ChiPhiEpsFunc API

As introduced in data structure, ChiPhiEpsFunc is a list-like class containing scalars and ChiPhiFunc's. It is the primary data structure pyAQSC stores results in.

ChiPhiEpsFunc manages the power-Fourier series: $$F(\psi, \chi, \phi)\\ =\sum_{n=0}^{n_{max}}\epsilon^nF_n(\chi,\phi) (\epsilon\equiv\sqrt{\psi})\\ =\sum_{n=0}^{n_{max}}\epsilon^n\sum_{m=0|1}^n e^{im} F_{n,m}(\phi) + e^{-im} F_{n,-m}(\phi).$$

ChiPhiEpsFunc supports +, -, * with scalars, ChiPhiFuncs and ChiPhiEpsFuncs.

Class attributes

self.chiphifunc_list : int (list of traced)

The list containing all power coefficients. A power coefficient can be a scalar or a ChiPhiFunc.

self.nfp : int (static)

Required number of field period of the ChiPhiFunc's in self.chiphifunc_list.

self.square_eps_series : bool (static)

Whether the object represents a series containing only even powers of $\epsilon$. One example is: $$B_\alpha(\psi) = \sum_{n=0}^\infty\epsilon^{2n}B_{\alpha n}$$

ChiPhiEpsFunc supports __getitem__ and append, but not __setitem__. ChiPhiEpsFunc[n] Extracts the $n$-th order power coefficient, which may be a scalar or a ChiPhiFunc.

Constructor

aqsc.ChiPhiEpsFunc(self, list:list, nfp:int, check_consistency:bool=False) Parameters:

• chiphifunc_list : list (list of traced) - The list containing all power coefficients. A power coefficient can be a scalar or a ChiPhiFunc.
• nfp : int (static) - Required number of field period of the ChiPhiFunc's in self.chiphifunc_list.
• check_consistency : bool - Runs aqsc.ChiPhiEpsFunc.check_nfp_consistency() if set to True. The method checks for items with inconsistent nfp and replaes them with ChiPhiFunc(nfp=-14).

Functions

aqsc.ChiPhiEpsFunc.__getitem__(self, index)

Implements ChiPhiEpsFunc[n]. Finds the $n$-th order power coefficient. Returns ChiPhiFunc(nfp=0) for negative or out-of-bound index.

Parameters:

• index : int (static) - index of item.

Returns:

• A ChiPhiFunc or a scalar.

aqsc.ChiPhiEpsFunc.append(item)

Returns a new ChiPhiEpsFunc with a new item appended to the end. Checks consistency. Does not modify self. Returns a new ChiPhiEpsFunc.

Parameters:

• item (traced) - Power coefficient to append.

Returns: - A new ChiPhiEpsFunc.

aqsc.ChiPhiEpsFunc.eval(psi, chi=0, phi=0, n_max=float('inf'))

A vectorized function that evaluates the value of the ChiPhiEpsFunc, $f(\psi, \chi, \phi)$, at given psi, chi and phi. The $\phi$ interpolation is performed by jax.numpy.interp. When sq_eps_series is set to True, the series is treated as an even power series, which $\bar\iota$ and $B_\alpha$ are expanded as. $$F(\psi, \chi, \phi) = \sum_{n=0}^{n_{max}}F_n(\chi, \phi)\epsilon^{2n}.$$

Parameters:

• psi, chi, phi : array or scalar (traced) - $\psi$, $\chi$, $\phi$'s to evaluate at.
• n_max=float('inf') (static) - The order to evaluate to. If larger than highest available $n$, evaluates to highest available $n$.

Returns: - An jnp.array evaluation result.

aqsc.ChiPhiEpsFunc.deps(), aqsc.ChiPhiEpsFunc.dchi(), aqsc.ChiPhiEpsFunc.dphi()

Calculates the $\epsilon$, $\chi$ or $\phi$ derivative of a ChiPhiEpsFunc.

Returns: - A new aqsc.ChiPhiEpsFunc.

aqsc.ChiPhiEpsFunc.eval_eps(eps, chi=0, phi=0, n_max=float('inf'))

A vectorized function that evaluates the value of the ChiPhiEpsFunc, $f(\epsilon, \chi, \phi)$, at given psi, chi and phi. The $\phi$ interpolation is performed by jax.numpy.interp. When sq_eps_series is set to True, the series is treated as an even power series, which $\bar\iota$ and $B_\alpha$ are expanded as. $$F(\psi, \chi, \phi) = \sum_{n=0}^{n_{max}}F_n(\chi, \phi)\epsilon^{2n}.$$

Parameters:

• eps, chi, phi : array or scalar (traced) - $\psi$, $\chi$, $\phi$'s to evaluate at.
• n_max=float('inf') (static) - The order to evaluate to. If larger than highest available $n$, evaluates to highest available $n$.

Returns: - An jnp.array evaluation result.

aqsc.ChiPhiEpsFunc.deps(), aqsc.ChiPhiEpsFunc.dchi(), aqsc.ChiPhiEpsFunc.dphi()

Calculates the $\epsilon$, $\chi$ or $\phi$ derivative of a ChiPhiEpsFunc.

Returns: - A new aqsc.ChiPhiEpsFunc.

aqsc.ChiPhiEpsFunc.mask(n)

Produces a ChiPhiEpsFunc from self containing power coefficients up to (and including) order $n$. When $n$ is lower than the highest currently known order, returns a ChiPhiEpsFunc containing a sublist of self.chiphifunc_list. When $n$ is higher than the highest currently known order, fill in the unknown elements with ChiPhiFunc(nfp=0).

Does not modify self. Returns a new ChiPhiEpsFunc.

Parameters:

• n : int (static) - Maximum order to extract.

Returns: - A new ChiPhiEpsFunc.

aqsc.ChiPhiEpsFunc.get_order()

Returns the highest known order $n$ for a ChiPhiEpsFunc. Equivalent to len(self.chiphifunc_list).

Returns:

• n : int - The highest known order $n$.

aqsc.ChiPhiEpsFunc.get_max_order_by_order(n)

Calculating the maximum of the absolute value of the function represented by the Fourier coefficient of each order.

Parameters:

• n_chi, n_phi : int - The grid size for evaluation.

Returns:

• A list of real scalars.

aqsc.ChiPhiEpsFunc.zeros_like(other)

Produces a ChiPhiFunc(nfp=0)-filled ChiPhiEpsFunc with the same $n$ as another ChiPhiEpsFunc.

Returns:

• A ChiPhiEpsFunc.

aqsc.ChiPhiEpsFunc.remove_square(self)

If self represents an even power series, converts self to a typical power series.

Returns:

• A ChiPhiEpsFunc(square_eps_series=False).

aqsc.ChiPhiEpsFunc.__str__(self)

Overrides str(aqsc.ChiPhiEpsFunc). Produces a string summarizing all elements in self.chiphifunc_list.

aqsc.ChiPhiEpsFunc.to_content_list()

Converts a ChiPhiEpsFunc to a list of int's, array's and string's that can be saved and loaded by np.save(). For aqsc.Equilibrium.save(file_name).

aqsc.ChiPhiEpsFunc.from_content_list(content_list, nfp)

Loads a ChiPhiEpsFunc from a list of int's, array's and string's generated by aqsc.ChiPhiEpsFunc.to_content_list(). For aqsc.Equilibrium.load(file_name).