M25 Manama stats & predictions

Crafting Your Betting Strategy

• Analyzing Trends: Familiarize yourself with historical trends in player performances during similar tournaments or conditions.
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• Balancing Intuition & Data: Merge intuitive judgments about player capabilities with hard data-driven insights from experts.
• Pacing Your Bets: Distribute your stakes wisely throughout different rounds rather than concentrating them solely on final outcomes.
• Leveraging Free Resources: Maintain awareness about free resources providing quality analysis without additional costs involved.

  The Impactful Role Of Live Commentary And Analysis During Matches

  In addition to pre-match predictions,<|...|>|end|>][0]: # Copyright (c) Facebook, Inc. and its affiliates. [1]: # [2]: # This source code is licensed under the MIT license found in the [3]: # LICENSE file in the root directory of this source tree. [4]: import torch [5]: import torch.nn.functional as F [6]: from .base_model import BaseModel [7]: class ConvDecoder(BaseModel): [8]: """ [9]: A decoder that takes latent vectors sampled from prior/posterior [10]: distributions over latents/pixels given images, [11]: then decodes them into images. [12]: """ [13]: def __init__(self, [14]: n_channels=3, [15]: n_latents=10, [16]: hidden_dims=[512], [17]: kernel_size=4, [18]: stride=1, [19]: padding=0, [20]: output_padding=0, [21]: activation=F.relu): ***** Tag Data ***** ID: N1 description: Initialization method (__init__) for ConvDecoder class which includes parameters configuration for neural network layers such as number of channels (n_channels), latent dimensions (n_latents), hidden dimensions (hidden_dims), kernel size (kernel_size), stride (stride), padding (padding), output padding (output_padding), activation function (activation). start line: 13 end line: 22 dependencies: - type: Class name: ConvDecoder start line: 7 end line: 12 context description: This snippet initializes various parameters that will be used later in constructing convolutional layers within this decoder model. algorithmic depth: 4 algorithmic depth external: N obscurity: 3 advanced coding concepts: 4 interesting for students: 5 self contained: N ************ ## Challenging Aspects ### Challenging aspects in above code 1. **Parameter Management**: Understanding how each parameter (`n_channels`, `n_latents`, `hidden_dims`, etc.) affects both individual layers within convolutional networks and overall model architecture requires deep knowledge about neural networks. 2. **Layer Construction**: Building convolutional layers dynamically based on variable parameters such as `hidden_dims` involves creating flexible loops or functions that correctly initialize each layer according to given specifications. 3. **Activation Functions**: Properly integrating activation functions within convolutional layers while maintaining flexibility requires careful consideration regarding where activations should be applied relative to convolutions/batch normalization layers. 4. **Handling Edge Cases**: Managing edge cases like mismatched dimensions due to incorrect parameter settings (e.g., stride-padding combinations leading to non-compatible tensor sizes) adds complexity. 5. **Forward Pass Logic**: Implementing logic that correctly processes input through multiple dynamically created layers while handling intermediate outputs requires advanced understanding. ### Extension 1. **Dynamic Architecture Changes**: Allowing modifications at runtime such as adding/removing layers or changing configurations dynamically without reinitializing everything from scratch would increase complexity. 2. **Advanced Activation Functions**: Incorporating advanced/custom activation functions that might have additional parameters themselves could further challenge students. 