Rename variables

This commit is contained in:
99991 2024-10-10 08:00:18 +02:00
parent 818448b05d
commit 4522258980

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@ -1,8 +1,7 @@
import numpy as np
# ruff: noqa: N803,N806
def cholesky_decomposition(A: np.ndarray) -> np.ndarray:
def cholesky_decomposition(a: np.ndarray) -> np.ndarray:
"""Return a Cholesky decomposition of the matrix A.
The Cholesky decomposition decomposes the square, positive definite matrix A
@ -26,7 +25,7 @@ def cholesky_decomposition(A: np.ndarray) -> np.ndarray:
>>> np.allclose(np.tril(L), L)
True
The Cholesky decomposition can be used to solve the system of equations A x = y.
The Cholesky decomposition can be used to solve the linear system A x = y.
>>> x_true = np.array([1, 2, 3], dtype=float)
>>> y = A @ x_true
@ -43,28 +42,30 @@ def cholesky_decomposition(A: np.ndarray) -> np.ndarray:
True
"""
assert A.shape[0] == A.shape[1], f"Matrix A is not square, {A.shape=}"
assert np.allclose(A, A.T), "Matrix A must be symmetric"
assert a.shape[0] == a.shape[1], f"Matrix A is not square, {a.shape=}"
assert np.allclose(a, a.T), "Matrix A must be symmetric"
n = A.shape[0]
L = np.tril(A)
n = a.shape[0]
lower_triangle = np.tril(a)
for i in range(n):
for j in range(i + 1):
L[i, j] -= np.sum(L[i, :j] * L[j, :j])
lower_triangle[i, j] -= np.sum(
lower_triangle[i, :j] * lower_triangle[j, :j]
)
if i == j:
if L[i, i] <= 0:
if lower_triangle[i, i] <= 0:
raise ValueError("Matrix A is not positive definite")
L[i, i] = np.sqrt(L[i, i])
lower_triangle[i, i] = np.sqrt(lower_triangle[i, i])
else:
L[i, j] /= L[j, j]
lower_triangle[i, j] /= lower_triangle[j, j]
return L
return lower_triangle
def solve_cholesky(L: np.ndarray, Y: np.ndarray) -> np.ndarray:
def solve_cholesky(lower_triangle: np.ndarray, y: np.ndarray) -> np.ndarray:
"""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.
@ -75,32 +76,36 @@ def solve_cholesky(L: np.ndarray, Y: np.ndarray) -> np.ndarray:
True
"""
assert L.shape[0] == L.shape[1], f"Matrix L is not square, {L.shape=}"
assert np.allclose(np.tril(L), L), "Matrix L is not lower triangular"
assert (
lower_triangle.shape[0] == lower_triangle.shape[1]
), f"Matrix L is not square, {lower_triangle.shape=}"
assert np.allclose(
np.tril(lower_triangle), lower_triangle
), "Matrix L is not lower triangular"
# Handle vector case by reshaping to matrix and then flattening again
if len(Y.shape) == 1:
return solve_cholesky(L, Y.reshape(-1, 1)).ravel()
if len(y.shape) == 1:
return solve_cholesky(lower_triangle, y.reshape(-1, 1)).ravel()
n = Y.shape[0]
n = y.shape[0]
# Solve L W = B for W
W = Y.copy()
w = y.copy()
for i in range(n):
for j in range(i):
W[i] -= L[i, j] * W[j]
w[i] -= lower_triangle[i, j] * w[j]
W[i] /= L[i, i]
w[i] /= lower_triangle[i, i]
# Solve L^T X = W for X
X = W
x = w
for i in reversed(range(n)):
for j in range(i + 1, n):
X[i] -= L[j, i] * X[j]
x[i] -= lower_triangle[j, i] * x[j]
X[i] /= L[i, i]
x[i] /= lower_triangle[i, i]
return X
return x
if __name__ == "__main__":