Solver
The superscreen.solve
module contains the actual implementation
of Brandt’s method, as described here.
Solve
- superscreen.solve.solve_layer(*, device, layer, applied_field, kernel, weights, Del2, grad, Lambda_info, terminal_currents=None, circulating_currents=None, vortices=None, current_units='uA', check_inversion=False, gpu=False)[source]
Computes the stream function and magnetic field within a single layer of a
Device
.- Parameters
device (
Device
) – The Device to simulate.layer (
str
) – Name of the layer to analyze.applied_field (
ndarray
) – The applied magnetic field evaluated at the mesh vertices.weights (
ndarray
) – The Device’s weight vector.kernel (
ndarray
) – The Device’s kernel matrixQ
.Del2 (
ndarray
) – The Device’s Laplacian operator.grad (
ndarray
) – The Device’s vertex gradient matrix, shape (num_vertices, 2, num_vertices).Lambda_info (
LambdaInfo
) – A LambdaInfo instance defining Lambda(x, y).terminal_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{source_name: source_current}
for each source terminal. This argument is only allowed ifdevice
as an instance ofTransportDevice
.circulating_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{hole_name: circulating_current}
. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Optional
[List
[Vortex
]]) – A list of Vortex objects located in films in this layer.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of{current_units} / {device.length_units}
.check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA).
- Return type
- Returns
stream function, current density, total field, film screening field
- superscreen.solve.solve(device, *, applied_field=None, terminal_currents=None, circulating_currents=None, vortices=None, field_units='mT', current_units='uA', check_inversion=False, iterations=0, return_solutions=True, directory=None, cache_memory_cutoff=inf, log_level=20, gpu=False, _solver='superscreen.solve')[source]
Computes the stream functions and magnetic fields for all layers in a
Device
.The simulation strategy is:
1. Compute the stream functions and fields for each layer given only the applied field.
2. If iterations > 1 and there are multiple layers, then for each layer, calculate the screening field from all other layers and recompute the stream function and fields based on the sum of the applied field and the screening fields from all other layers.
Repeat step 2 (iterations - 1) times.
- Parameters
device (
Device
) – The Device to simulate.applied_field (
Optional
[Callable
]) – A callable that computes the applied magnetic field as a function of x, y, z coordinates.terminal_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{source_name: source_current}
for each source terminal. This argument is only allowed ifdevice
as an instance ofTransportDevice
.circulating_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{hole_name: circulating_current}
. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Optional
[List
[Vortex
]]) – A list of Vortex objects located in the Device.field_units (
str
) – Units of the applied field. Can either be magnetic field H or magnetic flux density B = mu0 * H.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of [current_units / device.length_units].check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.iterations (
int
) – Number of times to compute the interactions between layers.return_solutions (
bool
) – Whether to return a list of Solution objects.directory (
Optional
[str
]) – If not None, resulting Solutions will be saved in this directory.cache_memory_cutoff (
float
) – If the memory needed for layer-to-layer kernel matrices exceedscache_memory_cutoff
times the current available system memory, then the kernel matrices will be cached to disk rather than in memory. Setting this value toinf
disables caching to disk. In this case, the arrays will remain in memory unless they are swapped to disk by the operating system.log_level (
int
) – Logging level to use, if any.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA)._solver (
str
) – Name of the solver method used.
- Return type
- Returns
If
return_solutions
is True, returns a list of Solutions of lengthiterations + 1
.
Solve Many
- superscreen.solve.solve_many(device, *, parallel_method=None, applied_fields=None, circulating_currents=None, vortices=None, layer_updater=None, layer_update_kwargs=None, field_units='mT', current_units='uA', check_inversion=False, iterations=0, product=False, directory=None, return_solutions=False, keep_only_final_solution=False, cache_memory_cutoff=inf, log_level=20, use_shared_memory=True, num_cpus=None, gpu=False)[source]
Solves many models involving the same device, optionally in parallel using multiple processes.
- Parameters
device (
Device
) – The Device to simulate.parallel_method (
Optional
[str
]) – The method to use for multiprocessing (None, “mp”, or “ray”).applied_fields (
Union
[Parameter
,List
[Parameter
],None
]) – A callable or list of callables that compute(s) the applied magnetic field as a function of x, y, z coordinates.circulating_currents (
Union
[Dict
[str
,Union
[float
,str
,Quantity
]],List
[Dict
[str
,Union
[float
,str
,Quantity
]]],None
]) – A dict of{hole_name: circulating_current}
or list of such dicts. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Union
[List
[Vortex
],List
[List
[Vortex
]],None
]) – A list (list of lists) ofVortex
objects.layer_updater (
Optional
[Callable
]) – A callable with signaturelayer_updater(layer: Layer, **kwargs) -> Layer
that updates parameter(s) of each layer in a device.layer_update_kwargs (
Optional
[List
[Dict
[str
,Any
]]]) – A list of dicts of keyword arguments passed tolayer_updater
.field_units (
str
) – Units of the applied field. Can either be magnetic field H or magnetic flux density B = mu0 * H.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of [current_units / device.length_units].check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.iterations (
int
) – Number of times to compute the interactions between layersproduct (
bool
) – If True, then all combinations of applied_fields, circulating_currrents, and layer_update_kwargs are simulated (the behavior is given by itertools.product(), i.e. a nested for loop). Otherwise, the behavior is similar to zip(). See superscreen.parallel.create_models for more details.directory (
Optional
[str
]) – The directory in which to save the results. If None is given, then the results are not automatically saved to disk.return_solutions (
bool
) – Whether to return the Solution objects.keep_only_final_solution (
bool
) – Whether to keep/save only the Solution from the final iteration of superscreen.solve.solve for each setup.cache_memory_cutoff (
float
) – If the memory needed for layer-to-layer kernel matrices exceedscache_memory_cutoff
times the current available system memory, then the kernel matrices will be cached to disk rather than in memory. Setting this value toinf
disables caching to disk. In this case, the arrays will remain in memory unless they are swapped to disk by the operating system.log_level (
int
) – Logging level to use, if any.use_shared_memory (
bool
) – Whether to use shared memory if parallel_method is not None.num_cpus (
Optional
[int
]) – The number of processes to utilize.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA). gpu = True is only allowed for serial execution, i.e.,parallel_method in {None, False, "serial"}
.
