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question:**Question: Double Conversion and String Formatting** Implement a Python function `convert_and_format_double` that takes a string representing a floating-point number and converts it to a float. The function should then format this float into a string using a specified format code and precision. Additionally, the function should handle potential exceptions that could arise during conversion and ensure the output is as specified. # Function Definition ```python def convert_and_format_double(s: str, format_code: str, precision: int, flags: int = 0) -> str: Convert a string representing a floating-point number to a float, and format it to a string using the given format code and precision. Parameters: s (str): The string representing the floating-point number. format_code (str): The format code to use for string conversion ('e', 'E', 'f', 'F', 'g', 'G', 'r'). precision (int): The number of digits of precision desired. flags (int): Flags to modify the resulting format (defaults to 0). Returns: str: The formatted float as a string, or an appropriate error message if conversion fails. pass ``` # Input 1. `s` (str): A string representing a valid floating-point number (e.g., '123.456', '1e10'). 2. `format_code` (str): A single character format code, which must be one of `'e'`, `'E'`, `'f'`, `'F'`, `'g'`, `'G'`, `'r'`. 3. `precision` (int): The number of digits of precision to include in the formatted string. 4. `flags` (int): An integer representing flags for formatting (optional, default is 0). # Output A string that represents the formatted version of the converted float or an appropriate error message if the conversion fails. # Constraints - You may assume that the input string `s` is always a valid floating-point number. - The `format_code` should always be one of the accepted values. - `precision` will be an integer within a reasonable range for float precision (e.g., 0 <= precision <= 20). - If conversion fails, the function should return "Conversion Error". - If formatting fails, the function should return "Formatting Error". # Example ```python assert convert_and_format_double("123.456", 'f', 2) == "123.46" assert convert_and_format_double("1e10", 'E', 1) == "1.0E+10" assert convert_and_format_double("not_a_number", 'g', 3) == "Conversion Error" ``` # Notes - Use appropriate error handling mechanisms to catch and handle errors during conversion and formatting. - Consider edge cases such as extremely large values, invalid format codes, etc.
answer:def convert_and_format_double(s: str, format_code: str, precision: int, flags: int = 0) -> str: Convert a string representing a floating-point number to a float, and format it to a string using the given format code and precision. Parameters: s (str): The string representing the floating-point number. format_code (str): The format code to use for string conversion ('e', 'E', 'f', 'F', 'g', 'G', 'r'). precision (int): The number of digits of precision desired. flags (int): Flags to modify the resulting format (defaults to 0). Returns: str: The formatted float as a string, or an appropriate error message if conversion fails. try: value = float(s) except ValueError: return "Conversion Error" try: format_spec = f".{precision}{format_code}" return format(value, format_spec) except (ValueError, TypeError): return "Formatting Error"
question:Problem Statement: You are required to implement a custom iterator class in Python, which replicates the functionality discussed in the documentation. 1. **SeqIterator**: This class should iterate over a sequence until an `IndexError` is thrown. 2. **CallIterator**: This class should iterate over a callable object until a sentinel value is returned. Requirements: 1. Implement a class `SeqIterator`: - **Constructor**: `__init__(self, seq: Sequence)` - **Methods**: - `__iter__(self) -> SeqIterator`: Returns the iterator object. - `__next__(self) -> Any`: Returns the next item in the sequence. Raises `StopIteration` if the sequence ends. 2. Implement a class `CallIterator`: - **Constructor**: `__init__(self, callable: Callable[[], Any], sentinel: Any)` - **Methods**: - `__iter__(self) -> CallIterator`: Returns the iterator object. - `__next__(self) -> Any`: Returns the next item from the callable. Raises `StopIteration` when the sentinel value is returned. Input and Output Format: - For `SeqIterator`: - **Input**: ```python seq = [1, 2, 3] seq_iter = SeqIterator(seq) ``` - **Output**: Calling `next(seq_iter)` repeatedly should return `1`, `2`, `3`, and then raise `StopIteration`. - For `CallIterator`: - **Input**: ```python def gen(): for i in range(4): return i sentinel = -1 call_iter = CallIterator(gen, sentinel) ``` - **Output**: Calling `next(call_iter)` repeatedly should return `0`, `1`, `2`, `3`, and then raise `StopIteration`. Constraints: - The sequence provided to `SeqIterator` can be any iterable (e.g., list, tuple, etc.). - The callable object provided to `CallIterator` must be a function with no parameters. - Ensure that your implementation handles edge cases, such as empty sequences or callable objects that immediately return the sentinel value. Performance Requirements: - Your iterators should have a time complexity of O(1) for the `__next__` method. Implement the classes as described and demonstrate their usage with example inputs and expected outputs.
