Linear algebra (scipy.linalg)¶
Basics¶
| inv(a[, overwrite_a]) | Compute the inverse of a matrix. |
| solve(a, b[, sym_pos, lower, overwrite_a, ...]) | Solve the equation a x = b for x |
| solve_banded(l, ab, b[, overwrite_ab, ...]) | Solve the equation a x = b for x, assuming a is banded matrix. |
| solveh_banded(ab, b[, overwrite_ab, ...]) | Solve equation a x = b. |
| solve_triangular(a, b[, trans, lower, ...]) | Solve the equation a x = b for x, assuming a is a triangular matrix. |
| det(a[, overwrite_a]) | Compute the determinant of a matrix |
| norm(a[, ord]) | Matrix or vector norm. |
| lstsq(a, b[, cond, overwrite_a, overwrite_b]) | Compute least-squares solution to equation Ax = b. |
| pinv(a[, cond, rcond]) | Compute the (Moore-Penrose) pseudo-inverse of a matrix. |
| pinv2(a[, cond, rcond]) | Compute the (Moore-Penrose) pseudo-inverse of a matrix. |
Eigenvalue Problem¶
| eig(a[, b, left, right, overwrite_a, ...]) | Solve an ordinary or generalized eigenvalue problem of a square matrix. |
| eigvals(a[, b, overwrite_a]) | Compute eigenvalues from an ordinary or generalized eigenvalue problem. |
| eigh(a[, b, lower, eigvals_only, ...]) | Solve an ordinary or generalized eigenvalue problem for a complex |
| eigvalsh(a[, b, lower, overwrite_a, ...]) | Solve an ordinary or generalized eigenvalue problem for a complex |
| eig_banded(a_band[, lower, eigvals_only, ...]) | Solve real symmetric or complex hermitian band matrix eigenvalue problem. |
| eigvals_banded(a_band[, lower, ...]) | Solve real symmetric or complex hermitian band matrix eigenvalue problem. |
Decompositions¶
| lu(a[, permute_l, overwrite_a]) | Compute pivoted LU decompostion of a matrix. |
| lu_factor(a[, overwrite_a]) | Compute pivoted LU decomposition of a matrix. |
| lu_solve(lu, b[, trans, overwrite_b]) | Solve an equation system, a x = b, given the LU factorization of a |
| svd(a[, full_matrices, compute_uv, overwrite_a]) | Singular Value Decomposition. |
| svdvals(a[, overwrite_a]) | Compute singular values of a matrix. |
| diagsvd(s, M, N) | Construct the sigma matrix in SVD from singular values and size M,N. |
| orth(A) | Construct an orthonormal basis for the range of A using SVD |
| cholesky(a[, lower, overwrite_a]) | Compute the Cholesky decomposition of a matrix. |
| cholesky_banded(ab[, overwrite_ab, lower]) | Cholesky decompose a banded Hermitian positive-definite matrix |
| cho_factor(a[, lower, overwrite_a]) | Compute the Cholesky decomposition of a matrix, to use in cho_solve |
| cho_solve(c, b[, overwrite_b]) | Solve the linear equations A x = b, given the Cholesky factorization of A. |
| cho_solve_banded(cb, b[, overwrite_b]) | Solve the linear equations A x = b, given the Cholesky factorization of A. |
| qr(a[, overwrite_a, lwork, mode]) | Compute QR decomposition of a matrix. |
| schur(a[, output, lwork, overwrite_a]) | Compute Schur decomposition of a matrix. |
| rsf2csf(T, Z) | Convert real Schur form to complex Schur form. |
| hessenberg(a[, calc_q, overwrite_a]) | Compute Hessenberg form of a matrix. |
Matrix Functions¶
| expm(A[, q]) | Compute the matrix exponential using Pade approximation. |
| expm2(A) | Compute the matrix exponential using eigenvalue decomposition. |
| expm3(A[, q]) | Compute the matrix exponential using Taylor series. |
| logm(A[, disp]) | Compute matrix logarithm. |
| cosm(A) | Compute the matrix cosine. |
| sinm(A) | Compute the matrix sine. |
| tanm(A) | Compute the matrix tangent. |
| coshm(A) | Compute the hyperbolic matrix cosine. |
| sinhm(A) | Compute the hyperbolic matrix sine. |
| tanhm(A) | Compute the hyperbolic matrix tangent. |
| signm(a[, disp]) | Matrix sign function. |
| sqrtm(A[, disp]) | Matrix square root. |
| funm(A, func[, disp]) | Evaluate a matrix function specified by a callable. |
Special Matrices¶
| block_diag(*arrs) | Create a block diagonal matrix from provided arrays. |
| circulant(c) | Construct a circulant matrix. |
| companion(a) | Create a companion matrix. |
| hadamard(n[, dtype]) | Construct a Hadamard matrix. |
| hankel(c[, r]) | Construct a Hankel matrix. |
| kron(a, b) | Kronecker product of a and b. |
| leslie(f, s) | Create a Leslie matrix. |
| toeplitz(c[, r]) | Construct a Toeplitz matrix. |
| tri(N[, M, k, dtype]) | Construct (N, M) matrix filled with ones at and below the k-th diagonal. |
| tril(m[, k]) | Construct a copy of a matrix with elements above the k-th diagonal zeroed. |
| triu(m[, k]) | Construct a copy of a matrix with elements below the k-th diagonal zeroed. |
