import streamlit as st
import numpy as np
import matplotlib.pyplot as plt

st.title('Fitting simple models with JAX')
st.header('A quadratric regression example')

st.markdown('*\"Parametrised models are simply functions that depend on inputs and trainable parameters. There is no fundamental difference between the two, except that trainable parameters are shared across training samples whereas the input varies from sample to sample.\"* [(Yann LeCun, Deep learning course)](https://atcold.github.io/pytorch-Deep-Learning/en/week02/02-1/#Parametrised-models)')

st.latex(r'''h(\boldsymbol x, \boldsymbol w)= \sum_{k=1}^{K}\boldsymbol w_{k} \phi_{k}(\boldsymbol x)''')

number_of_observations = st.sidebar.slider('Number of observations', min_value=50, max_value=150, value=50)
noise_standard_deviation = st.sidebar.slider('Standard deviation of the noise', min_value = 0.0, max_value=2.0, value=0.25)

np.random.seed(2)

X = np.column_stack((np.ones(number_of_observations), 
                     np.random.random(number_of_observations)))      

w = np.array([3.0, -20.0, 32.0])  # coefficients                                    

X = np.column_stack((X, X[:,1] ** 2))   # add x**2 column
additional_noise = 8 * np.random.binomial(1, 0.03, size = number_of_observations)
y = np.dot(X, w) + noise_standard_deviation * np.random.randn(number_of_observations) \
        + additional_noise	


fig, ax = plt.subplots(dpi=320)
ax.set_xlim((0,1))
ax.set_ylim((-5,20))
ax.scatter(X[:,1], y, c='r', edgecolors='black')

st.pyplot(fig)
st.write(X[:5, :])