Lattice.h

Classes

Lattice -- A templated, abstract base class for array-like objects. (full description)

template <class T> class Lattice : public LatticeBase

Interface

Public Members

virtual ~Lattice()

virtual Lattice<T>* clone() const = 0

T operator() (const IPosition& where) const

virtual T getAt (const IPosition& where) const

virtual void putAt (const T& value, const IPosition& where)

Bool get (COWPtr<Array<T> >& buffer, Bool removeDegenerateAxes=False) const

Bool getSlice (COWPtr<Array<T> >& buffer, const Slicer& section, Bool removeDegenerateAxes=False) const

Bool getSlice (COWPtr<Array<T> >& buffer, const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False) const

Bool getSlice (COWPtr<Array<T> >& buffer, const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False) const

Bool get (Array<T>& buffer, Bool removeDegenerateAxes=False)

Bool getSlice (Array<T>& buffer, const Slicer& section, Bool removeDegenerateAxes=False)

Bool getSlice (Array<T>& buffer, const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False)

Bool getSlice (Array<T>& buffer, const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False)

Array<T> get (Bool removeDegenerateAxes=False) const

Array<T> getSlice (const Slicer& section, Bool removeDegenerateAxes=False) const

Array<T> getSlice (const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False) const

Array<T> getSlice (const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False) const

void putSlice (const Array<T>& sourceBuffer, const IPosition& where, const IPosition& stride)

void putSlice (const Array<T>& sourceBuffer, const IPosition& where)

void put (const Array<T>& sourceBuffer)

virtual void set (const T& value)

virtual void apply (T (*function)(T))

virtual void apply (T (*function)(const T&))

virtual void apply (const Functional<T,T>& function)

void operator+= (const Lattice<T>& other)

void operator-= (const Lattice<T>& other)

void operator*= (const Lattice<T>& other)

void operator/= (const Lattice<T>& other)

virtual void copyData (const Lattice<T>& from)

virtual void copyDataTo (Lattice<T>& to) const

virtual uInt advisedMaxPixels() const

virtual LatticeIterInterface<T>* makeIter (const T& navigator, Bool useRef) const

virtual Bool doGetSlice (Array<T>& buffer, const Slicer& section) = 0

virtual void doPutSlice (const Array<T>& buffer, const IPosition& where, const IPosition& stride) = 0

Protected Members

Lattice()

virtual void handleMath (const Lattice<T>& from, int oper)

virtual void handleMathTo (Lattice<T>& to, int oper) const

Lattice (const Lattice<T>&)

Lattice<T>& operator= (const Lattice<T>&)

See Also

ArrayLattice - a memory based Lattice.

PagedArray - a disk based Lattice.

Description

Review Status

Reviewed By:

Peter Barnes

Date Reviewed:

1999/10/30

Programs:

Demos:

dLattice.cc

Tests:

tArrayLattice.cc

Prerequisite

IPosition
Array
LatticeBase
Abstract Base class Inheritance - try "Advanced C++" by James O. Coplien, Ch. 5.

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 items, on regular orthogonal axes.

Synopsis

This pure abstract base class defines the operations which may be performed on any concrete class derived from it. It has only a few non-pure virtual member functions. The fundamental contribution of this class, therefore, is that it defines the operations derived classes must provide:

how to extract a "slice" (or sub-array, or subsection) from a Lattice.
how to copy a slice in.
how to get and put a single element
how to apply a function to all elements
various shape related functions.

The base class contains several functions not dependent on the template parameter.

Lattices always have a zero origin.

Example

Because Lattice is an abstract base class, an actual instance of this class cannot be constructed. However the interface it defines can be used inside a function. This is always recommended as it allows functions which have Lattices as arguments to work for any derived class.

I will give a few examples here and then refer the reader to the ArrayLattice class (a memory resident Lattice) and the PagedArray class (a disk based Lattice) which contain further examples with concrete classes (rather than an abstract one). All the examples shown below are used in the dLattice.cc demo program.

Example 1:

This example calculates the mean of the Lattice. Because Lattices can be too large to fit into physical memory it is not good enough to simply use getSlice to read all the elements into an Array. Instead the Lattice is accessed in chunks which can fit into memory (the size is determined by the advisedMaxPixels and niceCursorShape functions). The LatticeIterator::cursor() function then returns each of these chunks as an Array and the standard Array based functions are used to calculate the mean on each of these chunks. Functions like this one are the recommended way to access Lattices as the LatticeIterator will correctly setup any required caches.

