iwopy.utils.discretization.RegularDiscretizationGrid

class iwopy.utils.discretization.RegularDiscretizationGrid[source]

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)[source]

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)[source]

all_gridpoints(pts, allow_outer=True)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

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)[source]

Prints basic information

Parameters:: spaces (int) – The prepending spaces