- Return type
Tuple
[Union
[List
[Solution
],List
[List
[Solution
]],None
],Optional
[List
[str
]]]- Returns
solutions, paths. If return_solutions is True, solutions is either a list of lists of Solutions (if keep_only_final_solution is False), or a list of Solutions (the final iteration for each setup). If directory is True, paths is a list of paths to the saved solutions, otherwise paths is None.
Solution
- class superscreen.solution.Solution(*, device, streams, current_densities, fields, screening_fields, applied_field, field_units, current_units, circulating_currents=None, terminal_currents=None, vortices=None, solver='superscreen.solve')[source]
A container for the calculated stream functions and fields, with some convenient data processing methods.
- Parameters
device (
Device
) – TheDevice
that was solvedstreams (
Dict
[str
,ndarray
]) – A dict of{layer_name: stream_function}
current_densities (
Dict
[str
,ndarray
]) – A dict of{layer_name: current_density}
fields (
Dict
[str
,ndarray
]) – A dict of{layer_name: total_field}
screening_fields (
Dict
[str
,ndarray
]) – A dict of{layer_name: screening_field}
applied_field (
Callable
) – The function defining the applied fieldfield_units (
str
) – Units of the applied fieldcurrent_units (
str
) – Units used for current quantities.circulating_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{hole_name: circulating_current}
.terminal_currents (
Optional
[Dict
[str
,Union
[float
,str
,Quantity
]]]) – A dict of{terminal_name: terminal_current}
.vortices (
Optional
[List
[Vortex
]]) – A list ofVortex
objects located in theDevice
.solver (
str
) – The solver method that generated the solution.
- grid_data(dataset, *, layers=None, grid_shape=(200, 200), method='linear', with_units=False, **kwargs)[source]
Interpolates results from the triangular mesh to a rectangular grid.
Keyword arguments are passed to scipy.interpolate.griddata().
- Parameters
dataset (
str
) – Name of the dataset to interpolate (one of “streams”, “fields”, or “screening_fields”, “current_densities”).layers (
Union
[str
,List
[str
],None
]) – Name(s) of the layer(s) for which to interpolate results.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer N is given, then the grid will be square, shape = (N, N).method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).with_units (
bool
) – Whether to return arrays of pint.Quantities with units attached.
- Return type
- Returns
x grid, y grid, dict of interpolated data for each layer
- grid_current_density(*, layers=None, grid_shape=(200, 200), method='linear', units=None, with_units=False, **kwargs)[source]
Computes the current density
J = [dg/dy, -dg/dx]
on a rectangular grid.Keyword arguments are passed to scipy.interpolate.griddata().
- Parameters
layers (
Union
[str
,List
[str
],None
]) – Name(s) of the layer(s) for which to interpolate current density.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer N is given, then the grid will be square, shape = (N, N).method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).units (
Optional
[str
]) – The desired units for the current density. Defaults toself.current_units / self.device.length_units
.with_units (
bool
) – Whether to return arrays of pint.Quantities with units attached.
- Return type
- Returns
x grid, y grid, dict of interpolated current density for each layer
- interp_current_density(positions, *, layers=None, grid_shape=(200, 200), method='linear', units=None, with_units=False, **kwargs)[source]
Computes the current density
J = [dg/dy, -dg/dx]
at unstructured coordinates via interpolation.Keyword arguments are passed to scipy.interpolate.griddata().
- Parameters
positions (
ndarray
) – Shape(m, 2)
array of x, y coordinates at which to evaluate the current density.layers (
Union
[str
,List
[str
],None
]) – Name(s) of the layer(s) for which to interpolate current density.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer N is given, then the grid will be square, shape = (N, N).method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).units (
Optional
[str
]) – The desired units for the current density. Defaults toself.current_units / self.device.length_units
.with_units (
bool
) – Whether to return arrays of pint.Quantities with units attached.
- Returns
A dict of interpolated current density for each layer.
- interp_fields(positions, *, layers=None, method='linear', units=None, with_units=False, **kwargs)[source]
Interpolates the fields in one or more layers.
