Boost Python Linear Algebra Performance with SciPy.linalg

Linear Algebra (scipy.linalg)

Built on ATLAS LAPACK and BLAS libraries, SciPy provides very fast linear algebra capabilities.

All linear algebra routines accept two‑dimensional arrays as input and output.

scipy.linalg and numpy.linalg

scipy.linalg = numpy.linalg + more advanced algorithms.

scipy.linalg is compiled with BLAS/LAPACK, making it faster.

numpy.matrix and 2‑D numpy.ndarray are matrix types; numpy.matrix offers a more convenient interface for matrix operations, supports MATLAB‑like syntax such as the * operator for matrix multiplication, and provides I and T members for inverse and transpose.

Example

We fit a quadratic polynomial y = a + b·x² by forming a design matrix with a constant column and a column of x² values, then solving the least‑squares problem M·p = y.

<code>from scipy.linalg import lstsq
import matplotlib.pyplot as plt
x = np.array([1, 2.5, 3.5, 4, 5, 7, 8.5])
y = np.array([0.3, 1.1, 1.5, 2.0, 3.2, 6.6, 8.6])
M = x[:, np.newaxis]**[0, 2]
p, res, rnk, s = lstsq(M, y)
p
</code>

<code>_= plt.plot(x, y, 'o', label='data')
xx = np.linspace(0, 9, 101)
yy = p[0] + p[1]*xx**2
_= plt.plot(xx, yy, label='least squares fit, $y = a + bx^2$')
_= plt.xlabel('x')
_= plt.ylabel('y')
_= plt.legend(framealpha=1, shadow=True)
_= plt.grid(alpha=0.25)
_= plt.show()
</code>