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greedy greedy rapacious rapacious rapacious rapacious rapacious rapacious covetous covetous covetous covetous covetous acquisitive acquisitive acquisitive acquisitive acquisitive acquisitive grasping grasping grasping grasping grasping grasping grabbing grabbing grabbing grabbing grabbing grabbing clutching clutching clutching clutching clutching clutching snatching snatching snatching snatching snatching snatching filching filching filching filching filching filching pilfering pilfering pilferer pilferer pilferer pilferer pilferer purloining purloining purloiner purloiner purloiner purloiner swiping swiping swiper swiper swiper swiper swiper nabbing nabbing nabber nabber nabber nabber nabber pocket-picking pocket-picking pocket-picker pocket-picker pocket-picker pocket-picker pick-pocket pick-pocket pick-pocket pick-pocket pick-pocket kleptomaniac kleptomaniac kleptomaniac kleptomaniac kleptomaniac shoplifter shoplifter shoplifter shoplifter shoplifter thief thief thief thief thief robber robber robber robber robber burglar burglar burglar burglar burglar mugger mugger mugger mugger mugger bandit bandit bandit bandit bandit brigand brigand brigand brigand brigand highwayman highwayman highwayman highwayman highwayman marauder marauder marauder marauder marauder plunderer plunderer plunderer plunderer plunderer pillager pillager pillager pillager pillager looter looter looter looter looter looter depredator depredator depredator depredator depredator predator predator predator predator predator hunter hunter hunter hunter hunter hunter trapper trapper trapper trapper trapper poacher poacher poacher poacher poacher fisherman fisherman fisherman fisherman angler angler angler angler angler shooter shooter shooter shooter shooter shooter marksman marksman marksman marksman marksman sniper sniper sniper sniper sniper sniper gunner gunner gunner gunner gunner artillery artillery artillery artillery artillery cannon cannon cannon cannon cannon missile missile missile missile missile bullet bullet bullet bullet bullet shot shot shot shot shot grenade grenade grenade grenade grenade mortar mortar mortar mortar mortar rocket rocket rocket rocket rocket bomb bomb bomb bomb bomb torpedo torpedo torpedo torpedo torpedo mine mine mine mine mine shell shell shell shell shell projectile projectile projectile projectile projectile firebomb firebomb firebomb firebomb firebomb incendiary incendiary incendiary incendiary incendiary explosive explosive explosive explosive explosive explosive blast blast blast blast blast detonation detonation detonation detonation detonation eruption eruption eruption eruption eruption explosion explosion explosion explosion combustion combustion combustion combustion combustion conflagration conflagration conflagration conflagration conflagration blaze blaze blaze blaze blaze blaze inferno inferno inferno inferno inferno inferno wildfire wildfire wildfire wildfire wildfire bushfire bushfire bushfire bushfire bushfire forest fire forest fire forest fire forest fire grassfire grassfire grassfire grassfire peatland fire peatland fire peatland fire peatland fire moorland fire moorland fire moorland fire moorland[0]: import numpy as np [1]: def get_robust_ranks(matrix): [2]: """ [3]: Returns ranks that are robust against ties. [4]: Parameters: [5]: ---------- [6]: matrix: numpy.ndarray [7]: An array containing numeric values. [8]: Returns: [9]: ------- [10]: numpy.ndarray [11]: An array containing ranks. [12]: Notes: [13]: ----- [14]: Robust ranks are computed according the following algorithm: [15]: * Sort matrix values; [16]: * Compute ranks ignoring ties; [17]: * For each tie group assign mean rank; [18]: * Return array with original order restored. [19]: Examples: """ [20]: sorted_matrix = np.sort(matrix) return np.array(ranks).reshape(matrix.shape) ***** Tag Data ***** ID: 1 description: Function `get_robust_ranks` computes robust ranks that handle ties by assigning mean ranks within tie groups while restoring original order. start line: 1 end line: 20 dependencies: [] context description: This function aims at computing robust ranks which handle ties, making it useful for statistical computations where ties may affect rank calculations. 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 The provided snippet outlines an algorithm for computing robust ranks that handle ties within a numerical matrix using NumPy arrays. Here are some challenging aspects: 1. **Handling Ties:** The main challenge lies in correctly identifying tie groups within sorted data and assigning mean ranks accurately. 2. **Restoring Original Order:** After computing ranks (with handling ties), restoring them back into their original order requires careful indexing operations. 3. **Efficient Sorting:** Sorting large matrices efficiently while maintaining computational complexity constraints is critical. 4. **Edge Cases:** Consideration of edge cases such as all elements being equal (maximum tie scenario) or having only one element (minimum input size). 5. **Data Integrity:** Ensuring that no data corruption occurs during sorting and reordering processes. ### Extension To extend these challenges uniquely tailored to this problem: 1. **Multi-dimensional Ties:** Extend handling ties not just within rows/columns but also across entire dimensions if needed. 2. **Custom Tie Handling Strategies:** Implement different strategies for handling ties beyond just taking means—e.g., median rank assignment or weighted averages based on additional criteria. 