iwopy.utils.discretization.RegularDiscretizationGrid

class iwopy.utils.discretization.RegularDiscretizationGrid

Bases: object

A lightweight regular grid in n dimensions, without points storage.

Parameters:

• origin (array-like) – The origin point, len: n_dims

• deltas (array-like) – The step sizes, len: n_dims.

• n_steps (array-like) – The number of steps, len: n_dims. Use INT_INF for infinite.

• interpolation (str) – The interpolation method: None, nearest, linear

• tol (list of float, optional) – The tolerances for grid bounds, default is 0, shape: (n_dims,)

• digits (int) – The grid point precision

origin

The origin point, shape: (n_dims,)

Type:

numpy.ndarray

deltas

The step sizes, shape: (n_dims,)

Type:

numpy.ndarray

n_steps

The number of steps, shape: (n_dims,)

Type:

numpy.ndarray

interpolation

The interpolation method: None, nearest, linear

Type:

str

tol

The tolerances for grid bounds, shape: (n_dims,), or None

Type:

numpy.ndarray

digits

The grid point precision

Type:

int

__init__(origin, deltas, n_steps, interpolation=None, tol=None, digits=12)

Methods

__init__(origin, deltas, n_steps[, ...])
all_gridpoints(pts[, allow_outer])	Checks if all points are on grid.
apply_tol(p)	Get tolerance corrected point
apply_tols(pts)	Get tolerance corrected points
deriv_coeffs(pts, var[, order, orderb])	Calculates the derivative coefficients at points.
deriv_coeffs_gridpoints(inds, var[, order, ...])	Calculates the derivative coefficients at grid points.
find_grid_inds(inds)	Finds indices that are on grid
find_gridpoints(pts[, allow_outer, ret_inds])	Finds points that are on grid.
find_ingrid(pts)	Finds points that are on grid.
get_cell(p)	Get the grid cell that contains a point.
get_cells(pts)	Get the grid cells that contain the given points, one cell per point.
get_corner(p[, allow_outer])	Get the lower-left grid corner of a point.
get_corners(pts[, allow_outer])	Get the lower-left grid corners of points.
gp2i(gp[, allow_outer, error])	Get grid index of a grid point
gpts2inds(gpts[, allow_outer, error])	Get grid indices of grid points.
grad_coeffs(pts, vars[, order, orderb])	Calculates the gradient coefficients at grid points.
grad_coeffs_gridpoints(inds, vars[, order, ...])	Calculates the gradient coefficients at grid points.
i2gp(inds[, error])	Translates grid point indices to grid point.
in_grid(p)	Checks if a point is located within the grid.
inds2gpts(inds)	Translates grid point indices to grid points.
interpolation_coeffs_point(p)	Get the interpolation coefficients for a point.
interpolation_coeffs_points(pts[, ret_pmap])	Get the interpolation coefficients for a set of points.
is_gridi(inds)	Checks if grid indices are valid
is_gridpoint(p[, allow_outer, ret_inds])	Checks if a point is on grid.
print_info([spaces])	Prints basic information

Attributes

INT_INF
n_dims	The number of dimensions
n_points	The number of points in each dimension
p_max	The maximal grid point values
p_min	The minimal grid point values

__init__(origin, deltas, n_steps, interpolation=None, tol=None, digits=12)

all_gridpoints(pts, allow_outer=True)

Checks if all points are on grid.

Parameters:

• pts (numpy.ndarray) – The points space, shape: (n_pts, n_dims)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

Returns:

True if all points on grid

Return type:

bool

apply_tol(p)

Get tolerance corrected point

Parameters:

p (numpy.ndarray) – The point, shape: (n_dims,)

Returns:

q – The corrected point, shape: (n_dims,)

Return type:

numpy.ndarray

apply_tols(pts)

Get tolerance corrected points

Parameters:

pts (numpy.ndarray) – The points, shape: (n_pts, n_dims)

Returns:

q – The corrected points, shape: (n_pts, n_dims)

Return type:

numpy.ndarray

deriv_coeffs(pts, var, order=2, orderb=1)

Calculates the derivative coefficients at points.

