ó ʽ÷Xc @`s¿dZddlmZmZmZddlmZddlTddlTddl Tddl Tddl Tddl Tddl TddlTddlTddlTddlTddlTddlTddlTddlTddlTddlTgeƒD]Zejdƒsæe^qæZddlmZxZdd d d d d dddddg D]1ZyeeeeƒƒWq?e k roq?Xq?Wyede!ƒWne k r˜nX[[ddl"m#Z#e#ƒj$Z$dS(s ==================================== Linear algebra (:mod:`scipy.linalg`) ==================================== .. currentmodule:: scipy.linalg Linear algebra functions. .. 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 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 pinv2 - Pseudo-inverse using svd pinvh - Pseudo-inverse of hermitian matrix kron - Kronecker product of two arrays tril - Construct a lower-triangular matrix from a given matrix triu - Construct an upper-triangular matrix from a given matrix orthogonal_procrustes - Solve an orthogonal Procrustes problem matrix_balance - Balance matrix entries with a similarity transformation LinAlgError 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 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 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 .. 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_discrete_lyapunov - Solve the discrete-time Lyapunov equation solve_lyapunov - Solve the (continous-time) Lyapunov equation Special Matrices ================ .. autosummary:: :toctree: generated/ block_diag - Construct a block diagonal matrix from submatrices circulant - Circulant matrix companion - Companion matrix dft - Discrete Fourier transform 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 tri - Construct a matrix filled with ones at and below a given diagonal 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 i(tdivisiontprint_functiontabsolute_importi(tlinalg_version(t*t_(t register_functnormtinvtsvdtsolvetdetteigteighteigvalsteigvalshtlstsqtcholeskytpinv(tTesterN(%t__doc__t __future__RRRRt __version__tmisctbasictdecompt decomp_lutdecomp_choleskyt decomp_qrt _decomp_qzt decomp_svdt decomp_schurt _decomp_polartmatfuncstblastlapacktspecial_matricest_solverst _procrustest_decomp_updatetdirtst startswitht__all__t numpy.dualRtktevalt ValueErrortpinv2t numpy.testingRttest(((s4/tmp/pip-build-7oUkmx/scipy/scipy/linalg/__init__.pyt©sD                 +