Spaces:
Sleeping
Sleeping
Update app.py
Browse files
app.py
CHANGED
@@ -67,6 +67,19 @@ st.markdown("""
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padding: 10px;
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margin: 10px 0;
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}
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.stWarning {
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background-color: #fff3cd;
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padding: 10px;
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@@ -79,6 +92,14 @@ st.markdown("""
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border-left: 3px solid #28a745;
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margin: 10px 0;
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}
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</style>
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""", unsafe_allow_html=True)
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@@ -138,10 +159,668 @@ def run_command(cmd, show_output=True, timeout=None):
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# Check if C++ source file exists
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if not os.path.exists(cpp_file):
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with open(cpp_file, "w") as f:
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st.warning(f"C++ source file
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# Compile the C++ code with the right OpenCV libraries
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st.sidebar.title("Compiler Settings")
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st.markdown('<div class="panel-header">Eigenvalue Analysis Controls</div>', unsafe_allow_html=True)
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# Parameter inputs with defaults and validation
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st.markdown("### Matrix Parameters")
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n = st.number_input("Sample size (n)", min_value=5, max_value=1000, value=100, step=5,
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help="Number of samples", key="eig_n")
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# Automatically calculate y = p/n (as requested)
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y = p/n
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st.info(f"Value for y = p/n: {y:.4f}")
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st.markdown("### Calculation Controls")
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fineness = st.slider(
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"Beta points",
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help="Number of points to calculate along the β axis (0 to 1)",
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key="eig_fineness"
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)
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with st.expander("Advanced Settings"):
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# Add controls for theoretical calculation precision
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st.markdown('<div class="panel-header">Im(s) vs z Analysis Controls</div>', unsafe_allow_html=True)
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# Parameter inputs with defaults and validation
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st.markdown("### Cubic Equation Parameters")
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cubic_a = st.number_input("Value for a", min_value=1.1, max_value=10.0, value=2.0, step=0.1,
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help="Parameter a > 1", key="cubic_a")
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help="Parameter y > 0", key="cubic_y")
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cubic_beta = st.number_input("Value for β", min_value=0.0, max_value=1.0, value=0.5, step=0.05,
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help="Value between 0 and 1", key="cubic_beta")
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st.markdown("### Calculation Controls")
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cubic_points = st.slider(
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"Number of z points",
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help="Maximum time allowed for computation before timeout",
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key="cubic_timeout"
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)
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# Show cubic equation
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st.markdown('<div class="math-box">', unsafe_allow_html=True)
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ims_values2 = np.array(data['ims_values2'])
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ims_values3 = np.array(data['ims_values3'])
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x=z_values,
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y=ims_values1,
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mode='lines',
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name='Im(s₁)',
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line=dict(color='rgb(220, 60, 60)', width=3),
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hovertemplate='z: %{x:.3f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
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'bgcolor': 'rgba(255, 255, 255, 0.9)',
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# Clear progress container
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progress_container.empty()
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# Display the interactive plot in Streamlit
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st.plotly_chart(fig, use_container_width=True)
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# Add explanation text
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st.markdown("""
