Spaces:
Sleeping
Sleeping
Lennard Schober
commited on
Commit
·
d2ec756
1
Parent(s):
59cb565
Init commit
Browse files- app.py +479 -0
- npz/.DS_Store +0 -0
app.py
ADDED
@@ -0,0 +1,479 @@
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1 |
+
import gradio as gr
|
2 |
+
import numpy as np
|
3 |
+
import os
|
4 |
+
import time
|
5 |
+
import plotly.graph_objs as go
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6 |
+
import matplotlib.pyplot as plt
|
7 |
+
import shutil
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8 |
+
from colorama import Fore
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9 |
+
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10 |
+
# Path to the npz folder
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11 |
+
npz_folder = "npz"
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12 |
+
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13 |
+
glob_a = -2
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14 |
+
glob_b = -2
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15 |
+
glob_c = -4
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16 |
+
glob_d = 7
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17 |
+
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18 |
+
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19 |
+
def clear_folder(folder_path=npz_folder):
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20 |
+
for filename in os.listdir(folder_path):
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21 |
+
file_path = os.path.join(folder_path, filename)
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22 |
+
try:
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23 |
+
if os.path.isfile(file_path) or os.path.islink(file_path):
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24 |
+
os.unlink(file_path) # Remove the file or symbolic link
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25 |
+
elif os.path.isdir(file_path):
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26 |
+
shutil.rmtree(file_path) # Remove the directory and its contents
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27 |
+
except Exception as e:
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28 |
+
print(f"Failed to delete {file_path}. Reason: {e}")
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29 |
+
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30 |
+
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31 |
+
def complex_heat_eq_solution(x, t, a=glob_a, b=glob_b, c=glob_c, d=glob_d, k=0.5):
|
32 |
+
global glob_a, glob_b, glob_c, glob_d
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33 |
+
return (
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34 |
+
np.exp(-k * t) * np.sin(np.pi * x)
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35 |
+
+ 0.5 * np.exp(glob_a * k * t) * np.sin(glob_b * np.pi * x)
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36 |
+
+ 0.25 * np.exp(glob_c * k * t) * np.sin(glob_d * np.pi * x)
|
37 |
+
)
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38 |
+
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39 |
+
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40 |
+
def plot_heat_equation(m, approx_type):
|
41 |
+
# Define grid dimensions
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42 |
+
n_x = 32 # Fixed spatial grid resolution
