app.py

import gradio as gr
import numpy as np
import matplotlib.pyplot as plt

def create_error_plot(error_message):
    fig, ax = plt.subplots(figsize=(10, 6))
    ax.text(0.5, 0.5, error_message, color='red', fontsize=16, ha='center', va='center', wrap=True)
    ax.axis('off')
    return fig

def linear_interpolation(x, y, x_interp):
    return np.interp(x_interp, x, y)

def quadratic_interpolation(x, y, x_interp):
    coeffs = np.polyfit(x, y, 2)
    return np.polyval(coeffs, x_interp)

def lagrange_interpolation(x, y, x_interp):
    n = len(x)
    y_interp = np.zeros_like(x_interp, dtype=float)
    
    for i in range(n):
        p = y[i]
        for j in range(n):
            if i != j:
                p = p * (x_interp - x[j]) / (x[i] - x[j])
        y_interp += p
    
    return y_interp

def newton_forward_interpolation(x, y, x_interp):
    n = len(x)
    h = x[1] - x[0]  # Assuming uniform spacing for simplicity
    F = [[0 for _ in range(n)] for _ in range(n)]
    for i in range(n):
        F[i][0] = y[i]
    
    for j in range(1, n):
        for i in range(n - j):
            F[i][j] = F[i+1][j-1] - F[i][j-1]
    
    def newton_forward(x_val):
        u = (x_val - x[0]) / h
        result = y[0]
        term = 1
        for i in range(1, n):
            term *= (u - i + 1) / i
            result += term * F[0][i]
        return result
    
    return np.array([newton_forward(xi) for xi in x_interp])

def newton_backward_interpolation(x, y, x_interp):
    n = len(x)
    h = x[1] - x[0]  # Assuming uniform spacing for simplicity
    F = [[0 for _ in range(n)] for _ in range(n)]
    for i in range(n):
        F[i][0] = y[i]
    
    for j in range(1, n):
        for i in range(n - 1, j - 1, -1):
            F[i][j] = F[i][j-1] - F[i-1][j-1]
    
    def newton_backward(x_val):
        u = (x_val - x[-1]) / h
        result = y[-1]
        term = 1
        for i in range(1, n):
            term *= (u + i - 1) / i
            result += term * F[n-1][i]
        return result
    
    return np.array([newton_backward(xi) for xi in x_interp])

def create_and_edit_plot(x, y, x_interp, y_interp, method, plot_title, x_label, y_label, legend_position, label_size, x_predict=None, y_predict=None):
    fig, ax = plt.subplots(figsize=(10, 6))
    ax.scatter(x, y, color='red', label='Input points')
    ax.plot(x_interp, y_interp, label=f'{method} interpolant')
    ax.set_xlabel(x_label, fontsize=label_size)
    ax.set_ylabel(y_label, fontsize=label_size)
    ax.set_title(plot_title, fontsize=label_size + 2)
    ax.legend(loc=legend_position, fontsize=label_size - 2)
    ax.tick_params(axis='both', which='major', labelsize=label_size - 2)
    ax.grid(True)

    if x_predict is not None and y_predict is not None:
        ax.scatter([x_predict], [y_predict], color='green', s=100, label='Predicted point')
        ax.legend(loc=legend_position, fontsize=label_size - 2)

    return fig

def interpolate_and_plot(x_input, y_input, x_predict, method, plot_title, x_label, y_label, legend_position, label_size):
    try:
        x = np.array([float(val.strip()) for val in x_input.split(',')])
        y = np.array([float(val.strip()) for val in y_input.split(',')])
    except ValueError:
        error_msg = "Error: Invalid input. Please enter comma-separated numbers."
        return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
    
    if len(x) != len(y):
        error_msg = "Error: Number of x and y values must be the same."
        return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
    
    if len(x) < 2:
        error_msg = "Error: At least two points are required for interpolation."
        return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
    
    x_interp = np.linspace(min(x), max(x), 100)
    
    # Interpolation method selection
    if method == "Linear":
        if len(x) < 2:
            error_msg = "Error: At least two points are required for linear interpolation."
            return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
        y_interp = linear_interpolation(x, y, x_interp)
    elif method == "Quadratic":
        if len(x) < 3:
            error_msg = "Error: At least three points are required for quadratic interpolation."
            return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
        y_interp = quadratic_interpolation(x, y, x_interp)
    elif method == "Lagrange":
        y_interp = lagrange_interpolation(x, y, x_interp)
    elif method == "Newton Forward":
        if not np.allclose(np.diff(x), x[1] - x[0]):
            error_msg = "Error: Newton Forward method requires uniform x spacing."
            return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
        y_interp = newton_forward_interpolation(x, y, x_interp)
    elif method == "Newton Backward":
        if not np.allclose(np.diff(x), x[1] - x[0]):
            error_msg = "Error: Newton Backward method requires uniform x spacing."
            return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
        y_interp = newton_backward_interpolation(x, y, x_interp)
    else:
        error_msg = "Error: Invalid interpolation method selected."
        return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
    
    # Predict y value for given x
    if x_predict is not None:
        try:
            x_predict = float(x_predict)
            if x_predict < min(x) or x_predict > max(x):
                error_msg = f"Error: Prediction x value must be between {min(x)} and {max(x)}."
                return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
            
            y_predict = np.interp(x_predict, x_interp, y_interp)
            
            fig = create_and_edit_plot(x, y, x_interp, y_interp, method, plot_title, x_label, y_label, legend_position, label_size, x_predict, y_predict)
            return fig, f"Predicted y value for x = {x_predict}: {y_predict:.4f}"
        except ValueError:
            error_msg = "Error: Invalid input for x prediction. Please enter a number."
            return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
    
    fig = create_and_edit_plot(x, y, x_interp, y_interp, method, plot_title, x_label, y_label, legend_position, label_size)
    return fig, None

iface = gr.Interface(
    fn=interpolate_and_plot,
    inputs=[
        gr.Textbox(label="X values (comma-separated)"),
        gr.Textbox(label="Y values (comma-separated)"),
        gr.Number(label="X value to predict (optional)", value=lambda: None),
        gr.Radio(["Linear", "Quadratic", "Lagrange", "Newton Forward", "Newton Backward"], label="Interpolation Method", value="Linear"),
        gr.Textbox(label="Plot Title", value="Interpolation Plot"),
        gr.Textbox(label="X-axis Label", value="x"),
        gr.Textbox(label="Y-axis Label", value="y"),
        gr.Dropdown(["best", "upper right", "upper left", "lower left", "lower right", "right", "center left", "center right", "lower center", "upper center", "center"], label="Legend Position", value="best"),
        gr.Slider(minimum=8, maximum=24, step=1, label="Label Size", value=12)
    ],
    outputs=[
        gr.Plot(label="Interpolation Plot"),
        gr.HTML(label="Result or Error Message")
    ],
    title="Interpolation App",
    description="Enter x and y values to see the interpolation graph. Choose the interpolation method using the radio buttons. Optionally, enter an x value (between min and max of input x values) to predict its corresponding y value. Note: Newton Forward and Backward methods require uniform x spacing. You can also customize the plot labels, legend position, and label size."
)

iface.launch()