Tessero\ScipyLinalg

apply(string $name, mixed ...$args): mixed

Call a function by its SciPy/NumPy name: ScipyLinalg::apply('log_ndtr', $x).

bandwidth(mixed $a): mixed

Lower and upper bandwidths of a 2-D array (scipy.linalg.bandwidth).

blockDiag(mixed ...$arrs): mixed

Assemble 2-D blocks on the diagonal of a larger zero matrix (scipy.linalg.block_diag).

cdf2rdf(mixed $w, mixed $v): mixed

Convert complex eigenvalues/eigenvectors to real block-diagonal form (scipy.linalg.cdf2rdf).

choFactor(mixed $a, mixed $lower = false): mixed

Cholesky factor for cho_solve, other triangle left as input (scipy.linalg.cho_factor).

choSolve(mixed $c, mixed $lower, mixed $b): mixed

Solve a x = b from a Cholesky factor; takes c, lower, b unpacked (scipy.linalg.cho_solve).

choSolveBanded(mixed $cb, mixed $lower, mixed $b): mixed

Solve A x = b from a banded Cholesky factor via dpbtrs (scipy.linalg.cho_solve_banded).

cholesky(mixed $a, mixed $lower = false): mixed

Cholesky factor, upper by default (scipy.linalg.cholesky).

choleskyBanded(mixed $ab, mixed $lower = false): mixed

Cholesky factor of a symmetric positive-definite banded matrix via dpbtrf (scipy.linalg.cholesky_banded).

circulant(mixed $c): mixed

Circulant matrix with first column c (scipy.linalg.circulant).

companion(mixed $a): mixed

Companion matrix of a polynomial (scipy.linalg.companion).

convolutionMatrix(mixed $a, mixed $n, mixed $mode = 'full'): mixed

Toeplitz matrix A with A @ v = convolve(a, v, mode) (scipy.linalg.convolution_matrix).

coshm(mixed $a): mixed

Matrix hyperbolic cosine via the Schur-Parlett method (scipy.linalg.coshm; real spectrum).

cosm(mixed $a): mixed

Matrix cosine via the Schur-Parlett method (scipy.linalg.cosm; real spectrum).

cossin(mixed $X, mixed $p, mixed $q): mixed

Cosine-sine decomposition of a partitioned orthogonal matrix via dorcsd (scipy.linalg.cossin).

det(mixed $a): mixed

Determinant of a square matrix (scipy.linalg.det).

dft(mixed $n, mixed $scale = null): mixed

The n x n discrete Fourier transform matrix (scipy.linalg.dft).

diagsvd(mixed $s, mixed $M, mixed $N): mixed

M x N matrix with s on the diagonal (scipy.linalg.diagsvd).

eig(mixed $a): mixed

Eigenvalues and right eigenvectors of a general matrix, complex (scipy.linalg.eig).

eigBanded(mixed $ab, mixed $lower = false, mixed $eigvalsOnly = false): mixed

Eigenvalues and eigenvectors of a symmetric banded matrix via dsbevd (scipy.linalg.eig_banded).

eigh(mixed $a): mixed

Eigenvalues and eigenvectors of a symmetric matrix (scipy.linalg.eigh).

eighTridiagonal(mixed $d, mixed $e): mixed

Eigenvalues and eigenvectors of a symmetric tridiagonal matrix via dstev (scipy.linalg.eigh_tridiagonal).

eigvals(mixed $a): mixed

Eigenvalues of a general matrix, complex, sorted (scipy.linalg.eigvals).

eigvalsBanded(mixed $aBand, mixed $lower = false): mixed

Eigenvalues of a symmetric banded matrix in band storage via dsbevd (scipy.linalg.eigvals_banded).

eigvalsh(mixed $a): mixed

Eigenvalues of a symmetric matrix, ascending (scipy.linalg.eigvalsh).

eigvalshTridiagonal(mixed $d, mixed $e): mixed

Eigenvalues of a symmetric tridiagonal matrix via dsterf (scipy.linalg.eigvalsh_tridiagonal).

expm(mixed $a): mixed

Matrix exponential via the Schur-Parlett method (scipy.linalg.expm; real spectrum).

expmCond(mixed $A): mixed

Relative condition number of the matrix exponential from the Kronecker form of its Frechet derivative (scipy.linalg.expm_cond).

expmFrechet(mixed $A, mixed $E): mixed

Matrix exponential and its Frechet derivative in direction E via the block-enlarge identity (scipy.linalg.expm_frechet).

fiedler(mixed $a): mixed

Symmetric Fiedler matrix of absolute differences |a_i - a_j| (scipy.linalg.fiedler).

fiedlerCompanion(mixed $a): mixed

Fiedler companion matrix of a polynomial (scipy.linalg.fiedler_companion).

fractionalMatrixPower(mixed $a, mixed $t): mixed

Fractional matrix power a^t via the Schur-Parlett method (scipy.linalg.fractional_matrix_power; positive real spectrum).

