simsopt.field package

Submodules

simsopt.field.biotsavart module

class simsopt.field.biotsavart.BiotSavart(coils)

Bases: simsoptpp.BiotSavart, simsopt.field.magneticfield.MagneticField

Computes the MagneticField induced by a list of closed curves \(\Gamma_k\) with electric currents \(I_k\). The field is given by

\[B(\mathbf{x}) = \frac{\mu_0}{4\pi} \sum_{k=1}^{n_\mathrm{coils}} I_k \int_0^1 \frac{(\Gamma_k(\phi)-\mathbf{x})\times \Gamma_k'(\phi)}{\|\Gamma_k(\phi)-\mathbf{x}\|^3} d\phi\]

where \(\mu_0=4\pi 10^{-7}\) is the magnetic constant.

Parameters: coils – A list of simsopt.field.coil.Coil objects.

A(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_and_dB_vjp(v, vgrad): Same as simsopt.geo.biotsavart.BiotSavart.B_vjp but returns the vector Jacobian product for \(B\) and \(\nabla B\), i.e. it returns

\[\{ \sum_{i=1}^{n} \mathbf{v}_i \cdot \partial_{\mathbf{c}_k} \mathbf{B}_i \}_k, \{ \sum_{i=1}^{n} {\mathbf{v}_\mathrm{grad}}_i \cdot \partial_{\mathbf{c}_k} \nabla \mathbf{B}_i \}_k.\]

B_cyl(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

B_vjp(v): Assume the field was evaluated at points \(\mathbf{x}_i, i\in \{1, \ldots, n\}\) and denote the value of the field at those points by \(\{\mathbf{B}_i\}_{i=1}^n\). These values depend on the shape of the coils, i.e. on the dofs \(\mathbf{c}_k\) of each coil. This function returns the vector Jacobian product of this dependency, i.e.

\[\{ \sum_{i=1}^{n} \mathbf{v}_i \cdot \partial_{\mathbf{c}_k} \mathbf{B}_i \}_k.\]

GradAbsB(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

property coils

compute(self: simsoptpp.BiotSavart, arg0: int) → None

compute_A(compute_derivatives=0)

Compute the potential of a BiotSavart field

\[A(\mathbf{x}) = \frac{\mu_0}{4\pi} \sum_{k=1}^{n_\mathrm{coils}} I_k \int_0^1 \frac{\Gamma_k'(\phi)}{\|\Gamma_k(\phi)-\mathbf{x}\|} d\phi\]

as well as the derivatives of A if requested.

d2A_by_dXdX(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdcoilcurrents(compute_derivatives=1)

d3B_by_dXdXdcoilcurrents(compute_derivatives=2)

dA_by_dX(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dcoilcurrents(compute_derivatives=0)

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fieldcache_get_or_create(self: simsoptpp.BiotSavart, arg0: str, arg1: List[int]) → numpy.ndarray[numpy.float64]

fieldcache_get_status(self: simsoptpp.BiotSavart, arg0: str) → bool

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.BiotSavart) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.BiotSavart) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.BiotSavart, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.BiotSavart, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.BiotSavart, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

simsopt.field.coil module

class simsopt.field.coil.Coil(curve, current)

Bases: simsoptpp.Coil, simsopt._core.graph_optimizable.Optimizable

A Coil combines a Curve and a Current and is used as input for a BiotSavart field.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property current: Get the underlying current.

property curve: Get the underlying curve.

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

vjp(v_gamma, v_gammadash, v_current)

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.coil.Current(current)

Bases: simsoptpp.Current, simsopt._core.graph_optimizable.Optimizable

An optimizable object that wraps around a single scalar degree of freedom. It represents the electric current in a coil, or in a set of coils that are constrained to use the same current.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_dofs(self: simsoptpp.Current) → numpy.ndarray[numpy.float64]: Get the current.

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

get_value(self: simsoptpp.Current) → float: Get the current.

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_dofs(self: simsoptpp.Current, arg0: numpy.ndarray[numpy.float64]) → None: Set the current.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

vjp(v_current)

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.coil.ScaledCurrent(basecurrent, scale)

Bases: simsoptpp.ScaledCurrent, simsopt._core.graph_optimizable.Optimizable

Scales Current by a factor. To be used for example to flip currents for stellarator symmetric coils.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

get_value(self: simsoptpp.ScaledCurrent) → float: Get the current.

