Lattices
[lattices package (liblattices)]

---

Detailed Description

Regular N-dimensional data structures.

See below for an overview of the classes in this module.

Prerequisite

• Programmers of new Lattice classes should understand Inheritance
• Users of the Lattice classes should understand Polymorphism.
• class IPosition
• class Array

Review Status

Reviewed By:

Peter Barnes

Date Reviewed:

1999/10/30

Etymology

Lattice: "A regular, periodic configuration of points, particles, or objects, throughout an area of a space.\.." (American Heritage Directory) This definition matches our own: an N-dimensional arrangement of data on regular orthogonal axes.

In AIPS++, we have used the ability to call many things by one generic name (Lattice) to create a number of classes which have different storage techniques (e.g. core memory, disk, etc.\..). The name Lattice should make the user think of a class interface (or member functions) which all Lattice objects have in common. If functions require a Lattice argument, the classes described here may be used interchangeably, even though their actual internal workings are very different.

Synopsis

The Lattice module may be broken up into a few areas:

1. Lattices - the actual holders of lattice-like data which all share a common interface . The following items are all Lattices and may be used polymorphically wherever a Lattice is called for.
   • The ArrayLattice class adds the interface requirements of a Lattice to an AIPS++ Array . The data inside an ArrayLattice are not stored on disk. This n-dimensional array class is the simplest of the Lattices. Users construct the ArrayLattice with an argument which is either an IPosition which describes the array shape or a previously instantiated Array object that may already contain data. In the former case, some Lattice operation must be done to fill the data. The ArrayLattice, like all Lattices, may be iterated through with a LatticeIterator (see below).
     Iteration can also be done using LatticeApply and some helper classes. It makes it possible to concentrate on the algorithm.

         // Make an Array of shape 3x4x5
         
         Array<Float> simpleArray(IPosition(3,3,4,5));
        
         // fill it with a gradient
        
         for (Int k=0; k<5; k++)
           for (Int j=0; j<4; j++)
             for (Int i=0; i<3; i++) 
               simpleArray(IPosition(3,i,j,k)) = i+j+k;
        
         // use the array to create an ArrayLattice.
        
         ArrayLattice<Float> lattice(simpleArray);
     

   • The PagedArray class stores its data on disk and pages it into random access memory for use. Paging is used here to describe the process of getting pieces of data small enough to fit into active memory even if the whole data set is much too large. This class "feels" like an array but may hold very large amounts of data. The paging has an added effect: all the data may be made persistent, so it stays around after the application ends. When you use PagedArrays - use them because you need persistent data and/or paging into large data sets.
     The persistence is done using a Table , and uses the tiled storage manager . This means that accessing the data along any axis is equally efficient (depending on the tile shape used).
     A PagedArray constructor allows previously created PagedArrays to be recalled from disk. Much of the time, the PagedArray will be constructed with a TiledShape argument which describes the array and tile shape and a Table argument for use as the place of storage. Then the PagedArray may be filled using any of the access functions of Lattices (like the LatticeIterator.)

         // Create a PagedArray from a Table already existing on disk.  
        
         PagedArray<Float> lattice(fileName);
        
         // Create a LatticeIterator to access the Lattice in optimal tile
         // shaped chunks.
        
         LatticeIterator<Float> iter(lattice);
        
         // Iterate through and do something simple; here we just 
         // sum up all the values in the Lattice
        
         Float dSum = 0;
         for(iter.reset(); !iter.atEnd(); iter++) {
           dSum += sum(iter.cursor());
         }
     

