Tensor

class discopy.tensor.Tensor(dom, cod, array)

Bases: Box

Implements a tensor with dom, cod and numpy array.

Examples

>>> m = Tensor(Dim(2), Dim(2), [0, 1, 1, 0])
>>> v = Tensor(Dim(1), Dim(2), [0, 1])
>>> v >> m >> v.dagger()
Tensor(dom=Dim(1), cod=Dim(1), array=[0])

Notes

Tensors can have sympy symbols as free variables.

>>> from sympy.abc import phi, psi
>>> v = Tensor(Dim(1), Dim(2), [phi, psi])
>>> d = v >> v.dagger()
>>> assert v >> v.dagger() == Tensor(
...     Dim(1), Dim(1), [phi * phi.conjugate() + psi * psi.conjugate()])

These can be substituted and lambdifed.

>>> v.subs(phi, 0).lambdify(psi)(1)
Tensor(dom=Dim(1), cod=Dim(2), array=[0, 1])

We can also use jax.numpy using Tensor.backend.

>>> with Tensor.backend('jax'):
...     f = lambda *xs: d.lambdify(phi, psi)(*xs).array
...     import jax
...     assert jax.grad(f)(1., 2.) == 2.

property array

Numpy array.

transpose(left=False)

Returns the diagrammatic transpose.

Note

This is not the same as the algebraic transpose for complex dims.

conjugate(diagrammatic=True)

Returns the conjugate of a tensor.

Parameters:

diagrammatic (bool, default: True) – Whether to use the diagrammatic or algebraic conjugate.

property l

Returns the conjugate of a tensor.

Parameters:

diagrammatic (bool, default: True) – Whether to use the diagrammatic or algebraic conjugate.

property r

Returns the conjugate of a tensor.

Parameters:

diagrammatic (bool, default: True) – Whether to use the diagrammatic or algebraic conjugate.

round(decimals=0)

Rounds the entries of a tensor up to a number of decimals.

map(func)

Apply a function elementwise.

static zeros(dom, cod)

Returns the zero tensor of a given shape.

Examples

>>> assert Tensor.zeros(Dim(2), Dim(2))\
...     == Tensor(Dim(2), Dim(2), [0, 0, 0, 0])

grad(var, **params)

Gradient with respect to variables.

jacobian(variables, **params)

Jacobian with respect to variables.

Parameters:

variables (List[sympy.Symbol]) – Differentiated variables.

Returns:

tensor – with tensor.dom == self.dom and tensor.cod == Dim(len(variables)) @ self.cod.

Return type:

Tensor

Examples

>>> from sympy.abc import x, y, z
>>> vector = Tensor(Dim(1), Dim(2), [x ** 2, y * z])
>>> vector.jacobian([x, y, z])
Tensor(dom=Dim(1), cod=Dim(3, 2), array=[2.0*x, 0, 0, 1.0*z, 0, 1.0*y])