funm(mixed $a, mixed $func = 'exp'): mixed

Matrix function f(A) by name via the Schur-Parlett method; func one of exp/sqrt/log/sin/cos/sinh/cosh/tanh/tan (scipy.linalg.funm; real spectrum).

hadamard(mixed $n): mixed

Sylvester-Hadamard matrix of order n, a power of two (scipy.linalg.hadamard).

hankel(mixed $c, mixed $r = null): mixed

Hankel matrix with first column c and last row r (scipy.linalg.hankel).

helmert(mixed $n, mixed $full = false): mixed

Helmert matrix of order n (scipy.linalg.helmert).

hessenberg(mixed $a, mixed $calcQ = false): mixed

Upper Hessenberg form via dgehrd (scipy.linalg.hessenberg).

hilbert(mixed $n): mixed

Hilbert matrix of order n (scipy.linalg.hilbert).

inv(mixed $a): mixed

Inverse of a square matrix (scipy.linalg.inv).

invhilbert(mixed $n): mixed

Inverse of the Hilbert matrix of order n (scipy.linalg.invhilbert).

invpascal(mixed $n, mixed $kind = 'symmetric'): mixed

Inverse of the Pascal matrix of order n (scipy.linalg.invpascal).

ishermitian(mixed $a, mixed $atol = null, mixed $rtol = null): mixed

Whether a square matrix is Hermitian; for real input, symmetric (scipy.linalg.ishermitian).

issymmetric(mixed $a, mixed $atol = null, mixed $rtol = null): mixed

Whether a square matrix is symmetric (scipy.linalg.issymmetric).

khatriRao(mixed $a, mixed $b): mixed

Column-wise Kronecker (Khatri-Rao) product (scipy.linalg.khatri_rao).

ldl(mixed $a, mixed $lower = true): mixed

LDL^T factorisation of a symmetric matrix via dsytrf (scipy.linalg.ldl).

leslie(mixed $f, mixed $s): mixed

Leslie population matrix with first row f and sub-diagonal s (scipy.linalg.leslie).

logm(mixed $a, mixed $disp = true): mixed

Principal matrix logarithm via the Schur-Parlett method (scipy.linalg.logm; distinct positive real spectrum).

lstsq(mixed $a, mixed $b, mixed $cond = null): mixed

Least-squares solution (scipy.linalg.lstsq).

lu(mixed $a, mixed $permuteL = false): mixed

LU factorisation with partial pivoting, A = P L U (scipy.linalg.lu).

luFactor(mixed $a): mixed

LU factorisation for lu_solve: combined factors and 0-based pivots (scipy.linalg.lu_factor).

luSolve(mixed $lu, mixed $piv, mixed $b, mixed $trans = 0): mixed

Solve a x = b from an lu_factor result; takes lu, piv, b unpacked (scipy.linalg.lu_solve).

matmulToeplitz(mixed $cOrCr, mixed $x): mixed

The product of a Toeplitz matrix with x (scipy.linalg.matmul_toeplitz).

matrixBalance(mixed $A, mixed $permute = true, mixed $scale = true, mixed $separate = false): mixed

Balance a matrix via dgebal; returns the balanced matrix and the scaling transform (scipy.linalg.matrix_balance).

norm(mixed $a, mixed $ord = null, mixed $axis = null, mixed $keepdims = false): mixed

Vector or matrix norm (scipy.linalg.norm).

nullSpace(mixed $A, mixed $rcond = null): mixed

Orthonormal basis for the null space of A via SVD (scipy.linalg.null_space).

ordqz(mixed $A, mixed $B, mixed $sort = 'lhp', mixed $output = 'real'): mixed

Reordered generalised Schur (QZ) decomposition via dgges and dtgsen (scipy.linalg.ordqz).

orth(mixed $A, mixed $rcond = null): mixed

Orthonormal basis for the range of A via SVD (scipy.linalg.orth).

orthogonalProcrustes(mixed $A, mixed $B): mixed

Orthogonal Procrustes solution R minimising ||A R - B|| and scale (scipy.linalg.orthogonal_procrustes).

pascal(mixed $n, mixed $kind = 'symmetric'): mixed

Pascal matrix of order n (scipy.linalg.pascal).

pinv(mixed $a): mixed

Moore-Penrose pseudo-inverse via SVD (scipy.linalg.pinv).

pinvh(mixed $a): mixed

Moore-Penrose pseudo-inverse of a symmetric matrix via eigendecomposition (scipy.linalg.pinvh).

polar(mixed $a, mixed $side = 'right'): mixed

Polar decomposition a = u p (right) or p u (left) via SVD (scipy.linalg.polar).

qr(mixed $a, mixed $mode = 'full'): mixed

QR factorisation (scipy.linalg.qr; mode 'full' or 'economic').