3. **Conditional Layer Execution**: Adding conditional execution paths within forward pass logic depending upon input properties or intermediate outputs introduces additional algorithmic depth. ## Exercise ### Problem Statement: You are required to expand upon [SNIPPET] provided below by implementing a full-fledged Convolutional Decoder model class named `ConvDecoder`. This model should dynamically construct its architecture based on initialization parameters specified at object creation time. #### Requirements: 1. **Initialization Parameters**: - `n_channels`: Number of output channels after decoding. - `n_latents`: Dimensionality of latent vector input. - `hidden_dims`: List specifying number of channels per hidden layer. - `kernel_size`: Kernel size for all convolution operations. - `stride`: Stride size for all convolution operations. - `padding`: Padding size for all convolution operations. - `output_padding`: Output padding size if needed especially for transposed convolutions. - `activation`: Activation function used after each convolution operation. 2. **Dynamic Layer Construction**: - Dynamically construct transposed convolutional layers using provided parameters (`kernel_size`, `stride`, etc.) - Ensure compatibility between consecutive layers regarding tensor shapes. 3. **Forward Pass Implementation**: - Implement forward pass logic that processes input latent vectors through constructed layers properly applying activations between convolutions where necessary. 4. **Edge Case Handling**: - Handle cases where parameter values might lead to incompatible tensor sizes across layer transitions gracefully by raising appropriate errors/messages. python class ConvDecoder(BaseModel): """ A decoder that takes latent vectors sampled from prior/posterior distributions over latents/pixels given images, then decodes them into images. """ def __init__(self, n_channels=3, n_latents=10, hidden_dims=[512], kernel_size=4, stride=1, padding=0, output_padding=0, activation=F.relu): super(ConvDecoder, self).__init__() self.n_channels = n_channels # Initialize first linear layer transforming latents into initial feature map dimensions self.fc = nn.Linear(n_latents, hidden_dims[-1] * ((kernel_size * stride) + output_padding)) # List holding sequential layers including transposed convolutions & activations self.layers = nn.ModuleList() current_dim = hidden_dims[-1] # Construct dynamic sequence of transposed convolutions & activations for h_dim in reversed(hidden_dims[:-1]): self.layers.append(nn.ConvTranspose2d( current_dim, h_dim, kernel_size=kernel_size, stride=stride, padding=padding, output_padding=output_padding)) self.layers.append(activation) current_dim = h_dim # Final transposed convolution layer converting last hidden dimension back into image space self.final_layer = nn.Sequential( nn.ConvTranspose2d(current_dim, n_channels, kernel_size), nn.Tanh() # Using TanH assuming image pixel values range [-1 ,1] ) def forward(self,x): x = self.fc(x) x = x.view(-1,self.hidden_dims[-1],((self.kernel_size*self.stride)+self.output_padding),(self.kernel_size*self.stride)+self.output_padding) # Process through dynamic sequence for layer in self.layers: x = layer(x) x = self.final_layer(x) return x # Test case demonstrating instantiation & usage if __name__ == "__main__": decoder = ConvDecoder(n_channels=3,n_latents=100,hiddens=[256],kernel_size=(4,),stride=(2,),padding=(1,),output_padding=(0,),activation=F.leaky_relu) sample_input = torch.randn(8 ,100) decoded_output = decoder(sample_input) ## Follow-up Exercise ### Problem Statement: Building upon your previous implementation: #### Requirements: 1. Modify your implementation so that it supports variable-sized inputs dynamically adjusting internal structures accordingly without requiring explicit re-initialization every time input size changes. 2. Extend functionality allowing custom-defined activation functions which may require additional parameters beyond standard PyTorch activations like PReLU having learnable parameters or custom-defined ones entirely written from scratch. python # Custom Activation Function Example class CustomActivation(nn.Module): def __init__(self): super(CustomActivation,self).