# tensorplay.linalg API

Source: https://www.tensorplay.cn/docs/api/tensorplay.linalg.html

## Functions 44

[#](#api-tensorplay.linalg.cholesky_ex)

### cholesky_ex

function[Full reference ↗](/docs/generated/tensorplay.linalg.cholesky_ex.html)

```python
tensorplay.linalg.cholesky_ex(A, *, upper=False, check_errors=False)
```

[#](#api-tensorplay.linalg.cholesky)

### cholesky

function[Full reference ↗](/docs/generated/tensorplay.linalg.cholesky.html)

```python
tensorplay.linalg.cholesky(A, *, upper=False) → Tensor
```

[#](#api-tensorplay.linalg.cond)

### cond

function[Full reference ↗](/docs/generated/tensorplay.linalg.cond.html)

```python
tensorplay.linalg.cond(A, p=None) → Tensor
```

[#](#api-tensorplay.linalg.cross)

### cross

function[Full reference ↗](/docs/generated/tensorplay.linalg.cross.html)

```python
tensorplay.linalg.cross(input, other, *, dim=-1) → Tensor
```

[#](#api-tensorplay.linalg.det)

### det

function[Full reference ↗](/docs/generated/tensorplay.linalg.det.html)

```python
tensorplay.linalg.det(A) → Tensor
```

[#](#api-tensorplay.linalg.diagonal)

### diagonal

function[Full reference ↗](/docs/generated/tensorplay.linalg.diagonal.html)

```python
tensorplay.linalg.diagonal()
```

linalg_diagonal(A, *, offset=0, dim1=-2, dim2=-1) -> Tensor

Returns a view of the diagonals of A: the two dimensions selected by
dim1 and dim2 are collapsed into the trailing axis of the
output, holding the entries of the diagonal shifted by offset
(positive shifts above, negative below the main diagonal).

See tensorplay.diagonal()

[#](#api-tensorplay.linalg.eig)

### eig

function[Full reference ↗](/docs/generated/tensorplay.linalg.eig.html)

```python
tensorplay.linalg.eig(A)
```

[#](#api-tensorplay.linalg.eigh)

### eigh

function[Full reference ↗](/docs/generated/tensorplay.linalg.eigh.html)

```python
tensorplay.linalg.eigh(A, UPLO='L')
```

[#](#api-tensorplay.linalg.eigvals)

### eigvals

function[Full reference ↗](/docs/generated/tensorplay.linalg.eigvals.html)

```python
tensorplay.linalg.eigvals(A) → Tensor
```

[#](#api-tensorplay.linalg.eigvalsh)

### eigvalsh

function[Full reference ↗](/docs/generated/tensorplay.linalg.eigvalsh.html)

```python
tensorplay.linalg.eigvalsh(A, UPLO='L') → Tensor
```

[#](#api-tensorplay.linalg.householder_product)

### householder_product

function[Full reference ↗](/docs/generated/tensorplay.linalg.householder_product.html)

```python
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!)

[#](#api-tensorplay.linalg.inv_ex)

### inv_ex

function[Full reference ↗](/docs/generated/tensorplay.linalg.inv_ex.html)

```python
tensorplay.linalg.inv_ex(A, *, check_errors=False)
```

[#](#api-tensorplay.linalg.inv)

### inv

function[Full reference ↗](/docs/generated/tensorplay.linalg.inv.html)

```python
tensorplay.linalg.inv(A) → Tensor
```

[#](#api-tensorplay.linalg.ldl_factor_ex)

### ldl_factor_ex

function[Full reference ↗](/docs/generated/tensorplay.linalg.ldl_factor_ex.html)

```python
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)

[#](#api-tensorplay.linalg.ldl_factor)

### ldl_factor

function[Full reference ↗](/docs/generated/tensorplay.linalg.ldl_factor.html)

```python
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)

[#](#api-tensorplay.linalg.ldl_solve)

### ldl_solve

function[Full reference ↗](/docs/generated/tensorplay.linalg.ldl_solve.html)

```python
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!)