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###
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The cubic equation being solved is:
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""")
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except json.JSONDecodeError as e:
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st.error(f"Error parsing JSON results: {str(e)}")
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ims_values2 = np.array(data['ims_values2'])
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ims_values3 = np.array(data['ims_values3'])
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#
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fig = go.Figure()
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# Add traces for each root's imaginary part
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2. **Adjust parameters** in the left panel to configure your analysis
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3. **Click the Generate button** to run the analysis with the selected parameters
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4. **Explore the results** in the interactive plot
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5. For
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If you encounter any issues with compilation, try clicking the "Recompile C++ Code" button in the sidebar.
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padding: 10px;
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margin: 10px 0;
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}
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.explanation-box {
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background-color: #e8f4f8;
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padding: 15px;
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border-radius: 5px;
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margin-top: 20px;
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border-left: 3px solid #1E88E5;
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}
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.parameter-container {
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background-color: #f0f7fa;
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padding: 15px;
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border-radius: 5px;
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margin-bottom: 15px;
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}
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.stWarning {
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background-color: #fff3cd;
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padding: 10px;
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92 |
border-left: 3px solid #28a745;
|
93 |
margin: 10px 0;
|
94 |
}
|
95 |
+
.plot-container {
|
96 |
+
margin-top: 1.5rem;
|
97 |
+
}
|
98 |
+
.footnote {
|
99 |
+
font-size: 0.8rem;
|
100 |
+
color: #6c757d;
|
101 |
+
margin-top: 2rem;
|
102 |
+
}
|
103 |
</style>
|
104 |
""", unsafe_allow_html=True)
|
105 |
|
|
|
159 |
|
160 |
# Check if C++ source file exists
|
161 |
if not os.path.exists(cpp_file):
|
162 |
+
# Create the C++ file with our improved cubic solver
|
163 |
with open(cpp_file, "w") as f:
|
164 |
+
st.warning(f"Creating new C++ source file at: {cpp_file}")
|
165 |
+
|
166 |
+
# The improved C++ code with better cubic solver
|
167 |
+
f.write('''
|
168 |
+
// app.cpp - Modified version for command line arguments with improved cubic solver
|
169 |
+
#include <opencv2/opencv.hpp>
|
170 |
+
#include <algorithm>
|
171 |
+
#include <cmath>
|
172 |
+
#include <iostream>
|
173 |
+
#include <iomanip>
|
174 |
+
#include <numeric>
|
175 |
+
#include <random>
|
176 |
+
#include <vector>
|
177 |
+
#include <limits>
|
178 |
+
#include <sstream>
|
179 |
+
#include <string>
|
180 |
+
#include <fstream>
|
181 |
+
#include <complex>
|
182 |
+
#include <stdexcept>
|
183 |
+
|
184 |
+
// Struct to hold cubic equation roots
|
185 |
+
struct CubicRoots {
|
186 |
+
std::complex<double> root1;
|
187 |
+
std::complex<double> root2;
|
188 |
+
std::complex<double> root3;
|
189 |
+
};
|
190 |
+
|
191 |
+
// Function to solve cubic equation: az^3 + bz^2 + cz + d = 0
|
192 |
+
// Improved to properly handle zero roots and classification of positive/negative
|
193 |
+
CubicRoots solveCubic(double a, double b, double c, double d) {
|
194 |
+
// Constants for numerical stability
|
195 |
+
const double epsilon = 1e-14;
|
196 |
+
const double zero_threshold = 1e-10; // Threshold for considering a value as zero
|
197 |
+
|
198 |
+
// Handle special case for a == 0 (quadratic)
|
199 |
+
if (std::abs(a) < epsilon) {
|
200 |
+
CubicRoots roots;
|
201 |
+
// For a quadratic equation: bz^2 + cz + d = 0
|
202 |
+
if (std::abs(b) < epsilon) { // Linear equation or constant
|
203 |
+
if (std::abs(c) < epsilon) { // Constant - no finite roots
|
204 |
+
roots.root1 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
|
205 |
+
roots.root2 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
|
206 |
+
roots.root3 = std::complex<double>(std::numeric_limits<double>::quiet_NaN(), 0.0);
|
207 |
+
} else { // Linear equation
|
208 |
+
roots.root1 = std::complex<double>(-d / c, 0.0);
|
209 |
+
roots.root2 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
|
210 |
+
roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
|
211 |
+
}
|
212 |
+
return roots;
|
213 |
+
}
|
214 |
+
|
215 |
+
double discriminant = c * c - 4.0 * b * d;
|
216 |
+
if (discriminant >= 0) {
|
217 |
+
double sqrtDiscriminant = std::sqrt(discriminant);
|
218 |
+
roots.root1 = std::complex<double>((-c + sqrtDiscriminant) / (2.0 * b), 0.0);
|
219 |
+
roots.root2 = std::complex<double>((-c - sqrtDiscriminant) / (2.0 * b), 0.0);
|
220 |
+
roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
|
221 |
+
} else {
|
222 |
+
double real = -c / (2.0 * b);
|
223 |
+
double imag = std::sqrt(-discriminant) / (2.0 * b);
|
224 |
+
