topoptlab.utils module

topoptlab.utils.check_optimizer_kw(optimizer: str, n: int, ft: int, n_constr: int, optimizer_kw: Dict) → None[source]

Check that general optimuer parameters are sensible or implemented and insert missing ones based on the default dictionary.

Parameters:

  • optimizer (str) – name of optimizer.

  • n (int) – number of design variables.

  • ft (int) – code for filter.

  • n_constr (int) – number of constraints.

  • optimizer_kw (dictionary) – contains parameters for the optimizern . All relevant values can be found in default_outputkw.

Return type:

None

topoptlab.utils.check_output_kw(output_kw: Dict) → None[source]

Check that general output parameters are sensible or implemented and insert missing ones based on the default dictionary.

Parameters:

output_kw (dictionary) – contains general parameters for outputting information . All relevant values can be found in default_outputkw.

Return type:

None

topoptlab.utils.check_simulation_params(simulation_kw: Dict) → None[source]

Check that general simulation parameters are sensible or implemented.

Parameters:

simulation_kw (dictionary) – contains general information about simulation. At the moment, only “grid”,”element order”, “meshfile” are supported with contents “regular”,1,None.

Return type:

None

topoptlab.utils.cholesky_inverse(A: ndarray) → ndarray[source]

Form inverse via Cholesky decomposition:

A = L @ L.T

Parameters:

A (np.ndarray shape (k,k) or (n,k,k)) – Matrix/matrices to invert.

Returns:

Ainv – inverted matrix/matrices.

Return type:

np.ndarray shape (k,k) or (n,k,k)

topoptlab.utils.default_outputkw() → Dict[source]

Return the default dictionary containing general parameters for output and logging in the topology_optimization.main() function.

This dictionary defines the default for output-related behavior, such as file naming, verbosity, etc. It can be used as a reference or as a source for inserting missing keys in user-defined dictionaries.

Keys and Default Values

Key

Type

Default

Description

“file” “display” “export” “write_log” “profile” “output_movie” “verbosity”

str bool bool bool bool bool int

“topopt” True True True False False 20

Base name used for output files. Display intermediary design. Export final results to disk as VTK. Write a log file. Profile code execution. Generate a movie of intermediate designs. Level of verbosity (see SimpleLogger).
returns:

dictionary containing the default output parameters.

rtype:

output_kw

topoptlab.utils.dict_without(dictionary: Dict, keys: List) → Dict[source]

Return a copy of a dictionary without the given keys.

Parameters:

  • dictionary (dict) – full dictionary.

  • keys (list) – list of keys to not include in the copy

Returns:

dictionary_new – dictionary without given keys

Return type:

dict

topoptlab.utils.elid_to_coords(el: ndarray, nelx: int, nely: int, nelz: None | int = None, l: float | List = [1.0, 1.0, 1.0], **kwargs: Any) → ndarray[source]

Map element IDs to cartesian coordinates in the usual regular grid.

Parameters:

  • el (np.ndarray, shape (n)) – element IDs.

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

  • nelz (int or None) – number of elements in z direction.

  • l (float or list) – side length of element

Returns:

coords – element coordinates of shape shape (n,ndim).

Return type:

np.ndarray

topoptlab.utils.even_spaced_ternary(npoints: int) → ndarray[source]

Create even spaced points for a ternary phase system.

Parameters:

npoints (int) – number of points.

Returns:

fracs – phase fractions.

Return type:

np.ndarray shape (k+1,3)

topoptlab.utils.map_eltoimg(quant: ndarray, nelx: int, nely: int, **kwargs: Any) → ndarray[source]

Map quantity located on elements on the usual regular grid to an image.

Parameters:

  • quant (np.ndarray, shape (n,nchannel)) – some quantity defined on each element (e. g. element density).

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

Returns:

img – quantity mapped to image.

Return type:

np.ndarray, shape (nely,nelx,nchannel)

topoptlab.utils.map_eltovoxel(quant: ndarray, nelx: int, nely: int, nelz: int, **kwargs: Any) → ndarray[source]

Map quantity located on elements on the usual regular grid to a voxels.

Parameters:

  • quant (np.ndarray, shape (n,nchannel)) – some quantity defined on each element (e. g. element density).

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

  • nelz (int or None) – number of elements in z direction.