[#](#api-tensorplay.linalg.lstsq)

### lstsq

function[Full reference ↗](/docs/generated/tensorplay.linalg.lstsq.html)

```python
tensorplay.linalg.lstsq(A, B, rcond=None, *, driver=None)
```

[#](#api-tensorplay.linalg.lu_factor_ex)

### lu_factor_ex

function[Full reference ↗](/docs/generated/tensorplay.linalg.lu_factor_ex.html)

```python
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)

[#](#api-tensorplay.linalg.lu_factor)

### lu_factor

function[Full reference ↗](/docs/generated/tensorplay.linalg.lu_factor.html)

```python
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)

[#](#api-tensorplay.linalg.lu_solve)

### lu_solve

function[Full reference ↗](/docs/generated/tensorplay.linalg.lu_solve.html)

```python
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!)

[#](#api-tensorplay.linalg.lu)

### lu

function[Full reference ↗](/docs/generated/tensorplay.linalg.lu.html)

```python
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)

[#](#api-tensorplay.linalg.matmul)

### matmul

function[Full reference ↗](/docs/generated/tensorplay.linalg.matmul.html)

```python
tensorplay.linalg.matmul(input, other) → Tensor
```

[#](#api-tensorplay.linalg.matrix_exp)

### matrix_exp

function[Full reference ↗](/docs/generated/tensorplay.linalg.matrix_exp.html)

```python
tensorplay.linalg.matrix_exp(A) → Tensor
```

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.

[#](#api-tensorplay.linalg.matrix_norm)

### matrix_norm

function[Full reference ↗](/docs/generated/tensorplay.linalg.matrix_norm.html)

```python
tensorplay.linalg.matrix_norm(A, ord='fro', dim=(-2, -1), keepdim=False) → Tensor
```

[#](#api-tensorplay.linalg.matrix_power)

### matrix_power

function[Full reference ↗](/docs/generated/tensorplay.linalg.matrix_power.html)

```python
tensorplay.linalg.matrix_power(A, n) → Tensor
```

[#](#api-tensorplay.linalg.matrix_rank)

### matrix_rank

function[Full reference ↗](/docs/generated/tensorplay.linalg.matrix_rank.html)

```python
tensorplay.linalg.matrix_rank(A, *, atol=None, rtol=None, hermitian=False)
```

Computes the numerical rank of each matrix in A.

A singular value counts towards the rank when it exceeds the sum of an
absolute tolerance and a relative tolerance scaled by the largest
singular value of its matrix.

Parameters:

- A ([Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)) – tensor of shape (..., m, n) holding the matrices.

- atol ([float](https://docs.python.org/3/builtins/functions.html#float), [Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor), optional) – absolute threshold applied to the singular values. Defaults to 0.

- rtol ([float](https://docs.python.org/3/builtins/functions.html#float), [Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor), optional) – relative threshold applied to the largest singular value. Defaults to max(m, n) times the machine epsilon of A’s dtype.

- hermitian ([bool](https://docs.python.org/3/builtins/functions.html#bool)) – when True, A is treated as Hermitian and its rank is derived from eigenvalues instead of singular values.

Returns:

integer tensor with the rank of each matrix, with the batch
dimensions of A.

Return type:

[Tensor](/docs/generated/tensorplay.Tensor.html#tensorplay.Tensor)

[#](#api-tensorplay.linalg.matrix_sqrth)

### matrix_sqrth

function[Full reference ↗](/docs/generated/tensorplay.linalg.matrix_sqrth.html)

```python
tensorplay.linalg.matrix_sqrth(A) → Tensor
```

Matrix square root via the Denman-Beavers fixed-point iteration
(converges for matrices with no eigenvalues on the closed negative real axis).