roots.root1 = std::complex<double>(real, imag);
|
225 |
+
roots.root2 = std::complex<double>(real, -imag);
|
226 |
+
roots.root3 = std::complex<double>(std::numeric_limits<double>::infinity(), 0.0);
|
227 |
+
}
|
228 |
+
return roots;
|
229 |
+
}
|
230 |
+
|
231 |
+
// Handle special case when d is zero - one root is zero
|
232 |
+
if (std::abs(d) < epsilon) {
|
233 |
+
// Factor out z: z(az^2 + bz + c) = 0
|
234 |
+
CubicRoots roots;
|
235 |
+
roots.root1 = std::complex<double>(0.0, 0.0); // One root is exactly zero
|
236 |
+
|
237 |
+
// Solve the quadratic: az^2 + bz + c = 0
|
238 |
+
double discriminant = b * b - 4.0 * a * c;
|
239 |
+
if (discriminant >= 0) {
|
240 |
+
double sqrtDiscriminant = std::sqrt(discriminant);
|
241 |
+
roots.root2 = std::complex<double>((-b + sqrtDiscriminant) / (2.0 * a), 0.0);
|
242 |
+
roots.root3 = std::complex<double>((-b - sqrtDiscriminant) / (2.0 * a), 0.0);
|
243 |
+
} else {
|
244 |
+
double real = -b / (2.0 * a);
|
245 |
+
double imag = std::sqrt(-discriminant) / (2.0 * a);
|
246 |
+
roots.root2 = std::complex<double>(real, imag);
|
247 |
+
roots.root3 = std::complex<double>(real, -imag);
|
248 |
+
}
|
249 |
+
return roots;
|
250 |
+
}
|
251 |
+
|
252 |
+
// Normalize equation: z^3 + (b/a)z^2 + (c/a)z + (d/a) = 0
|
253 |
+
double p = b / a;
|
254 |
+
double q = c / a;
|
255 |
+
double r = d / a;
|
256 |
+
|
257 |
+
// Substitute z = t - p/3 to get t^3 + pt^2 + qt + r = 0
|
258 |
+
double p1 = q - p * p / 3.0;
|
259 |
+
double q1 = r - p * q / 3.0 + 2.0 * p * p * p / 27.0;
|
260 |
+
|
261 |
+
// Calculate discriminant
|
262 |
+
double D = q1 * q1 / 4.0 + p1 * p1 * p1 / 27.0;
|
263 |
+
|
264 |
+
// Precompute values
|
265 |
+
const double two_pi = 2.0 * M_PI;
|
266 |
+
const double third = 1.0 / 3.0;
|
267 |
+
const double p_over_3 = p / 3.0;
|
268 |
+
|
269 |
+
CubicRoots roots;
|
270 |
+
|
271 |
+
// Handle the special case where the discriminant is close to zero (all real roots, at least two equal)
|
272 |
+
if (std::abs(D) < zero_threshold) {
|
273 |
+
// Special case where all roots are zero
|
274 |
+
if (std::abs(p1) < zero_threshold && std::abs(q1) < zero_threshold) {
|
275 |
+
roots.root1 = std::complex<double>(-p_over_3, 0.0);
|
276 |
+
roots.root2 = std::complex<double>(-p_over_3, 0.0);
|
277 |
+
roots.root3 = std::complex<double>(-p_over_3, 0.0);
|
278 |
+
return roots;
|
279 |
+
}
|
280 |
+
|
281 |
+
// General case for D ≈ 0
|
282 |
+
double u = std::cbrt(-q1 / 2.0); // Real cube root
|
283 |
+
|
284 |
+
roots.root1 = std::complex<double>(2.0 * u - p_over_3, 0.0);
|
285 |
+
roots.root2 = std::complex<double>(-u - p_over_3, 0.0);
|
286 |
+
roots.root3 = roots.root2; // Duplicate root
|
287 |
+
|
288 |
+
// Check if any roots are close to zero and set them to exactly zero
|
289 |
+
if (std::abs(roots.root1.real()) < zero_threshold)
|
290 |
+
roots.root1 = std::complex<double>(0.0, 0.0);
|
291 |
+
if (std::abs(roots.root2.real()) < zero_threshold) {
|
292 |
+
roots.root2 = std::complex<double>(0.0, 0.0);
|
293 |
+
roots.root3 = std::complex<double>(0.0, 0.0);
|
294 |
+
}
|
295 |
+
|
296 |
+
return roots;
|
297 |
+
}
|
298 |
+
|
299 |
+
if (D > 0) { // One real root and two complex conjugate roots
|
300 |
+
double sqrtD = std::sqrt(D);
|
301 |
+
double u = std::cbrt(-q1 / 2.0 + sqrtD);
|
302 |
+
double v = std::cbrt(-q1 / 2.0 - sqrtD);
|
303 |
+
|
304 |
+
// Real root
|
305 |
+
roots.root1 = std::complex<double>(u + v - p_over_3, 0.0);
|
306 |
+
|
307 |
+
// Complex conjugate roots
|
308 |
+
double real_part = -(u + v) / 2.0 - p_over_3;
|
309 |
+
double imag_part = (u - v) * std::sqrt(3.0) / 2.0;
|
310 |
+
roots.root2 = std::complex<double>(real_part, imag_part);
|
311 |
+
roots.root3 = std::complex<double>(real_part, -imag_part);
|
312 |
+
|
313 |
+
// Check if any roots are close to zero and set them to exactly zero
|
314 |
+
if (std::abs(roots.root1.real()) < zero_threshold)
|
315 |
+
roots.root1 = std::complex<double>(0.0, 0.0);
|
316 |
+
|
317 |
+
return roots;
|
318 |
+
}
|
319 |
+
else { // Three distinct real roots
|
320 |
+
double angle = std::acos(-q1 / 2.0 * std::sqrt(-27.0 / (p1 * p1 * p1)));
|
321 |
+
double magnitude = 2.0 * std::sqrt(-p1 / 3.0);
|
322 |
+
|
323 |
+
// Calculate all three real roots
|
324 |
+
roots.root1 = std::complex<double>(magnitude * std::cos(angle / 3.0) - p_over_3, 0.0);
|
325 |
+
roots.root2 = std::complex<double>(magnitude * std::cos((angle + two_pi) / 3.0) - p_over_3, 0.0);
|
326 |
+
roots.root3 = std::complex<double>(magnitude * std::cos((angle + 2.0 * two_pi) / 3.0) - p_over_3, 0.0);
|
327 |
+
|
328 |
+
// Check if any roots are close to zero and set them to exactly zero
|
329 |
+
if (std::abs(roots.root1.real()) < zero_threshold)
|
330 |
+
roots.root1 = std::complex<double>(0.0, 0.0);
|
331 |
+
if (std::abs(roots.root2.real()) < zero_threshold)
|
332 |
+
roots.root2 = std::complex<double>(0.0, 0.0);
|
333 |
+
if (std::abs(roots.root3.real()) < zero_threshold)
|
334 |
+
roots.root3 = std::complex<double>(0.0, 0.0);
|
335 |
+
|
336 |
+
return roots;
|
337 |
+
}
|
338 |
+
}
|
339 |
+
|
340 |
+
// Function to compute the cubic equation for Im(s) vs z
|
341 |
+
std::vector<std::vector<double>> computeImSVsZ(double a, double y, double beta, int num_points) {
|
342 |
+
std::vector<double> z_values(num_points);
|
343 |
+
std::vector<double> ims_values1(num_points);
|
344 |
+
std::vector<double> ims_values2(num_points);
|
345 |
+
std::vector<double> ims_values3(num_points);
|
346 |
+
std::vector<double> real_values1(num_points);
|
347 |
+
std::vector<double> real_values2(num_points);
|
348 |
+
std::vector<double> real_values3(num_points);
|
349 |
+
|
350 |
+
// Generate z values from 0.01 to 10 (or adjust range as needed)
|
351 |
+
double z_start = 0.01; // Avoid z=0 to prevent potential division issues
|
352 |
+
double z_end = 10.0;
|
353 |
+
double z_step = (z_end - z_start) / (num_points - 1);
|
354 |
+
|
355 |
+
for (int i = 0; i < num_points; ++i) {
|
356 |
+
double z = z_start + i * z_step;
|
357 |
+
z_values[i] = z;
|
358 |
+
|
359 |
+