Additional keyword arguments are passed to the relevant interpolator: :class``scipy.interpolate.NearestNDInterpolator`,
scipy.interpolate.LinearNDInterpolator
, orscipy.interpolate.CloughTocher2DInterpolator
.- Parameters
positions (
ndarray
) – Shape(m, 2)
array of x, y coordinates at which to evaluate the fields.layers (
Union
[str
,List
[str
],None
]) – Name(s) of the layer(s) for which to interpolate fields.method (
str
) – Interpolation method to use: ‘nearest’, ‘linear’, or ‘cubic’.units (
Optional
[str
]) – The desired units for the current density. Defaults toself.field_units
.with_units (
bool
) – Whether to return arrays of pint.Quantities with units attached.
- Returns
A dict of interpolated fields for each layer.
- polygon_flux(*, polygons=None, units=None, with_units=True)[source]
Computes the flux through all polygons (films, holes, and flux regions) by integrating the calculated fields.
- Parameters
- Return type
- Returns
A dict of
{polygon_name: polygon_flux}
- polygon_fluxoid(polygon_points, layers=None, grid_shape=(200, 200), interp_method='linear', units='Phi_0', with_units=True)[source]
Computes the
Fluxoid
(flux + supercurrent) for a given polygonal region.The fluxoid for a closed region \(S\) with boundary \(\partial S\) is defined as:
\[\Phi^f_S = \underbrace{ \int_S \mu_0 H_z(\vec{r})\,\mathrm{d}^2r }_{\text{flux part}} + \underbrace{ \oint_{\partial S} \mu_0\Lambda(\vec{r})\vec{J}(\vec{r})\cdot\mathrm{d}\vec{r} }_{\text{supercurrent part}}\]- Parameters
polygon_points (
ndarray
) – A shape(n, 2)
array of(x, y)
coordinates of polygon vertices defining the closed region \(S\).layers (
Union
[str
,List
[str
],None
]) – Name(s) of the layer(s) for which to compute the fluxoid.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid to use for interpolation. If a single integer N is given, then the grid will be square, shape = (N, N).interp_method (
str
) – Interpolation method to use.units (
Optional
[str
]) – The desired units for the current density. Defaults to \(\Phi_0\).with_units (
bool
) – Whether to return values as pint.Quantities with units attached.
- Return type
- Returns
A dict of
{layer_name: fluxoid}
for each specified layer, wherefluxoid
is an instance ofFluxoid
.
- hole_fluxoid(hole_name, points=None, grid_shape=(200, 200), interp_method='linear', units='Phi_0', with_units=True)[source]
Calculcates the fluxoid for a polygon enclosing the specified hole.
- Parameters
hole_name (
str
) – The name of the hole for which to calculate the fluxoid.points (
Optional
[ndarray
]) – The vertices of the polygon enclosing the hole. If None is given, a polygon is generated usingsupercreen.fluxoid.make_fluxoid_polygons()
.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid to use for interpolation. If a single integer N is given, then the grid will be square, shape = (N, N).interp_method (
str
) – Interpolation method to use.units (
Optional
[str
]) – The desired units for the current density. Defaults to \(\Phi_0\).with_units (
bool
) – Whether to return values as pint.Quantities with units attached.
- Return type
- Returns
The hole’s Fluxoid.
- field_at_position(positions, *, zs=None, vector=False, units=None, with_units=True, return_sum=True)[source]
Calculates the field due to currents in the device at any point(s) in space.
- Parameters
positions (
ndarray
) – Shape (m, 2) array of (x, y) coordinates, or (m, 3) array of (x, y, z) coordinates at which to calculate the magnetic field. A single sequence like [x, y] or [x, y, z] is also allowed.zs (
Union
[float
,ndarray
,None
]) – z coordinates at which to calculate the field. If positions has shape (m, 3), then this argument is not allowed. If zs is a scalar, then the fields are calculated in a plane parallel to the x-y plane. If zs is any array, then it must be same length as positions.vector (
bool
) – Whether to return the full vector magnetic field or just the z component.units (
Optional
[str
]) – Units to which to convert the fields (can be either magnetic field H or magnetic flux density B = mu0 * H). If not given, then the fields are returned in units ofself.field_units
.with_units (
bool
) – Whether to return the fields aspint.Quantity
with units attached.return_sum (
bool
) – Whether to return the sum of the fields from all layers in the device, or a dict of{layer_name: field_from_layer}
.
- Return type
- Returns
An np.ndarray if return_sum is True, otherwise a dict of
{layer_name: field_from_layer}
. If with_units is True, then the array(s) will contain pint.Quantities.field_from_layer
will have shape(m, )
if vector is False, or shape(m, 3)
ifvector
is True.
- vector_potential_at_position(positions, *, zs=None, units=None, with_units=True, return_sum=True)[source]
Calculates the vector potential due to currents in the device at any point(s) in space. Note that this only considers the vector potential due to currents in the device, so only represents the total vector potential in cases where the applied field is zero (e.g. models with only vortices and/or circulating currents).