[#](#api-tensorplay.linalg.multi_dot)

### multi_dot

function[Full reference ↗](/docs/generated/tensorplay.linalg.multi_dot.html)

```python
tensorplay.linalg.multi_dot(tensors) → Tensor
```

Chained matrix product evaluated in the parenthesization that minimizes
the scalar multiplication count (matrix-chain dynamic program).

[#](#api-tensorplay.linalg.norm)

### norm

function[Full reference ↗](/docs/generated/tensorplay.linalg.norm.html)

```python
tensorplay.linalg.norm(input, ord=None, dim=None, keepdim=False) → Tensor
```

[#](#api-tensorplay.linalg.pinv)

### pinv

function[Full reference ↗](/docs/generated/tensorplay.linalg.pinv.html)

```python
tensorplay.linalg.pinv(A, *, atol=None, rtol=None, hermitian=False) → Tensor
```

Moore-Penrose pseudo-inverse.  Singular values (eigenvalue magnitudes
when hermitian) at or below max(atol, rtol * sigma_max) are
treated as zero; rtol defaults to eps * max(m, n), or to zero
when only a positive atol is given.  The tolerances may be floats or
tensors that broadcast against the batch.

[#](#api-tensorplay.linalg.polar)

### polar

function[Full reference ↗](/docs/generated/tensorplay.linalg.polar.html)

```python
tensorplay.linalg.polar(A) → (Tensor Q, Tensor R) with A = Q R
```

[#](#api-tensorplay.linalg.qr)

### qr

function[Full reference ↗](/docs/generated/tensorplay.linalg.qr.html)

```python
tensorplay.linalg.qr(A, mode='reduced')
```

[#](#api-tensorplay.linalg.slogdet)

### slogdet

function[Full reference ↗](/docs/generated/tensorplay.linalg.slogdet.html)

```python
tensorplay.linalg.slogdet(A)
```

[#](#api-tensorplay.linalg.solve_ex)

### solve_ex

function[Full reference ↗](/docs/generated/tensorplay.linalg.solve_ex.html)

```python
tensorplay.linalg.solve_ex(A, B, *, left=True, check_errors=False)
```

[#](#api-tensorplay.linalg.solve_triangular)

### solve_triangular

function[Full reference ↗](/docs/generated/tensorplay.linalg.solve_triangular.html)

```python
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!)

[#](#api-tensorplay.linalg.solve)

### solve

function[Full reference ↗](/docs/generated/tensorplay.linalg.solve.html)

```python
tensorplay.linalg.solve(A, B, *, left=True) → Tensor
```

[#](#api-tensorplay.linalg.svd)

### svd

function[Full reference ↗](/docs/generated/tensorplay.linalg.svd.html)

```python
tensorplay.linalg.svd(A, full_matrices=True, *, driver=None)
```

[#](#api-tensorplay.linalg.svdvals)

### svdvals

function[Full reference ↗](/docs/generated/tensorplay.linalg.svdvals.html)

```python
tensorplay.linalg.svdvals(A, *, driver=None) → Tensor
```

[#](#api-tensorplay.linalg.tensorinv)

### tensorinv

function[Full reference ↗](/docs/generated/tensorplay.linalg.tensorinv.html)

```python
tensorplay.linalg.tensorinv(A, ind=2) → Tensor
```

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.

[#](#api-tensorplay.linalg.tensorsolve)

### tensorsolve

function[Full reference ↗](/docs/generated/tensorplay.linalg.tensorsolve.html)

```python
tensorplay.linalg.tensorsolve(A, B, dims=None) → Tensor
```

Solves the tensor equation A X = B after flattening the contracted
dimensions into a square matrix.  dims identifies dimensions of A
that should be moved to the trailing side before the flattening step.

[#](#api-tensorplay.linalg.vander)

### vander

function[Full reference ↗](/docs/generated/tensorplay.linalg.vander.html)

```python
tensorplay.linalg.vander(x, N=None) → Tensor
```

[#](#api-tensorplay.linalg.vdot)

### vdot

function[Full reference ↗](/docs/generated/tensorplay.linalg.vdot.html)