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

property scale: Get the scaling factor.

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

vjp(v_current)

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

simsopt.field.coil.coils_via_symmetries(curves, currents, nfp, stellsym): Take a list of n curves and return n * nfp * (1+int(stellsym)) Coil objects obtained by applying rotations and flipping corresponding to nfp fold rotational symmetry and optionally stellarator symmetry.

simsopt.field.magneticfield module

class simsopt.field.magneticfield.MagneticField(**kwargs)

Bases: simsoptpp.MagneticField, simsopt._core.graph_optimizable.Optimizable

Generic class that represents any magnetic field from which each magnetic field class inherits. The usage of MagneticField is as follows:

bfield = BiotSavart(coils, currents) # An instance of a MagneticField
points = ... # points is a (n, 3) numpy array
bfield.set_points(points)
B = bfield.B() # returns the Magnetic field at `points`
dA = bfield.dA_by_dX() # returns the gradient of the potential of the field at `points`

MagneticField has a cache to avoid repeated calculations. To clear this cache manually, call the clear_cached_properties() function. The cache is automatically cleared when set_points is called or one of the dependencies changes.

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfield.MagneticFieldMultiply(scalar, Bfield)

Bases: simsopt.field.magneticfield.MagneticField

Class used to multiply a magnetic field by a scalar. It takes as input a MagneticField class and a scalar and multiplies B, A and their derivatives by that value.

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfield.MagneticFieldSum(Bfields)

Bases: simsopt.field.magneticfield.MagneticField

Class used to sum two or more magnetic field together. It can either be called directly with a list of magnetic fields given as input and outputing another magnetic field with B, A and its derivatives added together or it can be called by summing magnetic fields classes as Bfield1 + Bfield1

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

B_vjp(v)

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

simsopt.field.magneticfieldclasses module

class simsopt.field.magneticfieldclasses.ChebyshevInterpolationRule

Bases: simsoptpp.ChebyshevInterpolationRule

property degree: The degree of the polynomial. The number of interpolation points in degree+1.

class simsopt.field.magneticfieldclasses.CircularCoil(r0=0.1, center=[0, 0, 0], I=159154.94309189534, normal=[0, 0])

Bases: simsopt.field.magneticfield.MagneticField

Magnetic field created by a single circular coil evaluated using analytical functions, including complete elliptic integrals of the first and second kind. As inputs, it takes the radius of the coil (r0), its center, current (I) and its normal vector [either spherical angle components (normal=[theta,phi]) or (x,y,z) components of a vector (normal=[x,y,z])]).

Parameters

r0 – radius of the coil
center – point at the coil center
I – current of the coil in Ampere’s
normal – if list with two values treats it as spherical angles theta and phi of the normal vector to the plane of the coil centered at the coil center, if list with three values treats it a vector

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.Dommaschk(mn=[[0, 0]], coeffs=[[0, 0]])

Bases: simsopt.field.magneticfield.MagneticField

Vacuum magnetic field created by an explicit representation of the magnetic field scalar potential as proposed by W. Dommaschk (1986), Computer Physics Communications 40, 203-218. As inputs, it takes the arrays for the harmonics m, n and its corresponding coefficients.

Parameters

m – first harmonic array
n – second harmonic array
coeffs – coefficient for Vml for each of the ith index of the harmonics m and n

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.InterpolatedField(field, degree, rrange, phirange, zrange, extrapolate=True, nfp=1, stellsym=False)

Bases: simsoptpp.InterpolatedField, simsopt.field.magneticfield.MagneticField

This field takes an existing field and interpolates it on a regular grid in \(r,\phi,z\). This resulting interpolant can then be evaluated very quickly.

