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Rename variables

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99991 2024-10-10 08:46:05 +02:00
parent 4522258980
commit 7808f21e1c
1 changed files with 18 additions and 12 deletions
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30
maths/cholesky_decomposition.py
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@ -1,7 +1,7 @@
import numpy as np import numpy as np
def cholesky_decomposition(a: np.ndarray) -> np.ndarray: def cholesky_decomposition(matrix: np.ndarray) -> np.ndarray:
"""Return a Cholesky decomposition of the matrix A. """Return a Cholesky decomposition of the matrix A.
The Cholesky decomposition decomposes the square, positive definite matrix A The Cholesky decomposition decomposes the square, positive definite matrix A
@ -42,11 +42,13 @@ def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
True True
""" """
assert a.shape[0] == a.shape[1], f"Matrix A is not square, {a.shape=}" assert (
assert np.allclose(a, a.T), "Matrix A must be symmetric" matrix.shape[0] == matrix.shape[1]
), f"Input matrix is not square, {matrix.shape=}"
assert np.allclose(matrix, matrix.T), "Input matrix must be symmetric"
n = a.shape[0] n = matrix.shape[0]
lower_triangle = np.tril(a) lower_triangle = np.tril(matrix)
for i in range(n): for i in range(n):
for j in range(i + 1): for j in range(i + 1):
@ -65,9 +67,13 @@ def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
return lower_triangle return lower_triangle
def solve_cholesky(lower_triangle: np.ndarray, y: np.ndarray) -> np.ndarray: def solve_cholesky(
lower_triangle: np.ndarray,
right_hand_side: np.ndarray,
) -> np.ndarray:
"""Given a Cholesky decomposition L L^T = A of a matrix A, solve the """Given a Cholesky decomposition L L^T = A of a matrix A, solve the
system of equations A X = Y where Y is either a matrix or a vector. system of equations A X = Y where the right-hand side Y is either
a matrix or a vector.
>>> L = np.array([[2, 0], [3, 4]], dtype=float) >>> L = np.array([[2, 0], [3, 4]], dtype=float)
>>> Y = np.array([[22, 54], [81, 193]], dtype=float) >>> Y = np.array([[22, 54], [81, 193]], dtype=float)
@ -84,13 +90,13 @@ def solve_cholesky(lower_triangle: np.ndarray, y: np.ndarray) -> np.ndarray:
), "Matrix L is not lower triangular" ), "Matrix L is not lower triangular"
# Handle vector case by reshaping to matrix and then flattening again # Handle vector case by reshaping to matrix and then flattening again
if len(y.shape) == 1: if len(right_hand_side.shape) == 1:
return solve_cholesky(lower_triangle, y.reshape(-1, 1)).ravel() return solve_cholesky(lower_triangle, right_hand_side.reshape(-1, 1)).ravel()
n = y.shape[0] n = right_hand_side.shape[0]
# Solve L W = B for W # Solve L W = Y for W
w = y.copy() w = right_hand_side.copy()
for i in range(n): for i in range(n):
for j in range(i): for j in range(i):
w[i] -= lower_triangle[i, j] * w[j] w[i] -= lower_triangle[i, j] * w[j]