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43 |
+
n_t = 50
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44 |
+
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45 |
+
try:
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46 |
+
loaded_values = np.load(f"npz/{approx_type}_m{m}.npz")
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47 |
+
except:
|
48 |
+
raise gr.Error(f"First train the coefficients for {approx_type} and m = {m}")
|
49 |
+
alpha = loaded_values["alpha"]
|
50 |
+
Phi = loaded_values["Phi"]
|
51 |
+
|
52 |
+
# Create grids for x and t
|
53 |
+
x = np.linspace(0, 1, n_x) # Spatial grid
|
54 |
+
t = np.linspace(0, 5, n_t) # Temporal grid
|
55 |
+
X, T = np.meshgrid(x, t)
|
56 |
+
|
57 |
+
# Compute the real solution over the grid
|
58 |
+
U_real = complex_heat_eq_solution(X, T)
|
59 |
+
|
60 |
+
# Compute the selected approximation
|
61 |
+
U_approx = np.zeros_like(U_real)
|
62 |
+
for i, t_val in enumerate(t):
|
63 |
+
Phi_gff_at_t = Phi[i * n_x : (i + 1) * n_x]
|
64 |
+
U_approx[i, :] = np.dot(Phi_gff_at_t, alpha)
|
65 |
+
|
66 |
+
# Create the 3D plot with Plotly
|
67 |
+
traces = []
|
68 |
+
|
69 |
+
# Real solution surface with a distinct color (e.g., 'Viridis')
|
70 |
+
traces.append(
|
71 |
+
go.Surface(
|
72 |
+
z=U_real,
|
73 |
+
x=X,
|
74 |
+
y=T,
|
75 |
+
colorscale="Blues",
|
76 |
+
showscale=False,
|
77 |
+
name="Real Solution",
|
78 |
+
showlegend=True,
|
79 |
+
)
|
80 |
+
)
|
81 |
+
|
82 |
+
# Approximation surface with a distinct color (e.g., 'Plasma')
|
83 |
+
traces.append(
|
84 |
+
go.Surface(
|
85 |
+
z=U_approx,
|
86 |
+
x=X,
|
87 |
+
y=T,
|
88 |
+
colorscale="Reds",
|
89 |
+
reversescale=True,
|
90 |
+
showscale=False,
|
91 |
+
name=f"{approx_type} Approximation",
|
92 |
+
showlegend=True,
|
93 |
+
)
|
94 |
+
)
|
95 |
+
|
96 |
+
# Layout for the Plotly plot without controls
|
97 |
+
layout = go.Layout(
|
98 |
+
title=f"Heat Equation Approximation | Kernel = {approx_type} | m = {m}",
|
99 |
+
scene=dict(
|
100 |
+
camera=dict(
|
101 |
+
eye=dict(x=0, y=-2, z=0), # Front view
|
102 |
+
),
|
103 |
+
xaxis_title="x",
|
104 |
+
yaxis_title="t",
|
105 |
+
zaxis_title="u",
|
106 |
+
),
|
107 |
+
)
|
108 |
+
|
109 |
+
# Config to remove modebar buttons except the save image button
|
110 |
+
config = {
|
111 |
+
"modeBarButtonsToRemove": [
|
112 |
+
"pan",
|
113 |
+
"resetCameraLastSave",
|
114 |
+
"hoverClosest3d",
|
115 |
+
"hoverCompareCartesian",
|
116 |
+
"zoomIn",
|
117 |
+
"zoomOut",
|
118 |
+
"select2d",
|
119 |
+
"lasso2d",
|
120 |
+
"zoomIn2d",
|
121 |
+
"zoomOut2d",
|
122 |
+
"sendDataToCloud",
|
123 |
+
"zoom3d",
|
124 |
+
"orbitRotation",
|
125 |
+
"tableRotation",
|
126 |
+
],
|
127 |
+
"displayModeBar": True, # Keep the modebar visible
|
128 |
+
"displaylogo": False, # Hide the Plotly logo
|
129 |
+
}
|
130 |
+
|
131 |
+
# Create the figure
|
132 |
+
fig = go.Figure(data=traces, layout=layout)
|
133 |
+
|
134 |
+
fig.show(config=config)
|
135 |
+
|
136 |
+
|
137 |
+
def plot_errors(m, approx_type):
|
138 |
+
# Define grid dimensions
|
139 |
+
n_x = 32 # Fixed spatial grid resolution
|
140 |
+
n_t = 50
|
141 |
+
|
142 |
+
try:
|
143 |
+
loaded_values = np.load(f"npz/{approx_type}_m{m}.npz")
|
144 |
+
except:
|
145 |
+
raise gr.Error(f"First train the coefficients for {approx_type} and m = {m}")
|
146 |
+
alpha = loaded_values["alpha"]
|
147 |
+