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__init__(field, degree, rrange, phirange, zrange, extrapolate=True, nfp=1, stellsym=False)

Parameters

field – the underlying simsopt.field.magneticfield.MagneticField to be interpolated.
degree – the degree of the piecewise polynomial interpolant.
rrange – a 3-tuple of the form (rmin, rmax, nr). This mean that the interval \([rmin, rmax]\) is split into nr many subintervals.
phirange – a 3-tuple of the form (phimin, phimax, nphi).
zrange – a 3-tuple of the form (zmin, zmax, nz).
extrapolate – whether to extrapolate the field when evaluate outside the integration domain or to throw an error.
nfp – Whether to exploit rotational symmetry. In this case any angle is always mapped into the interval \([0, 2\pi/\mathrm{nfp})\), hence it makes sense to use phimin=0 and phimax=2*np.pi/nfp.
stellsym – Whether to exploit stellarator symmetry. In this case z is always mapped to be positive, hence it makes sense to use zmin=0.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

estimate_error_B(self: simsoptpp.InterpolatedField, arg0: int) → Tuple[float, float]

estimate_error_GradAbsB(self: simsoptpp.InterpolatedField, arg0: int) → Tuple[float, float]

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

property phi_range

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

property r_range

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

property rule

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, h=0.1): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

property z_range

class simsopt.field.magneticfieldclasses.PoloidalField(R0, B0, q)

Bases: simsopt.field.magneticfield.MagneticField

Magnetic field purely in the poloidal direction, that is, in the theta direction of a poloidal-toroidal coordinate system. Its modulus is given by B = B0 * r / (R0 * q) so that, together with the toroidal field, it creates a safety factor equals to q

Parameters

B0 – modulus of the magnetic field at R0
R0 – major radius of the magnetic axis
q – safety factor/pitch angle of the magnetic field lines

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.Reiman(iota0=0.15, iota1=0.38, k=[6], epsilonk=[0.01], m0=1)

Bases: simsopt.field.magneticfield.MagneticField

Magnetic field model in section 5 of Reiman and Greenside, Computer Physics Communications 43 (1986) 157—167. This field allows for an analytical expression of the magnetic island width that can be used for island optimization. However, the field is not completely physical as it does not have nested flux surfaces.

Parameters

iota0 – unperturbed rotational transform
iota1 – unperturbed global magnetic shear
k – integer array specifying the Fourier modes used
epsilonk – coefficient of the Fourier modes
m0 – toroidal symmetry parameter (normally m0=1)

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.ScalarPotentialRZMagneticField(PhiStr)

Bases: simsopt.field.magneticfield.MagneticField

Vacuum magnetic field as a solution of B = grad(Phi) where Phi is the magnetic field scalar potential. It takes Phi as an input string, which should contain an expression involving the standard cylindrical coordinates (R, phi, Z) Example: ScalarPotentialRZMagneticField(“2*phi”) yields a magnetic field B = grad(2*phi) = (0,2/R,0). Note: this function needs sympy.

Parameters: PhiStr – string containing vacuum scalar potential expression as a function of R, Z and phi

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.ToroidalField(R0, B0)

Bases: simsopt.field.magneticfield.MagneticField

Magnetic field purely in the toroidal direction, that is, in the phi direction with (R,phi,Z) the standard cylindrical coordinates. Its modulus is given by B = B0*R0/R where R0 is the first input and B0 the second input to the function.

Parameters

B0 – modulus of the magnetic field at R0
R0 – radius of normalization

A(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic potential (in cartesian coordinates). Denoting the indices by i and l, the result contains A_l(x_i).

A_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As A, but returns a reference to the array (this array should be read only).

AbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 1) array containing the absolute value of the magnetic field (in cartesian coordinates).

AbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As AbsB, but returns a reference to the array (this array should be read only).

B(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the magnetic field (in cartesian coordinates). Denoting the indices by i and l, the result contains B_l(x_i).

B_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Return a (npoints, 3) array containing the magnetic field (in cylindrical coordinates) (the order is \((B_r, B_\phi, B_z)\)).

B_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B_cyl, but returns a reference to the array (this array should be read only).

B_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As B, but returns a reference to the array (this array should be read only).

GradAbsB(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3) array containing the gradient of the absolute value of the magnetic field (in cartesian coordinates).

GradAbsB_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]

GradAbsB_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As GradAbsB, but returns a reference to the array (this array should be read only).

