scipy.linalg

Linear algebra (scipy.linalg)

• linalg.blas

• linalg.cython_blas

• linalg.cython_lapack

• linalg.interpolative

• linalg.lapack

Linear algebra functions.

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
    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

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