Coverage for src / cvx / linalg / __init__.py: 100%

1"""Linear algebra utilities for risk models. 

2 

3This subpackage provides linear algebra utilities commonly used in risk modeling, 

4including Cholesky decomposition, Principal Component Analysis, matrix norms, 

5linear-system solving, and matrix validation. 

6 

7Example: 

8 >>> import numpy as np 

9 >>> from cvx.linalg import a_norm, cholesky, eigh, inv_a_norm, pca, qr, rand_cov, solve, svd, valid 

10 >>> # Cholesky decomposition 

11 >>> cov = np.array([[4.0, 2.0], [2.0, 5.0]]) 

12 >>> R = cholesky(cov) 

13 >>> np.allclose(R.T @ R, cov) 

14 True 

15 

16Functions: 

17 a_norm: Compute the matrix norm of a vector 

18 cholesky: Compute upper triangular Cholesky decomposition 

19 cond: Return the condition number of a matrix (NaN-aware) 

20 det: Compute the determinant of a square matrix 

21 eigvals: Compute eigenvalues of a general square matrix 

22 eigh: Compute eigenvalues and eigenvectors of a symmetric/Hermitian matrix 

23 eigvalsh: Compute eigenvalues of a symmetric/Hermitian matrix 

24 inv: Invert a matrix with NaN-aware matrix filtering and condition-number guarding 

25 inv_a_norm: Compute the inverse matrix norm of a vector 

26 lstsq: Solve least-squares problems with NaN-aware row filtering 

27 norm: Compute the norm of a vector or matrix, ignoring non-finite entries 

28 pca: Compute principal components of return data 

29 qr: Compute reduced QR decomposition of a matrix 

30 rand_cov: Generate a random positive semi-definite covariance matrix 

31 solve: Solve linear systems with NaN-aware matrix filtering 

32 svd: Compute compact singular value decomposition 

33 valid: Extract valid submatrix from a matrix with NaN values 

34 

35""" 

36 

37from .cholesky import cholesky as cholesky 

38from .cholesky import is_positive_definite as is_positive_definite 

39from .det import det as det 

40from .eigh import eigh as eigh 

41from .eigh import eigvalsh as eigvalsh 

42from .eigvals import eigvals as eigvals 

43from .exceptions import DimensionMismatchError as DimensionMismatchError 

44from .exceptions import IllConditionedMatrixWarning as IllConditionedMatrixWarning 

45from .exceptions import NonSquareMatrixError as NonSquareMatrixError 

46from .exceptions import NotAMatrixError as NotAMatrixError 

47from .exceptions import SingularMatrixError as SingularMatrixError 

48from .exceptions import check_and_warn_condition as check_and_warn_condition 

49from .exceptions import cond as cond 

50from .inv import inv as inv 

51from .lstsq import lstsq as lstsq 

52from .norm import a_norm as a_norm 

53from .norm import inv_a_norm as inv_a_norm 

54from .norm import norm as norm 

55from .pca import pca as pca 

56from .qr import qr as qr 

57from .rand_cov import rand_cov as rand_cov 

58from .solve import solve as solve 

59from .svd import svd as svd 

60from .types import Matrix as Matrix 

61from .valid import valid as valid