tensorplay.linalg

Common linear algebra operations. See Linear algebra (tensorplay.linalg) for some common numerical edge-cases.

Matrix Properties

`tensorplay.linalg.norm`
`tensorplay.linalg.vector_norm`	`dim=None` norms the whole tensor: the input is flattened first, and `keepdim` then restores the reduced axes as ones.
`tensorplay.linalg.matrix_norm`
`tensorplay.linalg.diagonal`	linalg_diagonal(A, *, offset=0, dim1=-2, dim2=-1) -> Tensor
`tensorplay.linalg.det`
`tensorplay.linalg.slogdet`
`tensorplay.linalg.cond`
`tensorplay.linalg.matrix_rank`	Computes the numerical rank of each matrix in `A`.

Decompositions

`tensorplay.linalg.cholesky`
`tensorplay.linalg.qr`
`tensorplay.linalg.polar`
`tensorplay.linalg.lu`	`linalg_lu(Tensor A, , bool pivot=True) -> (Tensor P, Tensor L, Tensor U)` `linalg_lu.out(Tensor A, , bool pivot=True, Tensor(a!) P, Tensor(b!) L, Tensor(c!) U) -> (Tensor(a!) P, Tensor(b!) L, Tensor(c!) U)`
`tensorplay.linalg.lu_factor`	`linalg_lu_factor(Tensor A, , bool pivot=True) -> (Tensor LU, Tensor pivots)` `linalg_lu_factor.out(Tensor A, , bool pivot=True, Tensor(a!) LU, Tensor(b!) pivots) -> (Tensor(a!) LU, Tensor(b!) pivots)`
`tensorplay.linalg.eig`
`tensorplay.linalg.eigvals`
`tensorplay.linalg.eigh`
`tensorplay.linalg.eigvalsh`
`tensorplay.linalg.svd`
`tensorplay.linalg.svdvals`

Solvers

`tensorplay.linalg.solve`
`tensorplay.linalg.solve_triangular`	`linalg_solve_triangular(Tensor A, Tensor B, , bool upper, bool left=True, bool unitriangular=False) -> Tensor` `linalg_solve_triangular.out(Tensor self, Tensor B, , bool upper, bool left=True, bool unitriangular=False, Tensor(a!) out) -> Tensor(a!)`
`tensorplay.linalg.lu_solve`	`linalg_lu_solve(Tensor LU, Tensor pivots, Tensor B, , bool left=True, bool adjoint=False) -> Tensor` `linalg_lu_solve.out(Tensor LU, Tensor pivots, Tensor B, , bool left=True, bool adjoint=False, Tensor(a!) out) -> Tensor(a!)`
`tensorplay.linalg.lstsq`

Inverses

`tensorplay.linalg.inv`
`tensorplay.linalg.pinv`	Moore-Penrose pseudo-inverse.

Matrix Functions

`tensorplay.linalg.matrix_exp`	Square matrix exponential via the degree-13 Pade approximant with scaling and squaring: `A` is halved until its 1-norm falls under the approximant's accuracy threshold, then the result is squared back.
`tensorplay.linalg.matrix_sqrth`	Matrix square root via the Denman-Beavers fixed-point iteration (converges for matrices with no eigenvalues on the closed negative real axis).
`tensorplay.linalg.matrix_power`

Matrix Products

`tensorplay.linalg.cross`
`tensorplay.linalg.matmul`
`tensorplay.linalg.vecdot`	Dot product along dim with the first argument conjugated for complex inputs.
`tensorplay.linalg.vdot`	Conjugating dot product over 1-D operands: sum(conj(self) * other).
`tensorplay.linalg.multi_dot`	Chained matrix product evaluated in the parenthesization that minimizes the scalar multiplication count (matrix-chain dynamic program).
`tensorplay.linalg.householder_product`	`linalg_householder_product(Tensor input, Tensor tau) -> Tensor` `linalg_householder_product.out(Tensor input, Tensor tau, *, Tensor(a!) out) -> Tensor(a!)`

Tensor Operations

`tensorplay.linalg.tensorinv`	Inverse of `A` seen as a square matrix over the split at `ind`: the product of the leading `ind` dimensions must equal that of the rest.
`tensorplay.linalg.tensorsolve`	Solves the tensor equation `A X = B` after flattening the contracted dimensions into a square matrix.

Misc

tensorplay.linalg.vander

Experimental Functions

`tensorplay.linalg.cholesky_ex`
`tensorplay.linalg.inv_ex`
`tensorplay.linalg.solve_ex`
`tensorplay.linalg.lu_factor_ex`	`linalg_lu_factor_ex(Tensor A, , bool pivot=True, bool check_errors=False) -> (Tensor LU, Tensor pivots, Tensor info)` `linalg_lu_factor_ex.out(Tensor A, , bool pivot=True, bool check_errors=False, Tensor(a!) LU, Tensor(b!) pivots, Tensor(c!) info) -> (Tensor(a!) LU, Tensor(b!) pivots, Tensor(c!) info)`
`tensorplay.linalg.ldl_factor`	`linalg_ldl_factor(Tensor A, , bool hermitian=False) -> (Tensor LD, Tensor pivots)` `linalg_ldl_factor.out(Tensor self, , bool hermitian=False, Tensor(a!) LD, Tensor(b!) pivots) -> (Tensor(a!) LD, Tensor(b!) pivots)`
`tensorplay.linalg.ldl_factor_ex`	`linalg_ldl_factor_ex(Tensor A, , bool hermitian=False, bool check_errors=False) -> (Tensor LD, Tensor pivots, Tensor info)` `linalg_ldl_factor_ex.out(Tensor self, , bool hermitian=False, bool check_errors=False, Tensor(a!) LD, Tensor(b!) pivots, Tensor(c!) info) -> (Tensor(a!) LD, Tensor(b!) pivots, Tensor(c!) info)`
`tensorplay.linalg.ldl_solve`	`linalg_ldl_solve(Tensor LD, Tensor pivots, Tensor B, , bool hermitian=False) -> Tensor` `linalg_ldl_solve.out(Tensor LD, Tensor pivots, Tensor B, , bool hermitian=False, Tensor(a!) out) -> Tensor(a!)`

Result Types

Solvers and decompositions that return several tensors package them in the named tuples below; the _ex variants report failures through an info field instead of raising.

`tensorplay.linalg.LinAlgError`	Raised when a decomposition or solve fails on a numerically invalid input.
`tensorplay.linalg.EigResult`
`tensorplay.linalg.EighResult`
`tensorplay.linalg.LstsqResult`
`tensorplay.linalg.QRResult`
`tensorplay.linalg.SVDResult`
`tensorplay.linalg.SlogdetResult`
`tensorplay.linalg.CholeskyExResult`