// Coefficients for the cubic equation:
|
360 |
+
// zas³ + [z(a+1)+a(1-y)]s² + [z+(a+1)-y-yβ(a-1)]s + 1 = 0
|
361 |
+
double coef_a = z * a;
|
362 |
+
double coef_b = z * (a + 1) + a * (1 - y);
|
363 |
+
double coef_c = z + (a + 1) - y - y * beta * (a - 1);
|
364 |
+
double coef_d = 1.0;
|
365 |
+
|
366 |
+
// Solve the cubic equation
|
367 |
+
CubicRoots roots = solveCubic(coef_a, coef_b, coef_c, coef_d);
|
368 |
+
|
369 |
+
// Extract imaginary and real parts
|
370 |
+
ims_values1[i] = std::abs(roots.root1.imag());
|
371 |
+
ims_values2[i] = std::abs(roots.root2.imag());
|
372 |
+
ims_values3[i] = std::abs(roots.root3.imag());
|
373 |
+
|
374 |
+
real_values1[i] = roots.root1.real();
|
375 |
+
real_values2[i] = roots.root2.real();
|
376 |
+
real_values3[i] = roots.root3.real();
|
377 |
+
}
|
378 |
+
|
379 |
+
// Create output vector, now including real values for better analysis
|
380 |
+
std::vector<std::vector<double>> result = {
|
381 |
+
z_values, ims_values1, ims_values2, ims_values3,
|
382 |
+
real_values1, real_values2, real_values3
|
383 |
+
};
|
384 |
+
|
385 |
+
return result;
|
386 |
+
}
|
387 |
+
|
388 |
+
// Function to save Im(s) vs z data as JSON
|
389 |
+
bool saveImSDataAsJSON(const std::string& filename,
|
390 |
+
const std::vector<std::vector<double>>& data) {
|
391 |
+
std::ofstream outfile(filename);
|
392 |
+
|
393 |
+
if (!outfile.is_open()) {
|
394 |
+
std::cerr << "Error: Could not open file " << filename << " for writing." << std::endl;
|
395 |
+
return false;
|
396 |
+
}
|
397 |
+
|
398 |
+
// Start JSON object
|
399 |
+
outfile << "{\n";
|
400 |
+
|
401 |
+
// Write z values
|
402 |
+
outfile << " \"z_values\": [";
|
403 |
+
for (size_t i = 0; i < data[0].size(); ++i) {
|
404 |
+
outfile << data[0][i];
|
405 |
+
if (i < data[0].size() - 1) outfile << ", ";
|
406 |
+
}
|
407 |
+
outfile << "],\n";
|
408 |
+
|
409 |
+
// Write Im(s) values for first root
|
410 |
+
outfile << " \"ims_values1\": [";
|
411 |
+
for (size_t i = 0; i < data[1].size(); ++i) {
|
412 |
+
outfile << data[1][i];
|
413 |
+
if (i < data[1].size() - 1) outfile << ", ";
|
414 |
+
}
|
415 |
+
outfile << "],\n";
|
416 |
+
|
417 |
+
// Write Im(s) values for second root
|
418 |
+
outfile << " \"ims_values2\": [";
|
419 |
+
for (size_t i = 0; i < data[2].size(); ++i) {
|
420 |
+
outfile << data[2][i];
|
421 |
+
if (i < data[2].size() - 1) outfile << ", ";
|
422 |
+
}
|
423 |
+
outfile << "],\n";
|
424 |
+
|
425 |
+
// Write Im(s) values for third root
|
426 |
+
outfile << " \"ims_values3\": [";
|
427 |
+
for (size_t i = 0; i < data[3].size(); ++i) {
|
428 |
+
outfile << data[3][i];
|
429 |
+
if (i < data[3].size() - 1) outfile << ", ";
|
430 |
+
}
|
431 |
+
outfile << "],\n";
|
432 |
+
|
433 |
+
// Write Real(s) values for first root
|
434 |
+
outfile << " \"real_values1\": [";
|
435 |
+
for (size_t i = 0; i < data[4].size(); ++i) {
|
436 |
+
outfile << data[4][i];
|
437 |
+
if (i < data[4].size() - 1) outfile << ", ";
|
438 |
+
}
|
439 |
+
outfile << "],\n";
|
440 |
+
|
441 |
+
// Write Real(s) values for second root
|
442 |
+
outfile << " \"real_values2\": [";
|
443 |
+
for (size_t i = 0; i < data[5].size(); ++i) {
|
444 |
+
outfile << data[5][i];
|
445 |
+
if (i < data[5].size() - 1) outfile << ", ";
|
446 |
+
}
|
447 |
+
outfile << "],\n";
|
448 |
+
|
449 |
+
// Write Real(s) values for third root
|
450 |
+
outfile << " \"real_values3\": [";
|
451 |
+
for (size_t i = 0; i < data[6].size(); ++i) {
|
452 |
+
outfile << data[6][i];
|
453 |
+
if (i < data[6].size() - 1) outfile << ", ";
|
454 |
+
}
|
455 |
+
outfile << "]\n";
|
456 |
+
|
457 |
+
// Close JSON object
|
458 |
+
outfile << "}\n";
|
459 |
+
|
460 |
+
outfile.close();
|
461 |
+
return true;
|
462 |
+
}
|
463 |
+
|
464 |
+
// Function to compute the theoretical max value
|
465 |
+
double compute_theoretical_max(double a, double y, double beta, int grid_points, double tolerance) {
|
466 |
+
auto f = [a, y, beta](double k) -> double {
|
467 |
+
return (y * beta * (a - 1) * k + (a * k + 1) * ((y - 1) * k - 1)) /
|
468 |
+
((a * k + 1) * (k * k + k));
|
469 |
+
};
|
470 |
+
|
471 |
+
// Use numerical optimization to find the maximum
|
472 |
+
// Grid search followed by golden section search
|
473 |
+
double best_k = 1.0;
|
474 |
+
double best_val = f(best_k);
|
475 |
+
|
476 |
+
// Initial grid search over a wide range
|
477 |
+
const int num_grid_points = grid_points;
|
478 |
+
for (int i = 0; i < num_grid_points; ++i) {
|
479 |
+
double k = 0.01 + 100.0 * i / (num_grid_points - 1); // From 0.01 to 100
|
480 |
+
double val = f(k);
|
481 |
+
if (val > best_val) {
|
482 |
+
best_val = val;
|
483 |
+
best_k = k;
|
484 |
+
}
|
485 |
+
}
|
486 |
+
|
487 |
+
// Refine with golden section search
|
488 |
+
double a_gs = std::max(0.01, best_k / 10.0);
|
489 |
+
double b_gs = best_k * 10.0;
|
490 |
+
const double golden_ratio = (1.0 + std::sqrt(5.0)) / 2.0;
|
491 |
+
|
492 |
+
double c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
|
493 |
+
double d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
|
494 |
+
|
495 |
+
while (std::abs(b_gs - a_gs) > tolerance) {
|
496 |
+
if (f(c_gs) > f(d_gs)) {
|
497 |
+
b_gs = d_gs;
|
498 |
+
d_gs = c_gs;
|
499 |
+
c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
|
500 |
+
} else {
|
501 |
+
a_gs = c_gs;
|
502 |
+
c_gs = d_gs;
|
503 |
+
d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
|
504 |
+
}
|
505 |
+
}
|
506 |
+
|
507 |
+
// Return the value without multiplying by y (as per correction)
|
508 |
+
return f((a_gs + b_gs) / 2.0);
|
509 |
+
}
|
510 |
+
|
511 |
+
// Function to compute the theoretical min value
|
512 |
+
double compute_theoretical_min(double a, double y, double beta, int grid_points, double tolerance) {
|
513 |
+
auto f = [a, y, beta](double t) -> double {
|
514 |
+
return (y * beta * (a - 1) * t + (a * t + 1) * ((y - 1) * t - 1)) /
|
515 |
+
((a * t + 1) * (t * t + t));
|
516 |
+
};
|
517 |
+
|
518 |
+
// Use numerical optimization to find the minimum
|
519 |
+
// Grid search followed by golden section search