2. LatticeIterator - the object which allows iteration through any Lattice's data. This comes in two types: the RO_LatticeIterator which should be used if you are not going to change the Lattice's data, and the LatticeIterator if you need to change the data in the Lattice.
   Note that iteration can also be done using LatticeApply and some helper classes. It makes it possible to concentrate on the algorithm.
   • The RO_LatticeIterator class name reflects its role as a means of iterating a "Read-Only" array (hereafter refered to as a "cursor") through a Lattice based object, from beginning to end. Think of a window into the Lattice that moves to a new location when requested. The Lattice doesn't change but you may see all or part of its data as the cursor "window" moves around. This class allows optimized read-only iteration through any instance of a class derived from Lattice. The cursor's shape is defined by the user and moved through the Lattice in an orderly fashion also defined by the user. Since the cursor is "read-only" it can only be used to "get" the data out of the Lattice. RO_LatticeIterators are constructed with the Lattice to be iterated as the first argument. The optional second constructor argument is either an IPosition which defines the shape of the cursor or a LatticeNavigator argument. The IPosition argument cause the iterator to move the cursor in a simple pattern; the cursor starts at the Lattice's origin and moves in the direction of the x-axis, then the y-axis, then the z-axis, etc.\. If a LatticeNavigator argument is given, more control over the cursor shape and path are available. If no second argument is given, the optimal TileStepper navigator will be used.

         // simple route - define a cursor shape that is the xy plane of our
         lattice.
        
         IPosition cursorShape(2, lattice.shape()(0), lattice.shape()(1));
         LatticeIterator<Float> iter(lattice, cursorShape);
         for (iter.reset(); !iter.atEnd(); iter++) {
           minMax(iter.cursor(), min, max);
         }
     

   • The LatticeIterator class name reflects its role as a means of iterating a read and write cursor through a Lattice based object. Not only does the cursor allow you to inspect the Lattice data but you may also change the Lattice via operations on the cursor. This class provides optimized read and write iteration through any class derived from Lattice. The technique is identical to the RO_LatticeIterator. But the cursor, in this case, is a reference back to the data in the Lattice. This means that changes made to the cursor propagate back to the Lattice. This is especially useful for the PagedArray and PagedImage classes. These two classes are constructed empty and need iteration to fill in the Lattice data.

         // make an empty PagedArray and fill it.   The Table that stores the 
         // PagedArray is deleted when the PagedArray goes out of scope
        
         PagedArray<Float> lattice(IPosition(4,100,200,300,50));
         LatticeIterator<Float> iter(lattice, IPosition(2, 100, 200));
        
         // fill each plane with the "distance" of the iterator from the origin
        
         for(iter.reset();!iter.atEnd(); iter++) {
            iter.woCursor() = iter.nsteps();
         }
     

3. LatticeNavigators - the objects which define the method and path used by a LatticeIterator to move the cursor through a Lattice. Many different paths are possible. We leave it you to choose the LatticeNavigator (method and path) when using a LatticeIterator.
   • The LatticeStepper class is used to define the steps which the cursor takes during its path through the Lattice. Every element of the Lattice will be covered, starting at the origin and ending at the "top right corner." This class provides the information needed by a LatticeIterator to do non-standard movements of the cursor during iteration. The shape of the cursor is specified by the second IPosition argument of the LatticeStepper. The order of the axis is important. An IPosition(1,5) is a five element vector along the x-axis. An IPosition(3,1,1,5) is a five element vector along the z-axis. The degenerate axes (axes with lengths of one) act as place holders. The third argument in the LatticeStepper constructor is the "orientation" IPosition. This describes the order of the axis for the cursor to follow. Again, we treat the elements, in order, of the IPosition as the designators of the appropriate axis. The zeroth element indicates which axis is the fastest moving, the first element indicates which axis is the second fastest moving etc. eg. The IPosition(3,2,0,1) says the LatticeIterator should start with the z-axis, next follow the x-axis, and finish with the y-axis. A single element cursor would thus move through a cube of dimension(x,y,z) from (0,0,0) up the z-axis until reaching the maximum (0,0,z-1) and then start on (1,0,0) and move to (1,0,z-1), etc.

