1. tomotok.core package

1.2. Submodules

1.3. tomotok.core.derivative module

Contains functions for derivative matrix computation.

  • new functions (isotropic) derivative_matrix and laplace_matrix
  • compute_aniso_dmats and compute_iso_dmats takes care of obtaining flux dependent or flux independent derivative matrices,
  • prepare_mag_data is an auxiliary function to calculate magnetic flux gradients and
  • px_norm is a simple auxiliary function to calculate norms for coefficients
tomotok.core.derivative.compute_aniso_dmats(grid, magflux, derivative=4, mask=None)

Prepares matrix of finite differences, magnetic configuration dependent or fixed simple differences. First or second derivative can be used

Parameters:

grid : RegularGrid

A reconstruction grid

magflux : numpy.ndarray

values of psi normalized mapped to grid

mask : numpy.ndarray, optional

bool mask

derivative : int in {1,2,3,4}

specifies type of derivative scheme, default is 4
Returns:

tuple of scipy.sparse.csrmatrix pairs

derivative matrix
tomotok.core.derivative.compute_iso_dmats(grid, derivatives=[1, 2], mask=None)

Computes isotropic derivative matrix pairs for given differential schemes.

Parameters:

grid : RegularGrid

mask : np.ndarray, optional

derivatives : list of int/str, optional
Returns:

list of dmat pairs
tomotok.core.derivative.derivative_matrix(grid: tomotok.core.geometry.grids.RegularGrid, direction: str, scheme: str = ‘forward’, mask: numpy.ndarray = None, compensate_edges=False)

Creates a derivative matrix using numerical differences

Parameters:

grid : RegularGrid

direction : str

Determines one of the 8 possible directions that can be used. Specified using the over edge neighbor ‘right’, ‘top’, ‘left’, ‘bottom’ or combination over corner directions like ‘top-left’

scheme : str, optional

Selects numerical scheme to be used. Can be ‘forward’, ‘backward’, ‘central’, ‘second’. The default value is ‘forward’.

mask : numpy.ndarray, optional

A bool mask determining nodes of regular grid to keep, by default None. Rows and columns representing False nodes are removed from derivative matrix. If mask is None, all rows and columns are returned.

compensate_edges : bool, optional

Subtracts from diagonal so that sum of each row is zero, by default False.
Returns:

scipy.sparse.csc_matrix
tomotok.core.derivative.generate_anizo_matrix(grid, atan2, derivative)

Write prepared directions atan2 into the derivative matrix. Main magic of this algorithm. Rewrite arctan into the directions and decompose directions to parallel and oblique direction.

Parameters:

grid : RegularGrid

Object with pixel grid gridinates

atan2 : numpy.ndarray

3D array of arcus tangents of Psi(R,z) evolution

derivative : int

derivative type identificator
Returns:

bper : scipy.sparse

sparse matrix with perpendicular derivatives

bpar : scipy.sparse

sparse matrix with parallel derivatives

bpar_tmp: numpy.array

(optional) dense matrix with parallel derivatives

bper_tmp: numpy.array

(optional) dense matrix with perpendicular derivatives
tomotok.core.derivative.generate_iso_dmat(grid: tomotok.core.geometry.grids.RegularGrid, derivative=4)

Computes isotropic derivative matrix.

Parameters:

grid : RegularGrid

derivative : list of int
Returns:

scipy.sparse.csc_matrix, scipy.sparse.csc_matrix
tomotok.core.derivative.get_index_shift(col_num: int, direction: str, distance: int = 1) → int

Computes the index difference of a node neighbor on a flatten grid.

Parameters:

col_num : int

number of columns in reconstruction grid

direction : str

Determines one of the 8 possible directions that can be used. Specified using the over edge neighbor ‘right’, ‘top’, ‘left’, ‘bottom’ or combination over corner directions like ‘top-left’

distance : int, optional

expressed in number of nodes, by default 1
Returns:

int

relative index of neighbor in flattened grid
tomotok.core.derivative.laplace_matrix(grid: tomotok.core.geometry.grids.RegularGrid, mask=None, compensate_edge=False, diagonals=True)

Creates sparse laplace matrix.

Parameters:

grid : RegularGrid

mask : numpy.ndarray, optional

A bool mask determining nodes of regular grid to keep, by default None. Rows and columns representing False nodes are removed from derivative matrix. If mask is None, all rows and columns are returned.

compensate_edges : bool, optional

Subtracts from diagonal so that sum of each row is zero, by default False.

diagonals : bool, optional

Selects whether to use diagonal neighbors in matrix, by default True.
Returns:

scipy.sparse.csc_matrix
tomotok.core.derivative.prepare_mag_data(flux)

Calculates gradient map of magnetic flux function Psi(R,z) and returns arcus tangens of dPsi_y/-dPsi_x that is a suitable funciton for anizotropic diffusion matrix calculation

Parameters:

flux : numpy.ndarray

array of Psi(R,z) evolution, with axes (z, R, t)

Returns

——

numpy.ndarray

arcus tangens of Psi gradient
tomotok.core.derivative.px_norm(direc)

Computed (normalised?) distance between centers of nodes.

tomotok.core.derivative.reduce_dmats(dmats, idx)

Creates reduced derivative matrices by cutting out rows and columns representing unwanted nodes.

Parameters:

dmats : tuples of scipy.sparse.csr_matrix

tuple containing full derivative matrices

idx : numpy.ndarray of bool

array or mask array to select desired nodes
Returns:

list of scipy.sparse.csr_matrix pairs

derivative matrices with removed rows and columns representing nodes outside the bdr polygon (vacuum vessel)

1.4. tomotok.core.phantoms module

Contains functions that can create emissivity phantoms.

Both isotropic one or based on the shape of flux surfaces.

tomotok.core.phantoms.gauss(x, w=0.1, lim=1, amp=1, cen=0.0)

Creates anisotropic gaussian artificial emissivity by 1D transform of x

\[f = amp \left( \mathrm{e}^{-(x-cen)^2 / w } - \mathrm{e}^{-(lim-cen)^2 / w)} \right)\]

Can be used on np.ndarray. Lim should be greater than cen.

Parameters:

x : float, array, np.ndarray

Contains values to be transformed, usually psi

w : float, optional

width of gaussian profile

lim : float, optional

minimal value of x where transform gives zero if x > lim emissivity is set to zero

amp : float, optional

amplitude of gaussian profile,

cen : float, optional

center of gaussian profile allows hollow profile generation when mapped on psi
Returns:

numpy.ndarray

Transformed values of x with same dimensions
tomotok.core.phantoms.gauss_iso(nx, ny, span=1.2, w=0.1, lim=1, amp=1, cen=0)

Creates isotropic gaussian distribution. See references for iso_psi and gauss

tomotok.core.phantoms.islands(psi, w=0.01, lim=1, amp=1, cen=0.4, num=3, shift=0)

Creates island like phantom from given psi profile. See references for gauss and polar_phase.

tomotok.core.phantoms.iso_psi(nx, ny, span=1.5)

Creates matrix of artificial isotropic psi profile with border values for each axis equal to span.

Parameters:

nx : int

Number of pixels on x axis

ny : int

Number of pixels on y axis

span : float, optional

Value of result on the center of border
Returns:

numpy.ndarray

Matrix with generated profile
tomotok.core.phantoms.polar_phase(x, num=3, shift=0)

Applies sine phase in radial angle direction to given profile x.

Parameters:

x : numpy.ndarray

Profile for application of polar phase.

num : int, optional

number of periods per one rotation

shift : float, optional

initial phase shift
Returns:

numpy.ndarray

Matrix with applied polar phase