qrDelete(mixed $Q, mixed $R, mixed $k, mixed $p = 1, mixed $which = 'row'): mixed

Economic QR after deleting rows/columns, canonicalised (scipy.linalg.qr_delete).

qrInsert(mixed $Q, mixed $R, mixed $u, mixed $k, mixed $which = 'row'): mixed

Economic QR after inserting a row/column, canonicalised (scipy.linalg.qr_insert).

qrMultiply(mixed $a, mixed $c, mixed $mode = 'right'): mixed

Product of c with the economic orthogonal factor Q of a, plus R (scipy.linalg.qr_multiply).

qrUpdate(mixed $Q, mixed $R, mixed $u, mixed $v): mixed

Economic QR of (Q R + u v^T), canonicalised (scipy.linalg.qr_update).

qz(mixed $A, mixed $B, mixed $output = 'real'): mixed

Generalised real Schur decomposition via dgges (scipy.linalg.qz).

rq(mixed $a, mixed $mode = 'full'): mixed

RQ decomposition a = R Q of a square matrix via dgerqf (scipy.linalg.rq).

rsf2csf(mixed $T, mixed $Z): mixed

Convert a real Schur form to the complex (upper-triangular) Schur form (scipy.linalg.rsf2csf).

schur(mixed $a, mixed $output = 'real'): mixed

Real Schur decomposition A = Z T Z^T via dgees (scipy.linalg.schur).

signm(mixed $A): mixed

Matrix sign function via the Schur-Parlett method (scipy.linalg.signm; real, well-separated spectrum).

sinhm(mixed $a): mixed

Matrix hyperbolic sine via the Schur-Parlett method (scipy.linalg.sinhm; real spectrum).

sinm(mixed $a): mixed

Matrix sine via the Schur-Parlett method (scipy.linalg.sinm; real spectrum).

solve(mixed $a, mixed $b): mixed

Solve a linear system a x = b (scipy.linalg.solve).

solveBanded(mixed $l, mixed $u, mixed $ab, mixed $b): mixed

Solve a banded linear system via dgbsv; takes l, u, ab, b unpacked (scipy.linalg.solve_banded).

solveCirculant(mixed $c, mixed $b): mixed

Solve a circulant system C x = b (scipy.linalg.solve_circulant).

solveContinuousAre(mixed $a, mixed $b, mixed $q, mixed $r): mixed

Stabilising solution of the continuous-time algebraic Riccati equation (scipy.linalg.solve_continuous_are).

solveContinuousLyapunov(mixed $a, mixed $q): mixed

Solve the continuous Lyapunov equation a x + x a^H = q (scipy.linalg.solve_continuous_lyapunov).

solveDiscreteAre(mixed $a, mixed $b, mixed $q, mixed $r): mixed

Stabilising solution of the discrete-time algebraic Riccati equation (scipy.linalg.solve_discrete_are).

solveDiscreteLyapunov(mixed $a, mixed $q): mixed

Solve the discrete Lyapunov equation a x a^H - x + q = 0 (scipy.linalg.solve_discrete_lyapunov).

solveLyapunov(mixed $a, mixed $q): mixed

Solve the continuous Lyapunov equation a x + x a^H = q; alias of solve_continuous_lyapunov (scipy.linalg.solve_lyapunov).

solveSylvester(mixed $a, mixed $b, mixed $q): mixed

Solve the Sylvester equation a x + x b = q (scipy.linalg.solve_sylvester).

solveToeplitz(mixed $cOrCr, mixed $b): mixed

Solve a Toeplitz system T x = b (scipy.linalg.solve_toeplitz).

solveTriangular(mixed $a, mixed $b, mixed $trans = 0, mixed $lower = false, mixed $unitDiagonal = false): mixed

Solve a triangular system (scipy.linalg.solve_triangular).

solvehBanded(mixed $ab, mixed $b, mixed $lower = false): mixed

Solve a Hermitian positive-definite banded system via dpbsv (scipy.linalg.solveh_banded).

sqrtm(mixed $a, mixed $disp = true): mixed

Principal matrix square root via the Schur method (scipy.linalg.sqrtm; real spectrum).

subspaceAngles(mixed $A, mixed $B): mixed

Principal angles between the column spaces of A and B (scipy.linalg.subspace_angles).

svd(mixed $a, mixed $fullMatrices = true): mixed

Singular value decomposition (scipy.linalg.svd).

svdvals(mixed $a): mixed

Singular values of a matrix (scipy.linalg.svdvals).

tanhm(mixed $a): mixed

Matrix hyperbolic tangent via the Schur-Parlett method (scipy.linalg.tanhm; real spectrum).

tanm(mixed $a): mixed

Matrix tangent via the Schur-Parlett method (scipy.linalg.tanm; real spectrum).

toeplitz(mixed $c, mixed $r = null): mixed

Toeplitz matrix with first column c and first row r (scipy.linalg.toeplitz).