The vector potential \(\vec{A}\) at position \(\vec{r}\) due to sheet current density \(\vec{J}(\vec{r}')\) flowing in a film with lateral geometry \(S\) is:
\[\vec{A}(\vec{r}) = \frac{\mu_0}{4\pi} \int_S\frac{\vec{J}(\vec{r}')}{|\vec{r}-\vec{r}'|}\mathrm{d}^2r'.\]- Parameters
positions (
ndarray
) – Shape (m, 2) array of (x, y) coordinates, or (m, 3) array of (x, y, z) coordinates at which to calculate the vector potential. A single list like [x, y] or [x, y, z] is also allowed.zs (
Union
[float
,ndarray
,None
]) – z coordinates at which to calculate the potential. If positions has shape (m, 3), then this argument is not allowed. If zs is a scalar, then the fields are calculated in a plane parallel to the x-y plane. If zs is any array, then it must be same length as positions.units (
Optional
[str
]) – Units to which to convert the vector potential.with_units (
bool
) – Whether to return the vector potential as apint.Quantity
with units attached.return_sum (
bool
) – Whether to return the sum of the potential from all layers in the device, or a dict of{layer_name: potential_from_layer}
.
- Return type
- Returns
An np.ndarray if return_sum is True, otherwise a dict of
{layer_name: potential_from_layer}
. If with_units is True, then the array(s) will contain pint.Quantities.potential_from_layer
will have shape(m, 3)
.
- to_file(directory, save_mesh=True, compressed=True, to_zip=False)[source]
Saves a Solution to disk.
- Parameters
directory (
str
) – The name of the directory in which to save the solution (must either be empty or not yet exist).save_mesh (
bool
) – Whether to save the device mesh.compressed (
bool
) – Whether to use numpy.savez_compressed rather than numpy.savez.to_zip (
bool
) – Whether to save the Solution to a zip file.
- Return type
- plot_streams(layers=None, units=None, max_cols=3, cmap='magma', levels=101, colorbar=True, filled=True, **kwargs)[source]
Alias for
superscreen.visualization.plot_streams()
.Plots the stream function for multiple layers in a Device.
Additional keyword arguments are passed to plt.subplots().
- Parameters
layers (
Union
[str
,List
[str
],None
]) – Name(s) of layer(s) for which to plot the stream function. By default, the stream function is plotted for all layers in the Device.units (
Optional
[str
]) – Units in which to plot the stream function. Defaults to solution.current_units.max_cols (
int
) – Maximum number of columns in the grid of subplots.cmap (
str
) – Name of the matplotlib colormap to use.levels (
int
) – Number of contour levels to used.colorbar (
bool
) – Whether to add a colorbar to each subplot.filled (
bool
) – If True, plots filled contours.solution (Solution) –
- Return type
- Returns
matplotlib figure and axes
- plot_currents(layers=None, units=None, grid_shape=(200, 200), grid_method='cubic', max_cols=3, cmap='inferno', colorbar=True, auto_range_cutoff=None, share_color_scale=False, symmetric_color_scale=False, vmin=None, vmax=None, streamplot=True, min_stream_amp=0.025, cross_section_coords=None, **kwargs)[source]
Alias for
superscreen.visualization.plot_currents()
.Plots the current density (sheet current) for each layer in a Device.
Additional keyword arguments are passed to plt.subplots().
- Parameters
layers (
Union
[str
,List
[str
],None
]) – Name(s) of layer(s) for which to plot the sheet current. By default, the stream function is plotted for all layers in the Device.units (
Optional
[str
]) – Units in which to plot the current density. Defaults to solution.current_units / solution.device.length_units.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer n is given, then the grid will be square, shape = (n, n).grid_method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).max_cols (
int
) – Maximum number of columns in the grid of subplots.cmap (
str
) – Name of the matplotlib colormap to use.colorbar (
bool
) – Whether to add a colorbar to each subplot.auto_range_cutoff (
Union
[float
,Tuple
[float
,float
],None
]) – Cutoff percentile forauto_range_iqr
.share_color_scale (
bool
) – Whether to force all layers to use the same color scale.symmetric_color_scale (
bool
) – Whether to use a symmetric color scale (vmin = -vmax).vmin (
Optional
[float
]) – Color scale minimum to use for all layers (ignored if share_color_scale is True).vmax (
Optional
[float
]) – Color scale maximum to use for all layers (ignored if share_color_scale is True).streamplot (
bool
) – Whether to overlay current streamlines on the plot.min_stream_amp (
float
) – Streamlines will not be drawn anywhere the current density is less than min_stream_amp * max(current_density). This avoids streamlines being drawn where there is no current flowing.cross_section_coords (
Union
[ndarray
,Sequence
[ndarray
],None
]) – Shape (m, 2) array of (x, y) coordinates for a cross-section (or a list of such arrays).solution (Solution) –
- Return type
- Returns
matplotlib figure and axes
- plot_fields(layers=None, dataset='fields', normalize=False, units=None, grid_shape=(200, 200), grid_method='cubic', max_cols=3, cmap='cividis', colorbar=True, auto_range_cutoff=None, share_color_scale=False, symmetric_color_scale=False, vmin=None, vmax=None, cross_section_coords=None, **kwargs)[source]
Alias for
superscreen.visualization.plot_fields()
.Plots either the total field or the screening field for multiple layers in a Device.
Additional keyword arguments are passed to plt.subplots().