Returns:

voxel – quantity mapped to voxels.

Return type:

np.ndarray shape (nelz,nely,nelx,nchannel)

topoptlab.utils.map_imgtoel(img: ndarray, nelx: int, nely: int, **kwargs: Any) → ndarray[source]

Map image of quantity back to 1D np.ndarray with correct (!) ordering.

Parameters:

  • img (np.ndarray, shape (nely,nelx)) – image of quantity (e. g. of element densities).

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

Returns:

quant – quantity mapped back to 1D np.ndarray with hopefully correct ordering.

Return type:

np.ndarray, shape (n)

topoptlab.utils.map_voxeltoel(voxel: ndarray, nelx: int, nely: int, nelz: int, **kwargs: Any) → ndarray[source]

Map voxels of quantity back to on elements on the usual regular grid.

Parameters:

  • voxel (np.ndarray, shape (nelz,nely,nelx,nchannel)) – voxels of quantity (e. g. of element densities).

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

  • nelz (int or None) – number of elements in z direction.

Returns:

quant – quantity mapped back to 1D np.ndarray with hopefully correct ordering.

Return type:

np.ndarray, shape (n,nchannel)

topoptlab.utils.nodeid_to_coords(nd: ndarray, nelx: int, nely: int, nelz: None | int = None, l: float | List = [1.0, 1.0, 1.0], **kwargs: Any) → ndarray[source]

Map node IDs to cartesian coordinates in the usual regular grid.

Parameters:

  • nd (np.ndarray, shape (n)) – node IDs.

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

  • nelz (int or None) – number of elements in z direction.

  • l (float or List) – side length of element

Returns:

coords – node coordinates of shape shape (n,ndim).

Return type:

np.ndarray

topoptlab.utils.solve_inverse(A: ndarray) → ndarray[source]

Form inverse via solving:

solve(A,eye)

Parameters:

A (np.ndarray shape (k,k) or (n,k,k)) – Matrix/matrices to invert.

Returns:

Ainv – inverted matrix/matrices.

Return type:

np.ndarray shape (k,k) or (n,k,k)

topoptlab.utils.svd_inverse(A: ndarray, check_singular: bool = True) → ndarray[source]

Form inverse via singular value decomposition (SVD). Not recommended as numerically unstable.

Parameters:

  • A (np.ndarray shape (k,k) or (n,k,k)) – Matrix/matrices to invert.

  • check_singular (bool) – Check if singular. If not True, raise ValueError.

Returns:

Ainv – inverted matrix/matrices.

Return type:

np.ndarray shape (k,k) or (n,k,k)

topoptlab.utils.unique_sort(iM: ndarray, jM: ndarray, combine: bool = False) → Tuple[ndarray, ndarray, ndarray][source]

Sort first according to iM, then sort values of equal value iM according to jM.

Parameters:

  • iM (np.ndarray, shape (n)) – first array.

  • jM (np.ndarray, shape (n)) – second array.

  • combine (scalar bool) – if True, stack both to to a column array of shape (n,2)

Returns:

  • iM (np.ndarray shape (n)) – if not combine returns sorted iM

  • jM (np.ndarray shape (n)) – if not combine returns sorted jM

  • M (np.ndarray shape (n,2)) – if combine returns column stack of sort iM and jM.

topoptlab.utils.upsampling(x: ndarray, magnification: float | int | List, nelx: int, nely: int, nelz: None | int = None, return_flat: bool = True, order: int = 0) → ndarray[source]

Upsample current design variables defined on the standard regular grid to a larger design by interpolation. With order 0 the design is replicated on a finer scale in a volume conserving fashion, otherwise spline interpolation might violate this.

Parameters:

  • x (np.ndarray shape (n,nchannel)) – design variables.

  • magnification (float) – magnification factor.

  • nelx (int) – number of elements in x direction.

  • nely (int) – number of elements in y direction.

  • nelz (int or None, optional) – number of elements in z direction. The default is None.

  • return_flat (bool, optional) – return the design variables flattened. If false returns an image or a voxel graphic. The default is True.

  • order (int, optional) – order of spline interpolation for upsampling. The default is 0.

Returns:

x_new – upsampled design variables.

Return type:

np.ndarray shape (n) or shape (nely,nelx) or shape (nelz,nely,nelx)