__add__(other): Add two magnetic fields.

__eq__(other: simsopt._core.graph_optimizable.Optimizable) → bool

Checks the equality condition

Parameters: other – Another object of subclass of Optimizable

Returns: True only if both are the same objects.

__mul__(other): Multiply a field with a scalar.

__rmul__(other): Multiply a field with a scalar.

_add_child(child: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as child. All the required processing of the dependencies is done in the child node. This method is used mainly to maintain 2-way link between parent and child.

Parameters: child – Direct dependent (child) of the Optimizable object

_get_ancestors() → list[Optimizable]

Get all the ancestors of the current Optimizable object

Returns: List of Optimizable objects that are parents of current Optimizable objects

_remove_child(other: simsopt._core.graph_optimizable.Optimizable) → None

Remove the specific Optimizable object from the children list.

Parameters: child – Direct dependent (child) of the Optimizable object

_update_free_dof_size_indices() → None

Updates the DOFs lengths for the Optimizable object as well as those of the descendent (dependent) Optimizable objects.

Call this function whenever DOFs are fixed or unfixed or when parents are added/deleted. Recursively calls the same function in children

_update_full_dof_size_indices() → None

Updates the full DOFs lengths for this instance and those of the children.

Call this function whenever parents are added or removed. Recursively calls the same function in children.

add_parent(index: int, other: simsopt._core.graph_optimizable.Optimizable) → None

Adds another Optimizable object as parent at specified index.

Parameters

int – Index of the parent’s list
other – Another Optimizable object to be added as parent

add_return_fn(child: simsopt._core.graph_optimizable.Optimizable, fn: Union[str, Callable]) → None

Add return function to the list of the return functions called by the child Optimizable object

Parameters

child – an Optimizable object that is direct dependent of the current Optimizable instance
fn – method of the Optimizable object needed by the child

append_parent(other: simsopt._core.graph_optimizable.Optimizable) → None

Appends another Optimizable object to parents list

Parameters: other – New parent Optimizable object

property bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

clear_cached_properties(): Clear the cache.

d2A_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the hessian of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j A_l(x_i).

d2A_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2A_by_dXdX, but returns a reference to the array (this array should be read only).

d2B_by_dXdX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3, 3) array containing the hessian of magnetic field (in cartesian coordinates). Denoting the indices by i, j, k and l, the result contains partial_kpartial_j B_l(x_i).

d2B_by_dXdX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As d2B_by_dXdX, but returns a reference to the array (this array should be read only).

dA_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of the magnetic potential (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j A_l(x_i).

dA_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dA_by_dX, but returns a reference to the array (this array should be read only).

dB_by_dX(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Returns a (npoints, 3, 3) array containing the gradient of magnetic field (in cartesian coordinates). Denoting the indices by i, j and l, the result contains partial_j B_l(x_i).

dB_by_dX_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As dB_by_dX, but returns a reference to the array (this array should be read only).

property dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with the current Optimizable object and those of its ancestors

property dof_size: numbers.Integral: Total number of free DOFs associated with the Optimizable object as well as parent Optimizable objects.

property dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current and ancestors Optimizable objects are free or not

fix(key: Union[numbers.Integral, str]) → None

Set the fixed attribute for the given degree of freedom.

Parameters: key – DOF identifier

fix_all() → None: Set the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property full_dof_size: numbers.Integral: Total number of all (free and fixed) DOFs associated with the Optimizable object as well as parent Optimizable objects.

property full_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of all the DOFs associated with the current Optimizable object and those of its ancestors

get(key: Union[numbers.Integral, str]) → numbers.Real

Get the value of specified DOF Even fixed dofs can be obtained individually.

Parameters: key – DOF identifier

get_parent_return_fns_list() → List[List[Callable]]

Get a list of the funcs returned by the parents as list of lists

Returns: The funcs returned by all the parents of the Optimizable object

get_points_cart(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cartesian coordinates.

get_points_cart_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cart, but returns a reference to the array (this array should be read only).

get_points_cyl(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: Get the point where the field should be evaluated in cylindrical coordinates (the order is \((r, \phi, z)\)).

get_points_cyl_ref(self: simsoptpp.MagneticField) → numpy.ndarray[numpy.float64]: As get_points_cyl, but returns a reference to the array (this array should be read only).

get_return_fn_list() → List[List[Callable]]

Gets return functions from this Optimizable object used by all the child Optimizable objects

Returns: List of methods that return a value when the current Optimizable object is called from the children.

get_return_fn_names() → List[str]

Return the names of the functions that could be used as objective functions.