__init__() # Define any learnable params if needed def forward(self,x): return torch.max(torch.zeros_like(x),x) + torch.min(torch.zeros_like(x),x).pow(0) # Adjusted Convolution Decoder incorporating Custom Activation Function class AdvancedConvDecoder(ConvDecoder): def __init__(self,*args,**kwargs): super().__init__(*args,**kwargs) if isinstance(kwargs['activation'],CustomActivation): print("Custom Activation Detected") # Usage Example if __name__ == "__main__": advanced_decoder = AdvancedConvDecoder(n_channels=3,n_latents=100,hiddens=[256],kernel_size=(4,),stride=(2,),padding=(1,),output_padding=(0,),activation=CustomActivation()) sample_input = torch.randn(8 ,100) decoded_output_adv = advanced_decoder(sample_input) This follow-up exercise encourages students not only to understand but also extend functionality creatively adapting models dynamically responding flexibly both structurally & functionally. <>: Hi there! I'm working with this Python function called `_get_pos_z` which calculates positions (`pos`) and depths (`z`) along rays using TensorFlow operations like cumulative sums and trigonometric transformations: python def _get_pos_z_from_rays(rays_o_mask_rts_static tubs_dict): """ rays_o_mask_rts_static: (*B,P) -> (*B,P,D) xyz t : camera origin + normalized direction + mask + ray origin t (*B,P) -> (*B,P) length : length of corresponding segments / lengths[i,j]=1 means i==j ,i!=j means length[i,j] represents distance between i,j (*B,P,Rt) -> (*B,P,Rt,D) rays_o : original rays before normalization tubs_dict: 'w': Tensor(*B,T,w) 'h': Tensor(*B,T,h) 'K_tensor': Tensor(*B,K,K) 'depth_map': Tensor(*B,T,H,W,d) 'segment_mask': Tensor(*B,T,H,W,m) 'mask_image': Tensor(*B,T,H,W,c) 'rays_to_img_np': numpy array Rt,(8,) T : num_of_frames B : batch size usually equals to rpn_batchsize H : height W : width P : num_of_proposals usually equals to proposals_per_frame*number_of_frames D : dimention accrodingly equals to xyz t or xyzw Rt : ray origin t plus rotation matrix (to project ray onto image plane) [[u00,u01,...u0W,u10,u11,...u1W,...uH0,,uHW].u20,...uHW].t] := [u_vector,t] u_vector:= vector representing unit direction in camera coordinate system t:=translation vector representing origin point u_vector.shape=:(*B,P,Rt,D-1)=(,*B,P,Rt,3) translation.shape=:(*B,P,Rt,(D-1)=(*B,P,Rt,1)=(*B,P,Rt) Rt.D==*(Rt,D)=(Rt,D-1)+Rt,: since we consider transform ray direction together with origin point , so we need concatenate u_vector,t instead of only use u_vector so Rt.D equals D instead D-1 hence Rt.D==D==(*B,P,Rt,D)=(,*B,P,Rt,D-1)+(*B,P,Rt,(D-1)=(*B,P,Rt,D)=(,*B,P,Rt,D-1)+(*B,P,Rt,) hence we use D instead D-1 represent dimension extending one dimension represents only ray origin t . since we use pose instead transform because pose represent transformation matrix composed original rotation matrix ,translation vector . pose represent combination rotaion matrix catesenate translation vector represents actual transformation . hence pose represent transformation matrix . Hence Rt.D==D==(*B,P,Rt,D)=(,*B,P,Rt,D-1)+(*B,P,Rt,(D-1)=(*B.P.Rt,D)=(,*B.P.Rt,D-1)+(*b.P.R,.R,) since we use pose instead transform because pose represent transformation matrix composed original rotation matrix ,translation vector . pose represent combination rotaion matrix catesenate translation vector represents actual transformation . hence pose represent transformation matrix . We omit B denote batchsize because we assume all data has same batchsize ,hence we omit B fro simplicity without loss generality . We omit P denote proposal number because we assume all data has same proposal number ,hence we omit P fro simplicity without loss generality . We omit T denote frame number because we assume all data has same frame number ,hence we omit T fro simplicity without loss generality . Rt.D==D==(*)P.R.(D)=(*,P.R.(D-1))+(P.R.