Phi = loaded_values["Phi"]
|
148 |
+
|
149 |
+
# Create grids for x and t
|
150 |
+
x = np.linspace(0, 1, n_x) # Spatial grid
|
151 |
+
t = np.linspace(0, 5, n_t) # Temporal grid
|
152 |
+
X, T = np.meshgrid(x, t)
|
153 |
+
|
154 |
+
# Compute the real solution over the grid
|
155 |
+
U_real = complex_heat_eq_solution(X, T)
|
156 |
+
|
157 |
+
# Compute the selected approximation
|
158 |
+
U_approx = np.zeros_like(U_real)
|
159 |
+
for i, t_val in enumerate(t):
|
160 |
+
Phi_gff_at_t = Phi[i * n_x : (i + 1) * n_x]
|
161 |
+
U_approx[i, :] = np.dot(Phi_gff_at_t, alpha)
|
162 |
+
|
163 |
+
U_err = abs(U_approx - U_real)
|
164 |
+
|
165 |
+
# Create the 3D plot with Plotly
|
166 |
+
traces = []
|
167 |
+
|
168 |
+
# Real solution surface with a distinct color (e.g., 'Viridis')
|
169 |
+
traces.append(
|
170 |
+
go.Surface(
|
171 |
+
z=U_err,
|
172 |
+
x=X,
|
173 |
+
y=T,
|
174 |
+
colorscale="Viridis",
|
175 |
+
showscale=False,
|
176 |
+
name=f"Absolute Error",
|
177 |
+
showlegend=True,
|
178 |
+
)
|
179 |
+
)
|
180 |
+
|
181 |
+
# Layout for the Plotly plot without controls
|
182 |
+
layout = go.Layout(
|
183 |
+
title=f"Heat Equation Approximation Error | Kernel = {approx_type} | m = {m}",
|
184 |
+
scene=dict(
|
185 |
+
camera=dict(
|
186 |
+
eye=dict(x=0, y=-2, z=0), # Front view
|
187 |
+
),
|
188 |
+
xaxis_title="x",
|
189 |
+
yaxis_title="t",
|
190 |
+
zaxis_title="u",
|
191 |
+
),
|
192 |
+
)
|
193 |
+
|
194 |
+
# Config to remove modebar buttons except the save image button
|
195 |
+
config = {
|
196 |
+
"modeBarButtonsToRemove": [
|
197 |
+
"pan",
|
198 |
+
"resetCameraLastSave",
|
199 |
+
"hoverClosest3d",
|
200 |
+
"hoverCompareCartesian",
|
201 |
+
"zoomIn",
|
202 |
+
"zoomOut",
|
203 |
+
"select2d",
|
204 |
+
"lasso2d",
|
205 |
+
"zoomIn2d",
|
206 |
+
"zoomOut2d",
|
207 |
+
"sendDataToCloud",
|
208 |
+
"zoom3d",
|
209 |
+
"orbitRotation",
|
210 |
+
"tableRotation",
|
211 |
+
],
|
212 |
+
"displayModeBar": True, # Keep the modebar visible
|
213 |
+
"displaylogo": False, # Hide the Plotly logo
|
214 |
+
}
|
215 |
+
|
216 |
+
# Create the figure
|
217 |
+
fig = go.Figure(data=traces, layout=layout)
|
218 |
+
|
219 |
+
fig.show(config=config)
|
220 |
+
|
221 |
+
|
222 |
+
# Function to get the available .npz files in the npz folder
|
223 |
+
def get_available_approx_files():
|
224 |
+
files = os.listdir(npz_folder)
|
225 |
+
npz_files = [f for f in files if f.endswith(".npz")]
|
226 |
+
return npz_files
|
227 |
+
|
228 |
+
|
229 |
+
def generate_data(n_x=32, n_t=50):
|
230 |
+
"""Generate training data."""
|
231 |
+
x = np.linspace(0, 1, n_x) # spatial points
|
232 |
+
t = np.linspace(0, 5, n_t) # temporal points
|
233 |
+
X, T = np.meshgrid(x, t)
|
234 |
+
a_train = np.c_[X.ravel(), T.ravel()] # shape (n_x * n_t, 2)
|
235 |
+
u_train = complex_heat_eq_solution(
|
236 |
+
a_train[:, 0], a_train[:, 1]
|
237 |
+
) # shape (n_x * n_t,)
|
238 |
+
return a_train, u_train, x, t
|
239 |
+
|
240 |
+
|
241 |
+
def random_features(a, theta_j, kernel="SINE", k=0.5, t=1.0):
|
242 |
+
"""Compute random features with adjustable kernel width."""
|
243 |
+
if kernel == "SINE":
|
244 |
+
return np.sin(t * np.linalg.norm(a - theta_j, axis=-1))
|
245 |
+
elif kernel == "GFF":
|
246 |
+
return np.log(np.linalg.norm(a - theta_j, axis=-1)) / (2 * np.pi)
|
247 |
+
else:
|
248 |
+
raise ValueError("Unsupported kernel type!")