Returns: List of function names that could be used as objective functions

get_return_fns(child: simsopt._core.graph_optimizable.Optimizable) → List[Callable]

Gets return functions from this Optimizable object used by the child Optimizable object

Parameters: child – Dependent Optimizable object
Returns: List of methods that return a value when the current Optimizable object is called from the child

invalidate_cache(self: simsoptpp.MagneticField) → None: Clear the cache. Called automatically after each call to set_points[…].

is_fixed(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is fixed

Parameters: key – DOF identifier

is_free(key: Union[numbers.Integral, str]) → bool

Checks if the specified dof is free

Parameters: key – DOF identifier

property local_bounds: Tuple[Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]], Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]]: Lower and upper bounds of the free DOFs associated with this Optimizable object

property local_dof_names: Union[Sequence[str], nptyping.types._ndarray.NDArray[None, nptyping.types._unicode.Unicode]]: Names (Identifiers) of the DOFs associated with this Optimizable object

property local_dof_size: numbers.Integral

Number of free DOFs associated with the Optimizable object.

Returns: Number of free DOFs associated with the Optimizable object.

property local_dofs_free_status: Union[Sequence[bool], nptyping.types._ndarray.NDArray[None, nptyping.types._bool.Bool]]: Boolean array denoting whether the DOFs associated with the current Optimizable object are free or not

property local_full_dof_size: numbers.Integral

Number of all (free and fixed) DOFs associated with the Optimizable object.

Returns: Total number of free and fixed DOFs associated with the Optimizable object.

property local_full_x: Numeric values of all DOFs associated with this Optimizable object

property local_lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with this Optimizable object

property local_upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with this Optimizable object

property local_x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with this Optimizable object

property lower_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Lower bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property parent_return_fns_no: int

Compute the total number of the return funcs of all the parents of the Optimizable object

Returns: The total number of the return funcs of the Optimizable object’s parents.

pop_parent(index: int = - 1) → simsopt._core.graph_optimizable.Optimizable

Removes the parent Optimizable object at specified index.

Parameters: index – Index of the list of the parents
Returns: The removed parent Optimizable object

recompute_bell(parent=None)

Function to be called whenever new DOFs input is given or if the parent Optimizable’s data changed, so the output from the current Optimizable object is invalid.

This method gets called by various DOF setters. If only the local DOFs of an object are being set, the recompute_bell method is called in that object and also in the descendent objects that have a dependency on the object, whose local DOFs are being changed. If gloabl DOFs of an object are being set, the recompute_bell method is called in the object, ancestors of the object, as well as the descendents of the object.

Need to be implemented by classes that provide a dof_setter for external handling of DOFs.

remove_parent(other: simsopt._core.graph_optimizable.Optimizable)

Removes the specified Optimizable object from the list of parents.

Parameters: other – The Optimizable object to be removed from the list of parents

return_fn_map = NotImplemented

set(key: Union[numbers.Integral, str], new_val: numbers.Real) → None

Update the value held the specified DOF. Even fixed dofs can be set this way

Parameters

key – DOF identifier
new_val – New value of the DOF

set_points(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Shorthand for set_points_cart.

set_points_cart(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cartesian coordinates.

set_points_cyl(self: simsoptpp.MagneticField, arg0: numpy.ndarray[numpy.float64]) → simsoptpp.MagneticField: Set the points where to evaluate the magnetic fields, in cylindrical coordinates (the order is \((r, \phi, z)\)).

to_vtk(filename, nr=10, nphi=10, nz=10, rmin=1.0, rmax=2.0, zmin=- 0.5, zmax=0.5): Export the field evaluated on a regular grid for visualisation with e.g. Paraview.

unfix(key: Union[numbers.Integral, str]) → None

Unset the fixed attribute for the given degree of freedom

Parameters: key – DOF identifier

unfix_all() → None: Unset the ‘fixed’ attribute for all degrees of freedom associated with the current Optimizable object.