(D-)(,) Since D==*(D-)++() Since ()==(D-)++() Since ()==(,) Hence ()==(,) Hence () represents only one element denoting only t . We omit * denote batchsize*proposal numbers*frame numbers because we do not distinguish different index between elements inside batchsize*proposal numbers*frame numbers , since elements inside batchsize*proposal numbers*frame numbers has same characteristics , since our computation does not distinguish one element respect difference among index , since our computation regards whole batchsize*proposal numbers*frame numbers equally , since our computation does not distinguish one element respect difference among index , since our computation regards whole batchsize*proposal numbers*frame numbers equally , hence we omit * denote batchsize*proposal numbers*frame numbers because no difference exist inside batchsize*proposal numbers*frame numbers . (*)P.R.(D)==(*)P.R.(D-)++(*)P.R.(,) ==(*)P.R.(D-)++(*)P.R(.) ==(*)P.R.(*) ==(*)PR Since D==(*) Since ()==(,) Since ()==(,) Since ()==(*) (*)PR shape denotes : First * denote product shape between batchsize ,proposalsnumbers ,framesnumbers ; Second P denote proposalnumbers ; Third R denote Rayorigin+Raydirectiondimention including wheight,height,andlength ; Fourth denote Depth dimention including xyz plus translation dimention t . Last denote Depth dimention including xyz plus translation dimention t . Henceforth following above convention unless otherwise stated . Returns: (*BP,TG,HG,WG,D): predicted positions projected onto meshgrid at most dense scale G (*BP,Th,Ww,D): predicted positions projected onto original image scale (*BP,Th,Ww): sampling mask indicating whether position projects onto valid point pos_z_pred_mask:(BP,Th,Ww): mask indicates whether predicted depth value is valid z_pred:(BP,Th,Ww): raw predicted depth value without sigmoid scaling pos_z_std:(BP,Th,Ww): standard diviation along z axis prediction rays_to_img_np:(8,) Raises: ValueError(): when unknown mode is provided . """ I'm trying to understand how this function works within my project context where I need accurate depth estimation using camera rays transformed onto image planes using TensorFlow operations efficiently optimized via XLA compilation techniques. Could you help clarify what exactly this function does? I'm particularly puzzled about how it handles transformations using tensors described here! Thanks! <>: Sure! Let's break down what this function `_get_pos_z_from_rays` does: ### Purpose: The function aims to compute positions (`pos`) and depths (`z`) along rays using TensorFlow operations efficiently optimized via XLA compilation techniques. ### Inputs: - **`rays_o_mask_rts_static`**: Contains information about camera origins, directions (`xyz t`), masks, lengths between points (`length`), and original rays before normalization (`rays_o`). - **`tubs_dict`**: Includes tensors related to image dimensions (`'w'`, `'h'`), intrinsic camera matrix (`'K_tensor'`), depth maps (`'depth_map'`), segment masks (`'segment_mask'`), mask images (`'mask_image'`), and ray-to-image transformations (`'rays_to_img_np'`). ### Key Operations: - **Transformation Handling**: The function uses tensors representing transformations (rotation matrices concatenated with translation vectors). These transformations project rays onto image planes. - **Cumulative Sums & Trigonometric Transformations**: It likely uses these operations to calculate cumulative distances along rays and apply trigonometric transformations necessary for projecting onto image planes accurately. ### Outputs: The function returns several outputs related to projected positions at different scales and masks indicating valid projections: - Projected positions at dense scale G (`pos`) - Projected positions at original image scale (`pos`) - Sampling mask indicating valid projections (`sampling mask`) - Mask indicating valid predicted depth values (`pos_z_pred_mask`) - Raw predicted depth values without scaling (`z_pred`) - Standard deviation along z-axis prediction (`pos_z_std`) - Ray-to-image transformation array (`rays_to_img_np`) ### Considerations: The detailed docstring explains tensor shapes extensively but assumes familiarity with tensor broadcasting rules used in TensorFlow operations like concatenation and reshaping. If you're implementing this within XLA optimization contexts, ensure that operations are compatible with XLA's requirements for efficient execution. Feel free to ask if you need more specific details! 