import warnings; warnings.filterwarnings("ignore")
# Let us import the basics we will need
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Data setup
url = "https://raw.githubusercontent.com/jbrownlee/Datasets/master/airline-passengers.csv"
df = pd.read_csv(url)
print(df.shape)
df.head()

# Convert 'Month' to datetime
df['Month'] = pd.to_datetime(df['Month'])
df = df.set_index('Month')
df.head()

# Plot the data
plt.figure(figsize=(10,4))
plt.plot(df.index, df['Passengers'])
plt.title("Monthly Airline Passengers")
plt.ylabel("Passengers")
plt.xlabel("Date")
plt.show()

# Create time-step numbers for each row
df['t'] = np.arange(len(df))
df.head()

# Basic Fourier (one cycle per year)
period = 12  # 12 months in a year
df['sin1'] = np.sin(2 * np.pi * df['t'] / period)
df['cos1'] = np.cos(2 * np.pi * df['t'] / period)
df[['sin1','cos1']].head()

# Plot sine and cosine waves
plt.figure(figsize=(10,4))
plt.plot(df.index, df['sin1'], label='sin1')
plt.plot(df.index, df['cos1'], label='cos1')
plt.legend()
plt.title("First Order Fourier Terms")
plt.show()

# Higher-order Fourier terms: add more waves
order = 2
for k in range(2, order*2+1):
    df[f'sin{k}'] = np.sin(2 * np.pi * k * df['t'] / period)
    df[f'cos{k}'] = np.cos(2 * np.pi * k * df['t'] / period)

df[[f'sin{k}' for k in range(2, order*2+1)] + [f'cos{k}' for k in range(2, order*2+1)]].head()

# Combine and plot all Fourier terms up to chosen order
plt.figure(figsize=(10,6))
for k in range(1, order*2+1):
    plt.plot(df.index, df[f'sin{k}'], label=f'sin{k}')
    plt.plot(df.index, df[f'cos{k}'], label=f'cos{k}')
plt.legend(ncol=2)
plt.title("All Fourier Term Waves (Order 2)")
plt.show()

# Add Fourier terms to a model
from sklearn.linear_model import LinearRegression
X = df[[f'sin{k}' for k in range(1, order*2+1)] + [f'cos{k}' for k in range(1, order*2+1)]]
y = df['Passengers']
model = LinearRegression()
model.fit(X, y)
preds = model.predict(X)

plt.figure(figsize=(10,4))
plt.plot(df.index, y, label='Actual')
plt.plot(df.index, preds, label='Model', linestyle='--')
plt.legend()
plt.title("Passengers: Actual vs Fourier Model")
plt.show()

# What happens if you use only t (time) as input?
model2 = LinearRegression()
model2.fit(df[['t']], y)
preds2 = model2.predict(df[['t']])

plt.figure(figsize=(10,4))
plt.plot(df.index, y, label='Actual')
plt.plot(df.index, preds2, label='Time-only Model', linestyle='--')
plt.legend()
plt.title("Passengers: Actual vs Time-only Model")
plt.show()

# Practice! How would you add weekly patterns?
print("How many months are there in a year?")
months = input()
print("The period for yearly seasonality would be:", months)

# Challenge! Make your own fourier feature
feature = np.sin(2 * np.pi * df['t'] / 6)
plt.plot(df.index, feature)
plt.title("Custom Sine Wave: 6 Month Seasonality")
plt.show()

# Best practice: Test different orders and period values
for trial_period in [3, 6, 12]:
    feature = np.sin(2 * np.pi * df['t'] / trial_period)
    plt.plot(df.index, feature, label=f'period={trial_period}')
plt.legend()
plt.title("Comparing Different Fourier Periods")
plt.show()

# Tip: Use sklearn's FunctionTransformer for pipelines
from sklearn.preprocessing import FunctionTransformer

def make_fourier(X, period=12, order=2):
    t = np.arange(len(X)).reshape(-1, 1)
    feats = []
    for k in range(1, order*2+1):
        feats.append(np.sin(2 * np.pi * k * t / period))
        feats.append(np.cos(2 * np.pi * k * t / period))
    return np.concatenate(feats, axis=1)

# Example use with pipeline:
trans = FunctionTransformer(make_fourier, kw_args={'period':12, 'order':2})
fourier_feats = trans.fit_transform(df[['Passengers']])
fourier_feats.shape

# Troubleshooting: Watch for overfitting with high orders
order = 10
X_big = df[[f'sin{k}' for k in range(1, order*2+1)] + [f'cos{k}' for k in range(1, order*2+1)]]
model_big = LinearRegression()
model_big.fit(X_big, y)
preds_big = model_big.predict(X_big)

plt.figure(figsize=(10, 4))
plt.plot(df.index, y, label='Actual')
plt.plot(df.index, preds_big, label='High-order Fourier Model', linestyle='--')
plt.legend()
plt.title("Model with Many Fourier Features")
plt.show()