- Parameters
layers (
Union
[str
,List
[str
],None
]) – Name(s) of layer(s) for which to plot the fields. By default, the stream function is plotted for all layers in the Device.dataset (
str
) – Which set of fields to plot, either “fields” or “screening_fields”.normalize (
bool
) – Whether to normalize the fields by the applied field.units (
Optional
[str
]) – Units in which to plot the fields. Defaults to solution.field_units. This argument is ignored if normalize is True.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer n is given, then the grid will be square, shape = (n, n).grid_method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).max_cols (
int
) – Maximum number of columns in the grid of subplots.cmap (
str
) – Name of the matplotlib colormap to use.colorbar (
bool
) – Whether to add a colorbar to each subplot.auto_range_cutoff (
Union
[float
,Tuple
[float
,float
],None
]) – Cutoff percentile forauto_range_iqr
.share_color_scale (
bool
) – Whether to force all layers to use the same color scale.symmetric_color_scale (
bool
) – Whether to use a symmetric color scale (vmin = -vmax).vmin (
Optional
[float
]) – Color scale minimum to use for all layersvmax (
Optional
[float
]) – Color scale maximum to use for all layerscross_section_coords (
Union
[ndarray
,Sequence
[ndarray
],None
]) – Shape (m, 2) array of (x, y) coordinates for a cross-section (or a list of such arrays).solution (Solution) –
- Return type
- Returns
matplotlib figure and axes
- plot_field_at_positions(positions, zs=None, vector=False, units=None, grid_shape=(200, 200), grid_method='cubic', cmap='cividis', colorbar=True, auto_range_cutoff=None, share_color_scale=False, symmetric_color_scale=False, vmin=None, vmax=None, cross_section_coords=None, **kwargs)[source]
Alias for
superscreen.visualization.plot_field_at_positions()
.Plots the total field (either all three components or just the z component) at a given set of positions (x, y, z) outside of the device.
Additional keyword arguments are passed to plt.subplots().
- Parameters
positions (
ndarray
) – Shape (m, 2) array of (x, y) coordinates, or (m, 3) array of (x, y, z) coordinates at which to calculate the magnetic field. A single list like [x, y] or [x, y, z] is also allowed.zs (
Union
[float
,ndarray
,None
]) – z coordinates at which to calculate the field. If positions has shape (m, 3), then this argument is not allowed. If zs is a scalar, then the fields are calculated in a plane parallel to the x-y plane. If zs is any array, then it must be same length as positions.vector (
bool
) – Whether to return the full vector magnetic field or just the z component.units (
Optional
[str
]) – Units in which to plot the fields. Defaults to solution.field_units. This argument is ignored if normalize is True.grid_shape (
Union
[int
,Tuple
[int
,int
]]) – Shape of the desired rectangular grid. If a single integer n is given, then the grid will be square, shape = (n, n).grid_method (
str
) – Interpolation method to use (see scipy.interpolate.griddata).max_cols – Maximum number of columns in the grid of subplots.
cmap (
str
) – Name of the matplotlib colormap to use.colorbar (
bool
) – Whether to add a colorbar to each subplot.auto_range_cutoff (
Union
[float
,Tuple
[float
,float
],None
]) – Cutoff percentile forauto_range_iqr
.share_color_scale (
bool
) – Whether to force all layers to use the same color scale.symmetric_color_scale (
bool
) – Whether to use a symmetric color scale (vmin = -vmax).vmin (
Optional
[float
]) – Color scale minimum to use for all layersvmax (
Optional
[float
]) – Color scale maximum to use for all layerscross_section_coords (
Union
[float
,List
[float
],None
]) – Shape (m, 2) array of (x, y) coordinates for a cross-section (or a list of such arrays).solution (Solution) –
- Return type
- Returns
matplotlib figure and axes
Fluxoid
- class superscreen.solution.Fluxoid(flux_part, supercurrent_part)[source]
Bases:
tuple
The fluxoid for a closed region \(S\) with boundary \(\partial S\) is defined as:
\[\Phi^f_S = \underbrace{ \int_S \mu_0 H_z(\vec{r})\,\mathrm{d}^2r }_{\text{flux part}} + \underbrace{ \oint_{\partial S} \mu_0\Lambda(\vec{r})\vec{J}(\vec{r})\cdot\mathrm{d}\vec{r} }_{\text{supercurrent part}}\]
- class superscreen.solution.Vortex(x, y, layer, nPhi0=1)[source]
Bases:
tuple
A vortex located at position
(x, y)
inlayer
containing a total fluxnPhi0
in units of the flux quantum \(\Phi_0\).
- superscreen.fluxoid.make_fluxoid_polygons(device, holes=None, join_style='mitre', interp_points=None)[source]
Generates polygons enclosing the given holes to calculate the fluxoid.
- Parameters
device (
Device
) – The Device for which to generate polygons.holes (
Union
[str
,List
[str
],None
]) – Name(s) of the hole(s) in the device for which to generate polygons. Defaults to all holes in the device.join_style (
str
) – Seesuperscreen.components.Polygon.buffer()
.interp_points (
Optional
[int
]) – If provided, the resulting polygons will be interpolated tointerp_points
vertices.
- Return type
- Returns
A dict of
{hole_name: fluxoid_polygon}
.
- superscreen.fluxoid.find_fluxoid_solution(device, *, fluxoids=None, **solve_kwargs)[source]
Calculates the current(s) circulating around hole(s) in the device required to realize the specified fluxoid state.