|
520 |
+
double best_t = -0.5 / a; // Midpoint of (-1/a, 0)
|
521 |
+
double best_val = f(best_t);
|
522 |
+
|
523 |
+
// Initial grid search over the range (-1/a, 0)
|
524 |
+
const int num_grid_points = grid_points;
|
525 |
+
for (int i = 1; i < num_grid_points; ++i) {
|
526 |
+
// From slightly above -1/a to slightly below 0
|
527 |
+
double t = -0.999/a + 0.998/a * i / (num_grid_points - 1);
|
528 |
+
if (t >= 0 || t <= -1.0/a) continue; // Ensure t is in range (-1/a, 0)
|
529 |
+
|
530 |
+
double val = f(t);
|
531 |
+
if (val < best_val) {
|
532 |
+
best_val = val;
|
533 |
+
best_t = t;
|
534 |
+
}
|
535 |
+
}
|
536 |
+
|
537 |
+
// Refine with golden section search
|
538 |
+
double a_gs = -0.999/a; // Slightly above -1/a
|
539 |
+
double b_gs = -0.001/a; // Slightly below 0
|
540 |
+
const double golden_ratio = (1.0 + std::sqrt(5.0)) / 2.0;
|
541 |
+
|
542 |
+
double c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
|
543 |
+
double d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
|
544 |
+
|
545 |
+
while (std::abs(b_gs - a_gs) > tolerance) {
|
546 |
+
if (f(c_gs) < f(d_gs)) {
|
547 |
+
b_gs = d_gs;
|
548 |
+
d_gs = c_gs;
|
549 |
+
c_gs = b_gs - (b_gs - a_gs) / golden_ratio;
|
550 |
+
} else {
|
551 |
+
a_gs = c_gs;
|
552 |
+
c_gs = d_gs;
|
553 |
+
d_gs = a_gs + (b_gs - a_gs) / golden_ratio;
|
554 |
+
}
|
555 |
+
}
|
556 |
+
|
557 |
+
// Return the value without multiplying by y (as per correction)
|
558 |
+
return f((a_gs + b_gs) / 2.0);
|
559 |
+
}
|
560 |
+
|
561 |
+
// Function to save data as JSON
|
562 |
+
bool save_as_json(const std::string& filename,
|
563 |
+
const std::vector<double>& beta_values,
|
564 |
+
const std::vector<double>& max_eigenvalues,
|
565 |
+
const std::vector<double>& min_eigenvalues,
|
566 |
+
const std::vector<double>& theoretical_max_values,
|
567 |
+
const std::vector<double>& theoretical_min_values) {
|
568 |
+
|
569 |
+
std::ofstream outfile(filename);
|
570 |
+
|
571 |
+
if (!outfile.is_open()) {
|
572 |
+
std::cerr << "Error: Could not open file " << filename << " for writing." << std::endl;
|
573 |
+
return false;
|
574 |
+
}
|
575 |
+
|
576 |
+
// Start JSON object
|
577 |
+
outfile << "{\n";
|
578 |
+
|
579 |
+
// Write beta values
|
580 |
+
outfile << " \"beta_values\": [";
|
581 |
+
for (size_t i = 0; i < beta_values.size(); ++i) {
|
582 |
+
outfile << beta_values[i];
|
583 |
+
if (i < beta_values.size() - 1) outfile << ", ";
|
584 |
+
}
|
585 |
+
outfile << "],\n";
|
586 |
+
|
587 |
+
// Write max eigenvalues
|
588 |
+
outfile << " \"max_eigenvalues\": [";
|
589 |
+
for (size_t i = 0; i < max_eigenvalues.size(); ++i) {
|
590 |
+
outfile << max_eigenvalues[i];
|
591 |
+
if (i < max_eigenvalues.size() - 1) outfile << ", ";
|
592 |
+
}
|
593 |
+
outfile << "],\n";
|
594 |
+
|
595 |
+
// Write min eigenvalues
|
596 |
+
outfile << " \"min_eigenvalues\": [";
|
597 |
+
for (size_t i = 0; i < min_eigenvalues.size(); ++i) {
|
598 |
+
outfile << min_eigenvalues[i];
|
599 |
+
if (i < min_eigenvalues.size() - 1) outfile << ", ";
|
600 |
+
}
|
601 |
+
outfile << "],\n";
|
602 |
+
|
603 |
+
// Write theoretical max values
|
604 |
+
outfile << " \"theoretical_max\": [";
|
605 |
+
for (size_t i = 0; i < theoretical_max_values.size(); ++i) {
|
606 |
+
outfile << theoretical_max_values[i];
|
607 |
+
if (i < theoretical_max_values.size() - 1) outfile << ", ";
|
608 |
+
}
|
609 |
+
outfile << "],\n";
|
610 |
+
|
611 |
+
// Write theoretical min values
|
612 |
+
outfile << " \"theoretical_min\": [";
|
613 |
+
for (size_t i = 0; i < theoretical_min_values.size(); ++i) {
|
614 |
+
outfile << theoretical_min_values[i];
|
615 |
+
if (i < theoretical_min_values.size() - 1) outfile << ", ";
|
616 |
+
}
|
617 |
+
outfile << "]\n";
|
618 |
+
|
619 |
+
// Close JSON object
|
620 |
+
outfile << "}\n";
|
621 |
+
|
622 |
+
outfile.close();
|
623 |
+
return true;
|
624 |
+
}
|
625 |
+
|
626 |
+
// Eigenvalue analysis function
|
627 |
+
bool eigenvalueAnalysis(int n, int p, double a, double y, int fineness,
|
628 |
+
int theory_grid_points, double theory_tolerance,
|
629 |
+
const std::string& output_file) {
|
630 |
+
|
631 |
+
std::cout << "Running eigenvalue analysis with parameters: n = " << n << ", p = " << p
|
632 |
+
<< ", a = " << a << ", y = " << y << ", fineness = " << fineness
|
633 |
+
<< ", theory_grid_points = " << theory_grid_points
|
634 |
+
<< ", theory_tolerance = " << theory_tolerance << std::endl;
|
635 |
+
std::cout << "Output will be saved to: " << output_file << std::endl;
|
636 |
+
|
637 |
+
// ─── Beta range parameters ────────────────────────────────────────
|
638 |
+
const int num_beta_points = fineness; // Controlled by fineness parameter
|
639 |
+
std::vector<double> beta_values(num_beta_points);
|
640 |
+
for (int i = 0; i < num_beta_points; ++i) {
|
641 |
+
beta_values[i] = static_cast<double>(i) / (num_beta_points - 1);
|
642 |
+
}
|
643 |
+
|
644 |
+
// ─── Storage for results ────────────────────────────────────────
|
645 |
+
std::vector<double> max_eigenvalues(num_beta_points);
|
646 |
+
std::vector<double> min_eigenvalues(num_beta_points);
|
647 |
+
std::vector<double> theoretical_max_values(num_beta_points);
|
648 |
+
std::vector<double> theoretical_min_values(num_beta_points);
|
649 |
+
|
650 |
+
try {
|
651 |
+
// ─── Random‐Gaussian X and S_n ────────────────────────────────
|
652 |
+
std::random_device rd;
|
653 |
+
std::mt19937_64 rng{rd()};
|
654 |
+
std::normal_distribution<double> norm(0.0, 1.0);
|
655 |
+
|
656 |
+
cv::Mat X(p, n, CV_64F);
|
657 |
+
for(int i = 0; i < p; ++i)
|
658 |
+
for(int j = 0; j < n; ++j)
|
659 |
+
X.at<double>(i,j) = norm(rng);
|
660 |
+
|
661 |
+
// ─── Process each beta value ─────────────────────────────────
|
662 |
+
for (int beta_idx = 0; beta_idx < num_beta_points; ++beta_idx) {
|
663 |
+
double beta = beta_values[beta_idx];
|
664 |
+
|
665 |
+
// Compute theoretical values with customizable precision
|
666 |
+
theoretical_max_values[beta_idx] = compute_theoretical_max(a, y, beta, theory_grid_points, theory_tolerance);
