The class "pgrid" (for pixel grid) represents regular quantizations of measures on
(bounded subsets of) \(R^d\). Currently only square quantizations of measures on a rectangles
are supported, which in 2-d can be thought of as grey scale images.
Dominic Schuhmacher dschuhm1@uni-goettingen.de
Objects of class "pgrid" can be created by the function
pgrid, and are most commonly used as input to the function
transport. There are methods plot, print and
summary for this class.
An object of class "pgrid" contains the following elements:
structure | the structure of the grid. Currently only "square" and "rectangular" are supported. |
dimension | the dimension \(d\) of the space in which the grid is embedded. Must be \(\geq 2\). |
n | the number of pixels along the various coordinates, a vector of length dimension. |
N | the total number of pixels. |
boundary | the outer boundary of the "picture" (i.e. of the support of the measure). A vector of |
length 2*dimension, where the odd entries contain the left and the even entries | |
| contain the right endpoints of the various coordinates. | |
gridtriple | the rule for generating the pixel centres along the various coordinates. |
A dim by 3 matrix where each row is of the form c(start, end, step). | |
generators | the pixel centres along the various coordinates. A list of length dim where the |
i-th element is a vector of length n[i]. | |
mass | the array of masses in each pixel / at each pixel centre. In 2-d orientation corresponds |
to the standard orientation of images, see e.g. image. This means that | |
| pixels are arranged on coordinate axes in the order of their indices. |
Constructor function pgrid.