matrix

© 2005,2008,2011,2016 John Abbott, Anna M. Bigatti
GNU Free Documentation License, Version 1.2

CoCoALib Documentation Index

User documentation for the classes matrix, MatrixView and ConstMatrixView

IMPORTANT: in CoCoALib row/column indices start from 0.

CoCoALib offers two distinct concepts for dealing with matrices: one is an explicit implementation of a matrix, the other is a way to "view" another existing object as though it were a matrix (possibly of a special form). An example of a MatrixView is seeing a std::vector<RingElem> as a row matrix (see MatrixView).

There are two categories of matrix view, namely ConstMatrixView and MatrixView. The only difference between them is that the former does not allow you to change the entries while the latter allows you to change them (or at least some of them).

There are also two categories of explicit matrix. A ConstMatrix is a matrix whose entries and dimensions are fixed. In contrast, a (non-const) matrix offers operations for assigning to entries, exchanging rows and columns, and even varying the dimensions -- see the maintainer documentation if you're curious about why these operations are not allowed on a MatrixView.

Here are some guidelines for writing a function or procedure which takes matrices as arguments. If the function/procedure does not change the structure of the matrix, then use ConstMatrixView or MatrixView. If the structure of the matrix parameter may be modified then you must use matrix& as the parameter type.

Examples

Constructors and Pseudo-constructors

The following create a matrix:

The following create a ConstMatrix:

The following create matrix views: for instance, changing an entry in RowMat(v) will also change the vector v, see MatrixView PseudoConstructors for more details.

The following create a matrix and come from MatrixSpecial. See there for more details.

Operations on ConstMatrixView, MatrixView, ConstMatrix, matrix

The following come from MatrixOps, see there for more details.

Operations on MatrixView, matrix

NOTE: You cannot set a matrix entry the obvious way, i.e. M(i,j) = value; You must use SetEntry(M,i,j,value).

Operations on matrix

With sanity checks

Without sanity checks

NOTE: these are not permitted on MatrixView because of various problems which could arise e.g. with aliasing in block matrices (see maintainer documentation). myResize simply truncates rows/columns if they are too long, and any new entries are filled with zeroes. So, if you resize to a smaller matrix, you get just the "top left hand" part of the original.

At the moment assignment of matrices is not allowed. The only way to make a copy of a matrix (view) is by calling a genuine constructor (so far only NewDenseMat comes into this category).

Utility functions

Library contributor documentation

The classes ConstMatrixView , MatrixView, ConstMatrix and matrix are just reference counting smart-pointers to objects of type derived from the abstract base classes ConstMatrixViewBase, MatrixViewBase, ConstMatrixBase and MatrixBase respectively; this is analogous to the way rings are implemented. Consequently every concrete matrix class or matrix view class must be derived from these abstract classes. At the moment, it is better to derive from MatrixViewBase rather than ConstMatrixViewBase because of the way BlockMat is implemented.

The base class ConstMatrixViewBase declares the following pure virtual member fns:

These are the additional virtual functions present in MatrixViewBase:

The class ConstMatrixBase is almost identical to ConstMatrixViewBase; the only real difference is that an instance of a concrete class derived from ConstMatrixBase should be self-contained (i.e. not refer to any external data structure) whereas a ConstMatrixView may refer to an external object (and typically should do so, unless it is derived from ConstMatrixBase).

These are the additional virtual functions present in MatrixBase:

Default definitions:

Maintainer documentation for the matrix classes

I shall assume that you have already read the User Documentation and Library Contributor Documentation.

The implementation underwent a big structural change in April 2008. I believe most of the design is sensible now, but further important changes could still occur. The implementation of the four matrix classes is wholly analogous to that of ring: they are simply reference counting smart-pointer classes (which may have derived classes). If assignment of matrices becomes permitted then some extra complication will be needed -- e.g. MakeUnique, and the pointed object must be able to clone itself.

The only delicate part of the implementation is in myMulByRow and myMulByCol where a buffer is used for the answer so that the fns can be exception clean and not suffer from aliasing problems between the args.

Recall that by convention member functions of the base class do not perform sanity checks on their arguments; though it is wise to include such checks inside CoCoA_ASSERT calls to help during debugging. The sanity check should be conducted in the functions which present a nice user interface.

Q: Why did I create both MatrixView and ConstMatrixView?

A: Because the usual C++ const mechanism doesn't work the way I want it to. Consider a function which takes an argument of type const MatrixView&. One would not expect that function to be able to modify the entries of the matrix view supplied as argument. However, you can create a new non const MatrixView using the default copy ctor, and since MatrixView is a smart pointer the copy refers to the same underlying object. Currently, a MatrixView object does not perform copy on write if the reference count of the underlying object is greater than 1 -- it is not at all clear what copy on write would mean for a matrix view (Should the underlying object be duplicated??? I don't like that idea!).

Q: Why are row, column and resizing operations which are allowed on matrix objects not allowed on MatrixView objects?

A: I disallowed them because there are cases where it is unclear what should happen. For example, suppose M is a square matrix, and someone creates the view MtrM defined to be ConcatHor(M, transpose(M)) then there is non-trivial aliasing between the entries of MtrM. What should happen if you try to multiply the second row of MtrM by 2? What should happen if you try to add a new column to MtrM? In general, resizing MtrM would be problematic. Here's another case: it is not clear how a resize operation should work on a matrix view based on a vector<RingElem>; would the underlying vector be resized too?

I chose to offer member fns for checking indices so that error messages could be uniform in appearance. I chose to have two index checking member fns myCheckRowIndex and myCheckColIndex rather than a single unified fn, as a single fn would have to have the ugly possibility of throwing either of two different exceptions.

I declared (and defined) explicitly the default ctor and dtor of the four base classes, to prohibit/discourage improper use of pointers to these classes.

The default dense definition of MatrixBase::myOutput seems a reasonable starting point -- but see the bugs section below!

Bugs, Shortcomings and other ideas

The use of std::vector<RingElem> should be replaced by ModuleElem which automatically guarantees that all its components are in the same ring.

Should the default dense definitions of the output functions be removed? They could be quite inappropriate for a large sparse matrix.

Should the OpenMath output function send the ring with every value sent (given that the ring is also specified in the header)?

Should the index checking fns myCheckRowIndex and myCheckColIndex really throw? Perhaps there should be an alternative which merely returns a boolean value? When would the boolean version be genuinely beneficial?

Why can you not simply write M(i,j) = NewValue;? It is non-trivial because if M is a sparse matrix then use of M(i,j) in that context will require a structural modification to M if NewValue is non-zero and currently M has no [i,j] element. This natural syntax could be made possible by using a proxy class for M(i,j); in a RHS context it simply produces a ConstRefRingElem for the value of the entry; in a LHS context the appropriate action depends on the implementation of the matrix.

I'm quite unsure about the signatures of several functions. I am not happy about requiring the user to use member functions for self-modifying operations (e.g. swap rows, etc) since elsewhere member functions by convention do not check the validity of their arguments.

Virtual member fn myIsWritable is not really intended for public use, but an arcane C++ rule prevents me from declaring it to be protected. Apparently a protected name in the base class is accessible only through a ptr/ref to the derived class (and not through one to the base class) -- no idea why!

Should assignment of matrices be allowed? Ref counting should make this relatively cheap, but must beware of the consequences for iterators (e.g. if it is possible to have a reference to a row/column of a matrix).

Would it be useful/helpful/interesting to have row-iterators and col-iterators for matrices?

Main changes

2016

2012

2011