L i]dZddlddlddlddlddlddlddlddlddl ddl ddl ddl ddl ddlddlddlddlddlddlddlddlddlmZmZmZmZmZmZmZmZmZm Z e!Dcgc]}|jEdr|c}Z#ddl$m%Z%e%e&Z'[%ycc}w)a ==================================== Linear algebra (:mod:`scipy.linalg`) ==================================== .. currentmodule:: scipy.linalg .. toctree:: :hidden: linalg.blas linalg.cython_blas linalg.cython_lapack linalg.interpolative linalg.lapack Linear algebra functions. .. eventually, we should replace the numpy.linalg HTML link with just `numpy.linalg` .. seealso:: `numpy.linalg `__ for more linear algebra functions. Note that although `scipy.linalg` imports most of them, identically named functions from `scipy.linalg` may offer more or slightly differing functionality. Basics ====== .. autosummary:: :toctree: generated/ inv - Find the inverse of a square matrix solve - Solve a linear system of equations solve_banded - Solve a banded linear system solveh_banded - Solve a Hermitian or symmetric banded system solve_circulant - Solve a circulant system solve_triangular - Solve a triangular matrix solve_toeplitz - Solve a toeplitz matrix matmul_toeplitz - Multiply a Toeplitz matrix with an array. det - Find the determinant of a square matrix norm - Matrix and vector norm lstsq - Solve a linear least-squares problem pinv - Pseudo-inverse (Moore-Penrose) using lstsq pinvh - Pseudo-inverse of hermitian matrix kron - Kronecker product of two arrays khatri_rao - Khatri-Rao product of two arrays orthogonal_procrustes - Solve an orthogonal Procrustes problem matrix_balance - Balance matrix entries with a similarity transformation subspace_angles - Compute the subspace angles between two matrices bandwidth - Return the lower and upper bandwidth of an array issymmetric - Check if a square 2D array is symmetric ishermitian - Check if a square 2D array is Hermitian LinAlgError LinAlgWarning Eigenvalue Problems =================== .. autosummary:: :toctree: generated/ eig - Find the eigenvalues and eigenvectors of a square matrix eigvals - Find just the eigenvalues of a square matrix eigh - Find the e-vals and e-vectors of a Hermitian or symmetric matrix eigvalsh - Find just the eigenvalues of a Hermitian or symmetric matrix eig_banded - Find the eigenvalues and eigenvectors of a banded matrix eigvals_banded - Find just the eigenvalues of a banded matrix eigh_tridiagonal - Find the eigenvalues and eigenvectors of a tridiagonal matrix eigvalsh_tridiagonal - Find just the eigenvalues of a tridiagonal matrix Decompositions ============== .. autosummary:: :toctree: generated/ lu - LU decomposition of a matrix lu_factor - LU decomposition returning unordered matrix and pivots lu_solve - Solve Ax=b using back substitution with output of lu_factor svd - Singular value decomposition of a matrix svdvals - Singular values of a matrix diagsvd - Construct matrix of singular values from output of svd orth - Construct orthonormal basis for the range of A using svd null_space - Construct orthonormal basis for the null space of A using svd ldl - LDL.T decomposition of a Hermitian or a symmetric matrix. cholesky - Cholesky decomposition of a matrix cholesky_banded - Cholesky decomp. of a sym. or Hermitian banded matrix cho_factor - Cholesky decomposition for use in solving a linear system cho_solve - Solve previously factored linear system cho_solve_banded - Solve previously factored banded linear system polar - Compute the polar decomposition. qr - QR decomposition of a matrix qr_multiply - QR decomposition and multiplication by Q qr_update - Rank k QR update qr_delete - QR downdate on row or column deletion qr_insert - QR update on row or column insertion rq - RQ decomposition of a matrix qz - QZ decomposition of a pair of matrices ordqz - QZ decomposition of a pair of matrices with reordering schur - Schur decomposition of a matrix rsf2csf - Real to complex Schur form hessenberg - Hessenberg form of a matrix cdf2rdf - Complex diagonal form to real diagonal block form cossin - Cosine sine decomposition of a unitary or orthogonal matrix .. seealso:: `scipy.linalg.interpolative` -- Interpolative matrix decompositions Matrix Functions ================ .. autosummary:: :toctree: generated/ expm - Matrix exponential logm - Matrix logarithm cosm - Matrix cosine sinm - Matrix sine tanm - Matrix tangent coshm - Matrix hyperbolic cosine sinhm - Matrix hyperbolic sine tanhm - Matrix hyperbolic tangent signm - Matrix sign sqrtm - Matrix square root funm - Evaluating an arbitrary matrix function expm_frechet - Frechet derivative of the matrix exponential expm_cond - Relative condition number of expm in the Frobenius norm fractional_matrix_power - Fractional matrix power Matrix Equation Solvers ======================= .. autosummary:: :toctree: generated/ solve_sylvester - Solve the Sylvester matrix equation solve_continuous_are - Solve the continuous-time algebraic Riccati equation solve_discrete_are - Solve the discrete-time algebraic Riccati equation solve_continuous_lyapunov - Solve the continuous-time Lyapunov equation solve_discrete_lyapunov - Solve the discrete-time Lyapunov equation Sketches and Random Projections =============================== .. autosummary:: :toctree: generated/ clarkson_woodruff_transform - Applies the Clarkson Woodruff Sketch (a.k.a CountMin Sketch) Special Matrices ================ .. autosummary:: :toctree: generated/ block_diag - Construct a block diagonal matrix from submatrices circulant - Circulant matrix companion - Companion matrix convolution_matrix - Convolution matrix dft - Discrete Fourier transform matrix fiedler - Fiedler matrix fiedler_companion - Fiedler companion matrix hadamard - Hadamard matrix of order 2**n hankel - Hankel matrix helmert - Helmert matrix hilbert - Hilbert matrix invhilbert - Inverse Hilbert matrix leslie - Leslie matrix pascal - Pascal matrix invpascal - Inverse Pascal matrix toeplitz - Toeplitz matrix Low-level routines ================== .. autosummary:: :toctree: generated/ get_blas_funcs get_lapack_funcs find_best_blas_type .. seealso:: `scipy.linalg.blas` -- Low-level BLAS functions `scipy.linalg.lapack` -- Low-level LAPACK functions `scipy.linalg.cython_blas` -- Low-level BLAS functions for Cython `scipy.linalg.cython_lapack` -- Low-level LAPACK functions for Cython )*) decompdecomp_cholesky decomp_lu decomp_qr decomp_svd decomp_schurbasicmiscspecial_matricesmatfuncs_) PytestTesterN)(__doc___misc_cythonized_array_utils_basic_decomp _decomp_lu _decomp_ldl_decomp_cholesky _decomp_qr _decomp_qz _decomp_svd _decomp_schur _decomp_polar _matfuncsblaslapack_special_matrices_solvers _procrustes_decomp_update _sketches_decomp_cossinrrrrrr r r r r dir startswith__all__scipy._lib._testutilsr__name__test)ss0[/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/scipy/linalg/__init__.pyr0sHT&  e 51<<#41 5/H 6s B;$B;