\name{ArrayGrid-class}
\docType{class}

\alias{class:ArrayViewport}
\alias{ArrayViewport-class}
\alias{ArrayViewport}

\alias{class:DummyArrayViewport}
\alias{DummyArrayViewport-class}
\alias{DummyArrayViewport}

\alias{class:SafeArrayViewport}
\alias{SafeArrayViewport-class}
\alias{SafeArrayViewport}

\alias{refdim}
\alias{refdim,ArrayViewport-method}
\alias{ranges,DummyArrayViewport-method}
\alias{ranges,SafeArrayViewport-method}
\alias{start,ArrayViewport-method}
\alias{width,ArrayViewport-method}
\alias{end,ArrayViewport-method}
\alias{dim,ArrayViewport-method}

\alias{classNameForDisplay,ArrayViewport-method}
\alias{show,ArrayViewport-method}

\alias{makeNindexFromArrayViewport}

\alias{class:ArrayGrid}
\alias{ArrayGrid-class}
\alias{ArrayGrid}

\alias{class:DummyArrayGrid}
\alias{DummyArrayGrid-class}
\alias{DummyArrayGrid}

\alias{class:ArbitraryArrayGrid}
\alias{ArbitraryArrayGrid-class}
\alias{ArbitraryArrayGrid}

\alias{class:RegularArrayGrid}
\alias{RegularArrayGrid-class}
\alias{RegularArrayGrid}

\alias{refdim,DummyArrayGrid-method}
\alias{refdim,ArbitraryArrayGrid-method}
\alias{refdim,RegularArrayGrid-method}
\alias{dim,DummyArrayGrid-method}
\alias{dim,ArbitraryArrayGrid-method}
\alias{dim,RegularArrayGrid-method}
\alias{as.character.ArrayGrid}
\alias{as.character,ArrayGrid-method}
\alias{dims}
\alias{dims,ArrayGrid-method}
\alias{lengths,ArrayGrid-method}
\alias{lengths,DummyArrayGrid-method}
\alias{maxlength}
\alias{maxlength,ANY-method}
\alias{maxlength,ArbitraryArrayGrid-method}
\alias{maxlength,RegularArrayGrid-method}
\alias{show,ArrayGrid-method}

\alias{aperm.DummyArrayGrid}
\alias{aperm,DummyArrayGrid-method}
\alias{aperm.ArbitraryArrayGrid}
\alias{aperm,ArbitraryArrayGrid-method}
\alias{aperm.RegularArrayGrid}
\alias{aperm,RegularArrayGrid-method}

\alias{downsample}
\alias{downsample,ArbitraryArrayGrid-method}
\alias{downsample,RegularArrayGrid-method}

\title{ArrayGrid and ArrayViewport objects}

\description{
  A \emph{grid} is a partitioning of an array-like object into block-shaped
  regions called \emph{viewports}.

  The \pkg{S4Arrays} package defines two S4 classes to formally represent
  grids and viewports: the ArrayGrid and ArrayViewport classes.
  Note that ArrayGrid and ArrayViewport objects are used extensively in
  the context of block processing of array-like objects.

  There are two variants of ArrayGrid objects:
  \itemize{
    \item RegularArrayGrid objects: for grids where all the blocks have
          the same geometry (except maybe for the edge blocks).
    \item ArbitraryArrayGrid objects: for grids where blocks don't
          necessarily have the same geometry.
  }
}

\usage{
## Constructor functions:
RegularArrayGrid(refdim, spacings=refdim)
ArbitraryArrayGrid(tickmarks)

downsample(x, ratio=1L)
}

\arguments{
  \item{refdim}{
    An integer vector containing the dimensions of the reference array.
  }
  \item{spacings}{
    An integer vector specifying the grid spacing along each dimension.
  }
  \item{tickmarks}{
    A list of integer vectors, one along each dimension of the reference
    array, representing the tickmarks along that dimension. Each integer
    vector must be sorted in ascending order. NAs or negative values are
    not allowed.
  }
  \item{x}{
    An ArrayGrid object.
  }
  \item{ratio}{
    An integer vector specifying the ratio of the downsampling along
    each dimension. Can be of length 1, in which case the same ratio is
    used along all the dimensions.
  }
}

\details{
  RegularArrayGrid and ArbitraryArrayGrid are concrete subclasses of
  ArrayGrid, which itself is a virtual class.

  Note that an ArrayGrid or ArrayViewport object doesn't store any array
  data, only the geometry of the grid or viewport. This makes these objects
  extremely light-weight, even for grids made of millions of blocks.
}

\value{
  For \code{RegularArrayGrid()}, a RegularArrayGrid instance.

  For \code{ArbitraryArrayGrid()}, an ArbitraryArrayGrid instance.

  For \code{downsample()}, an ArrayGrid object on the same reference
  array than \code{x}.
}

\seealso{
  \itemize{
    \item \code{\link{read_block}} to read a block of data from an
          array-like object.

    \item \code{\link[DelayedArray]{blockApply}} and family, in the
          \pkg{DelayedArray} package, for convenient block processing
          of an array-like object.

    \item \code{\link{mapToGrid}} for mapping reference array positions to
          grid positions and vice-versa.