- Parameters
device (
Device
) – The Device for which to find the given fluxoid solution.fluxoids (
Optional
[Dict
[str
,float
]]) – A dict of{hole_name: fluxoid_value}
, wherefluxoid_value
is in units of \(\Phi_0\). The fluxoid for any holes not in this dict will default to 0.solve_kwargs – Additional keyword arguments are passed to
superscreen.solve.solve()
.
- Return type
- Returns
The optimized
superscreen.solution.Solution
.
IO
- superscreen.io.save_solutions(solutions, base_directory, save_mesh=True, return_paths=False, to_zip=False)[source]
Saves a list of Solutions to disk.
- Parameters
base_directory (
PathLike
) – The name of the directory in which to save the solutions (must either be empty or not yet exist).save_mesh (
bool
) – Whether to save the full mesh.return_paths (
bool
) – Whether to return a list of resulting paths.to_zip (
bool
) – Whether to save Solutions as zip archives.
- Return type
- Returns
If
return_paths
is True, returns a list of paths where each solution was saved.
- superscreen.io.iload_solutions(base_directory)[source]
An iterator that loads a sequence of Solutions from disk.
Supporting Functions
Brandt Core
- superscreen.solve.q_matrix(points, dtype=None)[source]
Computes the denominator matrix, q:
\[q_{ij} = \frac{1}{4\pi|\vec{r}_i-\vec{r}_j|^3}\]See Eq. 7 in [Brandt-PRB-2005], Eq. 8 in [Kirtley-RSI-2016], and Eq. 8 in [Kirtley-SST-2016].
- superscreen.solve.C_vector(points, dtype=None)[source]
Computes the edge vector, C:
\[\begin{split}C_i &= \frac{1}{4\pi}\sum_{p,q=\pm1}\sqrt{(\Delta x - px_i)^{-2} + (\Delta y - qy_i)^{-2}}\\ \Delta x &= \frac{1}{2}(\mathrm{max}(x) - \mathrm{min}(x))\\ \Delta y &= \frac{1}{2}(\mathrm{max}(y) - \mathrm{min}(y))\end{split}\]See Eq. 12 in [Brandt-PRB-2005], Eq. 16 in [Kirtley-RSI-2016], and Eq. 15 in [Kirtley-SST-2016].
- superscreen.solve.Q_matrix(q, C, weights, dtype=None)[source]
Computes the kernel matrix, Q:
\[Q_{ij} = (\delta_{ij}-1)q_{ij} + \delta_{ij}\frac{1}{w_{ij}}\left(C_i + \sum_{l\neq i}q_{il}w_{il}\right)\]See Eq. 10 in [Brandt-PRB-2005], Eq. 11 in [Kirtley-RSI-2016], and Eq. 11 in [Kirtley-SST-2016].
- superscreen.solve.convert_field(value, new_units, old_units=None, ureg=None, with_units=True)[source]
Converts a value between different field units, either magnetic field H [current] / [length] or flux density B = mu0 * H [mass] / ([curret] [time]^2)).
- Parameters
value (
Union
[ndarray
,float
,str
,Quantity
]) – The value to convert. It can either be a numpy array (no units), a float (no units), a string like “1 uA/um”, or a scalar or arraypint.Quantity
. If value is not a string wiht units or apint.Quantity
, then old_units must specify the units of the float or array.old_units (
Union
[str
,Unit
,None
]) – The old units ofvalue
. This argument is required ifvalue
is not a string with units or apint.Quantity
.ureg (
Optional
[UnitRegistry
]) – Thepint.UnitRegistry
to use for conversion. If None is given, a new instance is created.with_units (
bool
) – Whether to return apint.Quantity
with units attached.
- Return type
- Returns
The converted value, either a pint.Quantity (scalar or array with units), or an array or float without units, depending on the
with_units
argument.
- superscreen.solve.field_conversion_factor(field_units, current_units, length_units='m', ureg=None)[source]
Returns a conversion factor from
field_units
tocurrent_units / length_units
.- Parameters
field_units (
str
) – Magnetic field/flux unit to convert, having dimensionality either of magnetic fieldH
(e.g. A / m or Oe) or of magnetic flux densityB = mu0 * H
(e.g. Tesla or Gauss).current_units (
str
) – Current unit to use for the conversion.length_units (
str
) – Lenght/distance unit to use for the conversion.ureg (
Optional
[UnitRegistry
]) – pint UnitRegistry to use for the conversion. If None is provided, a new UnitRegistry is created.
- Return type
Quantity
- Returns
Conversion factor as a
pint.Quantity
.conversion_factor.magnitude
gives you the numerical value of the conversion factor.
Parallel Processing
- superscreen.parallel.create_models(device, applied_fields=None, circulating_currents=None, vortices=None, layer_updater=None, layer_update_kwargs=None, product=False)[source]
Generate a list of (device, applied_field, circulating_currents).
