axis) newmat = _append_med(newmat, pad_after, chunk_after, axis) elif mode == 'minimum': for axis, ((pad_before, pad_after), (chunk_before, chunk_after)) \ in enumerate(zip(pad_width, kwargs['stat_length'])): newmat = _prepend_min(newmat, pad_before, chunk_before, axis) newmat = _append_min(newmat, pad_after, chunk_after, axis) elif mode == 'reflect': for axis, (pad_before, pad_after) in enumerate(pad_width): if narray.shape[axis] == 0: # Axes with non-zero padding cannot be empty. if pad_before > 0 or pad_after > 0: raise ValueError("There aren't any elements to reflect" " in axis {} of `array`".format(axis)) # Skip zero padding on empty axes. continue # Recursive padding along any axis where `pad_amt` is too large # for indexing tricks. We can only safely pad the original axis # length, to keep the period of the reflections consistent. if ((pad_before > 0) or (pad_after > 0)) and newmat.shape[axis] == 1: # Extending singleton dimension for 'reflect' is legacy # behavior; it really should raise an error. newmat = _prepend_edge(newmat, pad_before, axis) newmat = _append_edge(newmat, pad_after, axis) continue method = kwargs['reflect_type'] safe_pad = newmat.shape[axis] - 1 while ((pad_before > safe_pad) or (pad_after > safe_pad)): pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad)) pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad)) newmat = _pad_ref(newmat, (pad_iter_b, pad_iter_a), method, axis) pad_before -= pad_iter_b pad_after -= pad_iter_a safe_pad += pad_iter_b + pad_iter_a newmat = _pad_ref(newmat, (pad_before, pad_after), method, axis) elif mode == 'symmetric': for axis, (pad_before, pad_after) in enumerate(pad_width): # Recursive padding along any axis where `pad_amt` is too large # for indexing tricks. We can only safely pad the original axis # length, to keep the period of the reflections consistent. method = kwargs['reflect_type'] safe_pad = newmat.shape[axis] while ((pad_before > safe_pad) or (pad_after > safe_pad)): pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad)) pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad)) newmat = _pad_sym(newmat, (pad_iter_b, pad_iter_a), method, axis) pad_before -= pad_iter_b pad_after -= pad_iter_a safe_pad += pad_iter_b + pad_iter_a newmat = _pad_sym(newmat, (pad_before, pad_after), method, axis) elif mode == 'wrap': for axis, (pad_before, pad_after) in enumerate(pad_width): # Recursive padding along any axis where `pad_amt` is too large # for indexing tricks. We can only safely pad the original axis # length, to keep the period of the reflections consistent. safe_pad = newmat.shape[axis] while ((pad_before > safe_pad) or (pad_after > safe_pad)): pad_iter_b = min(safe_pad, safe_pad * (pad_before // safe_pad)) pad_iter_a = min(safe_pad, safe_pad * (pad_after // safe_pad)) newmat = _pad_wrap(newmat, (pad_iter_b, pad_iter_a), axis) pad_before -= pad_iter_b pad_after -= pad_iter_a safe_pad += pad_iter_b + pad_iter_a newmat = _pad_wrap(newmat, (pad_before, pad_after), axis) return newmat