    Complex latMean(const Lattice<Complex>& lat) {
      const uInt cursorSize = lat.advisedMaxPixels();
      const IPosition cursorShape = lat.niceCursorShape(cursorSize);
      const IPosition latticeShape = lat.shape();
      Complex currentSum = 0.0f;
      uInt nPixels = 0u;
      RO_LatticeIterator<Complex> iter(lat, 
    				   LatticeStepper(latticeShape, cursorShape));
      for (iter.reset(); !iter.atEnd(); iter++){
        currentSum += sum(iter.cursor());
        nPixels += iter.cursor().nelements();
      }
      return currentSum/nPixels;
    }

Example 2:

Sometimes it will be neccesary to access slices of a Lattice in a nearly random way. Often this can be done using the subSection commands in the LatticeStepper class. But it is also possible to use the getSlice and putSlice functions. The following example does a two-dimensional Real to Complex Fourier transform. This example is restricted to four-dimensional Arrays (unlike the previous example) and does not set up any caches (caching is currently only used with PagedArrays). So only use getSlice and putSlice when things cannot be done using LatticeIterators.

    void FFT2DReal2Complex(Lattice<Complex>& result, 
    		       const Lattice<Float>& input){
      AlwaysAssert(input.ndim() == 4, AipsError);
      const IPosition shape = input.shape();
      const uInt nx = shape(0);
      AlwaysAssert (nx > 1, AipsError);
      const uInt ny = shape(1);
      AlwaysAssert (ny > 1, AipsError);
      const uInt npol = shape(2);
      const uInt nchan = shape(3); 
      const IPosition resultShape = result.shape();
      AlwaysAssert(resultShape.nelements() == 4, AipsError);
      AlwaysAssert(resultShape(3) == nchan, AipsError);
      AlwaysAssert(resultShape(2) == npol, AipsError);
      AlwaysAssert(resultShape(1) == ny, AipsError);
      AlwaysAssert(resultShape(0) == nx/2 + 1, AipsError);
    
      const IPosition inputSliceShape(4,nx,ny,1,1);
      const IPosition resultSliceShape(4,nx/2+1,ny,1,1);
      COWPtr<Array<Float> > 
        inputArrPtr(new Array<Float>(inputSliceShape.nonDegenerate()));
      Array<Complex> resultArray(resultSliceShape.nonDegenerate());
      FFTServer<Float, Complex> FFT2D(inputSliceShape.nonDegenerate());
     
      IPosition start(4,0);
      Bool isARef;
      for (uInt c = 0; c < nchan; c++){
        for (uInt p = 0; p < npol; p++){
          isARef = input.getSlice(inputArrPtr,
                                  Slicer(start,inputSliceShape), True);
          FFT2D.fft(resultArray, *inputArrPtr);
          result.putSlice(resultArray, start);
          start(2) += 1;
        }
        start(2) = 0;
        start(3) += 1;
      }
    }

Note that the LatticeFFT class offers a nice way to do lattice based FFTs.

Example 3:

Occasionally you may want to access a few elements of a Lattice without all the difficulty involved in setting up Iterators or calling getSlice and putSlice. This is demonstrated in the example below. Setting a single element can be done with the putAt function, while getting a single element can be done with the parenthesis operator. Using these functions to access many elements of a Lattice is not recommended as this is the slowest access method.

In this example an ideal point spread function will be inserted into an empty Lattice. As with the previous examples all the action occurs inside a function because Lattice is an interface (abstract) class.

    void makePsf(Lattice<Float>& psf) {
      const IPosition centrePos = psf.shape()/2;
      psf.set(0.0f);       // this sets all the elements to zero
                           // As it uses a LatticeIterator it is efficient
      psf.putAt (1, centrePos);  // This sets just the centre element to one
      AlwaysAssert(near(psf(centrePos), 1.0f, 1E-6), AipsError);
      AlwaysAssert(near(psf(centrePos*0), 0.0f, 1E-6), AipsError);
    }

Motivation

Creating an abstract base class which provides a common interface between memory and disk based arrays has a number of advantages.

It allows functions common to all arrays to be written independent of the way the data is stored. This is illustrated in the three examples above.
It reduces the learning curve for new users who only have to become familiar with one interface (ie. Lattice) rather than distinct interfaces for different array types.

To Do

Make PagedArray cache functions virtual in this base class.

Member Description

virtual ~Lattice()

a virtual destructor is needed so that it will use the actual destructor in the derived class

virtual Lattice<T>* clone() const = 0

Make a copy of the derived object (reference semantics).

T operator() (const IPosition& where) const
virtual T getAt (const IPosition& where) const

Return the value of the single element located at the argument IPosition.
The default implementation uses getSlice.

virtual void putAt (const T& value, const IPosition& where)

Put the value of a single element.
The default implementation uses putSlice.

Bool get (COWPtr<Array<T> >& buffer, Bool removeDegenerateAxes=False) const
Bool getSlice (COWPtr<Array<T> >& buffer, const Slicer& section, Bool removeDegenerateAxes=False) const
Bool getSlice (COWPtr<Array<T> >& buffer, const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False) const
Bool getSlice (COWPtr<Array<T> >& buffer, const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False) const
Bool get (Array<T>& buffer, Bool removeDegenerateAxes=False)
Bool getSlice (Array<T>& buffer, const Slicer& section, Bool removeDegenerateAxes=False)
Bool getSlice (Array<T>& buffer, const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False)
Bool getSlice (Array<T>& buffer, const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False)
Array<T> get (Bool removeDegenerateAxes=False) const
Array<T> getSlice (const Slicer& section, Bool removeDegenerateAxes=False) const
Array<T> getSlice (const IPosition& start, const IPosition& shape, Bool removeDegenerateAxes=False) const
Array<T> getSlice (const IPosition& start, const IPosition& shape, const IPosition& stride, Bool removeDegenerateAxes=False) const