|
667 |
+
theoretical_min_values[beta_idx] = compute_theoretical_min(a, y, beta, theory_grid_points, theory_tolerance);
|
668 |
+
|
669 |
+
// ─── Build T_n matrix ──────────────────────────────────
|
670 |
+
int k = static_cast<int>(std::floor(beta * p));
|
671 |
+
std::vector<double> diags(p, 1.0);
|
672 |
+
std::fill_n(diags.begin(), k, a);
|
673 |
+
std::shuffle(diags.begin(), diags.end(), rng);
|
674 |
+
|
675 |
+
cv::Mat T_n = cv::Mat::zeros(p, p, CV_64F);
|
676 |
+
for(int i = 0; i < p; ++i){
|
677 |
+
T_n.at<double>(i,i) = diags[i];
|
678 |
+
}
|
679 |
+
|
680 |
+
// ─── Form B_n = (1/n) * X * T_n * X^T ────────────
|
681 |
+
cv::Mat B = (X.t() * T_n * X) / static_cast<double>(n);
|
682 |
+
|
683 |
+
// ─── Compute eigenvalues of B ────────────────────────────
|
684 |
+
cv::Mat eigVals;
|
685 |
+
cv::eigen(B, eigVals);
|
686 |
+
std::vector<double> eigs(n);
|
687 |
+
for(int i = 0; i < n; ++i)
|
688 |
+
eigs[i] = eigVals.at<double>(i, 0);
|
689 |
+
|
690 |
+
max_eigenvalues[beta_idx] = *std::max_element(eigs.begin(), eigs.end());
|
691 |
+
min_eigenvalues[beta_idx] = *std::min_element(eigs.begin(), eigs.end());
|
692 |
+
|
693 |
+
// Progress indicator for Streamlit
|
694 |
+
double progress = static_cast<double>(beta_idx + 1) / num_beta_points;
|
695 |
+
std::cout << "PROGRESS:" << progress << std::endl;
|
696 |
+
|
697 |
+
// Less verbose output for Streamlit
|
698 |
+
if (beta_idx % 20 == 0 || beta_idx == num_beta_points - 1) {
|
699 |
+
std::cout << "Processing beta = " << beta
|
700 |
+
<< " (" << beta_idx+1 << "/" << num_beta_points << ")" << std::endl;
|
701 |
+
}
|
702 |
+
}
|
703 |
+
|
704 |
+
// Save data as JSON for Python to read
|
705 |
+
if (!save_as_json(output_file, beta_values, max_eigenvalues, min_eigenvalues,
|
706 |
+
theoretical_max_values, theoretical_min_values)) {
|
707 |
+
return false;
|
708 |
+
}
|
709 |
+
|
710 |
+
std::cout << "Data saved to " << output_file << std::endl;
|
711 |
+
return true;
|
712 |
+
}
|
713 |
+
catch (const std::exception& e) {
|
714 |
+
std::cerr << "Error in eigenvalue analysis: " << e.what() << std::endl;
|
715 |
+
return false;
|
716 |
+
}
|
717 |
+
catch (...) {
|
718 |
+
std::cerr << "Unknown error in eigenvalue analysis" << std::endl;
|
719 |
+
return false;
|
720 |
+
}
|
721 |
+
}
|
722 |
+
|
723 |
+
// Cubic equation analysis function
|
724 |
+
bool cubicAnalysis(double a, double y, double beta, int num_points, const std::string& output_file) {
|
725 |
+
std::cout << "Running cubic equation analysis with parameters: a = " << a
|
726 |
+
<< ", y = " << y << ", beta = " << beta << ", num_points = " << num_points << std::endl;
|
727 |
+
std::cout << "Output will be saved to: " << output_file << std::endl;
|
728 |
+
|
729 |
+
try {
|
730 |
+
// Compute Im(s) vs z data
|
731 |
+
std::vector<std::vector<double>> ims_data = computeImSVsZ(a, y, beta, num_points);
|
732 |
+
|
733 |
+
// Save to JSON
|
734 |
+
if (!saveImSDataAsJSON(output_file, ims_data)) {
|
735 |
+
return false;
|
736 |
+
}
|
737 |
+
|
738 |
+
std::cout << "Cubic equation data saved to " << output_file << std::endl;
|
739 |
+
return true;
|
740 |
+
}
|
741 |
+
catch (const std::exception& e) {
|
742 |
+
std::cerr << "Error in cubic analysis: " << e.what() << std::endl;
|
743 |
+
return false;
|
744 |
+
}
|
745 |
+
catch (...) {
|
746 |
+
std::cerr << "Unknown error in cubic analysis" << std::endl;
|
747 |
+
return false;
|
748 |
+
}
|
749 |
+
}
|
750 |
+
|
751 |
+
int main(int argc, char* argv[]) {
|
752 |
+
// Print received arguments for debugging
|
753 |
+
std::cout << "Received " << argc << " arguments:" << std::endl;
|
754 |
+
for (int i = 0; i < argc; ++i) {
|
755 |
+
std::cout << " argv[" << i << "]: " << argv[i] << std::endl;
|
756 |
+
}
|
757 |
+
|
758 |
+
// Check for mode argument
|
759 |
+
if (argc < 2) {
|
760 |
+
std::cerr << "Error: Missing mode argument." << std::endl;
|
761 |
+
std::cerr << "Usage: " << argv[0] << " eigenvalues <n> <p> <a> <y> <fineness> <theory_grid_points> <theory_tolerance> <output_file>" << std::endl;
|
762 |
+
std::cerr << " or: " << argv[0] << " cubic <a> <y> <beta> <num_points> <output_file>" << std::endl;
|
763 |
+
return 1;
|
764 |
+
}
|
765 |
+
|
766 |
+
std::string mode = argv[1];
|
767 |
+
|
768 |
+
try {
|
769 |
+
if (mode == "eigenvalues") {
|
770 |
+
// ─── Eigenvalue analysis mode ───────────────────────────────────────────
|
771 |
+
if (argc != 10) {
|
772 |
+
std::cerr << "Error: Incorrect number of arguments for eigenvalues mode." << std::endl;
|
773 |
+
std::cerr << "Usage: " << argv[0] << " eigenvalues <n> <p> <a> <y> <fineness> <theory_grid_points> <theory_tolerance> <output_file>" << std::endl;
|
774 |
+
std::cerr << "Received " << argc << " arguments, expected 10." << std::endl;
|
775 |
+
return 1;
|
776 |
+
}
|
777 |
+
|
778 |
+
int n = std::stoi(argv[2]);
|
779 |
+
int p = std::stoi(argv[3]);
|
780 |
+
double a = std::stod(argv[4]);
|
781 |
+
double y = std::stod(argv[5]);
|
782 |
+
int fineness = std::stoi(argv[6]);
|
783 |
+
int theory_grid_points = std::stoi(argv[7]);
|
784 |
+
double theory_tolerance = std::stod(argv[8]);
|
785 |
+
std::string output_file = argv[9];
|
786 |
+
|
787 |
+
if (!eigenvalueAnalysis(n, p, a, y, fineness, theory_grid_points, theory_tolerance, output_file)) {
|
788 |
+
return 1;
|
789 |
+
}
|
790 |
+
|
791 |
+
} else if (mode == "cubic") {
|
792 |
+
// ─── Cubic equation analysis mode ───────────────────────────────────────────
|
793 |
+
if (argc != 7) {
|
794 |
+
std::cerr << "Error: Incorrect number of arguments for cubic mode." << std::endl;
|
795 |
+
std::cerr << "Usage: " << argv[0] << " cubic <a> <y> <beta> <num_points> <output_file>" << std::endl;
|
796 |
+
std::cerr << "Received " << argc << " arguments, expected 7." << std::endl;
|
797 |
+
return 1;
|
798 |
+
}
|
799 |
+
|
800 |
+
double a = std::stod(argv[2]);
|
801 |
+
double y = std::stod(argv[3]);
|
802 |
+
double beta = std::stod(argv[4]);
|
803 |
+
int num_points = std::stoi(argv[5]);
|
804 |
+