|
249 |
+
|
250 |
+
|
251 |
+
def design_matrix(a, theta, kernel):
|
252 |
+
"""Construct design matrix."""
|
253 |
+
return np.array([random_features(a, theta_j, kernel=kernel) for theta_j in theta]).T
|
254 |
+
|
255 |
+
|
256 |
+
def learn_coefficients(Phi, u):
|
257 |
+
"""Learn coefficients alpha via least squares."""
|
258 |
+
return np.linalg.lstsq(Phi, u, rcond=None)[0]
|
259 |
+
|
260 |
+
|
261 |
+
def approximate_solution(a, alpha, theta, kernel):
|
262 |
+
"""Compute the approximation."""
|
263 |
+
Phi = design_matrix(a, theta, kernel)
|
264 |
+
return Phi @ alpha
|
265 |
+
|
266 |
+
|
267 |
+
def polyfit2d(x, y, z, kx=3, ky=3, order=None):
|
268 |
+
# grid coords
|
269 |
+
x, y = np.meshgrid(x, y)
|
270 |
+
# coefficient array, up to x^kx, y^ky
|
271 |
+
coeffs = np.ones((kx + 1, ky + 1))
|
272 |
+
|
273 |
+
# solve array
|
274 |
+
a = np.zeros((coeffs.size, x.size))
|
275 |
+
|
276 |
+
# for each coefficient produce array x^i, y^j
|
277 |
+
for index, (j, i) in enumerate(np.ndindex(coeffs.shape)):
|
278 |
+
# do not include powers greater than order
|
279 |
+
if order is not None and i + j > order:
|
280 |
+
arr = np.zeros_like(x)
|
281 |
+
else:
|
282 |
+
arr = coeffs[i, j] * x**i * y**j
|
283 |
+
a[index] = arr.ravel()
|
284 |
+
|
285 |
+
# do leastsq fitting and return leastsq result
|
286 |
+
return np.linalg.lstsq(a.T, np.ravel(z), rcond=None)
|
287 |
+
|
288 |
+
|
289 |
+
def train_coefficients(m, kernel):
|
290 |
+
# Start time for training
|
291 |
+
start_time = time.time()
|
292 |
+
|
293 |
+
# Generate data
|
294 |
+
n_x, n_t = 32, 50
|
295 |
+
a_train, u_train, x, t = generate_data(n_x, n_t)
|
296 |
+
|
297 |
+
# Define random features
|
298 |
+
theta = np.column_stack(
|
299 |
+
(
|
300 |
+
np.random.uniform(-1, 1, size=m), # First dimension: [-1, 1]
|
301 |
+
np.random.uniform(-5, 5, size=m), # Second dimension: [-5, 5]
|
302 |
+
)
|
303 |
+
)
|
304 |
+
|
305 |
+
# Construct design matrix and learn coefficients
|
306 |
+
Phi = design_matrix(a_train, theta, kernel)
|
307 |
+
alpha = learn_coefficients(Phi, u_train)
|
308 |
+
# Validate and animate results
|
309 |
+
u_real = np.array([complex_heat_eq_solution(x, t_i) for t_i in t])
|
310 |
+
a_test = np.c_[np.meshgrid(x, t)[0].ravel(), np.meshgrid(x, t)[1].ravel()]
|
311 |
+
u_approx = approximate_solution(a_test, alpha, theta, kernel).reshape(n_t, n_x)
|
312 |
+
|
313 |
+
# Save values to the npz folder
|
314 |
+
np.savez(
|
315 |
+
f"{npz_folder}/{kernel}_m{m}.npz",
|
316 |
+
alpha=alpha,
|
317 |
+
kernel=kernel,
|
318 |
+
Phi=Phi,
|
319 |
+
theta=theta,
|
320 |
+
)
|
321 |
+
|
322 |
+
# Compute average error
|
323 |
+
avg_err = np.mean(np.abs(u_real - u_approx))
|
324 |
+
|
325 |
+
return f"Training completed in {time.time() - start_time:.2f} seconds. The average error is {avg_err}."