property upper_bounds: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Upper bounds of the free DOFs associated with the current Optimizable object and those of its ancestors

property x: Union[Sequence[numbers.Real], nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]]]: Numeric values of the free DOFs associated with the current Optimizable object and those of its ancestors

class simsopt.field.magneticfieldclasses.UniformInterpolationRule

Bases: simsoptpp.UniformInterpolationRule

property degree: The degree of the polynomial. The number of interpolation points in degree+1.

simsopt.field.sampling module

simsopt.field.sampling.draw_uniform_on_curve(curve, nsamples, safetyfactor=10)

Uses rejection sampling to sample points on a curve. Warning: assumes that the underlying quadrature points on the Curve are uniformly distributed.

Parameters

curve – The simsopt.geo.curve.Curve to spawn the particles on.
nsamples – number of samples.
safetyfactor – how many more samples than nsamples to generate for rejection/acceptance.

simsopt.field.sampling.draw_uniform_on_surface(surface, nsamples, safetyfactor=10)

Uses rejection sampling to sample points on a surface. Warning: assumes that the underlying quadrature points on the surface are uniformly distributed.

Parameters

surface – The simsopt.geo.surface.Surface to spawn the particles on.
nsamples – number of samples.
safetyfactor – how many more samples than nsamples to generate for rejection/acceptance.

simsopt.field.tracing module

class simsopt.field.tracing.IterationStoppingCriterion

Bases: simsoptpp.IterationStoppingCriterion

Stop the iteration once the maximum number of iterations is reached.

class simsopt.field.tracing.LevelsetStoppingCriterion(classifier)

Bases: simsoptpp.LevelsetStoppingCriterion

Based on a scalar function \(f:R^3\to R\), this criterion checks whether \(f(x, y, z) < 0\) and stops the iteration once this is true.

The idea is to use this for example with signed distance functions to a surface.

simsopt.field.tracing.compute_fieldlines(field, R0, Z0, tmax=200, tol=1e-07, phis=[], stopping_criteria=[], comm=None)

Compute magnetic field lines by solving

\[[\dot x, \dot y, \dot z] = B(x, y, z)\]

Parameters

field – the magnetic field \(B\)
R0 – list of radial components of initial points
Z0 – list of vertical components of initial points
tmax – for how long to trace. will do roughly |B|*tmax/(2*pi*r0) revolutions of the device
tol – tolerance for the adaptive ode solver
phis – list of angles in [0, 2pi] for which intersection with the plane corresponding to that phi should be computed
stopping_criteria – list of stopping criteria, mostly used in combination with the LevelsetStoppingCriterion accessed via simsopt.field.tracing.SurfaceClassifier.

Returns: 2 element tuple containing

res_tys:
A list of numpy arrays (one for each particle) describing the solution over time. The numpy array is of shape (ntimesteps, 4). Each row contains the time and the position, i.e.`[t, x, y, z]`.
res_phi_hits:
A list of numpy arrays (one for each particle) containing information on each time the particle hits one of the phi planes or one of the stopping criteria. Each row of the array contains [time, idx, x, y, z], where idx tells us which of the phis or stopping_criteria was hit. If idx>=0, then phis[int(idx)] was hit. If idx<0, then stopping_criteria[int(-idx)-1] was hit.

simsopt.field.tracing.compute_gc_radius(m, vperp, q, absb): Computes the gyro radius of a particle in a field with strenght absb`, that is r=m*vperp/(abs(q)*absb).

simsopt.field.tracing.gc_to_fullorbit_initial_guesses(field, xyz_inits, speed_pars, speed_total, m, q, eta=0): Takes in guiding center positions xyz_inits as well as a parallel speeds speed_pars and total velocities speed_total to compute orbit positions for a full orbit calculation that matches the given guiding center. The phase angle can be controll via the eta parameter

simsopt.field.tracing.parallel_loop_bounds(comm, n): Split up an array [0, 1, …, n-1] across an mpi communicator. Example: n = 8, comm with size=2 will return (0, 4) on core 0, (4, 8) on core 1, meaning that the array is split up as [0, 1, 2, 3] + [4, 5, 6, 7].

