Update app.py

app.py

@@ -28,7 +28,68 @@ def lagrange_interpolation(x, y, x_interp):
     
     return y_interp
 
-def interpolate_and_plot(x_input, y_input, x_predict):
+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(',')])
@@ -46,24 +107,32 @@ def interpolate_and_plot(x_input, y_input, x_predict):
     
     x_interp = np.linspace(min(x), max(x), 100)
     
-    if len(x) == 2:
+    # 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)
-        method = "Linear"
-    elif len(x) == 3:
+    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)
-        method = "Quadratic"
-    else:
+    elif method == "Lagrange":
         y_interp = lagrange_interpolation(x, y, x_interp)
-        method = "Lagrange"
-    
-    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')
-    ax.set_ylabel('y')
-    ax.set_title(f'{method} Interpolation')
-    ax.legend()
-    ax.grid(True)
+    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:
@@ -71,23 +140,17 @@ def interpolate_and_plot(x_input, y_input, x_predict):
             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 fig, f'<p style="color: red;">{error_msg}</p>'
-            
-            if len(x) == 2:
-                y_predict = linear_interpolation(x, y, [x_predict])[0]
-            elif len(x) == 3:
-                y_predict = quadratic_interpolation(x, y, [x_predict])[0]
-            else:
-                y_predict = lagrange_interpolation(x, y, [x_predict])[0]
+                return create_error_plot(error_msg), f'<p style="color: red;">{error_msg}</p>'
             
-            ax.scatter([x_predict], [y_predict], color='green', s=100, label='Predicted point')
-            ax.legend()
+            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(
@@ -95,14 +158,20 @@ iface = gr.Interface(
     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.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. The method will be chosen based on the number of points:\n2 points: Linear, 3 points: Quadratic, >3 points: Lagrange. \nOptionally, enter an x value (between min and max of input x values) to predict its corresponding y value."
+    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()