         // The shape of our Lattice - a 4 dimensional image of shape (x,y,z,t) -
         // and the shape of the cursor
        
         IPosition latticeShape(image.shape());
         IPosition cursorShape(3, lattticeShape(0), 1, latticeShape(2));
        
         // Define the path the cursor should follow, we list x and z first, even though
         // no iterations will be done along those axes since the cursor is an 
         // integral subshape of the Lattice. The cursor will move along the y-axis
         // and then increment the t-axis.  The construct the Navigator and Iterator
        
         IPosition order(4,0,2,1,3);
         LatticeStepper nav(latticeShape, cursorShape, order);
         LatticeIterator<Float> iter(image, nav);
     

   • The TiledLineStepper class allows you to iterate through a Lattice with a Vector cursor. However, it steps through the Lattice in an order which is optimum with regard to the I/O of the tiles with which the Lattice is constructed.

         // Set up a TiledLineStepper to return profiles along the specified
         // axis from a PagedArray (not all Lattices have the tileShape member
         // function).  Then create the iterator as well.
         
         TiledLineStepper nav(lattice.shape(), lattice.tileShape(), axis);
         LatticeIterator<Complex> nav(lattice, nav);
     

   • The TileStepper class allows you to iterate through a Lattice in the optimum way. It steps through the lattice tile by tile minimizing I/O and memory usage. It is very well suited for pixel based operations. However, its iteration order is such that it cannot be used for a certain subset of pixels (e.g. a vector) is needed.
     This navigator is the default when no navigator is given when constructing a (RO_)LatticeIterator.

4. MaskedLattice - a Lattice with a mask. It is an abstract base class for various types of MaskedLattices. A MaskedLattice does not need to contain a mask (see e.g. SubLattice below), although the user can always ask for the mask. The function isMasked() tells if there is really a mask. If not, users could take advantage by shortcutting some code for better performance. I.e. a function can test if a the MaskedLattice is really masked and can take a special route if not. Of course, doing that requires more coding, so it should only be done where performance is a real issue.
   • A SubLattice represents a rectangular subset of a Lattice. The SubLattice can be a simple box, but it can also be a circle, polygon, etc. In the latter case the SubLattice contains a mask telling which pixels in the bounding box actually belong to the circle or polygon. In the case of a box there is no mask, because there is no need to (because a box is already rectangular).
     A SubLattice can be constructed from any Lattice and a LatticeRegion telling which part to take from the Lattice. If the SubLattice is constructed from a const Lattice, the SubLattice is not writable. Otherwise it is writable if the lattice is writable.

     There is a rich variety of region classes which can be used to define a LatticeRegion in pixel coordinates. The elementary ones are box , ellipsoid , polygon , pixelset , and good/bad mask . Compound region classes can be used to make a union , intersection , difference , concatenation , complement , or extension from one or more regions.
     Apart from these region classes, class LCSlicer can be used to define a box with optional strides. It also offers the opportunity to define the box in fractions or to define it relative to the center of the lattice or relative to a reference pixel.
     The final, and most general way, to define regions is by means of the world coordinates region classes in the Images module, in particular the WCRegion class. However, world coordinate regions can only be used with images.

   • A LatticeExpr represents a mathematical expression of lattices. All standard operators, regions, and many, many functions can be used in an expression.
     An expression is calculated on-the-fly. Thus only when the user gets a part of the lattice, is the expression calculated for that part. Subexpressions resulting in a scalar are calculated only once, on a get of the first part of the lattice expression.
     Note that a lattice expression is not writable, thus using the put function on such a lattice results in an exception.
     Note 223 gives a more detailed explanation of the capabilities of LEL (Lattice Expression Language).

     When the expression consists of images, the result can also be treated as an image using class ImageExpr . With the command function in ImageExprParse it is possible to parse and execute a LEL expression given as as a string.

5. LatticeLocker can be used to acquire a (user) lock on a lattice. The lock can be a read or write lock. The destructor releases the lock when needed.
   Lattices on disk can be used (read and write) by multiple processes. The Table locking/synchronization mechanism takes care that sharing such a lattice is done in an orderly way. Usually the default locking mechanism is sufficient. LatticeLocker is useful when finer locking control is needed for a disk-based lattice.

