Step a Vector cursor optimally through a tiled Lattice. More...

#include <TiledLineStepper.h>

Inheritance diagram for casa::TiledLineStepper:

Public Member Functions
	TiledLineStepper (const IPosition &latticeShape, const IPosition &tileShape, const uInt axis)
	Construct a TiledLineStepper by specifying the Lattice shape, a tile shape and the axis along which the Vector cursor will lie (0 means the x-axis).
	TiledLineStepper (const TiledLineStepper &other)
	The copy constructor uses copy semantics.
	~TiledLineStepper ()
TiledLineStepper &	operator= (const TiledLineStepper &other)
	The assignment operator uses copy semantics.
virtual Bool	operator++ (int)
	Increment operator (postfix or prefix version) - move the cursor forward one step.
virtual Bool	operator-- (int)
	Decrement operator (postfix or prefix version) - move the cursor backwards one step.
virtual void	reset ()
	Function to move the cursor to the beginning of the Lattice.
virtual Bool	atStart () const
	Function which returns "True" if the cursor is at the beginning of the Lattice, otherwise, returns "False".
virtual Bool	atEnd () const
	Function which returns "True" if an attempt has been made to increment the cursor beyond the end of the Lattice.
virtual uInt	nsteps () const
	Function to return the number of steps (increments & decrements) taken since construction (or since last reset).
virtual IPosition	position () const
	Function which returns the current position of the beginning of the cursor.
virtual IPosition	endPosition () const
	Function which returns the current position of the end of the cursor.
virtual IPosition	latticeShape () const
	Functions which returns the shape of the Lattice being iterated through.
virtual IPosition	subLatticeShape () const
virtual IPosition	cursorShape () const
	Function which returns the shape of the cursor.
virtual IPosition	cursorAxes () const
	Function which returns the axes of the cursor.
IPosition	tileShape () const
	Function which returns the shape of the "tile" the cursor will iterate through before moving onto the next tile.
virtual Bool	hangOver () const
	Function which returns "True" if the increment/decrement operators have moved the cursor position such that part of the cursor beginning or end is hanging over the edge of the Lattice.
virtual void	subSection (const IPosition &blc, const IPosition &trc)
	Functions to specify a "section" of the Lattice to step over.
virtual void	subSection (const IPosition &blc, const IPosition &trc, const IPosition &inc)
virtual IPosition	blc () const
	Return the bottom left hand corner (blc), top right corner (trc) or step size (increment) used by the current sub-Lattice.
virtual IPosition	trc () const
virtual IPosition	increment () const
virtual const IPosition &	axisPath () const
	Return the axis path.
virtual LatticeNavigator *	clone () const
	Function which returns a pointer to dynamic memory of an exact copy of this instance.
virtual Bool	ok () const
	Function which checks the internal data of this class for correct dimensionality and consistant values.
virtual uInt	calcCacheSize (const IPosition &cubeShape, const IPosition &tileShape, uInt maxCacheSize, uInt bucketSize) const
	Calculate the cache size (in tiles) for this type of access to a lattice in the given row of the tiled hypercube.
Private Member Functions
	TiledLineStepper ()
	Prevent the default constructor from being used.
Private Attributes
IPosition	itsBlc
IPosition	itsTrc
IPosition	itsInc
LatticeIndexer	itsSubSection
LatticeIndexer	itsIndexer
LatticeIndexer	itsTiler
IPosition	itsIndexerCursorPos
IPosition	itsTilerCursorPos
IPosition	itsCursorShape
IPosition	itsTileShape
IPosition	itsAxisPath
uInt	itsNsteps
uInt	itsAxis
Bool	itsEnd
Bool	itsStart

Detailed Description

Step a Vector cursor optimally through a tiled Lattice.

Intended use:

Public interface

 <h3>Review Status</h3><dl><dt>Reviewed By:<dd>Peter Barnes<dt>Date Reviewed:<dd>1999/10/30<dt>Test programs:<dd>tTiledLineStepper</dl>

Prerequisite

LatticeNavigator

Etymology

TiledLineStepper is used to step a Vector cursor optimally through a Lattice that is tiled.

Synopsis

When you wish to traverse a Lattice (say, a PagedArray or an Image) you will usually create a LatticeIterator. Once created, you may attach a LatticeNavigator to the iterator. A TiledLineStepper, is a concrete class derived from the abstract LatticeNavigator that allows you to move a Vector cursor through the Lattice in a way that will minimize the amount of cache memory consumed.

Some Lattices (in particular PagedArrays) are stored (on disk) in tiles. For an N-dimensional Lattice a tile is an N-dimensional subsection with fewer elements along each axis. For example a Lattice of shape [512,512,4,32] may have a tile shape of [32,16,4,16], and there will be 16*32*1*2 (=1024) tiles in the entire Lattice. To allow efficient access of the data in a Lattice some tiles are cached in memory. As each tile may consume a fair bit of memory (in this example 128kBytes, assuming each element consumes 4 bytes), it is desirable to minimise the number of tiles held in the cache. But it is also desirable to minimise the number of times a tiles must be read into or written from the cache as this may require a time consuming operation like disk I/O.

Now suppose you wanted to traverse a Lattice with a Vector cursor of length 512 pixel aligned along the x-axis. Using a LatticeStepper , each Vector is retrieved from the Lattice sequentially and without any consideration of the underlying tile shape. What is the optimal cache size for the above example?

