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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
import numpy as np from scipy import linalg def sor_solver (A, b, omega, initial_guess, convergence_criteria): """ This is an implementation of the pseudo-code provided in the Wikipedia article.
Matrix types (special types like bidiagonal/tridiagonal are not listed): Real – general (nonsymmetric) real; Complex – general (nonsymmetric) complex; SPD – symmetric positive definite (real)
In the Python library NumPy, the outer product can be computed with function np.outer(). [8] In contrast, np.kron results in a flat array. The outer product of multidimensional arrays can be computed using np.multiply.outer .
The Python package NumPy provides a pseudoinverse calculation through its functions matrix.I and linalg.pinv; its pinv uses the SVD-based algorithm. SciPy adds a function scipy.linalg.pinv that uses a least-squares solver. The MASS package for R provides a calculation of the Moore–Penrose inverse through the ginv function. [24]
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
#!/usr/bin/env python3 import numpy as np def power_iteration (A, num_iterations: int): # Ideally choose a random vector # To decrease the chance that our vector # Is orthogonal to the eigenvector b_k = np. random. rand (A. shape [1]) for _ in range (num_iterations): # calculate the matrix-by-vector product Ab b_k1 = np. dot (A, b_k) # calculate the norm b_k1_norm = np. linalg. norm (b_k1 ...
The following list contains syntax examples of how to determine the dimensions (index of the first element, the last element or the size in elements). Some languages index from zero. Some index from one. Some carry no such restriction, or even allow indexing by any enumerated type, not only integers.