   Warning: The following are listed for low-level programmers. Lattice users need not understand them. The Lattice directory contains several files relevant only to implementation.

   • LatticeBase - a non-templated abstract base class defining the type-independent interface to classes which must act as Lattices do.
   • Lattice - a templated abstract base class (derived from LatticeBase) defining the interface to classes which must act as Lattices do. The user simply publicly inherits from Lattice and defines the member functions declared as pure abstract in the Lattice header file.
   • The LatticeNavigator class name defines the interface used for navigating through a Lattice by iteration. This class is an abstract base. Classes derived from this (currently LatticeStepper , TiledLineStepper , and TileStepper ) must define the path the iterator cursor follows, the size of the movement of the cursor with each iteration, and the behaviour of that cursor shape as it moves through a Lattice.
   • LatticeIndexer - this class contains the currently defined Lattice and sub-Lattice shape. It is used only by navigator classes as it contains member functions for moving a cursor through a defined sub-Lattice.
   • The LatticeIterInterface class defines the interface for a specific Lattice's iterator. This class is a base class with a default iterator implementation. Lattice based classes may need to derive an iterator from LatticeIterInterface to optimize for the LatticeIterator internals which impact upon the new Lattice.
   • PagedArrIter - this class is the PagedArray's optimized method of iterating. This class is a "letter" utilized within the LatticeIterator "envelope" and cannot be instantiated by any user.
   • LCRegion - this class is the (abstract) base class for regions in pixel coordinates.

Motivation

Lattices allow the various holders of data to assume a general method of treatment; by making interfaces in terms of the Lattice class, the programmer can polymorphically operate on objects derived from the Lattice class.

To Do

• Make Lattice expressions mask aware.
• Set cache size correctly in expressions and sublattices.
• Make MaskedIterator class?