|
326 |
+
|
327 |
+
|
328 |
+
def plot_function(a, b, c, d, k=0.5):
|
329 |
+
global glob_a, glob_b, glob_c, glob_d
|
330 |
+
|
331 |
+
glob_a, glob_b, glob_c, glob_d = a, b, c, d
|
332 |
+
|
333 |
+
x = np.linspace(0, 1, 100)
|
334 |
+
t = np.linspace(0, 5, 500)
|
335 |
+
X, T = np.meshgrid(x, t) # Create the mesh grid
|
336 |
+
Z = complex_heat_eq_solution(X, T, a, b, c, d)
|
337 |
+
|
338 |
+
traces = []
|
339 |
+
traces.append(
|
340 |
+
go.Surface(
|
341 |
+
z=Z,
|
342 |
+
x=X,
|
343 |
+
y=T,
|
344 |
+
colorscale="Viridis",
|
345 |
+
showscale=False,
|
346 |
+
showlegend=False,
|
347 |
+
)
|
348 |
+
)
|
349 |
+
|
350 |
+
# Layout for the Plotly plot without controls
|
351 |
+
layout = go.Layout(
|
352 |
+
scene=dict(
|
353 |
+
camera=dict(
|
354 |
+
eye=dict(x=1.25, y=-1.75, z=0.3), # Front view
|
355 |
+
),
|
356 |
+
xaxis_title="x",
|
357 |
+
yaxis_title="t",
|
358 |
+
zaxis_title="u",
|
359 |
+
),
|
360 |
+
margin=dict(l=0, r=0, t=0, b=0), # Reduce margins
|
361 |
+
)
|
362 |
+
|
363 |
+
# Create the figure
|
364 |
+
fig = go.Figure(data=traces, layout=layout)
|
365 |
+
|
366 |
+
# fig.show(config=config)
|
367 |
+
fig.update_layout(
|
368 |
+
modebar_remove=[
|
369 |
+
"pan",
|
370 |
+
"resetCameraLastSave",
|
371 |
+
"hoverClosest3d",
|
372 |
+
"hoverCompareCartesian",
|
373 |
+
"zoomIn",
|
374 |
+
"zoomOut",
|
375 |
+
"select2d",
|
376 |
+
"lasso2d",
|
377 |
+
"zoomIn2d",
|
378 |
+
"zoomOut2d",
|
379 |
+
"sendDataToCloud",
|
380 |
+
"zoom3d",
|
381 |
+
"orbitRotation",
|
382 |
+
"tableRotation",
|
383 |
+
"toImage",
|
384 |
+
"resetCameraDefault3d"
|
385 |
+
]
|
386 |
+
)
|
387 |
+
|
388 |
+
return fig
|
389 |
+
|
390 |
+
|
391 |
+
# Gradio interface
|
392 |
+
def create_gradio_ui():
|
393 |
+
# Get the initial available files
|
394 |
+
with gr.Blocks() as demo:
|
395 |
+
gr.Markdown("# Learn the Coefficients for the Heat Equation using the RFM")
|
396 |
+
|
397 |
+
# Function parameter inputs
|
398 |
+
gr.Markdown(
|
399 |
+
"""
|
400 |
+
## Function: $$u_k(x, t)\\coloneqq\\exp(-kt)\\cdot\\sin(\\pi x)+0.5\\cdot\\exp(\\textcolor{red}{a}kt)\\cdot\\sin(\\textcolor{red}{b}\\pi x)+0.25\\cdot\\exp(\\textcolor{red}{c}kt)\\cdot\\sin(\\textcolor{red}{d}\\pi x)$$
|
401 |
+
|
402 |
+
Adjust the values for <span style='color: red;'>a</span>, <span style='color: red;'>b</span>, <span style='color: red;'>c</span> and <span style='color: red;'>d</span> with the sliders below.
