mrmustard.math

The math module

• ParameterSet
• Parameters
• Backend Manager

A class to manage the different backends supported by Mr Mustard.

Functions

Categorical(name)	Categorical distribution over integers.
DefaultEuclideanOptimizer()	Default optimizer for the Euclidean parameters.
J(num_modes)	Symplectic form.
MultivariateNormalTriL(scale_tril)	Multivariate normal distribution on R^k and parameterized by a (batch of) length-k loc vector (aka "mu") and a (batch of) k x k scale matrix; covariance = scale @ scale.T where @ denotes matrix-multiplication.
Xmat(num_modes)	The matrix \(X_n = \begin{bmatrix}0 & I_n\\ I_n & 0\end{bmatrix}.\)
Zmat(num_modes)	The matrix \(Z_n = \begin{bmatrix}I_n & 0\\ 0 & -I_n\end{bmatrix}.\)
abs()	The absolute value of array.
add_at_modes(new, modes)	Adds two phase-space tensors (cov matrices, displacement vectors, etc..) on the specified modes.
all_diagonals(real)	Returns all the diagonals of a density matrix.
allclose(array2[, atol])	Whether two arrays are equal within tolerance.
any()	Returns True if any element of array is True, False otherwise.
arange([limit, delta, dtype])	Returns an array of evenly spaced values within a given interval.
asnumpy()	Converts an array to a numpy array.
assign(value)	Assigns value to tensor.
astensor([dtype])	Converts a numpy array to a tensor.
atleast_1d([dtype])	Returns an array with at least one dimension.
atleast_2d([dtype])	Returns an array with at least two dimensions.
atleast_3d([dtype])	Returns an array with at least three dimensions by eventually inserting new axes at the beginning.
binomial_conditional_prob(dim_out, dim_in)	\(P(out|in) = binom(in, out) * (1-success_prob)**(in-out) * success_prob**out\).
block([axes])	Returns a matrix made from the given blocks.
block_diag(mat2)	Returns a block diagonal matrix from the given matrices.
boolean_mask(mask)	Returns a tensor based on the truth value of the boolean mask.
cast([dtype])	Casts array to dtype.
change_backend()	Changes the backend to a different one.
cholesky()	Computes the Cholesky decomposition of square matrices.
clip(a_min, a_max)	Clips array to the interval [a_min, a_max].
concat(axis)	Concatenates values along the given axis.
conj()	The complex conjugate of array.
constraint_func()	Returns a constraint function for the given bounds.
convolution(filters[, padding, data_format])	Performs a convolution on array with filters.
convolve_probs(other)	Convolve two probability distributions (up to 3D) with the same shape.
convolve_probs_1d(other_probs)	Convolution of a joint probability with a list of single-index probabilities.
cos()	The cosine of an array.
cosh()	The hyperbolic cosine of array.
custom_gradient(func)	A decorator to define a function with a custom gradient.
dagger()	The adjoint of array.
det()	The determinant of matrix.
diag([k])	The array made by inserting the given array along the \(k\)-th diagonal.
diag_part([k])	The array of the main diagonal of array.
eigh()	The eigenvalues and eigenvectors of a matrix.
eigvals()	The eigenvalues of a tensor.
einsum(*tensors)	The result of the Einstein summation convention on the tensors.
euclidean_to_symplectic(dS_euclidean)	Convert the Euclidean gradient to a Riemannian gradient on the tangent bundle of the symplectic manifold.
euclidean_to_unitary(dU_euclidean)	Convert the Euclidean gradient to a Riemannian gradient on the tangent bundle of the unitary manifold.
exp()	The exponential of array element-wise.
expand_dims(axis)	The array with an additional dimension inserted at the given axis.
expm()	The matrix exponential of matrix.
eye([dtype])	The identity matrix of size.
eye_like()	The identity matrix of the same shape and dtype as array.
from_backend()	Whether the given tensor is a tensor of the concrete backend.
gather(indices[, axis])	The values of the array at the given indices.
hermite_renormalized(B, C, shape)	Renormalized multidimensional Hermite polynomial given by the "exponential" Taylor series of \(exp(C + Bx + 1/2*Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\).
hermite_renormalized_1leftoverMode(B, C, cutoffs)	First, reorder A and B parameters of Bargmann representation to match conventions in mrmustard.math.compactFock~ Then, calculate the required renormalized multidimensional Hermite polynomial.
hermite_renormalized_1leftoverMode_reorderedAB(B, ...)	Renormalized multidimensional Hermite polynomial given by the "exponential" Taylor series of \(exp(C + Bx - Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\).
