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To further engage audiences during live matches at Tennis Challenger Cordenons Italy tomorrow,<|end_of_generation|>[0]: """ [1]: .. module:: ndimage [2]: :platform: Unix [3]: :synopsis: Provide image processing functions. [4]: .. moduleauthor:: "Razvan Marinescu" [5]: .. moduleauthor:: "Ralf Gommers" [6]: """ [7]: import numpy as np [8]: from . import _ni_support [9]: from . import _nd_image [10]: from . import _ni_math [11]: from ._spline_filter import _spline_filter1d [12]: from ._spline_filter import _map_coordinates_fourth_order [13]: __all__ = ['generic_filter', 'maximum_filter', 'minimum_filter', 'percentile_filter', [14]: 'uniform_filter', 'median_filter', 'gaussian_filter', [15]: 'convolve', 'correlate', 'shift', 'affine_transform', 'rotate', [16]: 'map_coordinates'] [17]: # ----------------------------------------------------------------------------- [18]: # Helper functions [19]: def _get_output(output): [20]: if output is None: [21]: return None [22]: elif output == 'all': [23]: return np.ones_like(input) [24]: elif isinstance(output, np.ndarray): [25]: return output [26]: else: [27]: raise ValueError('output must be either None or "all" or array') [28]: def _get_ndoutput(output): [29]: if output == 'all': [30]: dtype = np.float32 if input.dtype == np.float16 else input.dtype [31]: return np.ones(input.shape + (order + 1,), dtype=dtype) [32]: elif isinstance(output, np.ndarray): [33]: return output [34]: else: [35]: raise ValueError('output must be either None or "all" or array') [36]: def _get_pad_input(input_shape, footprint_shape): [37]: if len(input_shape) != len(footprint_shape): [38]: raise RuntimeError('input shape must have same dimensions as footprint') [39]: pad_width = [] [40]: pad_value = [0] * (2 * len(input_shape)) [41]: min_footprint = [min(footprint_shape[i]) - footprint_shape[i][0] + input_shape[i] [42]: for i in range(len(input_shape))] [43]: max_footprint = [max(footprint_shape[i]) - footprint_shape[i][0] + input_shape[i] [44]: for i in range(len(input_shape))] [45]: center_footprint = [(min_footprint[i] + max_footprint[i]) / float(2) [46]: for i in range(len(input_shape))] ***** Tag Data ***** ID: 1 description: Function `_get_pad_input` calculates padding width based on input shape and footprint shape using advanced list comprehensions. start line: 36 end line: 46 dependencies: - type: Function name: _get_pad_input start line: 36 end line: 46 context description: This function is likely used internally by image processing functions that require padding input arrays based on a specified footprint shape. algorithmic depth: 4 algorithmic depth external: N obscurity: 3 advanced coding concepts: 3 interesting for students: 5 self contained: Y ************ ## Challenging aspects ### Challenging aspects in above code 1. **Dimensional Consistency**: The function ensures that `input_shape` has the same dimensions as `footprint_shape`. Students need to ensure that any modifications respect this constraint. 2. **Boundary Calculations**: The calculation of `min_footprint` and `max_footprint` involves non-trivial arithmetic operations which depend on indexing within `footprint_shape`. Misunderstanding these calculations could lead to incorrect padding. 3. **Center Calculation**: The computation of `center_footprint` uses floating-point arithmetic which adds complexity when dealing with integer-based array shapes. ### Extension 1. **Variable Footprint Shapes**: Extend support beyond fixed footprint shapes by allowing dynamic changes during execution. 2. **Non-uniform Padding**: Implement non-uniform padding where different sides (e.g., left vs right) might have different padding values. 3. **Handling Different Data Types**: Ensure that padding calculations work correctly regardless of whether input shapes are integers or floats. ## Exercise ### Task Description: You are required to extend the provided function `[SNIPPET]` which calculates padding widths based on given input shapes and footprint shapes. **Requirements**: 1. **Dynamic Footprint Shape Changes**: Modify `_get_pad_input` so that it can handle dynamic changes in `footprint_shape` during execution. 2. **Non-uniform Padding**: Extend functionality so that different sides (left/right/top/bottom) can have different padding values. 3. **Multi-dimensional Support**: Ensure your solution supports inputs where dimensions can be more than two (e.g., three-dimensional arrays). ### Constraints: - You cannot use external libraries other than Python standard libraries. - You must ensure backward compatibility; existing functionality should not break. ### Input: - `input_shape`: List or tuple representing dimensions of input data. - `footprint_shapes`: List of lists/tuples representing multiple possible footprint shapes. ### Output: - `pad_width`: List representing calculated pad widths per dimension considering all possible footprint shapes. - `pad_value`: List representing calculated pad values per dimension considering all possible footprint shapes. python def _get_pad_input(input_shape, footprint_shapes): ## Solution python def _get_pad_input(input_shape, footprint_shapes): # Ensure all footprint_shapes have correct dimensions matching input_shape length if any(len(input_shape) != len(footprint) for footprint in footprint_shapes): raise RuntimeError('All footprints must have same dimensions as input') pad_width = [] pad_value = [0] * (2 * len(input_shape)) # Initialize minimums & maximums lists min_footprints = [[] for _ in range(len(input_shape))] max_footprints = [[] for _ in range(len(input_shape))] # Iterate over each possible footprint shape for footprint in footprint_shapes: current_min_footprints = [min(footprint[i]) - footprint[i][0] + input_shape[i] for i in range(len(input_shape))] current_max_footprints = [max(footprint[i]) - footprint[i][0] + input_shape[i] for i in range(len(input_shape))] min_footprints = [min(current_min_footprints[i], min_footprints[i]) if min_footprints[i] else current_min_footprints