Functions which extract an Array of values from a Lattice. All the IPosition arguments must have the same number of axes as the underlying Lattice, otherwise, an exception is thrown.
The parameters are:

buffer: a COWPtr<Array<T>> or an Array<T>. See example 2 above for an example.
start: The starting position (or Bottom Left Corner), within the Lattice, of the data to be extracted.
shape: The shape of the data to be extracted. This is not a position within the Lattice but the actual shape the buffer will have after this function is called. This argument added to the "start" argument should be the "Top Right Corner".
stride: The increment for each axis. A stride of one will return every data element, a stride of two will return every other element. The IPosition elements may be different for each respective axis. Thus, a stride of IPosition(3,1,2,3) says: fill the buffer with every element whose position has a first index between start(0) and start(0)+shape(0), a second index which is every other element between start(1) and (start(1)+shape(1))*2, and a third index of every third element between start(2) and (start(2)+shape(2))*3.
section: Another way of specifying the start, shape and stride
removeDegenerateAxes: a Bool which dictates whether to remove "empty" axis created in buffer. (e.g. extracting an n-dimensional from an (n+1)-dimensional will fill 'buffer' with an array that has a degenerate axis (i.e. one axis will have a length = 1.) Setting removeDegenerateAxes = True will return a buffer with a shape that doesn't reflect these superfluous axes.)

The derived implementations of these functions return 'True' if "buffer" is a reference to Lattice data and 'False' if it is a copy.

void putSlice (const Array<T>& sourceBuffer, const IPosition& where, const IPosition& stride)
void putSlice (const Array<T>& sourceBuffer, const IPosition& where)
void put (const Array<T>& sourceBuffer)

A function which places an Array of values within this instance of the Lattice at the location specified by the IPosition "where", incrementing by "stride". All of the IPosition arguments must be of the same dimensionality as the Lattice. The sourceBuffer array may (and probably will) have less axes than the Lattice. The stride defaults to one if not specified.

virtual void set (const T& value)

Set all elements in the Lattice to the given value.

virtual void apply (T (function)(T))
virtual void apply (T (function)(const T&))
virtual void apply (const Functional<T,T>& function)

Replace every element, x, of the Lattice with the result of f(x). You must pass in the address of the function -- so the function must be declared and defined in the scope of your program. All versions of apply require a function that accepts a single argument of type T (the Lattice template type) and return a result of the same type. The first apply expects a function with an argument passed by value; the second expects the argument to be passed by const reference; the third requires an instance of the class Functional<T,T>. The first form ought to run faster for the built-in types, which may be an issue for large Lattices stored in memory, where disk access is not an issue.

void operator+= (const Lattice<T>& other)
void operator-= (const Lattice<T>& other)
void operator*= (const Lattice<T>& other)
void operator/= (const Lattice<T>& other)

Add, subtract, multiple, or divide by another Lattice. The other Lattice can be a scalar (e.g. the result of LatticeExpr). Possible masks are not taken into account.

virtual void copyData (const Lattice<T>& from)

Copy the data from the given lattice to this one. The default implementation uses function copyDataTo.

virtual void copyDataTo (Lattice<T>& to) const

Copy the data from this lattice to the given lattice. The default implementation only copies data (thus no mask, etc.).

virtual uInt advisedMaxPixels() const

This function returns the advised maximum number of pixels to include in the cursor of an iterator. The default implementation returns a number that is a power of two and includes enough pixels to consume between 4 and 8 MBytes of memory.

virtual LatticeIterInterface<T>* makeIter (const T& navigator, Bool useRef) const

These functions are used by the LatticeIterator class to generate an iterator of the correct type for a specified Lattice. Not recommended for general use.
The default implementation creates a LatticeIterInterface object.

virtual Bool doGetSlice (Array<T>& buffer, const Slicer& section) = 0
virtual void doPutSlice (const Array<T>& buffer, const IPosition& where, const IPosition& stride) = 0

The functions (in the derived classes) doing the actual work. These functions are public, so they can be used internally in the various Lattice classes, which is especially useful for doGetSlice.
However, doGetSlice does not call Slicer::inferShapeFromSource to fill in possible unspecified section values. Therefore one should normally use one of the get(Slice) functions. doGetSlice should be used with care and only when performance is an issue.

Lattice()

Define default constructor to satisfy compiler.

virtual void handleMath (const Lattice<T>& from, int oper)
virtual void handleMathTo (Lattice<T>& to, int oper) const

Handle the Math operators (+=, -=, *=, /=). They work similarly to copyData(To). However, they are not defined for Bool types, thus specialized below.

Lattice (const Lattice<T>&)
Lattice<T>& operator= (const Lattice<T>&)

Copy constructor and assignment can only be used by derived classes.