```python
tensorplay.linalg.vdot(self, other) → Tensor
```

Conjugating dot product over 1-D operands: sum(conj(self) * other).

[#](#api-tensorplay.linalg.vecdot)

### vecdot

function[Full reference ↗](/docs/generated/tensorplay.linalg.vecdot.html)

```python
tensorplay.linalg.vecdot(x, y, *, dim=-1) → Tensor
```

Dot product along dim with the first argument conjugated for complex
inputs.

[#](#api-tensorplay.linalg.vector_norm)

### vector_norm

function[Full reference ↗](/docs/generated/tensorplay.linalg.vector_norm.html)

```python
tensorplay.linalg.vector_norm(x, ord=2, dim=None, keepdim=False) → Tensor
```

dim=None norms the whole tensor: the input is flattened first, and
keepdim then restores the reduced axes as ones.

## Classes 7

[#](#api-tensorplay.linalg.CholeskyExResult)

### CholeskyExResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.CholeskyExResult.html)

```python
class tensorplay.linalg.CholeskyExResult(L, info)
```

```python
L
```

Alias for field number 0

```python
count(value, /)
```

Return number of occurrences of value.

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

```python
info
```

Alias for field number 1

[#](#api-tensorplay.linalg.EighResult)

### EighResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.EighResult.html)

```python
class tensorplay.linalg.EighResult(eigenvalues, eigenvectors)
```

```python
count(value, /)
```

Return number of occurrences of value.

```python
eigenvalues
```

Alias for field number 0

```python
eigenvectors
```

Alias for field number 1

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

[#](#api-tensorplay.linalg.EigResult)

### EigResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.EigResult.html)

```python
class tensorplay.linalg.EigResult(eigenvalues, eigenvectors)
```

```python
count(value, /)
```

Return number of occurrences of value.

```python
eigenvalues
```

Alias for field number 0

```python
eigenvectors
```

Alias for field number 1

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

[#](#api-tensorplay.linalg.LstsqResult)

### LstsqResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.LstsqResult.html)

```python
class tensorplay.linalg.LstsqResult(solution, residuals, rank, singular_values)
```

```python
count(value, /)
```

Return number of occurrences of value.

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

```python
rank
```

Alias for field number 2

```python
residuals
```

Alias for field number 1

```python
singular_values
```

Alias for field number 3

```python
solution
```

Alias for field number 0

[#](#api-tensorplay.linalg.QRResult)

### QRResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.QRResult.html)

```python
class tensorplay.linalg.QRResult(Q, R)
```

```python
Q
```

Alias for field number 0

```python
R
```

Alias for field number 1

```python
count(value, /)
```

Return number of occurrences of value.

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

[#](#api-tensorplay.linalg.SlogdetResult)

### SlogdetResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.SlogdetResult.html)

```python
class tensorplay.linalg.SlogdetResult(sign, logabsdet)
```

```python
count(value, /)
```

Return number of occurrences of value.

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

```python
logabsdet
```

Alias for field number 1

```python
sign
```

Alias for field number 0

[#](#api-tensorplay.linalg.SVDResult)

### SVDResult

class[Full reference ↗](/docs/generated/tensorplay.linalg.SVDResult.html)

```python
class tensorplay.linalg.SVDResult(U, S, Vh)
```

```python
S
```

Alias for field number 1

```python
U
```

Alias for field number 0

```python
Vh
```

Alias for field number 2

```python
count(value, /)
```

Return number of occurrences of value.

```python
index(value, start=0, stop=9223372036854775807, /)
```

Return first index of value.

Raises ValueError if the value is not present.

## Exceptions 1

[#](#api-tensorplay.linalg.LinAlgError)

### LinAlgError

exception[Full reference ↗](/docs/generated/tensorplay.linalg.LinAlgError.html)

```python
exception tensorplay.linalg.LinAlgError
```

Raised when a decomposition or solve fails on a numerically invalid input.