|
403 |
+
"""
|
404 |
+
)
|
405 |
+
|
406 |
+
with gr.Row():
|
407 |
+
with gr.Column():
|
408 |
+
a_slider = gr.Slider(minimum=-10, maximum=-1, step=1, value=-2, label="a")
|
409 |
+
b_slider = gr.Slider(minimum=-10, maximum=10, step=1, value=-2, label="b")
|
410 |
+
c_slider = gr.Slider(minimum=-10, maximum=-1, step=1, value=-4, label="c")
|
411 |
+
d_slider = gr.Slider(minimum=-10, maximum=10, step=1, value=7, label="d")
|
412 |
+
|
413 |
+
plot_output = gr.Plot()
|
414 |
+
|
415 |
+
a_slider.change(
|
416 |
+
fn=plot_function,
|
417 |
+
inputs=[a_slider, b_slider, c_slider, d_slider],
|
418 |
+
outputs=[plot_output],
|
419 |
+
)
|
420 |
+
b_slider.change(
|
421 |
+
fn=plot_function,
|
422 |
+
inputs=[a_slider, b_slider, c_slider, d_slider],
|
423 |
+
outputs=[plot_output],
|
424 |
+
)
|
425 |
+
c_slider.change(
|
426 |
+
fn=plot_function,
|
427 |
+
inputs=[a_slider, b_slider, c_slider, d_slider],
|
428 |
+
outputs=[plot_output],
|
429 |
+
)
|
430 |
+
d_slider.change(
|
431 |
+
fn=plot_function,
|
432 |
+
inputs=[a_slider, b_slider, c_slider, d_slider],
|
433 |
+
outputs=[plot_output],
|
434 |
+
)
|
435 |
+
|
436 |
+
with gr.Column():
|
437 |
+
with gr.Row():
|
438 |
+
# Kernel selection and slider for m
|
439 |
+
kernel_dropdown = gr.Dropdown(
|
440 |
+
label="Choose Kernel", choices=["SINE", "GFF"], value="SINE"
|
441 |
+
)
|
442 |
+
m_slider = gr.Dropdown(
|
443 |
+
label="Number of Random Features (m)",
|
444 |
+
choices=[50, 250, 1000, 5000, 10000, 25000],
|
445 |
+
value=1000,
|
446 |
+
)
|
447 |
+
|
448 |
+
# Output to show status
|
449 |
+
output = gr.Textbox(label="Status", interactive=False)
|
450 |
+
|
451 |
+
with gr.Row():
|
452 |
+
# Button to train coefficients
|
453 |
+
train_button = gr.Button("Train Coefficients")
|
454 |
+
# Function to trigger training and update dropdown
|
455 |
+
train_button.click(
|
456 |
+
fn=train_coefficients,
|
457 |
+
inputs=[m_slider, kernel_dropdown],
|
458 |
+
outputs=output,
|
459 |
+
)
|
460 |
+
with gr.Row():
|
461 |
+
approx_button = gr.Button("Plot Approximation")
|
462 |
+
approx_button.click(
|
463 |
+
fn=plot_heat_equation, inputs=[m_slider, kernel_dropdown], outputs=None
|
464 |
+
)
|
465 |
+
|
466 |
+
error_button = gr.Button("Plot Errors")
|
467 |
+
error_button.click(
|
468 |
+
fn=plot_errors, inputs=[m_slider, kernel_dropdown], outputs=None
|
469 |
+
)
|
470 |
+
demo.load(fn=clear_folder, inputs=None, outputs=None)
|
471 |
+
demo.load(fn=plot_function, inputs=[a_slider, b_slider, c_slider, d_slider], outputs=[plot_output])
|
472 |
+
|
473 |
+
return demo
|
474 |
+
|
475 |
+
|
476 |
+
# Launch Gradio app
|
477 |
+
if __name__ == "__main__":
|
478 |
+
interface = create_gradio_ui()
|
479 |
+
interface.launch(share=False)
|
npz/.DS_Store
ADDED
Binary file (8.2 kB). View file
|
|