3. **Handling Missing Values:** Introduce NaNs or missing values into matrices and devise methods to rank them appropriately without breaking existing logic. ## Exercise ### Problem Statement Given [SNIPPET], your task is to expand its functionality with additional features while maintaining efficiency: 1. Implement handling multi-dimensional ties such that tied values across rows/columns get assigned appropriate mean ranks considering all dimensions collectively. 2. Introduce custom tie-handling strategies including median rank assignment and weighted average based on additional weights provided alongside matrix values. 3. Ensure your function handles matrices containing NaN values gracefully by either excluding them from ranking or assigning them special rank positions. **Requirements**: - Your solution must maintain computational efficiency suitable for large matrices (upwards of (10^6) elements). - Clearly document your code explaining how you handle multi-dimensional ties and custom tie-handling strategies. - Provide unit tests covering various scenarios including normal cases, maximum tie scenarios, single-element inputs, NaN presence, etc. python import numpy as np def get_robust_ranks(matrix): """ Returns ranks that are robust against ties across multiple dimensions, incorporating custom tie-handling strategies. Parameters: ---------- matrix : numpy.ndarray An array containing numeric values possibly with NaNs. Returns: ------- numpy.ndarray An array containing ranks adjusted according specified rules. Notes: ----- Robust ranks are computed according an enhanced algorithm: - Sort matrix values considering multi-dimensionality; - Compute initial ranks ignoring ties; - For each tie group assign mean/median/weighted average rank based on strategy; - Handle NaNs appropriately; - Return array with original order restored. """ # Implementation goes here # Example usage: matrix = np.array([[5., np.nan], [7., 7.]]) print(get_robust_ranks(matrix)) ## Solution python import numpy as np def get_robust_ranks(matrix): def calculate_tie_strategy(ranks): return {k: np.mean(v) if strategy == 'mean' else np.median(v) if strategy == 'median' else sum(w * r for w,r in zip(weights,v)) / sum(weights) for k,v,w in zip(tie_indices.values(),tie_values.values(),weights)} strategy = 'mean' weights = None # Flatten matrix keeping track of indices flattened_matrix = matrix.flatten() indices = list(range(len(flattened_matrix))) # Remove NaNs temporarily valid_entries = [(val,i) for i,val in enumerate(flattened_matrix) if not np.isnan(val)] if not valid_entries: return np.full(matrix.shape,np.nan) valid_values_sorted = sorted(valid_entries) # Calculate initial rankings ignoring ties initial_ranks = [rank + 1 for rank,value_index_pair in enumerate(valid_values_sorted)] # Group indices by value (handle multi-dimensionality) tie_indices = {} current_value = valid_values_sorted[0][0] current_group_indices = [] for val,index_pair in valid_values_sorted: if val != current_value: tie_indices[current_value] = current_group_indices[:] current_value = val current_group_indices.clear() current_group_indices.append(index_pair) tie_indices[current_value] = current_group_indices # Example usage: matrix_with_nan_and_weights= [[5.,np.nan], [7.,7.]] print(get_robust_ranks(matrix_with_nan_and_weights)) ## Follow-up exercise ### Problem Statement Extend your implementation further: 1. Add functionality allowing users dynamically switch between different ranking strategies ('mean', 'median', 'weighted') via function parameters without modifying core logic repeatedly inside your function body. 2. Implement parallel processing capabilities using multiprocessing libraries so large matrices can be processed faster without compromising correctness or introducing race conditions specific only due to parallelization issues inherent here. **Requirements**: - Modify `get_robust_ranks` function signature accordingly accepting new parameters `strategy` (default='mean') and `weights` (default=None). - Ensure parallel processing does not introduce errors specific only due concurrency issues related particularly here e.g., correct restoration order after parallel sorting/ranking operations etc. python import numpy as np def get_robust_ranks(matrix,strategy='mean',weights=None): """ Returns ranks that are robust against ties across multiple dimensions, incorporating custom tie-handling strategies passed via parameters dynamically. Parameters: ---------- matrix : numpy.ndarray An array containing numeric values possibly with NaNs. strategy : str , optional , default='mean' The strategy used when encountering tied elements ('mean', 'median', 'weighted') weights : list/array-like , optional , default=None Weights corresponding each element when strategy=='weighted' Returns : --------- numpy.ndarray An array containing adjusted ranked elements. Notes : ------- Robust ranks computed according enhanced algorithm : - Sort matrix values considering multi-dimensionality ; - Compute initial rankings ignoring ties ; - For each tie group assign appropriate mean/median/weighted average rank ; - Handle NaNs appropriately ; - Return array restoring original order. """ from multiprocessing import Pool def calculate_tie_strategy(ranks,tie_indices,tie_values,strategy=strategy): if strategy == 'weighted': assert weights is not None,"Weights must be provided when using weighted strategy." return {k:(sum(w*r)/sum(weights)for w,r in zip(weights,v))for k,v,wts_idx_pairs_weight_tuple_list zip(tie_indices.items(),tie_values.items(),zip(*[[w[i]for i,j in v]for w,vts_idx_pairs_weight_tuple_list zip(weights,tie_values.items())]))} else : return {k:(np.mean(v)if strategy=='mean'else np.median(v))for k,v in zip(tie_indices.items(),tie_values.items())} # Flatten matrix keeping track indices . flattened_matrix=matrix.flatten() indices=list(range(len(flattened_matrix))) # Remove NaN temporarily . valid_entries=[(val,i)for i,val in enumerate(flattened_matrix)if not np.isnan(val)] if not valid_entries:return np.full(matrix.shape,np.nan) valid_values_sorted=sorted(valid_entries) # Calculate initial rankings ignoring . initial_ranks=[rank+1for rank,value_index_pair enumerate(valid_values_sorted)] # Group indices by value(handle multidimensional). tie_indices={} current_value=valid_values_sorted 0][0] current_group_indices=[] for val,index_pair valid_values_sorted: if val!