answer:from typing import Sequence, Callable, Any class SeqIterator: def __init__(self, seq: Sequence): self.seq = seq self.index = 0 def __iter__(self): return self def __next__(self): if self.index < len(self.seq): result = self.seq[self.index] self.index += 1 return result else: raise StopIteration class CallIterator: def __init__(self, callable: Callable[[], Any], sentinel: Any): self.callable = callable self.sentinel = sentinel def __iter__(self): return self def __next__(self): result = self.callable() if result == self.sentinel: raise StopIteration return result # Example usage: # seq = [1, 2, 3] # seq_iter = SeqIterator(seq) # for value in seq_iter: # print(value) # # def gen(): # for i in range(4): # yield i # # sentinel = -1 # call_iter = CallIterator(gen().__next__, sentinel) # for value in call_iter: # print(value)
question:**Objective**: Demonstrate your understanding of seaborn by creating a complex, well-customized plot. **Scenario**: You are given a dataset containing two continuous variables, `X` and `Y`, and one categorical variable, `Category`. The dataset has 300 observations. Your task is to visualize the relationship between `X` and `Y` using seaborn, customizing the plot to ensure clarity and visual appeal. **Input**: A pandas DataFrame `df` with the following structure: - `X`: Continuous variable - `Y`: Continuous variable - `Category`: Categorical variable (up to 4 unique categories) **Requirements**: 1. Create a scatter plot to visualize the relationship between `X` and `Y`. 2. Use different colors for each category in `Category`. 3. Fit and plot a regression line for each category. 4. Use a dark-themed color palette for the categories. 5. Include appropriate labels for the axes and a legend. 6. Ensure the plot has a grid and customize the grid's appearance for better readability. **Constraints**: - Do not use Seaborn’s default settings for the plot. Customize the appearance based on the requirements above. **Output**: - Return the seaborn plot object. **Example**: Here's a sample function signature to get you started: ```python import pandas as pd import seaborn as sns import matplotlib.pyplot as plt def visualize_relationship(df: pd.DataFrame): sns.set_theme(style="darkgrid") # Define a dark-themed color palette with a sufficient number of colors palette = sns.dark_palette("seagreen", n_colors=len(df["Category"].unique())) # Create a scatter plot with a regression line per category sns.lmplot( data=df, x='X', y='Y', hue='Category', palette=palette, height=7, aspect=1.2, markers='o', scatter_kws={"s": 50, "alpha": 0.7}, line_kws={"lw": 2}) # Customizing the appearance of the plot plt.xlabel("X-axis Label") plt.ylabel("Y-axis Label") plt.title("Scatter Plot of X vs. Y with Regression Lines by Category") plt.legend(title='Category', loc='upper left') plt.grid(True, linestyle="--", linewidth=0.5, alpha=0.7) # Show plot plt.show() return plt ``` Use this template and modify it to meet all the requirements.