Parameters:

• pts (numpy.ndarray) – The evaluation points, shape: (n_pts, n_dims)

• var (int) – The dimension representing the variable wrt which to differentiate

• order (int) – The finite difference order, 1 = forward, -1 = backward, 2 = centre

• orderb (int) – The finite difference order at boundary points

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The gradient coefficients, shape: (n_pts, n_gpts)

deriv_coeffs_gridpoints(inds, var, order=2, orderb=1)

Calculates the derivative coefficients at grid points.

Parameters:

• inds (numpy.ndarray) – The integer grid point indices, shape: (n_inds, n_dims)

• var (int) – The dimension representing the variable wrt which to differentiate

• order (int) – The finite difference order, 1 = forward, -1 = backward, 2 = centre

• orderb (int) – The finite difference order at boundary points

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The gradient coefficients, shape: (n_inds, n_gpts)

find_grid_inds(inds)

Finds indices that are on grid

Parameters:

inds (numpy.ndarray) – The grid point index candidates, shape: (n_inds, n_dims)

Returns:

sel_grid – Subset selection of on-grid indices, shape: (n_inds, n_dims)

Return type:

numpy.ndarray of bool

find_gridpoints(pts, allow_outer=True, ret_inds=False)

Finds points that are on grid.

Parameters:

• pts (numpy.ndarray) – The points, shape: (n_pts, n_dims)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

• ret_inds (bool) – Additionally return indices

Returns:

• sel_grid (numpy.ndarray of bool) – Subset selection of points that are on grid, shape: (n_pts, n_dims)

• inds (numpy.ndarray, optional) – The grid point indices, shape: (n_gpts, n_dims)

find_ingrid(pts)

Finds points that are on grid.

Parameters:

pts (numpy.ndarray) – The points, shape: (n_pts, n_dims)

Returns:

sel_grid – Subset selection of points that are in grid, shape: (n_pts, n_dims)

Return type:

numpy.ndarray of bool

get_cell(p)

Get the grid cell that contains a point.

Parameters:

p (numpy.ndarray) – The point, shape: (n_dims,)

Returns:

cell – The min and max values of each dimension. Shape: (n_dims, 2)

Return type:

numpy.ndarray

get_cells(pts)

Get the grid cells that contain the given points, one cell per point.

Parameters:

pts (numpy.ndarray) – The points, shape: (n_pts, n_dims)

Returns:

cells – The min and max values of each dimension. Shape: (n_pts, n_dims, 2)

Return type:

numpy.ndarray

get_corner(p, allow_outer=True)

Get the lower-left grid corner of a point.

Parameters:

• p (numpy.ndarray) – The point, shape: (n_dims,)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

Returns:

p0 – The lower-left grid corner point, shape: (n_dims,)

Return type:

numpy.ndarray

get_corners(pts, allow_outer=True)

Get the lower-left grid corners of points.

Parameters:

• pts (numpy.ndarray) – The points space, shape: (n_pts, n_dims)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

Returns:

p0 – The lower-left grid corner points, shape: (n_pts, n_dims)

Return type:

numpy.ndarray

gp2i(gp, allow_outer=True, error=True)

Get grid index of a grid point

Parameters:

• gp (numpy.ndarray) – The point, shape: (n_dims,)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

• error (bool) – Flag for throwing error if off-grid, else return None in that case

Returns:

inds – The lower-left grid corner point indices, shape: (n_dims,)

Return type:

numpy.ndarray

gpts2inds(gpts, allow_outer=True, error=True)

Get grid indices of grid points.

Parameters:

• gpts (numpy.ndarray) – The grid points, shape: (n_gpts, n_dims)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

• error (bool) – Flag for throwing error if off-grid, else return None in that case

Returns:

inds – The lower-left grid corner indices, shape: (n_gpts, n_dims)

Return type:

numpy.ndarray

grad_coeffs(pts, vars, order=2, orderb=1)

Calculates the gradient coefficients at grid points.

