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To remove in the future –– scipy.linalg

Linear algebra (:mod:`scipy.linalg`)

{currentmodule}scipy.linalg

Linear algebra functions.

{seealso}

`numpy.linalg <https://www.numpy.org/devdocs/reference/routines.linalg.html>`__
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
    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
    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
    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

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.linalg._basic:solve_circulant

Local connectivity graph

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Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

scipy.linalg._basic:solve_circulant_basic:solve_circulant

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


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