3.5. wavesim.utilities

add_absorption(m, boundary_widths, n_roi, n_dims)

Add (weighted) absorption to the permittivity (refractive index squared)

Parameters:

• m – array (permittivity)

• boundary_widths – Boundary widths

• n_roi – Number of points in the region of interest

• n_dims – Number of dimensions

Returns:

m with absorption

analytical_solution(n_size0, pixel_size, wavelength=None)

Compute analytic solution for 1D case

boundary_(x)

Anti-reflection boundary layer (ARL). Linear window function

Parameters:

x – Size of the ARL

class chain

Bases: object

chain(*iterables) –> chain object

Return a chain object whose .__next__() method returns elements from the first iterable until it is exhausted, then elements from the next iterable, until all of the iterables are exhausted.

classmethod from_iterable(iterable, /)

Alternative chain() constructor taking a single iterable argument that evaluates lazily.

check_input_dims(x)

Expand arrays to 3 dimensions (e.g. permittivity (refractive index²) or source)

Parameters:

x – Input array

Returns:

x with 3 dimensions

check_input_len(x, e, n_dims)

Check the length of input arrays and expand them to 3 elements if necessary. Either repeat or add ‘e’

Parameters:

• x – Input array

• e – Element to add

• n_dims – Number of dimensions

Returns:

Array with 3 elements

combine(domains, device='cpu')

Concatenates a 3-d array of 3-d tensors

full_matrix(operator)

Converts operator to a 2D square matrix of size np.prod(d) x np.prod(d)

Parameters:

operator – Operator to convert to a matrix. This function must be able to accept a 0 scalar, and return a vector of the size and data type of the domain.

get_dims(x)

Get the number of dimensions of ‘x’

Parameters:

x – Input array

Returns:

Number of dimensions

is_zero(x)

Check if x is zero

Some functions allow specifying 0 or 0.0 instead of a torch tensor, to indicate that the array should be cleared. This function returns True if x is a scalar 0 or 0.0. It raises an error if x is a scalar that is not equal to 0 or 0.0, and returns False otherwise.

list_to_array(input, depth)

Convert a nested list of depth depth to a numpy object array

max_abs_error(e, e_true)

(Normalized) Maximum Absolute Error (MAE) ||e-e_true||_{inf} / ||e_true||

Parameters:

• e – Computed field

• e_true – True field

Returns:

(Normalized) MAE

max_relative_error(e, e_true)

Computes the maximum error, normalized by the rms of the true field

Parameters:

• e – Computed field

• e_true – True field

Returns:

(Normalized) Maximum Relative Error

normalize(x, min_val=None, max_val=None, a=0, b=1)

Normalize x to the range [a, b]

Parameters:

• x – Input array

• min_val – Minimum value (of x)

• max_val – Maximum value (of x)

• a – Lower bound for normalization

• b – Upper bound for normalization

Returns:

Normalized x

pad_boundaries(x, boundary_widths, boundary_post=None, mode='constant')

Pad ‘x’ with boundaries in all dimensions using numpy pad (if x is np.ndarray) or PyTorch nn.functional.pad (if x is torch.Tensor). If boundary_post is specified separately, pad with boundary_widths (before) and boundary_post (after).

Parameters:

• x – Input array

• boundary_widths – Boundary widths for padding before and after (or just before if boundary_post not None)

• boundary_post – Boundary widths for padding after

• mode – Padding mode

Returns:

Padded array

partition(array, n_domains)

Split a 3-D array into a 3-D set of sub-arrays of approximately equal sizes.

preprocess(permittivity, boundary_widths=10)

Preprocess the input parameters for the simulation. Add absorption and boundaries to the permittivity (refractive index²), and return the preprocessed permittivity and boundaries in the format (ax0, ax1, ax2).

Parameters:

• permittivity – Refractive index²

• boundary_widths – Boundary widths (in pixels)

Returns:

Preprocessed permittivity (refractive index²) with boundaries and absorption

relative_error(e, e_true)

Relative error ⟨|e-e_true|^2⟩ / ⟨|e_true|^2⟩

Parameters:

• e – Computed field

• e_true – True field

Returns:

Relative Error

squeeze_(x)

Squeeze the last dimension of ‘x’ if it is 1

Parameters:

x – Input array

Returns:

Squeezed array