Suppose we have a cache size of 16 ie., the number of tiles along the x-axis. Then Vectors beginning at positions [0,0,0,0] to [0,15,0,0] will be stored in the cache. But the next Vector beginning at position [0,16,0,0] will flush the cache and read in another 16 tiles. This I/O takes time and will occur 16 times for each plane in the four dimensional Lattice. Further when the cursor moves to position [0,0,1,0] the 16 tiles that where initially in the cache will need to be read again. To avoid all this cache I/O it is better to have a bigger cache.

Suppose the cache size is 16*32 (=512) ie., enough tiles to contain an (x,y)-plane. Then the cache size will not be flushed until the cursor is moved to position [0,0,0,16]. Further the cache will never need to read back into memory tiles that had previously been stored in there. The cache is big enough to store tiles until they have been completely used. But this cache is 64MBytes in size, and consumes too much memory for many computers.

This where a TiledLineStepper is useful. Because it knows the shape of the tiles in the underlying Lattice it moves the cursor to return all the Vectors in the smallest possible cache of tiles before moving on to the next set of tiles. Using the above example again, the TiledLineStepper will move the beginning of the Vector cursor in the following pattern.

    [0,0,0,0], [0,1,0,0], [0,2,0,0], ... [0,15,0,0]
    [0,0,1,0], [0,1,1,0],            ... [0,15,1,0], 
                                     ... [0,15,3,0],
    [0,0,0,1], ...                       [0,15,3,15]

Moving the Vector cursor through all 16*4*16 (=1024 positions) can be done by caching only 16 tiles in memory (those along the x-axis). Hence the cache size need only be 2MBytes in size. Further once all 1024 vectors have been returned it is not necessary to read these 16 tiles back into memory. All the data in those tiles has already been accessed. Using a TiledLineStepper rather than a LatticeStepper has, in this example, resulted in a drop in the required cache size from 64MBytes down to 2MBytes.

In constructing a TiledLineStepper, you specify the Lattice shape, the tile shape and the axis the Vector cursor will be aligned with. Specifying an axis=0 will align the cursor with the x-axis and axis=2 will produce a cursor that is along the z-axis. The length of the cursor is always the same as the number of elements in the Lattice along the axis the cursor is aligned with.
It is possible to use the function subSection to traverse only a subsection of the lattice.

The cursor position can be incremented or decremented to retrieve the next or previous Vector in the Lattice. The position of the next Vector in the Lattice will depend on the tile shape, and is described above. Within a tile the Vector cursor will move first through the x-axis and then the y-axis (assuming we have a cursor oriented along the z-axis). In general the lower dimensions will be exhausted (within a tile) before moving the cursor through higher dimensions. This intra-tile behaviour for cursor movement extends to the inter-tile movement of the cursor between tiles.

Example

This example is of a global function that will do a 2-D inplace complex Fourier transform of an arbitrary large Lattice (which must have at least two dimensions).

A two dimensional transform is done by successive one dimensional transforms along all the rows and then all the columns in the lattice. Scoping is used to destroy iterators once they have been used. This frees up the cache memory associated with the cursor in each iterator.

    void FFT2DComplex (Lattice<Complex>& cArray,
                      const Bool direction)
    {
      const uInt ndim = cArray.ndim();
      AlwaysAssert(ndim > 1, AipsError);
      const IPosition latticeShape = cArray.shape();
      const uInt nx=latticeShape(0);
      const uInt ny=latticeShape(1);
      const IPosition tileShape = cArray.niceCursorShape();
   
      {
        TiledLineStepper tsx(latticeShape, tileShape, 0);
        LatticeIterator<Complex> lix(cArray, tsx);
        FFTServer<Float,Complex> fftx(IPosition(1, nx));
        for (lix.reset();!lix.atEnd();lix++) {
          fftx.fft(lix.rwVectorCursor(), direction);
        }
      }
      {
        TiledLineStepper tsy(latticeShape, tileShape, 1);
        LatticeIterator<Complex> liy(cArray, tsy);
        FFTServer<Float,Complex> ffty(IPosition(1, ny));
        for (liy.reset();!liy.atEnd();liy++) {
          ffty.fft(liy.rwVectorCursor(), direction);
        }
      }
    }

Motivation

Moving through a Lattice by equal sized chunks, and without regard to the nature of the data, is a basic and common procedure.

To Do

Support for Matrix and higher dimensional cursors can be used.

Definition at line 192 of file TiledLineStepper.h.

Constructor & Destructor Documentation

casa::TiledLineStepper::TiledLineStepper	(	const IPosition &	latticeShape,
		const IPosition &	tileShape,
		const uInt	axis
	)

Construct a TiledLineStepper by specifying the Lattice shape, a tile shape and the axis along which the Vector cursor will lie (0 means the x-axis).

Is is nearly always advisable to make the tileShape identical to the Lattice tileShape. This can be obtained by lat.niceCursorShape(lat.advisedMaxPixels()) where lat is a Lattice object.

casa::TiledLineStepper::TiledLineStepper ( const TiledLineStepper & other )

The copy constructor uses copy semantics.

casa::TiledLineStepper::~TiledLineStepper ( )

casa::TiledLineStepper::TiledLineStepper ( ) [private]

Prevent the default constructor from being used.

Member Function Documentation

virtual Bool casa::TiledLineStepper::atEnd ( ) const [virtual]

Function which returns "True" if an attempt has been made to increment the cursor beyond the end of the Lattice.

virtual uInt casa::TiledLineStepper::calcCacheSize	(	const IPosition &	cubeShape,
		const IPosition &	tileShape,
		uInt	maxCacheSize,
		uInt	bucketSize
	)		const `[virtual]`

virtual void casa::TiledLineStepper::subSection	(	const IPosition &	blc,
		const IPosition &	trc
	)		`[virtual]`

Public Member Functions

Private Member Functions

Private Attributes