app.py

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

# Safe function evaluation
def safe_eval(func_str, x_val):
    """ Safely evaluates the function at a given x value. """
    allowed_names = {"x": x_val, "np": np}
    try:
        return eval(func_str, {"__builtins__": None}, allowed_names)
    except Exception as e:
        raise ValueError(f"Error evaluating the function: {e}")

# Function derivative using finite difference method
def derivative(func_str, x_val, h=1e-5):
    """ Numerically compute the derivative of the function at x using finite differences. """
    return (safe_eval(func_str, x_val + h) - safe_eval(func_str, x_val - h)) / (2 * h)

# Tangent line equation
def tangent_line(func_str, x_val, x_range):
    """ Compute the tangent line at a given x value. """
    y_val = safe_eval(func_str, x_val)
    slope = derivative(func_str, x_val)
    return slope * (x_range - x_val) + y_val

# Callback to reset session state
def reset_state():
    st.session_state.x = st.session_state.starting_point
    st.session_state.iteration = 0
    st.session_state.x_vals = [st.session_state.starting_point]
    st.session_state.y_vals = [safe_eval(st.session_state.func_input, st.session_state.starting_point)]

# Initialize session state variables
if "func_input" not in st.session_state:
    st.session_state.func_input = "x**2 + x"
if "x" not in st.session_state:
    st.session_state.x = 4.0
    st.session_state.iteration = 0
    st.session_state.x_vals = [4.0]
    st.session_state.y_vals = [safe_eval(st.session_state.func_input, 4.0)]

# Full-width layout
st.set_page_config(layout="wide")

# CSS Styles for Borders, Font, Reduced Padding, and Custom Border Color
st.markdown(
    """
    <style>
    * {
        font-family: Cambria, Arial, sans-serif !important;
    }
    h1, h2, h3, h4, h5 {
        text-align: center;
        margin-top: 0;
    }
    input, .stButton button, .stDownloadButton button {
        border: 2px solid #ea445a;
        border-radius: 5px;
        padding: 10px;
    }
    .stInfo, .stSuccess {
        border: 2px solid #ea445a;
        border-radius: 5px;
        padding: 10px;
    }
    .stButton {
        margin-top: 10px;
    }
    /* Reduced Padding at the top */
    .css-1d391kg {
        padding-top: 0.5rem;
    }
    /* Centering the legend in the plot */
    .stPlotlyChart {
        display: block;
        margin: 0 auto;
    }
    /* Adjusting for full width without scrolling */
    .css-1lcbvhc {
        padding-left: 0;
        padding-right: 0;
    }
    /* Custom borders for input fields */
    .stTextInput input, .stNumberInput input {
        border: 2px solid #001A6E;
        border-radius: 5px;
        padding: 10px;
    }
    /* Tooltip styling */
    .tooltip {
        position: relative;
        display: inline-block;
        cursor: pointer;
    }
    .tooltip .tooltiptext {
        visibility: hidden;
        opacity: 0;
        width: 300px;
        background-color: #001A6E;
        color: #fff;
        text-align: center;
        border-radius: 5px;
        padding: 5px;
        position: absolute;
        z-index: 1;
        bottom: 125%; /* Position the tooltip above */
        left: 50%;
        margin-left: -150px;
        transition: opacity 0.3s;
    }
    .tooltip:hover .tooltiptext {
        visibility: visible;
        opacity: 1;
    }
    </style>
    """,
    unsafe_allow_html=True,
)

# Page Layout
st.title("🌟 Gradient Descent Interactive Tool 🌟")

col1, col2 = st.columns([1, 2])

# Left Section: User Input
with col1:
    st.subheader("🔧 Define Your Function")

    # Tooltip with instructions when hovering over the function input label
    st.markdown(
        """
        <div class="tooltip">
            <label for="func_input">Enter a function of 'x':</label>
            <span class="tooltiptext">
                **How to input your function:**
                - Please give the inputs as mentioned below                
                - x^n as  x**n,                
                - sin(x) as np.sin(x)                
                - log(x) as np.log(x),                
                - e^x or exp(x) as np.exp(x).
            </span>
        </div>
        """,
        unsafe_allow_html=True
    )
    
