traverse_grid - Traverse an N-dimensional grid of points
The traverse_grid module defines three types with accompanying routines to traverse a block of grid points through N-dimensional space. The types have different purposes:
Objects of the type grid_traversing can be used to traverse a grid along all the grid points. These objects use integer coordinates only.
The type grid_coordinates traverses a grid along the same grid points but you can convert the indices to (real) coordinates of the midpoints.
The type grid_sampler is meant to sample the grid points in a quasi-random way. It is useful as an alternative to Monte Carlo, because the selected points are more uniformly distributed. (See the test program for an example.)
The idea is that the N-dimensional space in question is split up into rectangular cells with indices running from 0 up to but not including a maximum value. This maximum can differ per dimension.
Traversing such a grid, for instance a 4 by 3 grid, gives the following ordering of the points;
2| 9 10 11 12
1| 5 6 7 8
0| 1 2 3 4
+---+---+---+---+
0 1 2 3
That is, the grid points are visited in the shown order, with indices (0,0), (1,0), ... (0,1), (0,2), ..., (3,2).
All three types can return the raw indices, but the grid_coordinates and grid_sampler types can also return the actual coordinates (real numbers).
The grid_sampler type samples the grid points using steps of the size of a prime, so that the whole space is effectively covered in a fairly small number of samples.
Each type contains a number of methods:
Initialise a grid_traversing object with uniform dimensions, that is, each index runs from 0 to max_index-1.
The number of dimensions
The maximum index for each dimension (actually the index runs up to that value, but does not reach it)
Initialise a grid_traversing object with different dimensions, that is, index i runs from 0 to max_index(i)-1.
The maximum index per dimension. The number of dimensions is equal to the size of the array.
Initialise a grid_coordinates object with uniform dimensions, that is, each index runs from 0 to max_index-1. The range argument contains the minimum and maximum values of the coordinates. The number of dimensions is equal to the second dimension of range (that is, size(range,2)).
The maximum index for each dimension (actually the index runs up to that value, but does not reach it)
The minimum (range(1,:)) and the maximum (range(2,:)) coordinate per dimension. This is used to determine the midpoint coordinates of a cell.
Initialise a grid_coordinates object with uniform dimensions, that is, index i runs from 0 to max_index(i)-1. The range argument contains the minimum and maximum values of the coordinates. The number of dimensions is equal to the second dimension of range (that is, size(range,2)), but the size of max_index should be equal to that.
The maximum index per dimension
The minimum (range(1,:)) and the maximum (range(2,:)) coordinate per dimension.
Initialise a grid_sampler object, analogous to the initialisation of a grid_coordinates object. Both variants are allowed.
Resets the current point in a grid_traversing, grid_coordinates or grid_sampler object to the point with indices all zero.
Returns the indices of the current point in a grid_traversing, grid_coordinates or grid_sampler object. The receiving variable must be an array of the correct dimension.
Returns the coordinates of the current point in a grid_coordinates or grid_sampler object. The receiving variable must be an array of the correct dimension.
Determine the next point for a grid_traversing, grid_coordinates or grid_sampler object. The argument indices will contain the indices of this new point.
The indices for the new point.
Copyright © 2013 Arjen Markus <arjenmarkus at sourceforge dot net>