simsopt.field.tracing.particles_to_vtk(res_tys, filename): Export particle tracing or field lines to a vtk file. Expects that the xyz positions can be obtained by xyz[:, 1:4].

simsopt.field.tracing.plot_poincare_data(fieldlines_phi_hits, phis, filename, mark_lost=False, aspect='equal', dpi=300)

Create a poincare plot. Usage:

phis = np.linspace(0, 2*np.pi/nfp, nphis, endpoint=False)
res_tys, res_phi_hits = compute_fieldlines(
    bsh, R0, Z0, tmax=1000, phis=phis, stopping_criteria=[])
plot_poincare_data(res_phi_hits, phis, '/tmp/fieldlines.png')

Requires matplotlib to be installed.

simsopt.field.tracing.trace_particles(field: simsopt.field.magneticfield.MagneticField, xyz_inits: nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]], parallel_speeds: nptyping.types._ndarray.NDArray[None, nptyping.types._number.Float[float, numpy.floating]], tmax=0.0001, mass=6.69509884346e-27, charge=3.204353268e-19, Ekin=5.639661751679999e-13, tol=1e-09, comm=None, phis=[], stopping_criteria=[], mode='gc_vac', forget_exact_path=False, phase_angle=0)

Follow particles in a magnetic field.

In the case of mod='full' we solve

\[[\ddot x, \ddot y, \ddot z] = \frac{q}{m} [\dot x, \dot y, \dot z] \times B\]

in the case of mod='gc_vac' we solve the guiding center equations under the assumption \(\nabla p=0\), that is

\[\begin{split}[\dot x, \dot y, \dot z] &= v_{||}\frac{B}{|B|} + \frac{m}{q|B|^3} (0.5v_\perp^2 + v_{||}^2) B\times \nabla(|B|)\\ \dot v_{||} &= -\mu (B \cdot \nabla(|B|))\end{split}\]

where \(v_\perp = 2\mu|B|\). See equations (12) and (13) of [Guiding Center Motion, H.J. de Blank, https://doi.org/10.13182/FST04-A468].

Parameters

field – The magnetic field \(B\).
xyz_inits – A (nparticles, 3) array with the initial positions of the particles.
parallel_speeds – A (nparticles, ) array containing the speed in direction of the B field for each particle.
tmax – integration time
mass – particle mass in kg, defaults to the mass of an alpha particle
charge – charge in Coulomb, defaults to the charge of an alpha particle
Ekin – kinetic energy in Joule, defaults to 3.52MeV
tol – tolerance for the adaptive ode solver
comm – MPI communicator to parallelize over
phis – list of angles in [0, 2pi] for which intersection with the plane corresponding to that phi should be computed
stopping_criteria – list of stopping criteria, mostly used in combination with the LevelsetStoppingCriterion accessed via simsopt.field.tracing.SurfaceClassifier.
mode – how to trace the particles. options are gc: general guiding center equations, gc_vac: simplified guiding center equations for the case \(\nabla p=0\), full: full orbit calculation (slow!)
forget_exact_path – return only the first and last position of each particle for the res_tys. To be used when only res_phi_hits is of interest or one wants to reduce memory usage.
phase_angle – the phase angle to use in the case of full orbit calculations

Returns: 2 element tuple containing

res_tys:
A list of numpy arrays (one for each particle) describing the solution over time. The numpy array is of shape (ntimesteps, M) with M depending on the mode. Each row contains the time and the state. So for mode=’gc’ and mode=’gc_vac’ the state consists of the xyz position and the parallel speed, hence each row contains [t, x, y, z, v_par]. For mode=’full’, the state consists of position and velocity vector, i.e. each row contains [t, x, y, z, vx, vy, vz].
res_phi_hits:
A list of numpy arrays (one for each particle) containing information on each time the particle hits one of the phi planes or one of the stopping criteria. Each row of the array contains [time] + [idx] + state, where idx tells us which of the phis or stopping_criteria was hit. If idx>=0, then phis[int(idx)] was hit. If idx<0, then stopping_criteria[int(-idx)-1] was hit.

simsopt.field.tracing.trace_particles_starting_on_curve(curve, field, nparticles, tmax=0.0001, mass=6.69509884346e-27, charge=3.204353268e-19, Ekin=5.639661751679999e-13, tol=1e-09, comm=None, seed=1, umin=- 1, umax=1, phis=[], stopping_criteria=[], mode='gc_vac', forget_exact_path=False, phase_angle=0)

Follows particles spawned at random locations on the magnetic axis with random pitch angle. See simsopt.field.tracing.trace_particles for the governing equations.

