File size: 9,274 Bytes
fb0e940 9d41ddd 9f13c80 fb0e940 da45c29 5f50a36 da45c29 5f50a36 da45c29 5f50a36 9f13c80 fb0e940 9f13c80 fb0e940 da45c29 fb0e940 da45c29 fb0e940 da45c29 fb0e940 da45c29 fb0e940 9f13c80 cdd703d e8edd35 9f13c80 da45c29 9f13c80 5f50a36 9f13c80 fb0e940 5f50a36 9f13c80 fb0e940 5f50a36 567a44d 4ee8a04 83c0e71 caef810 5f50a36 ebbf7a2 5f50a36 28f0030 5f50a36 fb0e940 5f50a36 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 |
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, log_x, x_predict=None, y_predict=None):
fig, ax = plt.subplots(figsize=(10, 6))
if log_x:
# Ensure all x-values are positive before setting log scale
if np.any(np.array(x) <= 0):
return create_error_plot("Error: All x values must be positive for logarithmic scale."), \
'<p style="color: red;">Error: All x values must be positive for logarithmic scale.</p>'
ax.set_xscale('log')
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, log_x):
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)}."
fig = create_and_edit_plot(x, y, x_interp, y_interp, method, plot_title, x_label, y_label, legend_position, label_size, log_x)
return fig, f'<p style="color: red;">{error_msg}</p>'
#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, log_x, 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, log_x)
return fig, None
def toggle_plot_options(show_options):
return not show_options, gr.update(visible=not show_options)
with gr.Blocks(theme=gr.themes.Base()) as iface:
#gr.Markdown("# Interpolation App")
gr.Markdown('<h1 style="text-align:center;">Interpolation App</h1>')
gr.Markdown("Enter x and y values to see the interpolation graph")
show_options = gr.State(False)
with gr.Row():
with gr.Column():
x_input = gr.Textbox(label="X values (comma-separated)", value="1,2,3")
y_input = gr.Textbox(label="Y values (comma-separated)", value="1,8,27")
x_predict = gr.Number(label="X value to predict (optional)", value=lambda: None)
method = gr.Radio(["Linear", "Quadratic", "Lagrange", "Newton Forward", "Newton Backward"], label="Interpolation Method", value="Linear")
submit_btn = gr.Button("Generate Plot", variant="primary", elem_id="submit-btn")
edit_plot_btn = gr.Button("Edit Plot", variant="secondary")
with gr.Column():
plot_output = gr.Plot(label="Interpolation Plot")
result_output = gr.HTML(label="Result or Error Message")
plot_options = gr.Column(visible=False)
with plot_options:
plot_title = gr.Textbox(label="Plot Title", value="Interpolation Plot")
x_label = gr.Textbox(label="X-axis Label", value="x")
y_label = gr.Textbox(label="Y-axis Label", value="y")
legend_position = 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")
label_size = gr.Slider(minimum=8, maximum=24, step=1, label="Label Size", value=16)
log_x = gr.Checkbox(label="Log scale for X-axis", value=False)
edit_plot_btn.click(
toggle_plot_options,
inputs=[show_options],
outputs=[show_options, plot_options]
)
inputs = [x_input, y_input, x_predict, method, plot_title, x_label, y_label, legend_position, label_size, log_x]
outputs = [plot_output, result_output]
submit_btn.click(interpolate_and_plot, inputs=inputs, outputs=outputs)
iface.launch()
|