std::string output_file = argv[6];
|
805 |
+
|
806 |
+
if (!cubicAnalysis(a, y, beta, num_points, output_file)) {
|
807 |
+
return 1;
|
808 |
+
}
|
809 |
+
|
810 |
+
} else {
|
811 |
+
std::cerr << "Error: Unknown mode: " << mode << std::endl;
|
812 |
+
std::cerr << "Use 'eigenvalues' or 'cubic'" << std::endl;
|
813 |
+
return 1;
|
814 |
+
}
|
815 |
+
}
|
816 |
+
catch (const std::exception& e) {
|
817 |
+
std::cerr << "Error: " << e.what() << std::endl;
|
818 |
+
return 1;
|
819 |
+
}
|
820 |
+
|
821 |
+
return 0;
|
822 |
+
}
|
823 |
+
''')
|
824 |
|
825 |
# Compile the C++ code with the right OpenCV libraries
|
826 |
st.sidebar.title("Compiler Settings")
|
|
|
886 |
st.markdown('<div class="panel-header">Eigenvalue Analysis Controls</div>', unsafe_allow_html=True)
|
887 |
|
888 |
# Parameter inputs with defaults and validation
|
889 |
+
st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
|
890 |
st.markdown("### Matrix Parameters")
|
891 |
n = st.number_input("Sample size (n)", min_value=5, max_value=1000, value=100, step=5,
|
892 |
help="Number of samples", key="eig_n")
|
|
|
898 |
# Automatically calculate y = p/n (as requested)
|
899 |
y = p/n
|
900 |
st.info(f"Value for y = p/n: {y:.4f}")
|
901 |
+
st.markdown('</div>', unsafe_allow_html=True)
|
902 |
|
903 |
+
st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
|
904 |
st.markdown("### Calculation Controls")
|
905 |
fineness = st.slider(
|
906 |
"Beta points",
|
|
|
911 |
help="Number of points to calculate along the β axis (0 to 1)",
|
912 |
key="eig_fineness"
|
913 |
)
|
914 |
+
st.markdown('</div>', unsafe_allow_html=True)
|
915 |
|
916 |
with st.expander("Advanced Settings"):
|
917 |
# Add controls for theoretical calculation precision
|
|
|
1374 |
st.markdown('<div class="panel-header">Im(s) vs z Analysis Controls</div>', unsafe_allow_html=True)
|
1375 |
|
1376 |
# Parameter inputs with defaults and validation
|
1377 |
+
st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
|
1378 |
st.markdown("### Cubic Equation Parameters")
|
1379 |
cubic_a = st.number_input("Value for a", min_value=1.1, max_value=10.0, value=2.0, step=0.1,
|
1380 |
help="Parameter a > 1", key="cubic_a")
|
|
|
1382 |
help="Parameter y > 0", key="cubic_y")
|
1383 |
cubic_beta = st.number_input("Value for β", min_value=0.0, max_value=1.0, value=0.5, step=0.05,
|
1384 |
help="Value between 0 and 1", key="cubic_beta")
|
1385 |
+
st.markdown('</div>', unsafe_allow_html=True)
|
1386 |
|
1387 |
+
st.markdown('<div class="parameter-container">', unsafe_allow_html=True)
|
1388 |
st.markdown("### Calculation Controls")
|
1389 |
cubic_points = st.slider(
|
1390 |
"Number of z points",
|
|
|
1408 |
help="Maximum time allowed for computation before timeout",
|
1409 |
key="cubic_timeout"
|
1410 |
)
|
1411 |
+
st.markdown('</div>', unsafe_allow_html=True)
|
1412 |
|
1413 |
# Show cubic equation
|
1414 |
st.markdown('<div class="math-box">', unsafe_allow_html=True)
|
|
|
1489 |
ims_values2 = np.array(data['ims_values2'])
|
1490 |
ims_values3 = np.array(data['ims_values3'])
|
1491 |
|
1492 |
+
# Also extract real parts if available
|
1493 |
+
real_values1 = np.array(data.get('real_values1', [0] * len(z_values)))
|
1494 |
+
real_values2 = np.array(data.get('real_values2', [0] * len(z_values)))
|
1495 |
+
real_values3 = np.array(data.get('real_values3', [0] * len(z_values)))
|
1496 |
|
1497 |
+
# Create tabs for imaginary and real parts
|
1498 |
+
im_tab, real_tab = st.tabs(["Imaginary Parts", "Real Parts"])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1499 |
|
1500 |
+
# Tab for imaginary parts
|
1501 |
+
with im_tab:
|
1502 |
+
# Create an interactive plot for imaginary parts
|
1503 |
+
im_fig = go.Figure()
|
1504 |
+
|
1505 |
+
# Add traces for each root's imaginary part
|
1506 |
+
im_fig.add_trace(go.Scatter(
|
1507 |
+
x=z_values,
|
1508 |
+
y=ims_values1,
|
1509 |
+
mode='lines',
|
1510 |
+
name='Im(s₁)',
|
1511 |
+
line=dict(color='rgb(220, 60, 60)', width=3),
|
1512 |
+
hovertemplate='z: %{x:.3f}<br>Im(s₁): %{y:.6f}<extra>Root 1</extra>'
|
1513 |
+
))
|
1514 |
+
|
1515 |
+
im_fig.add_trace(go.Scatter(
|
1516 |
+
x=z_values,
|
1517 |
+
y=ims_values2,
|
1518 |
+
mode='lines',
|
1519 |
+
name='Im(s₂)',
|
1520 |
+
line=dict(color='rgb(60, 60, 220)', width=3),
|
1521 |
+
hovertemplate='z: %{x:.3f}<br>Im(s₂): %{y:.6f}<extra>Root 2</extra>'
|
1522 |
+
))
|
1523 |
+
|
1524 |
+
im_fig.add_trace(go.Scatter(
|
1525 |
+
x=z_values,
|
1526 |
+
y=ims_values3,
|
1527 |
+
mode='lines',
|
1528 |
+
name='Im(s₃)',
|
1529 |
+
line=dict(color='rgb(30, 180, 30)', width=3),
|
1530 |
+
hovertemplate='z: %{x:.3f}<br>Im(s₃): %{y:.6f}<extra>Root 3</extra>'
|
1531 |
+
))
|
1532 |
+
|
1533 |
+
# Configure layout for better appearance
|
1534 |
+
im_fig.update_layout(
|
1535 |
+
title={
|
1536 |
+
'text': f'Im(s) vs z Analysis: a={cubic_a}, y={cubic_y}, β={cubic_beta}',
|
1537 |
+
'font': {'size': 24, 'color': '#1E88E5'},
|
1538 |
+
'y': 0.95,
|
1539 |
+
'x': 0.5,
|
1540 |
+
'xanchor': 'center',
|
1541 |
+
'yanchor': 'top'
|
1542 |
+
},
|
1543 |
+
xaxis={
|
1544 |
+
'title': {'text': 'z (logarithmic scale)', 'font': {'size': 18, 'color': '#424242'}},
|
1545 |
+
'tickfont': {'size': 14},
|
1546 |
+
'gridcolor': 'rgba(220, 220, 220, 0.5)',
|
1547 |
+
'showgrid': True,
|
1548 |
+
'type': 'log' # Use logarithmic scale for better visualization
|
1549 |
+
},
|
1550 |
+
yaxis={
|
1551 |
+
'title': {'text': 'Im(s)', 'font': {'size': 18, 'color': '#424242'}},
|
1552 |
+
'tickfont': {'size': 14},
|
1553 |
+
'gridcolor': 'rgba(220, 220, 220, 0.5)',
|
1554 |
+
'showgrid': True
|
1555 |
+
},
|
1556 |
+
plot_bgcolor='rgba(240, 240, 240, 0.8)',
|
1557 |
+
paper_bgcolor='rgba(249, 249, 249, 0.8)',
|
1558 |
+
hovermode='closest',
|
1559 |
+
legend={
|
1560 |
+
'font': {'size': 14},
|
1561 |
'bgcolor': 'rgba(255, 255, 255, 0.9)',
|
1562 |
+
'bordercolor': 'rgba(200, 200, 200, 0.5)',
|
1563 |
+
'borderwidth': 1
|
1564 |
+
},
|
1565 |
+
margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
|
1566 |
+
height=500,
|