Parameters

curve – The simsopt.geo.curve.Curve to spawn the particles on. Uses rejection sampling to sample points on the curve. Warning: assumes that the underlying quadrature points on the Curve are uniformly distributed.
field – The magnetic field \(B\).
nparticles – number of particles to follow.
tmax – integration time
mass – particle mass in kg, defaults to the mass of an alpha particle
charge – charge in Coulomb, defaults to the charge of an alpha particle
Ekin – kinetic energy in Joule, defaults to 3.52MeV
tol – tolerance for the adaptive ode solver
comm – MPI communicator to parallelize over
seed – random seed
umin – the parallel speed is defined as v_par = u * speed_total where u is drawn uniformly in [umin, umax]
umax – see umin
phis – list of angles in [0, 2pi] for which intersection with the plane corresponding to that phi should be computed
stopping_criteria – list of stopping criteria, mostly used in combination with the LevelsetStoppingCriterion accessed via simsopt.field.tracing.SurfaceClassifier.
mode – how to trace the particles. options are gc: general guiding center equations, gc_vac: simplified guiding center equations for the case \(\nabla p=0\), full: full orbit calculation (slow!)
forget_exact_path – return only the first and last position of each particle for the res_tys. To be used when only res_phi_hits is of interest or one wants to reduce memory usage.
phase_angle – the phase angle to use in the case of full orbit calculations

Returns: see simsopt.field.tracing.trace_particles

simsopt.field.tracing.trace_particles_starting_on_surface(surface, field, nparticles, tmax=0.0001, mass=6.69509884346e-27, charge=3.204353268e-19, Ekin=5.639661751679999e-13, tol=1e-09, comm=None, seed=1, umin=- 1, umax=1, phis=[], stopping_criteria=[], mode='gc_vac', forget_exact_path=False, phase_angle=0)

Follows particles spawned at random locations on the magnetic axis with random pitch angle. See simsopt.field.tracing.trace_particles for the governing equations.

Parameters

surface – The simsopt.geo.surface.Surface to spawn the particles on. Uses rejection sampling to sample points on the curve. Warning: assumes that the underlying quadrature points on the Curve as uniformly distributed.
field – The magnetic field \(B\).
nparticles – number of particles to follow.
tmax – integration time
mass – particle mass in kg, defaults to the mass of an alpha particle
charge – charge in Coulomb, defaults to the charge of an alpha particle
Ekin – kinetic energy in Joule, defaults to 3.52MeV
tol – tolerance for the adaptive ode solver
comm – MPI communicator to parallelize over
seed – random seed
umin – the parallel speed is defined as v_par = u * speed_total where u is drawn uniformly in [umin, umax].
umax – see umin
phis – list of angles in [0, 2pi] for which intersection with the plane corresponding to that phi should be computed
stopping_criteria – list of stopping criteria, mostly used in combination with the LevelsetStoppingCriterion accessed via simsopt.field.tracing.SurfaceClassifier.
mode – how to trace the particles. options are gc: general guiding center equations, gc_vac: simplified guiding center equations for the case \(\nabla p=0\), full: full orbit calculation (slow!)
forget_exact_path – return only the first and last position of each particle for the res_tys. To be used when only res_phi_hits is of interest or one wants to reduce memory usage.
phase_angle – the phase angle to use in the case of full orbit calculations

Returns: see simsopt.field.tracing.trace_particles

simsopt.field package

Submodules

simsopt.field.biotsavart module

simsopt.field.coil module

simsopt.field.magneticfield module

simsopt.field.magneticfieldclasses module

simsopt.field.sampling module

simsopt.field.tracing module

Module contents