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import random
import math
import matplotlib.pyplot as plt
import matplotlib
from smolagents import tool
@tool
def generate_normal_distribution(mean: float, std_dev: float, count: int = 10000)->list:
"""Generate a list of random numbers from a normal distribution.
This function generates a list of random numbers drawn from a normal
distribution specified by the mean and standard deviation.
Args:
mean: The mean (average) of the normal distribution.
std_dev: The standard deviation of the normal distribution.
count: The number of random samples to generate (default: 10000).
Returns:
list: A list of samples drawn from the specified normal distribution.
"""
samples = []
for _ in range(count // 2): # Generate pairs of samples
u1 = random.random()
u2 = random.random()
# Box-Muller transform
z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2.0 * math.pi * u2)
z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2.0 * math.pi * u2)
# Scale and shift to the specified mean and standard deviation
samples.append(z0 * std_dev + mean)
samples.append(z1 * std_dev + mean)
return samples
@tool
def create_histogram_and_theorical_pdf(mean: float, std_dev:float, random_numbers:list)->str:
"""Generate a histogram of random numbers and overlay the theoretical
probability density function (PDF) of a normal distribution.
Return the histogram as a base64-encoded string.
Args:
mean: The mean (average) of the normal distribution.
std_dev: The standard deviation of the normal distribution.
random_numbers: A list of random numbers generated from a
normal distribution.
Returns:
str: The graphics for the histogram and probability density function (PDF) on string format
"""
# Prepare data for plotting
hist_data = [0] * 50 # Create a list to hold histogram data
min_value = min(random_numbers)
max_value = max(random_numbers)
bin_width = (max_value - min_value) / len(hist_data)
# Fill histogram data
for number in random_numbers:
bin_index = int((number - min_value) / bin_width)
if bin_index >= len(hist_data):
bin_index = len(hist_data) - 1
hist_data[bin_index] += 1
# Normalize histogram data
hist_data = [count / len(random_numbers) / bin_width for count in hist_data]
# Prepare x values for the theoretical PDF
x_values = [min_value + i * bin_width for i in range(len(hist_data))]
# Calculate the corresponding y values for the theoretical normal distribution
pdf_values = [
(1 / (std_dev * math.sqrt(2 * math.pi))) * math.exp(-0.5 * ((x - mean) / std_dev) ** 2) \
for x in x_values
]
# Scale for ASCII output
max_hist = max(hist_data) if hist_data else 1 # Avoid division by zero
max_pdf = max(pdf_values) if pdf_values else 1 # Avoid division by zero
max_height = 20 # Maximum height of the ASCII histogram
# Building the ASCII graph as a string
ascii_graph = "Histogram (|: Counts, -: PDF)\n"
for i in range(len(hist_data)):
hist_count = int((hist_data[i] / max_hist) * max_height)
pdf_count = int((pdf_values[i] / max_pdf) * max_height)
ascii_graph += f"{'|' * hist_count} {'-' * pdf_count} {x_values[i]:.2f}\n"
return ascii_graph |