    \item \link[base]{array} and \link[base]{matrix} objects in base R.
  }
}

\examples{
## ---------------------------------------------------------------------
## A. ArrayGrid OBJECTS
## ---------------------------------------------------------------------

## Create a regularly-spaced grid on top of a 3700 x 100 x 33 array:
grid1 <- RegularArrayGrid(c(3700, 100, 33), c(250, 100, 10))

## Dimensions of the reference array:
refdim(grid1)

## Number of grid elements along each dimension of the reference array:
dim(grid1)

## Total number of grid elements:
length(grid1)

## First element in the grid:
grid1[[1L]]             # same as grid1[[1L, 1L, 1L]]

## Last element in the grid:
grid1[[length(grid1)]]  # same as grid1[[15L, 1L, 4L]]

## Dimensions of the grid elements:
dims(grid1)             # one row per grid element

## Lengths of the grid elements:
lengths(grid1)          # same as rowProds(dims(grid1))
stopifnot(sum(lengths(grid1)) == prod(refdim(grid1)))

maxlength(grid1)        # does not need to compute lengths(grid1)) first
                        # so is more efficient than max(lengths(grid1))
stopifnot(maxlength(grid1) == max(lengths(grid1)))

## Create an arbitrary-spaced grid on top of a 15 x 9 matrix:
grid2 <- ArbitraryArrayGrid(list(c(2L, 7:10, 13L, 15L), c(5:6, 6L, 9L)))

refdim(grid2)
dim(grid2)
length(grid2)
grid2[[1L]]             # same as grid2[[1L, 1L]]
grid2[[length(grid2)]]  # same as grid2[[15L, 9L]]

dims(grid2)
lengths(grid2)
array(lengths(grid2), dim(grid2))  # display the grid element lengths in
                                   # an array of same shape as grid2

stopifnot(sum(lengths(grid2)) == prod(refdim(grid2)))

maxlength(grid2)        # does not need to compute lengths(grid2)) first
                        # so is more efficient than max(lengths(grid2))
stopifnot(maxlength(grid2) == max(lengths(grid2)))

## Max (i.e. highest) resolution grid:
Hgrid <- RegularArrayGrid(6:4, c(1, 1, 1))
Hgrid
dim(Hgrid)              # same as refdim(Hgrid)
stopifnot(identical(dim(Hgrid), refdim(Hgrid)))
stopifnot(all(lengths(Hgrid) == 1))

## Min (i.e. lowest) resolution grid:
Lgrid <- RegularArrayGrid(6:4, 6:4)
Lgrid
stopifnot(all(dim(Lgrid) == 1))
stopifnot(identical(dim(Lgrid[[1L]]), refdim(Lgrid)))
stopifnot(identical(dims(Lgrid), matrix(refdim(Lgrid), nrow=1)))

## ---------------------------------------------------------------------
## B. ArrayViewport OBJECTS
## ---------------------------------------------------------------------

## Grid elements are ArrayViewport objects:
grid1[[1L]]
stopifnot(is(grid1[[1L]], "ArrayViewport"))
grid1[[2L]]
grid1[[2L, 1L, 1L]]
grid1[[15L, 1L, 4L]]

## Construction of a standalong ArrayViewport object:
m0 <- matrix(1:30, ncol=5)
block_dim <- c(4, 3)
viewport1 <- ArrayViewport(dim(m0), IRanges(c(3, 2), width=block_dim))
viewport1

dim(viewport1)     # 'block_dim'
length(viewport1)  # number of array elements in the viewport
ranges(viewport1)

## ---------------------------------------------------------------------
## C. GRIDS CAN BE TRANSPOSED
## ---------------------------------------------------------------------

tgrid2 <- t(grid2)
dim(tgrid2)
refdim(tgrid2)

## Use aperm() if the grid has more than 2 dimensions:
tgrid1 <- aperm(grid1)
dim(tgrid1)
refdim(tgrid1)

aperm(grid1, c(3, 1, 2))
aperm(grid1, c(1, 3, 2))
aperm(grid1, c(3, 1))     # some dimensions can be dropped
aperm(grid1, c(3, 2, 3))  # and some can be repeated

## ---------------------------------------------------------------------
## D. DOWNSAMPLING AN ArrayGrid OBJECT
## ---------------------------------------------------------------------
## The elements (ArrayViewport) of an ArrayGrid object can be replaced
## with bigger elements obtained by merging adjacent elements. How many
## adjacent elements to merge along each dimension is specified via the
## 'ratio' vector (one integer per dimension). We call this operation
## "downsampling. It can be seen as reducing the "resolution" of a grid
## by the specified ratio (if we think of the grid elements as pixels).
downsample(grid2, 2)
downsample(grid2, 3)
downsample(grid2, 4)

## Downsampling preserves the dimensions of the reference array:
stopifnot(identical(refdim(downsample(grid2, 2)), refdim(grid2)))
stopifnot(identical(refdim(downsample(grid2, 3)), refdim(grid2)))
stopifnot(identical(refdim(downsample(grid2, 4)), refdim(grid2)))

## A big enough ratio will eventually produce the coarsest possible grid
## i.e. a grid with a single grid element covering the entire reference
## array:
grid3 <- downsample(grid2, 7)
length(grid3)
grid3[[1L]]
stopifnot(identical(dim(grid3[[1L]]), refdim(grid3)))

## Downsampling by a ratio of 1 is a no-op:
stopifnot(identical(downsample(grid2, 1), grid2))

## Using one ratio per dimension:
downsample(grid2, c(2, 1))

## Downsample a max resolution grid:
refdim <- c(45, 16, 20)
grid4 <- RegularArrayGrid(refdim, c(1, 1, 1))
ratio <- c(6, 1, 3)
stopifnot(identical(
    downsample(grid4, ratio),
    RegularArrayGrid(refdim, ratio)
))
}
\keyword{classes}
\keyword{methods}