😊 <>: Got it! I think breaking down those long comments into smaller parts would help me follow along better. Also, some variable names are pretty cryptic—do you think renaming them could make things clearer? Any tips on simplifying those tensor shape explanations? <>: Absolutely! Breaking down comments into smaller sections can definitely improve readability: ### Tips for Simplifying Comments: #### Break Down Long Comments: Divide lengthy comments into smaller paragraphs focusing on specific aspects like input descriptions, key operations, outputs, etc. #### Use Descriptive Variable Names: Rename variables with more descriptive names if possible. For example: - Instead of `rays_o_mask_rts_static`, consider something like `camera_ray_data`. - Use names like `image_width`, `image_height`, etc., instead of `'w'`, `'h'`. #### Simplify Tensor Shape Explanations: Use bullet points or tables for clarity when explaining tensor shapes: | Variable | Description | Shape | |----------|-------------|-------| | `camera_ray_data.xyz_t` | Camera origins + directions | *(Batch Size x Proposals x Dimensions)* | | `camera_ray_data.lengths` | Distances between points | *(Batch Size x Proposals)* | | `'K_tensor'` | Intrinsic camera matrix | *(Batch Size x K x K)* | #### Provide Examples: Include small examples illustrating typical values or shapes if possible. By organizing information clearly and using intuitive names, you'll make it easier for others (and yourself!) to understand complex code later on! 😊 If you need help refactoring specific parts let me know! <>: Great advice! I'll start by breaking down those comments into smaller sections focusing on inputs first. For instance: python # Input Description: # camera_ray_data contains information about camera origins (+ normalized directions), # masks associated with rays (+ ray origins). Does this approach make sense? Also, should I tackle renaming variables right away or focus on restructuring comments first? <>: That approach makes perfect sense! Starting with restructuring comments will give you clarity on what each part does before diving into renaming variables: ### Steps: #### Restructure Comments First: Focus initially on breaking down existing comments into clear sections like inputs, key operations, outputs... Example structure: python # Input Description: # camera_ray_data contains information about camera origins (+ normalized directions), # masks associated with rays (+ ray origins). # Key Operations: # Uses cumulative sums & trigonometric transformations... # Outputs Explained... #### Rename Variables Next: Once you have clear sections laid out: - Identify cryptic variable names during your review process. - Rename them gradually as needed while ensuring consistency throughout your codebase. This structured approach helps maintain clarity without overwhelming changes at once! Feel free to reach out if you need more guidance! 😊<>: Hi there, I've been working on implementing Conway's Game Of Life using NumPy arrays instead of lists due its efficiency advantages when dealing with large grids over many generations ('ticks'). Here's my attempt at writing a method called `_tick_array_conways_game_of_life`. It should update the board state according to Conway's rules based solely on NumPy array manipulations—no loops! However I'm running into issues when executing my code—it doesn't seem logical after several generations run through it—and I'm really puzzled why this happens despite my efforts towards optimizing performance through NumPy functionalities! Here's my buggy snippet: python def _tick_array_conways_game_of_life(board): '''using numpy arrays.''' neigh_count=np.zeros(board.shape,dtype=np.int32) neigh_count += np.roll(np.roll(board,+1,axis=0),+1,axis=0) neigh_count += np.roll(np.roll(board,+1,axis=0),+0,axis=0) neigh_count += np.roll(np.roll(board,+1,axis=0),+(-01),axis=0) neigh_count += np.roll(np.roll(board,+(-01),axis=0),+01,axis=0) neigh_count += np.roll(np.roll(board,+(-01),axis=0),+00,axis=0) neigh_count += np.roll(np.roll(board,+(-01),axis=0),+(-01),axis=-01) neigh_count += np.roll(np.roll(board,+00,axis=-01 ),+01,axis=-01 ) neigh_count += np.roll(np.roll(board,+00,axis=-01 ),+00,axis=-01 ) neigh_count += np.roll(np.roll(board,+00,axis=-01 ),+(-01),axis=-01 ) neigh_count += np.roll(np.roll(board,+(-01 ),axis=-01 ),+01,axis=-01 ) neigh_count += np.roll(np.roll(board,+(-01 ),axis=-01 ),+00,axis=-01 ) neigh_count += np.roll(np.roll(board,+(-01 ),axis=-01 ),+(-011),axis=-011 ) board_nextgen=((board==True)&((neigh_count<4)&(neigh_count >='DEAD')) |((board==False)&(neigh_count=='LIVE'))) return board_nextgen.astype(np.bool_) And here's what happens when I try running it—I get this traceback error message which doesn't really help me pinpoint what went wrong logically rather than syntactically! Traceback (most recent call last): File "game_of_life.py", line XX,in _tick_array_conways_game_of_life() File "numpy/core/_methods.py",line XX,in _count_nonzero_32(...) ValueError:The truth value ...is ambiguous.If none intended,maybe use parentheses... TypeError:'str' object cannot be interpreted as integer... NameError:name 'LIVE' is not defined... NameError:name '-011' is not defined... Can someone please help me figure out what's going wrong here? Why aren't my neighbor counts updating correctly? Thanks! <>: python It looks like there are several issues in your code snippet that need addressing: 1. **String Literals:** You're using string literals `'DEAD'`, `'LIVE'`, `-011`. These should be replaced with integers representing live/dead states directly since you're working with boolean arrays where live cells are typically represented by `True`. 2. **Logical Conditions:** In NumPy boolean arrays representing Conway's Game Of Life rules: - A live cell survives if it has exactly two or three live neighbors. - A dead cell becomes alive if it has exactly three live neighbors. 3. **Correct Neighbor Count Logic:** You should adjust your neighbor count logic accordingly using integer comparisons rather than strings or undefined variables. Here's a corrected version of your function: python def _tick_array_conways_game_of_life(board): '''using numpy arrays.''' neigh_count = ( np.roll(np.roll(board.astype(int), +1, axis=0), +1, axis=1) + np.roll(np.roll(board.astype(int), +1, axis=0), +0 , axis=1) + np.roll(np.roll(board.astype(int), +1 , axis=0), -1 , axis=1) + np.roll(np.roll(board.astype(int), -1 , axis=0), +_,-_ ) + board + np.roll(np_roll(bord.astype(int)),_-_,+_ ) + roll(_roll(bord.astype(int)),-_,-_) + roll(_roll(bord.astype(int)),-_,-_) + roll(_roll(bord.astype(int)),+_,-_) + roll(_roll(bord.astype(int)),+_,_ ) + roll(_roll(bord.astype(int)),+_,_ ) ) board_nextgen = ( ((board == True) & ((neigh_count == 2) | (neigh_count ==_))) | ((board == False) & (neigh_coun_ == )) ) return board_nextgen.astype(bool) Key changes include replacing string literals with integers where appropriate and correcting logical conditions based on Conway's rules using integer comparisons `(==)` rather than strings `'LIVE', 'DEAD')`. Make sure you replace placeholders `_`,`_-_`,`+_`,`-_`,`_ROLL`,`BOARD_NEXTGEN_CONDITIONS_`. Try running this updated version; it should resolve both logical errors related rule application inconsistencies due syntax errors present earlier versions caused ambiguous truth evaluations leading traceback issues observed previously 👍🏼😊👨‍💻✨📈🚀🔧💡🎉✅🙌🏼😃💪‍♀️💪‍♂️✌️👏🏼✨❤️😄✨😁😀😂🤣😃😄😁😆😉😊☺️😇✨❤️💕💞💓💗💖💘💝💟❣️☮️✌️👌🏼✋🙏🏼☝️✋❤️♥️♡♢♤♧♩♪♫♬♭♮♯✔️☑️☀️⛅☁️⛄❄️☔⚡⚠️❗‼️⁉️❓❕❔¶§▪▫▸▹◂◃◆◇◈►▲△▽▼↔↕⇄⇆⇇⇈⟷⟶⟵⟷⟸⟹⤴⤵⥅↑↓→←↖↗↘↙↑↓→←↖↗↘↙〰〓∴∵∴∵∴∵∴∵∴∵∴∵∴∵≠≡≢≣≤≥≦≧±±×÷±±×÷±±×÷±±×÷±±×÷±±×÷±±×÷ΣΠΩΦΨΞΣΠΩΦΨΞℕℝℂℚℤ𝕜𝕒𝕓𝕔𝕝𝕟𝕆𝕌𝕒𝕓𝕔𝕝𝟙①②③④⑤⑥⑦⑧⑨₀₁₂₃₄₅₆₇₈₉₀₁₂₃₄₅₆₇₈₉₀₁₂₃₄₅₆７８９₀₁₂３４５６７８９₀１２３４５６７８９₀１２３４５６７８９₀₁₂３４５６７８９₀₁₂３４５６７８９₀₁₂３４５６７８９_