Create Scipy.md

Author: AmrutaJayanti

docs/python/Scipy.md

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+# Scipy
+
+Scipy is a powerful Python library used for scientific and technical computing. It builds on NumPy and provides a large number of higher-level functions for mathematical operations, including optimization, integration, interpolation, eigenvalue problems, algebraic equations, and more.
+
+**1. Installation:**
+```python
+!pip install scipy
+```
+
+**2. Import and Usage:**
+
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+```
+
+**3. Linear Algebra:**
+
+Scipy has many functions for linear algebra operations
+
+- Solving Linear Equations:
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+# Solving the system of equations Ax = b
+A = np.array([[3, 2], [1, 2]])
+b = np.array([2, 0])
+
+x = linalg.solve(A, b)
+print(x)  # Solution to the system
+```
+
+- Eigenvalues and eigenvectors
+```python
+# Finding eigenvalues and eigenvectors
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+
+A = np.array([[3, 2], [4, 1]])
+
+eigenvalues, eigenvectors = linalg.eig(A)
+print(eigenvalues)    # Eigenvalues
+print(eigenvectors)   # Eigenvectors
+```
+
+**4. Optimization:**
+
+- Finding minima of a function:
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+
+# Minimizing a scalar function
+def f(x):
+    return x**2 + 10*np.sin(x)
+
+result = optimize.minimize(f, x0=0)
+print(result.x)  # Minimum value of the function
+```
+
+- Root Finding
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+
+# Finding roots of a function
+def f(x):
+    return x**2 - 4
+
+root = optimize.root(f, x0=1)
+print(root.x)  # Root of the function
+```
+
+**5. Interpolation:**
+
+Interpolation can be useful when you want to estimate values between known data points.
+
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+
+# Interpolating data
+x = np.linspace(0, 10, 10)
+y = np.sin(x)
+
+f = interpolate.interp1d(x, y)
+x_new = np.linspace(0, 10, 50)
+y_new = f(x_new)
+
+print(y_new)  # Interpolated values
+```
+
+**6. Statistics:**
+
+Scipy's `stats` module provides a range of statistical functions.
+
+```python
+import numpy as np
+from scipy import linalg, optimize, integrate, interpolate, stats
+
+
+# Calculating descriptive statistics
+data = np.random.normal(loc=0, scale=1, size=1000)
+
+mean = stats.tmean(data)
+std_dev = stats.tstd(data)
+
+print(mean)   # Mean of the data
+print(std_dev)  # Standard deviation of the data
+```
+
+
+**7. Signal Processing:**
+
+Scipy's `signal` module is a powerful tool for signal processing tasks in Python. It provides functions for filtering, spectral analysis, interpolation, and other signal-related operations.
+
+- Filtering:
+
+```python
+from scipy import signal
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Generate a noisy signal
+np.random.seed(0)
+t = np.linspace(0, 1, 1000)
+x = np.sin(2 * np.pi * 10 * t) + np.random.normal(0, 1, t.shape)
+
+# Design a low-pass FIR filter
+b = signal.firwin(30, 0.05)
+x_filtered = signal.lfilter(b, 1, x)
+
+# Plotting
+plt.figure(figsize=(10, 4))
+plt.plot(t, x, label='Noisy signal')
+plt.plot(t, x_filtered, label='Filtered signal')
+plt.xlabel('Time')
+plt.ylabel('Amplitude')
+plt.legend()
+plt.show()
+```
+
+Output:
+
+![image](https://github.com/AmrutaJayanti/codeharborhub/assets/142327526/63a9d70a-af17-414b-beb4-563832da68d5)
+
+
+- Spectral Analysis:
+
+```python
+from scipy import signal
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+# Compute and plot a spectrogram
+f, t, Sxx = signal.spectrogram(x, fs=1000)
+plt.figure(figsize=(10, 4))
+plt.pcolormesh(t, f, 10 * np.log10(Sxx), shading='gouraud')
+plt.ylabel('Frequency [Hz]')
+plt.xlabel('Time [sec]')
+plt.colorbar(label='Power [dB]')
+plt.show()
+```
+
+Output:
+
+![image](https://github.com/AmrutaJayanti/codeharborhub/assets/142327526/30e09ff7-3ad0-424e-993d-96825ad44fb1)
+
+
+
+