- Parameters
device (
Device
) – The Device to simulate.applied_fields (
Union
[Parameter
,List
[Parameter
],None
]) – A callable or list of callables that compute(s) the applied magnetic field as a function of x, y, z coordinates.circulating_currents (
Union
[Dict
[str
,Union
[float
,str
,Quantity
]],List
[Dict
[str
,Union
[float
,str
,Quantity
]]],None
]) – A dict of{hole_name: circulating_current}
or list of such dicts. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Union
[List
[Vortex
],List
[List
[Vortex
]],None
]) – A list (or list of lists) ofVortex
objects.layer_updater (
Optional
[Callable
]) – A callable with signaturelayer_updater(layer: Layer, **kwargs) -> Layer
that updates parameter(s) of each layer in a device.layer_update_kwargs (
Optional
[List
[Dict
[str
,Any
]]]) – A list of dicts of keyword arguments passed tolayer_updater
.product (
bool
) – If True, then all combinations of applied_fields, circulating_currrents, and layer_update_kwargs are simulated (the behavior is given by itertools.product()). Otherwise, the behavior is similar to zip().
- Return type
List
[Tuple
[Device
,Parameter
,Dict
[str
,Union
[float
,str
,Quantity
]]]]- Returns
A list of “models”, (device, applied_field, circulating_currents, vortices).
- superscreen.parallel.solve_many_serial(*, device, applied_fields=None, circulating_currents=None, vortices=None, layer_updater=None, layer_update_kwargs=None, field_units='mT', current_units='uA', check_inversion=False, iterations=1, product=False, directory=None, return_solutions=False, keep_only_final_solution=False, cache_memory_cutoff=inf, log_level=None, gpu=False, use_shared_memory=True, num_cpus=None)[source]
Solve many models in a single process.
- Parameters
device (
Device
) – The Device to simulate.applied_fields (
Union
[Parameter
,List
[Parameter
],None
]) – A callable or list of callables that compute(s) the applied magnetic field as a function of x, y, z coordinates.circulating_currents (
Union
[Dict
[str
,Union
[float
,str
,Quantity
]],List
[Dict
[str
,Union
[float
,str
,Quantity
]]],None
]) – A dict of{hole_name: circulating_current}
or list of such dicts. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Union
[List
[Vortex
],List
[List
[Vortex
]],None
]) – A list (list of lists) ofVortex
objects.layer_updater (
Optional
[Callable
]) – A callable with signaturelayer_updater(layer: Layer, **kwargs) -> Layer
that updates parameter(s) of each layer in a device.layer_update_kwargs (
Optional
[List
[Dict
[str
,Any
]]]) – A list of dicts of keyword arguments passed tolayer_updater
.field_units (
str
) – Units of the applied field. Can either be magnetic field H or magnetic flux density B = mu0 * H.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of [current_units / device.length_units].check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.iterations (
int
) – Number of times to compute the interactions between layersproduct (
bool
) – If True, then all combinations of applied_fields, circulating_currrents, and layer_update_kwargs are simulated (the behavior is given by itertools.product(), i.e. a nested for loop). Otherwise, the behavior is similar to zip(). See superscreen.parallel.create_models for more details.directory (
Optional
[str
]) – The directory in which to save the results. If None is given, then the results are not automatically saved to disk.return_solutions (
bool
) – Whether to return the Solution objects.keep_only_final_solution (
bool
) – Whether to keep/save only the Solution from the final iteration of superscreen.solve.solve for each setup.cache_memory_cutoff (
float
) – If the memory needed for layer-to-layer kernel matrices exceedscache_memory_cutoff
times the current available system memory, then the kernel matrices will be cached to disk rather than in memory. Setting this value toinf
disables caching to disk. In this case, the arrays will remain in memory unless they are swapped to disk by the operating system.use_shared_memory (
bool
) – Whether to use shared memory if parallel_method is not None.num_cpus (
Optional
[int
]) – The number of processes to utilize.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA). gpu = True is only allowed for serial execution, i.e.,parallel_method in {None, False, "serial"}
.
- Return type
Tuple
[Union
[List
[Solution
],List
[List
[Solution
]],None
],Optional
[List
[str
]]]- Returns
solutions, paths. If return_solutions is True, solutions is either a list of lists of Solutions (if keep_only_final_solution is False), or a list of Solutions (the final iteration for each setup). If directory is True, paths is a list of paths to the saved solutions, otherwise paths is None.
- superscreen.parallel.solve_many_mp(*, device, applied_fields=None, circulating_currents=None, vortices=None, layer_updater=None, layer_update_kwargs=None, field_units='mT', current_units='uA', check_inversion=False, iterations=0, product=False, directory=None, return_solutions=False, keep_only_final_solution=False, cache_memory_cutoff=inf, log_level=None, use_shared_memory=True, num_cpus=None)[source]
Solve many models in parallel using multiprocessing.
