entanglish.utilities module

entanglish.utilities.clip(x, limits)

This method clips x between limits[0] and limits[1]

Parameters:

• x (int|float) –
• limits (list[int|float]) –

Returns:

Return type:

int|float

entanglish.utilities.clipped_log_of_vec(vec, eps=1e-10, clip_to_zero=False)

This method takes as input a int|float or a 1D array of floats. It returns the log element-wise of that array, except when an element of the array is < eps, where eps is a positive but << 1 float. In that exceptional case, the method “clips the log”, meaning that it returns log(eps) if clip_to_zero=False and 0 if clip_to_zero=True

Parameters:

• vec (int|float|np.ndarray) –
• eps (float) –
• clip_to_zero (bool) –

Returns:

Return type:

np.ndarray

entanglish.utilities.comb(n, k)

This method returns the number of combinations of k picks (with return) out of n possible choices, “n choose k” = n!/[(n-k)! k!]

Parameters:

• n (int) –
• k (int) –

Returns:

Return type:

int

entanglish.utilities.fun_of_herm_arr(fun_of_evas, herm_arr, **fun_kwargs)

This method does the same as the method ut.fun_of_herm_arr_from_eigen(), except that it calculates evas and eigen_cols from the matrix herm_arr which it has as input.

Parameters:

• fun_of_evas (function) – np function acting on 1d array
• herm_arr (np.ndarray) – Hermitian array
• fun_kwargs (dict) – dict of keyword args that fun depends on

Returns:

Return type:

np.ndarray

entanglish.utilities.fun_of_herm_arr_from_eigen_sys(fun_of_evas, evas, evec_cols, **fun_kwargs)

eigen_sys= eigensystem= (eigenvalues, eigenvectors as columns)= (evas, evec_cols)

This method returns a function fun of a Hermitian matrix mat. This is calculated as fun(mat) = U.D.U^dag, where U=evec_cols is a unitary matrix with the eigenvectors of mat as columns, U^dag is the Hermitian conjugate of U, D= diag(fun(evas)) is a diagonal matrix whose diagonal is obtained by applying element-wise the function fun=fun_of_evas to the 1D array of eigenvalues evas.

Parameters:

• fun_of_evas (function) –
• evas (np.ndarray) –
• evec_cols (np.ndarray) –
• fun_kwargs (dict) – dict of keyword arguments that fun depends on

Returns:

Return type:

np.ndarray

entanglish.utilities.get_entropy_from_probs(probs)

This method returns the classical entropy of the probability distribution probs. It checks that probs is a prob distribution.

Parameters:probs (np.ndarray) – Returns: Return type:float

entanglish.utilities.get_equiv_classes(li)

This method is given as input a list li of floats, some of which may be equal within epsilon = 1e-6. The method then returns a list of equivalence classes, where each equivalence class is a list of the int positions in li of those floats that are equal to each other within epsilon.

Parameters:li (list[float]|np.ndarray) – Returns: Return type:list[list[int]]

entanglish.utilities.herm_arr_from_eigen_sys(evas, evec_cols)

Same as fun_of_herm_arr_from_eigen_sys() but for special case when fun_of_evas() is identity.

Parameters:

• evas (np.ndarray) –
• evec_cols (np.ndarray) –

Returns:

Return type:

np.ndarray

entanglish.utilities.is_hermitian_arr(arr)

Returns True iff arr is a Hermitian matrix.

Returns: Return type:bool

entanglish.utilities.is_nonnegative_arr(arr)

This method checks that all elements of arr are > -1e-6.

Parameters:arr (np.ndarray) – Returns: Return type:bool

entanglish.utilities.is_positive_arr(arr)

This method checks that all elements of arr are > 0.

Parameters:arr (np.ndarray) – Returns: Return type:bool

entanglish.utilities.is_prob_dist(prob_dist)

This method checks that the elements of arr define a probability distribution.

Parameters:prob_dist (np.ndarray) – Returns: Return type:bool

entanglish.utilities.is_unitary_arr(umat)

Returns True iff umat is a unitary matrix

Parameters:umat (np.ndarray) – Returns: Return type:bool

entanglish.utilities.kron_prod(mat_list)

This method returns the Kronecker product of the list of matrices which is has as input.

Parameters:mat_list (list[np.ndarray]) – Returns: Return type:np.ndarray

entanglish.utilities.mat_elem(v1, a, v2)

This method returns the matrix element <v1|a|v2>, where v1 and v2 are column vectors and ‘a’ a matrix.

Parameters:

• v1 (np.ndarray) –
• a (np.ndarray) –
• v2 (np.ndarray) –

Returns:

Return type:

complex

entanglish.utilities.positive_part(x)

This method returns max(0, x)

Parameters:x (int|float) – Returns: Return type:int|float

entanglish.utilities.positive_part_of_vec(vec)

This method takes as input a int|float or a 1D array of floats. It returns the array, with negative items replaced by zero

Parameters:vec (int|float|np.ndarray) – Returns: Return type:np.ndarray

entanglish.utilities.prob_hypergeometric(x, xx, n, nn)

This method returns

P(x | xx, n, nn) = comb(xx, x)*comb(nn-xx, n-x)/comb(nn, n)

where:

0 <= x <= xx
0 <= n-x <= nn-xx
0 <= n <= nn

This P(x | ) defines the hypergeometric distribution

References

1. https://en.wikipedia.org/wiki/Hypergeometric_distribution

Parameters:

• x (int) –
• xx (int) –
• n (int) –
• nn (int) –

Returns:

Return type:

float

entanglish.utilities.random_st_vec(dim)

This method returns a random complex 1D numpy array, normalized, of size dim.

Parameters:dim (int) – Returns: Return type:np.ndarray

entanglish.utilities.random_unitary(dim)

This method returns a random unitary matrix of size dim x dim

Parameters:dim (int) – Returns: Return type:np.ndarray

entanglish.utilities.scalar_prod(scalars_list)

This method returns the product of the list of scalars which it has as input.

Parameters:scalars_list (list[int|float|complex] | tuple[int|float|complex]) – Returns: Return type:complex|float|int

entanglish.utilities.switch_arr_basis(arr, umat, reverse=False)

This method takes as input a square array ‘arr’ and returns a new array which is a similarity transformation U^dag(arr)U of ‘arr’ that changes the basis of arr from inbasis to sbasis (or the reverse, U(arr)U^dag, from sbasis to inbasis if the input bool parameter ‘reverse’ is set to True.) U = umat , U^dag = Hermitian conjugate of U

Parameters:

• arr (np.ndarray) –
• umat (np.ndarray) –
• reverse (bool) –

Returns:

Return type:

np.ndarray