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from itertools import permutations
import numpy as np
from collections import defaultdict
from scipy.stats import kendalltau

# Define the input rankings: each ranking is a list from most to least preferred
rankings = [
    ['A', 'B', 'C'],
    ['B', 'C', 'A'],
    ['C', 'A', 'B']

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import numpy as np
import matplotlib.pyplot as plt

# Set seed for reproducibility
np.random.seed(123)

# Parameters
T = 10000       # number of time steps
s = 0.01        # step size
dim = 2         # 2D space

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import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

np.random.seed(42)

def g(x):
    return np.log(1 + x) - np.log(x)

def f(x):

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import torch
import torch.nn as nn

class MultiQueryAttention(nn.Module):
    def __init__(self, embed_dim, num_heads):
        super().__init__()
        self.embed_dim = embed_dim
        self.num_heads = num_heads
        self.head_dim = embed_dim // num_heads
        

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import numpy as np
import time
import torch
from transformers import AutoModelForCausalLM, AutoTokenizer

device = "cpu"
tokenizer = AutoTokenizer.from_pretrained("gpt2")
model = AutoModelForCausalLM.from_pretrained("gpt2").to(device)

dur = {}

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class Tensor:
    def __init__(self, value, requires_grad=False):
        self.value = value  # Store the value of the tensor
        self.grad = 0  # Gradient initialized to zero
        self.requires_grad = requires_grad
        self._backward = lambda: None  # Function to compute gradient
        self._prev = set()  # Track previous nodes for backpropagation

    def backward(self):
        """Computes gradients using reverse-mode automatic differentiation."""

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import torch
from transformers import GPT2LMHeadModel, GPT2Tokenizer

# Load GPT-2 model and tokenizer
tokenizer = GPT2Tokenizer.from_pretrained("gpt2")
model = GPT2LMHeadModel.from_pretrained("gpt2")
model.eval()

def compare_outputs(prompt):
    print('Prompt:', prompt)

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# Results

## Feature 1: Biden's health and cognitive abilities.

### Stats

F1 score: 0.5

Pearson Correlation: -0.38014296063485287

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import numpy as np
import matplotlib.pyplot as plt

# Parameters
T = 35  # Number of trials
beta = 0.5  # Probability parameter for z
alpha_1 = 0.2  # Probability parameter for x if z=0
alpha_2 = 0.6  # Probability parameter for x if z=1

# Simulate z

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def get_response_sql(user_query, chat_history, plot=False):
    
    # Specify the path to the SQLite database
    db_path = "metadataDB/output_database.db"

    # Connect to the SQLite database
    db = SQLDatabase.from_uri(f"sqlite:///{db_path}")

    underspecified = classify_underspecified_query(user_query , chat_history)