answer:import pandas as pd import seaborn as sns import matplotlib.pyplot as plt def visualize_relationship(df: pd.DataFrame): Creates a scatter plot to visualize the relationship between continuous variables X and Y with categories differentiated by colors. Fits and plots a regression line for each category. sns.set_theme(style="darkgrid") # Define a dark-themed color palette with a sufficient number of colors palette = sns.color_palette("dark", n_colors=df["Category"].nunique()) # Create a scatter plot with a regression line per category plot = sns.lmplot( data=df, x='X', y='Y', hue='Category', palette=palette, height=7, aspect=1.2, markers='o', scatter_kws={"s": 50, "alpha": 0.7}, line_kws={"lw": 2} ) # Customizing the appearance of the plot plot.set_axis_labels("X-axis", "Y-axis") plt.title("Scatter Plot of X vs. Y with Regression Lines by Category") plt.legend(title='Category', loc='upper left') plt.grid(True, linestyle="--", linewidth=0.5, alpha=0.7) return plot
question:# PyTorch Coding Assessment **Objective**: Demonstrate your ability to utilize PyTorch's `torch.func` functionality, particularly focusing on `vmap` and `grad`, while adhering to the limitations and constraints described. # Question You are to write a function `batched_cosine_similarity` that computes the cosine similarity between two batches of vectors. Implement this using PyTorch's `vmap` for batch processing and the `grad` function to compute the gradient of the cosine similarity with respect to the input vectors. Function Signature ```python def batched_cosine_similarity(batch1: torch.Tensor, batch2: torch.Tensor) -> torch.Tensor: Parameters: - batch1 (torch.Tensor): A tensor of shape (n, d) containing n vectors each of dimension d. - batch2 (torch.Tensor): A tensor of shape (n, d) containing n vectors each of dimension d. Returns: - torch.Tensor: A tensor of shape (n,) containing the cosine similarity for each pair of vectors. pass ``` # Instructions 1. **Inputs**: - `batch1`: A tensor of shape `(n, d)` where `n` is the number of vectors and `d` is the dimension of each vector. - `batch2`: A tensor of shape `(n, d)`. 2. **Outputs**: - Return a tensor of shape `(n,)` where each element is the cosine similarity between the corresponding vectors in `batch1` and `batch2`. 3. **Constraints**: - Use `vmap` to achieve batch processing. - Ensure your implementation does not involve assigning to global variables. - Handle the calculation purely within the function without any in-place operations that `vmap` might not support. - Cosine similarity is defined as: [ text{cosine_similarity}(x, y) = frac{x cdot y}{|x|_2 |y|_2} ] 4. **Gradient Calculation**: - After implementing `batched_cosine_similarity`, use `grad` to compute the gradient of the cosine similarity with respect to the first input `batch1`. # Example ```python import torch from torch.func import vmap, grad # Example inputs batch1 = torch.randn(5, 3) # 5 vectors of dimension 3 batch2 = torch.randn(5, 3) # Implement the function to compute batched cosine similarity def batched_cosine_similarity(batch1, batch2): def cosine_sim(x, y): return torch.dot(x, y) / (torch.norm(x) * torch.norm(y)) vmap_cosine_sim = vmap(cosine_sim, in_dims=(0, 0)) return vmap_cosine_sim(batch1, batch2) # Example usage cosine_similarities = batched_cosine_similarity(batch1, batch2) print(cosine_similarities) # Compute the gradient of the batched cosine similarity with respect to batch1 def func_for_grad(batch1): return batched_cosine_similarity(batch1, batch2).sum() grad_fn = grad(func_for_grad) batch1_grad = grad_fn(batch1) print(batch1_grad) ``` Your task is to implement the `batched_cosine_similarity` function correctly, adhering to the given constraints and requirements.
answer:import torch from torch.func import vmap, grad def batched_cosine_similarity(batch1: torch.Tensor, batch2: torch.Tensor) -> torch.Tensor: Computes the cosine similarity between two batches of vectors using vmap for batch processing. Parameters: - batch1 (torch.Tensor): A tensor of shape (n, d) containing n vectors each of dimension d. - batch2 (torch.Tensor): A tensor of shape (n, d) containing n vectors each of dimension d. Returns: - torch.Tensor: A tensor of shape (n,) containing the cosine similarity for each pair of vectors. def cosine_sim(x, y): return torch.dot(x, y) / (torch.norm(x) * torch.norm(y)) vmap_cosine_sim = vmap(cosine_sim, in_dims=(0, 0)) return vmap_cosine_sim(batch1, batch2) # Example for gradient calculation def grad_batched_cosine_similarity(batch1: torch.Tensor, batch2: torch.Tensor) -> torch.Tensor: def func_for_grad(batch1): return batched_cosine_similarity(batch1, batch2).sum() grad_fn = grad(func_for_grad) return grad_fn(batch1) # Example usage if __name__ == "__main__": batch1 = torch.randn(5, 3) batch2 = torch.randn(5, 3) cosine_similarities = batched_cosine_similarity(batch1, batch2) print(cosine_similarities) batch1_grad = grad_batched_cosine_similarity(batch1, batch2) print(batch1_grad)