Modules
	Lattices_internal_classes
	Internal Lattices classes and functions.
Classes
class	casa::ArrayLattice< T >
	A memory resident Lattice. More...
class	casa::CLIPNearest2D< T >
	Arbitrarily shaped 1-dim lattice crosscut. More...
class	casa::ExtendLattice< T >
	An extension of a Lattice or MaskedLattice. More...
class	casa::FITSMask
	Provides an on-the-fly mask for FITS images. More...
class	casa::Lattice< T >
	A templated, abstract base class for array-like objects. More...
class	casa::LatticeAddNoise
	Add noise from specified distribution to a lattice. More...
class	casa::LatticeApply< T, U >
	Optimally iterate through a Lattice and apply provided function object. More...
class	casa::LatticeBase
	A non-templated, abstract base class for array-like objects. More...
class	casa::LatticeCache< T >
	a class for caching image access via tiles More...
class	casa::CleanEnums
	Lists the different types of Convolutions that can be done. More...
class	casa::LatticeCleaner< T >
	A class for doing multi-dimensional cleaning. More...
class	casa::LatticeCleanProgress
	Abstract base class to monitor progress in lattice operations. More...
class	casa::LatticeConcat< T >
	Concatenates lattices along a specified axis. More...
class	casa::ConvEnums
	Lists the different types of Convolutions that can be done. More...
class	casa::LatticeConvolver< T >
	A class for doing multi-dimensional convolution. More...
class	casa::LatticeExpr< T >
	Class to allow C++ expressions involving lattices. More...
class	casa::LatticeExprNode
	Bridging class to allow C++ expressions involving lattices. More...
class	casa::LatticeFFT
	Functions for Fourier transforming Lattices. More...
class	casa::LatticeHistograms< T >
	Displays histograms of regions from a lattice. More...
class	casa::HistTiledCollapser< T >
	Generate histograms, tile by tile, from a masked lattice. More...
class	casa::LatticeHistSpecialize
	Specialized functions for LatticeHistograms. More...
class	casa::RO_LatticeIterator< T >
	A readonly iterator for Lattices. More...
class	casa::LatticeIterator< T >
	A read/write lattice iterator. More...
class	casa::LatticeLocker
	Class to hold a (user) lock on a lattice. More...
class	casa::LatticeProgress
	Abstract base class to monitor progress in lattice operations. More...
class	casa::LatticeSlice1D< T >
	Extract a 1-D slice from a Lattice. More...
class	casa::LatticeStatistics< T >
	Compute and display various statistics from a lattice. More...
class	casa::StatsTiledCollapser< T, U >
	Generate statistics, tile by tile, from a masked lattice. More...
class	casa::LatticeStatsBase
	Base class for LatticeStatistics class. More...
class	casa::LatticeStepper
	Traverse a Lattice by cursor shape. More...
class	casa::LatticeTwoPtCorr< T >
	Compute two point auto-correlation functions from a lattice. More...
class	casa::LatticeUtilities
	Static functions for Lattices. More...
struct	casa::LatticeUtilities_global_functions_LatticeUtilities
	Global functions on Lattices. More...
class	casa::LattRegionHolder
	Class to hold a region of interest in an image. More...
class	casa::LattStatsSpecialize
class	casa::LCBox
	Class to define a rectangular box of interest. More...
class	casa::LCComplement
	Make the complement of a region. More...
class	casa::LCConcatenation
	Combine multiple LCRegion's into a new dimension. More...
class	casa::LCDifference
	Make the difference of 2 regions. More...
class	casa::LCEllipsoid
	Define an N-dimensional ellipsoidal region of interest. More...
class	casa::LCExtension
	Extend an LCRegion along straight lines to other dimensions. More...
class	casa::LCIntersection
	Make the intersection of 2 or more regions. More...
class	casa::LCLELMask
	Class to define a mask as a LEL expression. More...
class	casa::LCMask
	Class to define a rectangular mask as a temporary region. More...
class	casa::LCPagedMask
	Class to define a rectangular mask as a region. More...
class	casa::LCPixelSet
	Class to define a rectangular mask as a region. More...
class	casa::LCPolygon
	Define a 2-dimensional region by a polygon. More...
class	casa::LCRegion
	Abstract base class to define a region of interest in lattice coordinates. More...
class	casa::LCRegionFixed
	Abstract base class to define a fixed region. More...
class	casa::LCRegionMulti
	Make the intersection of 2 or more regions. More...
class	casa::LCRegionSingle
	Abstract base class to define a single region. More...
class	casa::LCSlicer
	Class to define a rectangular box of interest with strides. More...
class	casa::LCStretch
	Stretch length 1 axes in an LCRegion along straight lines. More...
class	casa::LCUnion
	Make the union of 2 or more regions. More...
class	casa::LELCoordinates
	Envelope class to handle Lattice Coordinates in LEL. More...
class	casa::LineCollapser< T, U >
	Abstract base class for LatticeApply function signatures. More...
class	casa::MaskedLattice< T >
	A templated, abstract base class for array-like objects with masks. More...
class	casa::RO_MaskedLatticeIterator< T >
	A readonly iterator for masked Lattices. More...
class	casa::PagedArray< T >
	A Lattice that is read from or written to disk. More...
class	casa::PixelCurve1D
	Arbitrary 1-dim curve in a lattice plane. More...
class	casa::RegionType
	Define the various region types. More...
class	casa::SubLattice< T >
	A subset of a Lattice or MaskedLattice. More...
class	casa::TempLattice< T >
	A Lattice that can be used for temporary storage. More...
class	casa::TiledCollapser< T, U >
	Abstract base class to collapse chunks for LatticeApply. More...
class	casa::TiledLineStepper
	Step a Vector cursor optimally through a tiled Lattice. More...
class	casa::TiledShape
	Define the shape and tile shape. More...
class	casa::TileStepper
	traverse a tiled Lattice optimally with a tile cursor More...

---