import streamlit as st
import plotly.graph_objects as go
import numpy as np
import scipy.integrate as integrate

def _false_positive_probability(threshold, b, r):
    def _probability(s):
        return 1 - (1 - s ** float(r)) ** float(b)
    a, err = integrate.quad(_probability, 0.0, threshold)
    return a


def _false_negative_probability(threshold, b, r):
    def _probability(s):
        return 1 - (1 - (1 - s ** float(r)) ** float(b))

    a, err = integrate.quad(_probability, threshold, 1.0)
    return a


def _optimal_param(threshold, num_perm, false_positive_weight, false_negative_weight):
    """
    Compute the optimal `MinHashLSH` parameter that minimizes the weighted sum
    of probabilities of false positive and false negative.
    """
    min_error = float("inf")
    opt = (0, 0)
    for b in range(1, num_perm + 1):
        max_r = int(num_perm / b)
        for r in range(1, max_r + 1):
            fp = _false_positive_probability(threshold, b, r)
            fn = _false_negative_probability(threshold, b, r)
            error = fp * false_positive_weight + fn * false_negative_weight
            if error < min_error:
                min_error = error
                opt = (b, r)
    return opt


col1, col2 = st.columns(2)
s = col1.slider("Select a Jaccard similarity", 0.0, 1.0, 0.1)
p = col2.slider("Select a number of permutations", 0, 1000, 10)
optimal_b, optimal_r = _optimal_param(s, p, 1, 1)

b = col1.slider("Select a number of bands", 1, 100, 1)
r = col2.slider("Select a number of rows per band", 1, 100, 1)

col1.metric(label="Optimal number of bands", value=optimal_b)
col2.metric(label="Optimal number of rows per band", value=optimal_r)

st.markdown("---")

st.markdown(f"Two documents that have a Jaccard similarity of $s={s}$ will have:")
st.markdown(f"1. ${s * 100:.2f}\%$ of their k-shingles will be the same")
st.markdown(f"2. ${s * 100:.2f}\%$ of their k-shingles' hashes will be the same")
st.markdown(f"4. ${s * 100:.2f}\%$ of the time, a particular hash will be the same for two documents")
st.markdown(
    f"3. $s^r={100 * s ** r:.2f}\%$ of the time, they will have the same hashes for a particular band of $r={r}$ rows"
)
st.markdown(
    f"5. $1 - s^r = {100 * (1 - s ** r):.2f}\%$ of the time, they will have at least one different hash for a particular band"
)
st.markdown(
    f"6. $(1 - s^r)^b = {100 * (1 - s ** r)**b:.2f}\%$ of the time, they will have at least one different hash for all $b={b}$ bands"
)
st.markdown(
    f"7. $1 - (1 - s^r)^b={100 * (1 - (1 - s ** r)**b):.2f}\%$ of the time, they will have at least one band with the same hashes"
)

t = st.slider("Select a Jaccard similarity threshold", 0.0, 1.0, 0.1)

x = np.linspace(0, 1, 1000)
y = 1 - (1 - x**r) ** b

fig = go.Figure(
    data=go.Scatter(
        x=x,
        y=y,
        showlegend=False,
    )
)
fig = fig.add_shape(
    type="line",
    x0=t,
    y0=0,
    x1=t,
    y1=1,
    line=dict(
        color="Red",
        width=4,
    ),
)
false_positive_x = [d for d in x if d <= t] + [t]
false_positive_y = [d for i, d in enumerate(y) if x[i] <= t] + [0]
fig.add_trace(
    go.Scatter(
        x=false_positive_x,
        y=false_positive_y,
        fill="tozeroy",
        fillcolor="rgba(255, 0, 0, 0.2)",
        line_color="rgba(255, 0, 0, 0)",
        showlegend=False,
    )
)

false_negative_x = [d for d in x if d > t]
false_negative_y = [d for i, d in enumerate(y) if x[i] > t]
fig.add_trace(
    go.Scatter(
        x=[t] + false_negative_x + [1],
        y=[1] + false_negative_y + [1],
        fill="toself",
        fillcolor="rgba(0, 255, 0, 0.2)",
        line_color="rgba(0, 255, 0, 0)",
        showlegend=False,
    )
)

st.plotly_chart(fig)

false_positive = integrate.quad(lambda x: 1 - (1 - x**r) ** b, 0, t)[0]
false_negative = integrate.quad(lambda x: (1 - x**r) ** b, t, 1)[0]

cols = st.columns(2)
cols[0].metric(label="False positive area", value=f"{false_positive:.2f}")
cols[1].metric(label="False negative area", value=f"{false_negative:.2f}")