    # Use text input for the user to define a function, but no `value` argument
    func_input = st.text_input(
        "👇", 
        key="func_input", 
        on_change=reset_state
    )

    st.subheader("⚙️ Gradient Descent Parameters")
    starting_point = st.number_input(
        "Starting Point (X₀)", 
        value=4.0, 
        step=0.1, 
        format="%.2f", 
        key="starting_point", 
        on_change=reset_state
    )
    learning_rate = st.number_input(
        "Learning Rate (ŋ)", 
        value=0.25, 
        step=0.01, 
        format="%.2f", 
        key="learning_rate", 
        on_change=reset_state
    )

    col3, col4 = st.columns(2)
    with col3:
        if st.button("🔄 Set Up Function"):
            reset_state()
    with col4:
        if st.button("▶️ Next Iteration"):
            try:
                grad = derivative(st.session_state.func_input, st.session_state.x)
                st.session_state.x = st.session_state.x - learning_rate * grad
                st.session_state.iteration += 1
                st.session_state.x_vals.append(st.session_state.x)
                st.session_state.y_vals.append(safe_eval(st.session_state.func_input, st.session_state.x))
            except Exception as e:
                st.error(f"⚠️ Error: {str(e)}")

# Right Section: Visualization
with col2:
    st.subheader("📊 Gradient Descent Visualization")
    try:
        # Plot the function and all current and previous gradient descent points
        x_plot = np.linspace(-10, 10, 400)
        y_plot = [safe_eval(st.session_state.func_input, x) for x in x_plot]

        fig = go.Figure()

        # Function curve
        fig.add_trace(go.Scatter(
            x=x_plot, 
            y=y_plot, 
            mode="lines+markers", 
            line=dict(color="blue", width=2), 
            marker=dict(size=4, color="blue", symbol="circle"),
            name="Function"
        ))

        # All gradient descent points (red points without coordinates)
        fig.add_trace(go.Scatter(
            x=st.session_state.x_vals,
            y=st.session_state.y_vals,
            mode="markers",
            marker=dict(color="red", size=10),
            name="Gradient Descent Points"
        ))

        # Tangent line at the current gradient descent point
        current_x = st.session_state.x
        tangent_x = np.linspace(-10, 10, 200)  # Adjusting range to cover entire plot
        tangent_y = tangent_line(st.session_state.func_input, current_x, tangent_x)
        fig.add_trace(go.Scatter(
            x=tangent_x,
            y=tangent_y,
            mode="lines",
            line=dict(color="orange", width=3),
            name="Tangent Line"
        ))

        # Dynamic zoom for better visibility
        fig.update_layout(
            xaxis=dict(
                title="x-axis",
                range=[-10, 10],
                showline=True,
                linecolor="white",
                tickcolor="white",
                tickfont=dict(color="white"),
                ticks="outside",
            ),
            yaxis=dict(
                title="y-axis",
                range=[min(y_plot) - 5, min(max(y_plot) + 5, 1000)],  # Limiting the max y to 1000
                showline=True,
                linecolor="white",
                tickcolor="white",
                tickfont=dict(color="white"),
                ticks="outside",
            ),
            plot_bgcolor="black",
            paper_bgcolor="black",
            title="",
            margin=dict(l=10, r=10, t=10, b=10),
            width=800,
            height=400,
            showlegend=True,
            legend=dict(
                x=1.1,
                y=0.5,
                xanchor="left",
                yanchor="middle",
                orientation="v",
                font=dict(size=12, color="white"),
                bgcolor="black",
                bordercolor="white",
                borderwidth=2,
            )
        )

        # Axis lines for quadrants
        fig.add_shape(type="line", x0=-10, x1=10, y0=0, y1=0, line=dict(color="white", width=2))  # x-axis
        fig.add_shape(type="line", x0=0, x1=0, y0=-100, y1=100, line=dict(color="white", width=2))  # y-axis

        st.plotly_chart(fig, use_container_width=True)

    except Exception as e:
        st.error(f"⚠️ Error in visualization: {str(e)}")

    # Iteration stats and download
    col5, col6 = st.columns(2)
    col5.info(f"🧑‍💻 Iteration: {st.session_state.iteration}")
    col6.success(f"✅ Current x: {st.session_state.x:.4f}, Current f(x): {st.session_state.y_vals[-1]:.4f}")