- Parameters
device (
Device
) – The Device to simulate.applied_fields (
Union
[Parameter
,List
[Parameter
],None
]) – A callable or list of callables that compute(s) the applied magnetic field as a function of x, y, z coordinates.circulating_currents (
Union
[Dict
[str
,Union
[float
,str
,Quantity
]],List
[Dict
[str
,Union
[float
,str
,Quantity
]]],None
]) – A dict of{hole_name: circulating_current}
or list of such dicts. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Union
[List
[Vortex
],List
[List
[Vortex
]],None
]) – A list (list of lists) ofVortex
objects.layer_updater (
Optional
[Callable
]) – A callable with signaturelayer_updater(layer: Layer, **kwargs) -> Layer
that updates parameter(s) of each layer in a device.layer_update_kwargs (
Optional
[List
[Dict
[str
,Any
]]]) – A list of dicts of keyword arguments passed tolayer_updater
.field_units (
str
) – Units of the applied field. Can either be magnetic field H or magnetic flux density B = mu0 * H.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of [current_units / device.length_units].check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.iterations (
int
) – Number of times to compute the interactions between layersproduct (
bool
) – If True, then all combinations of applied_fields, circulating_currrents, and layer_update_kwargs are simulated (the behavior is given by itertools.product(), i.e. a nested for loop). Otherwise, the behavior is similar to zip(). See superscreen.parallel.create_models for more details.directory (
Optional
[str
]) – The directory in which to save the results. If None is given, then the results are not automatically saved to disk.return_solutions (
bool
) – Whether to return the Solution objects.keep_only_final_solution (
bool
) – Whether to keep/save only the Solution from the final iteration of superscreen.solve.solve for each setup.cache_memory_cutoff (
float
) – If the memory needed for layer-to-layer kernel matrices exceedscache_memory_cutoff
times the current available system memory, then the kernel matrices will be cached to disk rather than in memory. Setting this value toinf
disables caching to disk. In this case, the arrays will remain in memory unless they are swapped to disk by the operating system.use_shared_memory (
bool
) – Whether to use shared memory if parallel_method is not None.num_cpus (
Optional
[int
]) – The number of processes to utilize.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA). gpu = True is only allowed for serial execution, i.e.,parallel_method in {None, False, "serial"}
.
- Return type
Tuple
[Union
[List
[Solution
],List
[List
[Solution
]],None
],Optional
[List
[str
]]]- Returns
solutions, paths. If return_solutions is True, solutions is either a list of lists of Solutions (if keep_only_final_solution is False), or a list of Solutions (the final iteration for each setup). If directory is True, paths is a list of paths to the saved solutions, otherwise paths is None.
- superscreen.parallel.solve_many_ray(*, device, applied_fields=None, circulating_currents=None, vortices=None, layer_updater=None, layer_update_kwargs=None, field_units='mT', current_units='uA', check_inversion=False, iterations=0, product=False, directory=None, return_solutions=False, keep_only_final_solution=False, cache_memory_cutoff=inf, log_level=None, use_shared_memory=True, num_cpus=None)[source]
Solve many models in parallel using ray.
- Parameters
device (
Device
) – The Device to simulate.applied_fields (
Union
[Parameter
,List
[Parameter
],None
]) – A callable or list of callables that compute(s) the applied magnetic field as a function of x, y, z coordinates.circulating_currents (
Union
[Dict
[str
,Union
[float
,str
,Quantity
]],List
[Dict
[str
,Union
[float
,str
,Quantity
]]],None
]) – A dict of{hole_name: circulating_current}
or list of such dicts. If circulating_current is a float, then it is assumed to be in units of current_units. If circulating_current is a string, then it is converted to a pint.Quantity.vortices (
Union
[List
[Vortex
],List
[List
[Vortex
]],None
]) – A list (list of lists) ofVortex
objects.layer_updater (
Optional
[Callable
]) – A callable with signaturelayer_updater(layer: Layer, **kwargs) -> Layer
that updates parameter(s) of each layer in a device.layer_update_kwargs (
Optional
[List
[Dict
[str
,Any
]]]) – A list of dicts of keyword arguments passed tolayer_updater
.field_units (
str
) – Units of the applied field. Can either be magnetic field H or magnetic flux density B = mu0 * H.current_units (
str
) – Units to use for current quantities. The applied field will be converted to units of [current_units / device.length_units].check_inversion (
bool
) – Whether to verify the accuracy of the matrix inversion.iterations (
int
) – Number of times to compute the interactions between layersproduct (
bool
) – If True, then all combinations of applied_fields, circulating_currrents, and layer_update_kwargs are simulated (the behavior is given by itertools.product(), i.e. a nested for loop). Otherwise, the behavior is similar to zip(). See superscreen.parallel.create_models for more details.directory (
Optional
[str
]) – The directory in which to save the results. If None is given, then the results are not automatically saved to disk.return_solutions (
bool
) – Whether to return the Solution objects.keep_only_final_solution (
bool
) – Whether to keep/save only the Solution from the final iteration of superscreen.solve.solve for each setup.cache_memory_cutoff (
float
) – If the memory needed for layer-to-layer kernel matrices exceedscache_memory_cutoff
times the current available system memory, then the kernel matrices will be cached to disk rather than in memory. Setting this value toinf
disables caching to disk. In this case, the arrays will remain in memory unless they are swapped to disk by the operating system.use_shared_memory (
bool
) – Whether to use shared memory if parallel_method is not None.num_cpus (
Optional
[int
]) – The number of processes to utilize.gpu (
bool
) – Solve on a GPU if available (requires JAX and CUDA). gpu = True is only allowed for serial execution, i.e.,parallel_method in {None, False, "serial"}
.
- Return type
Tuple
[Union
[List
[Solution
],List
[List
[Solution
]],None
],Optional
[List
[str
]]]- Returns
solutions, paths. If return_solutions is True, solutions is either a list of lists of Solutions (if keep_only_final_solution is False), or a list of Solutions (the final iteration for each setup). If directory is True, paths is a list of paths to the saved solutions, otherwise paths is None.