1567 |
+
annotations=[
|
1568 |
+
{
|
1569 |
+
'text': f"Cubic Equation: {cubic_a}zs³ + [{cubic_a+1}z+{cubic_a}(1-{cubic_y})]s² + [z+{cubic_a+1}-{cubic_y}-{cubic_y*cubic_beta}({cubic_a-1})]s + 1 = 0",
|
1570 |
+
'xref': 'paper', 'yref': 'paper',
|
1571 |
+
'x': 0.5, 'y': 0.02,
|
1572 |
+
'showarrow': False,
|
1573 |
+
'font': {'size': 12, 'color': 'black'},
|
1574 |
+
'bgcolor': 'rgba(255, 255, 255, 0.9)',
|
1575 |
+
'bordercolor': 'rgba(0, 0, 0, 0.5)',
|
1576 |
+
'borderwidth': 1,
|
1577 |
+
'borderpad': 4,
|
1578 |
+
'align': 'center'
|
1579 |
+
}
|
1580 |
+
]
|
1581 |
+
)
|
1582 |
+
|
1583 |
+
# Display the interactive plot in Streamlit
|
1584 |
+
st.plotly_chart(im_fig, use_container_width=True)
|
1585 |
+
|
1586 |
+
# Tab for real parts
|
1587 |
+
with real_tab:
|
1588 |
+
# Create an interactive plot for real parts
|
1589 |
+
real_fig = go.Figure()
|
1590 |
+
|
1591 |
+
# Add traces for each root's real part
|
1592 |
+
real_fig.add_trace(go.Scatter(
|
1593 |
+
x=z_values,
|
1594 |
+
y=real_values1,
|
1595 |
+
mode='lines',
|
1596 |
+
name='Re(s₁)',
|
1597 |
+
line=dict(color='rgb(220, 60, 60)', width=3),
|
1598 |
+
hovertemplate='z: %{x:.3f}<br>Re(s₁): %{y:.6f}<extra>Root 1</extra>'
|
1599 |
+
))
|
1600 |
+
|
1601 |
+
real_fig.add_trace(go.Scatter(
|
1602 |
+
x=z_values,
|
1603 |
+
y=real_values2,
|
1604 |
+
mode='lines',
|
1605 |
+
name='Re(s₂)',
|
1606 |
+
line=dict(color='rgb(60, 60, 220)', width=3),
|
1607 |
+
hovertemplate='z: %{x:.3f}<br>Re(s₂): %{y:.6f}<extra>Root 2</extra>'
|
1608 |
+
))
|
1609 |
+
|
1610 |
+
real_fig.add_trace(go.Scatter(
|
1611 |
+
x=z_values,
|
1612 |
+
y=real_values3,
|
1613 |
+
mode='lines',
|
1614 |
+
name='Re(s₃)',
|
1615 |
+
line=dict(color='rgb(30, 180, 30)', width=3),
|
1616 |
+
hovertemplate='z: %{x:.3f}<br>Re(s₃): %{y:.6f}<extra>Root 3</extra>'
|
1617 |
+
))
|
1618 |
+
|
1619 |
+
# Configure layout for better appearance
|
1620 |
+
real_fig.update_layout(
|
1621 |
+
title={
|
1622 |
+
'text': f'Re(s) vs z Analysis: a={cubic_a}, y={cubic_y}, β={cubic_beta}',
|
1623 |
+
'font': {'size': 24, 'color': '#1E88E5'},
|
1624 |
+
'y': 0.95,
|
1625 |
+
'x': 0.5,
|
1626 |
+
'xanchor': 'center',
|
1627 |
+
'yanchor': 'top'
|
1628 |
+
},
|
1629 |
+
xaxis={
|
1630 |
+
'title': {'text': 'z (logarithmic scale)', 'font': {'size': 18, 'color': '#424242'}},
|
1631 |
+
'tickfont': {'size': 14},
|
1632 |
+
'gridcolor': 'rgba(220, 220, 220, 0.5)',
|
1633 |
+
'showgrid': True,
|
1634 |
+
'type': 'log' # Use logarithmic scale for better visualization
|
1635 |
+
},
|
1636 |
+
yaxis={
|
1637 |
+
'title': {'text': 'Re(s)', 'font': {'size': 18, 'color': '#424242'}},
|
1638 |
+
'tickfont': {'size': 14},
|
1639 |
+
'gridcolor': 'rgba(220, 220, 220, 0.5)',
|
1640 |
+
'showgrid': True
|
1641 |
+
},
|
1642 |
+
plot_bgcolor='rgba(240, 240, 240, 0.8)',
|
1643 |
+
paper_bgcolor='rgba(249, 249, 249, 0.8)',
|
1644 |
+
hovermode='closest',
|
1645 |
+
legend={
|
1646 |
+
'font': {'size': 14},
|
1647 |
+
'bgcolor': 'rgba(255, 255, 255, 0.9)',
|
1648 |
+
'bordercolor': 'rgba(200, 200, 200, 0.5)',
|
1649 |
+
'borderwidth': 1
|
1650 |
+
},
|
1651 |
+
margin={'l': 60, 'r': 30, 't': 100, 'b': 60},
|
1652 |
+
height=500
|
1653 |
+
)
|
1654 |
+
|
1655 |
+
# Display the interactive plot in Streamlit
|
1656 |
+
st.plotly_chart(real_fig, use_container_width=True)
|
1657 |
|
1658 |
# Clear progress container
|
1659 |
progress_container.empty()
|
1660 |
|
|
|
|
|
|
|
1661 |
# Add explanation text
|
1662 |
+
st.markdown('<div class="explanation-box">', unsafe_allow_html=True)
|
1663 |
st.markdown("""
|
1664 |
+
### Root Pattern Analysis
|
1665 |
|
1666 |
+
For the cubic equation in this analysis, we observe specific patterns in the roots:
|
|
|
1667 |
|
1668 |
+
- One root typically has negative real part
|
1669 |
+
- One root typically has positive real part
|
1670 |
+
- One root has zero or near-zero real part
|
1671 |
|
1672 |
+
The imaginary parts show oscillatory behavior, with some z values producing purely real roots
|
1673 |
+
(Im(s) = 0) and others producing complex roots with non-zero imaginary parts. This pattern
|
1674 |
+
is consistent with the expected behavior of cubic equations and has important implications
|
1675 |
+
for system stability analysis.
|
1676 |
|
1677 |
+
The imaginary parts represent oscillatory behavior in the system, while the real parts
|
1678 |
+
represent exponential growth (positive) or decay (negative).
|
1679 |
""")
|
1680 |
+
st.markdown('</div>', unsafe_allow_html=True)
|
1681 |
|
1682 |
except json.JSONDecodeError as e:
|
1683 |
st.error(f"Error parsing JSON results: {str(e)}")
|
|
|
1705 |
ims_values2 = np.array(data['ims_values2'])
|
1706 |
ims_values3 = np.array(data['ims_values3'])
|
1707 |
|
1708 |
+
# Also extract real parts if available
|
1709 |
+
real_values1 = np.array(data.get('real_values1', [0] * len(z_values)))
|
1710 |
+
real_values2 = np.array(data.get('real_values2', [0] * len(z_values)))
|
1711 |
+
real_values3 = np.array(data.get('real_values3', [0] * len(z_values)))
|
1712 |
+
|
1713 |
+
# Show previous results with Imaginary parts
|
1714 |
fig = go.Figure()
|
1715 |
|
1716 |
# Add traces for each root's imaginary part
|
|
|
1798 |
2. **Adjust parameters** in the left panel to configure your analysis
|
1799 |
3. **Click the Generate button** to run the analysis with the selected parameters
|
1800 |
4. **Explore the results** in the interactive plot
|
1801 |
+
5. For the Im(s) vs z Analysis, you can toggle between Imaginary and Real parts to see different aspects of the cubic roots
|
1802 |
|
1803 |
If you encounter any issues with compilation, try clicking the "Recompile C++ Code" button in the sidebar.
|
1804 |
+
|
1805 |
+
<div class="footnote">
|
1806 |
+
This dashboard analyzes the properties of cubic equations and eigenvalues for matrix analysis.
|
1807 |
+
The Im(s) vs z Analysis shows the behavior of cubic roots, with specific patterns of one negative, one positive, and one zero or near-zero root.
|
1808 |
+
</div>
|
1809 |
+
""", unsafe_allow_html=True)
|