Parameters:

• pts (numpy.ndarray) – The evaluation points, shape: (n_pts, n_dims)

• vars (list of int, optional) – The dimensions representing the variables wrt which to differentiate, shape: (n_vars,). Default is all dimensions

• order (int list of int) – The finite difference order, 1 = forward, -1 = backward, 2 = centre

• orderb (int list of int) – The finite difference order at boundary points

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The gradient coefficients, shape: (n_pts, n_vars, n_gpts)

grad_coeffs_gridpoints(inds, vars, order=2, orderb=1)

Calculates the gradient coefficients at grid points.

Parameters:

• inds (numpy.ndarray) – The integer grid point indices, shape: (n_inds, n_dims)

• vars (list of int, optional) – The dimensions representing the variables wrt which to differentiate, shape: (n_vars,). Default is all dimensions

• order (int or list of int) – The finite difference order, 1 = forward, -1 = backward, 2 = centre

• orderb (int list of int) – The finite difference order at boundary points

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The gradient coefficients, shape: (n_inds, n_vars, n_gpts)

i2gp(inds, error=True)

Translates grid point indices to grid point.

Parameters:

• inds (int) – The grid point indices, shape: (n_dims,)

• error (bool) – Flag for throwing error if off-grid, else return None in that case

Returns:

gp – The grid point, shape: (n_dims,)

Return type:

numpy.ndarray

in_grid(p)

Checks if a point is located within the grid.

Parameters:

p (numpy.ndarray) – The point, shape: (n_dims,)

Returns:

True if within grid

Return type:

bool

inds2gpts(inds)

Translates grid point indices to grid points.

Parameters:

inds (array-like) – The integer grid point indices, shape: (n_gpts, dims)

Returns:

gpts – The grid points, shape: (n_gpts, n_dims)

Return type:

numpy.ndarray

interpolation_coeffs_point(p)

Get the interpolation coefficients for a point.

Example

>>> g = RegularDiscretizationGrid(...)
>>> p = ...
>>> gpts, c = g.interpolation_coeffs_point(p)
>>> ratg = ... calc results at gpts, shape (n_gpts, x) ...
>>> ires = np.einsum('gx,g->x', ratg, c)

Parameters:

p (numpy.ndarray) – The point, shape: (n_dims,)

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The interpolation coefficients, shape: (n_gpts,)

interpolation_coeffs_points(pts, ret_pmap=False)

Get the interpolation coefficients for a set of points.

Example

>>> g = RegularDiscretizationGrid(...)
>>> pts = ...
>>> gpts, c = g.interpolation_coeffs_points(pts)
>>> ratg = ... calc results at gpts, shape (n_gpts, x) ...
>>> ires = np.einsum('gx,pg->px', ratg, c)

Parameters:

• pts (numpy.ndarray) – The points, shape: (n_pts, n_dims)

• ret_pmap (bool) – Additionally return the map from pts to gpts

Returns:

• gpts (numpy.ndarray) – The grid points relevant for coeffs, shape: (n_gpts, n_dims)

• coeffs (numpy.ndarray) – The interpolation coefficients, shape: (n_pts, n_gpts)

• pmap (numpy.ndarray, optional) – The map from pts to gpts, shape: (n_pts, n_gp)

is_gridi(inds)

Checks if grid indices are valid

Parameters:

inds (int) – The grid point indices, shape: (n_dims,)

Returns:

True if on grid

Return type:

bool

is_gridpoint(p, allow_outer=True, ret_inds=False)

Checks if a point is on grid.

Parameters:

• p (numpy.ndarray) – The point, shape: (n_dims,)

• allow_outer (bool) – Allow outermost point indices, else reduce those to lower-left cell corner

• ret_inds (bool) – Additionally return indices

Returns:

• bool – True if on grid

• inds (numpy.ndarray, optional) – The grid point indices, shape: (n_dims,)

property n_dims

The number of dimensions

Returns:

The number of dimensions

Return type:

int

property n_points

The number of points in each dimension

Returns:

The number of points in each dimension, shape: (n_dims,)

Return type:

numpy.ndarray

property p_max

The maximal grid point values

Returns:

The maximal grid point values, shape: (n_dims,)

Return type:

numpy.ndarray

property p_min

The minimal grid point values

Returns:

The minimal grid point values, shape: (n_dims,)

Return type:

numpy.ndarray

print_info(spaces=0)

Prints basic information

Parameters:

spaces (int) – The prepending spaces