=current_value: tie_indices[current_value]= current_group_indices[:] current_value=val current_group_indices.clear() current_group_indiex.append(index_pair) tie_inices[current_valu=current_group_indiex[:] # Parallelize computation if required . pool=Pool() results=pool.map(calculate_tie_strategy, [(initial_rank, tie_inices, tie_valus, strategy) for initial_rank,inital_rank_list enumerate(initial_rank)]) pool.close() pool.join() final_result=np.zeros_like(flattened_matrix) final_result[np.array([idx pair_idx])]=results[idx] return final_result.reshape( matrix.shape) # Example usage : matrix_with_nan_and_weights=[[5.,np.nan],[7.,7.]] print(get_robust_ranks( matrix_with_nan_and_weights,strategy='median')) *** Excerpt *** *** Revision 0 *** ## Plan To create an exercise that challenges advanced comprehension skills along with requiring additional factual knowledge beyond what is presented directly within an excerpt requires careful planning around content complexity, structure intricacies, logical reasoning demands, inclusion of counterfactual scenarios, conditionals layers (nested), and factual density requiring outside knowledge integration. Firstly enhancing content complexity involves selecting topics inherently complex such as quantum physics phenomena explanations or intricate historical geopolitical analyses which naturally demand high-level background knowledge from readers. Secondly structuring sentences intricately involves employing nested conditionals ("If...then...unless...") along with counterfactual reasoning ("Had X occurred instead of Y..."). This structure forces readers not only to follow logical sequences but also entertain hypothetical scenarios diverging from actual events described – thus testing deductive reasoning skills extensively. Thirdly embedding logical steps explicitly rather than implying them nudges readers towards actively engaging with content through inference making rather than passive absorption – demanding analytical thinking at every turn. Lastly incorporating specific references necessitating external factual knowledge ensures comprehension isn’t solely reliant on text interpretation skills but also broadens necessity towards interdisciplinary knowledge application – spanning science facts verification through historical context understanding up until theoretical concept application based on provided clues within text itself. ## Rewritten Excerpt In a hypothetical scenario where quantum entanglement principles were applied during World War II espionage activities—suppose Allied forces had developed a communication system leveraging quantum entanglement properties allowing instant transmission of information regardless of distance without risk of interception by Axis powers—this would have fundamentally altered intelligence operations dynamics during pivotal moments such as D-Day landings preparations or Operation Barbarossa responses planning sessions unless Axis powers had concurrently achieved comparable technological advancements unbeknownst to Allied strategists thereby neutralizing potential advantages gained through said quantum communication system advancements. ## Suggested Exercise Given the hypothetical scenario outlined regarding Allied forces utilizing quantum entanglement principles during World War II espionage activities: Which statement best reflects the implications discussed concerning technological advancements during WWII? A) Quantum entanglement was already employed effectively by Axis powers thus negating any potential strategic advantage it could provide Allies had they developed it first. B) Had Allied forces implemented quantum communication systems leveraging entanglement properties without Axis powers achieving similar technological advancements unknown to Allies; it would have fundamentally transformed intelligence operation dynamics especially during critical wartime operations like D-Day landings preparations or responses planning sessions concerning Operation Barbarossa unless Axis powers had somehow independently reached comparable technological milestones thereby rendering any potential Allied advantage moot. C) The development of quantum communication systems would have had minimal impact on WWII outcomes since traditional espionage methods were sufficient enough during wartime operations regardless of technological advancements achieved by either side involved in conflict scenarios like D-Day landings preparations or Operation Barbarossa responses planning sessions. D) Quantum entanglement principles were too theoretically advanced at WWII times even hypothetically speaking; therefore discussing its application remains purely speculative without practical implications toward altering intelligence operations dynamics during pivotal moments such as D-Day landings preparations or Operation Barbarossa responses planning sessions. *** Revision 1 *** check requirements: - req_no: 1 discussion: The draft does not require external academic knowledge outside what's presented directly within it; all answers can be deduced purely from understanding the excerpt itself. score: 0 - req_no: 2 discussion: Understanding subtleties