hermite_renormalized_batch(B, C, shape)	Renormalized multidimensional Hermite polynomial given by the "exponential" Taylor series of \(exp(C + Bx + 1/2*Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\).
hermite_renormalized_binomial(B, C, shape, ...)	Renormalized multidimensional Hermite polynomial given by the "exponential" Taylor series of \(exp(C + Bx + 1/2*Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\).
hermite_renormalized_diagonal(B, C, cutoffs)	Firsts, reorder A and B parameters of Bargmann representation to match conventions in mrmustard.math.compactFock~ Then, calculates the required renormalized multidimensional Hermite polynomial.
hermite_renormalized_diagonal_batch(B, C, ...)	First, reorder A and B parameters of Bargmann representation to match conventions in mrmustard.math.compactFock~ Then, calculates the required renormalized multidimensional Hermite polynomial.
hermite_renormalized_diagonal_reorderedAB(B, ...)	Renormalized multidimensional Hermite polynomial given by the "exponential" Taylor series of \(exp(C + Bx - Ax^2)\) at zero, where the series has \(sqrt(n!)\) at the denominator rather than \(n!\).
imag()	The imaginary part of array.
inv()	The inverse of tensor.
is_trainable()	Whether the given tensor is trainable.
kron(tensor2)	The Kroenecker product of the given tensors.
left_matmul_at_modes(b_full, modes)	Left matrix multiplication of a partial matrix and a full matrix.
lgamma()	The natural logarithm of the gamma function of x.
log()	The natural logarithm of x.
make_complex(imag)	Given two real tensors representing the real and imaginary part of a complex number, this operation returns a complex tensor.
map_fn(elements)	Transforms elems by applying fn to each element unstacked on axis 0.
matmul()	The matrix product of the given matrices.
matvec(b)	The matrix vector product of a (matrix) and b (vector).
matvec_at_modes(vec, modes)	Matrix-vector multiplication between a phase-space matrix and a vector in the specified modes.
maximum(b)	The element-wise maximum of a and b.
minimum(b)	The element-wise minimum of a and b.
new_constant(name[, dtype])	Returns a new constant with the given value.
new_variable(bounds, name[, dtype])	Returns a new variable with the given value and bounds.
norm()	The norm of array.
ones([dtype])	Returns an array of ones with the given shape and dtype.
ones_like()	Returns an array of ones with the same shape and dtype as array.
outer(array2)	The outer product of array1 and array2.
pad(paddings[, mode, constant_values])	The padded array.
pinv()	The pseudo-inverse of matrix.
poisson(rate)	Poisson distribution up to max_k.
pow(y)	Returns \(x^y\).
prod([axis])	The product of all elements in array.
random_orthogonal(N)	A random orthogonal matrix in \(O(N)\).
random_symplectic([max_r])	A random symplectic matrix in Sp(2*num_modes).
random_unitary()	a random unitary matrix in \(U(N)\)
real()	The real part of array.
reshape(shape)	The reshaped array.
right_matmul_at_modes(b_partial, modes)	Right matrix multiplication of a full matrix and a partial matrix.
rotmat(num_modes)	Rotation matrix from quadratures to complex amplitudes.
round(decimals)	The array rounded to the nearest integer.
set_diag(diag, k)	The array with the diagonal set to diag.
sin()	The sine of array.
single_mode_to_multimode_mat(num_modes)	Apply the same \(2\times 2\) matrix (i.e. single-mode) to a larger number of modes.
single_mode_to_multimode_vec(num_modes)	Apply the same 2-vector (i.e. single-mode) to a larger number of modes.
sinh()	The hyperbolic sine of array.
solve(rhs)	The solution of the linear system \(Ax = b\).
sort([axis])	Sort the array along an axis.
sqrt([dtype])	The square root of x.
sqrtm([dtype])	The matrix square root.
squeeze(axis)	Removes dimensions of size 1 from the shape of a tensor.
sum([axes])	The sum of array.
tensordot(b, axes)	The tensordot product of a and b.
tile(repeats)	The tiled array.
trace([dtype])	The trace of array.
transpose([perm])	The transposed arrays.
unitary_to_orthogonal(U)	Unitary to orthogonal mapping.
update_add_tensor(indices, values)	Updates a tensor in place by adding the given values.
update_tensor(indices, values)	Updates a tensor in place with the given values.
value_and_gradients(parameters)	The loss and gradients of the given cost function.
xlogy(y)	Returns 0 if x == 0 elementwise and x * log(y) otherwise.
zeros([dtype])	Returns an array of zeros with the given shape and dtype.
zeros_like()	Returns an array of zeros with the same shape and dtype as array.

Variables

backend
backend_name
euclidean_opt
instance

code/math

 

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