A MatrixView offers a means to view one or more
existing objects as though they were a matrix:
MatrixView changes;
MatrixView then the underlying objects change;
MatrixView may become invalid (and using it could lead to the
dreaded undefined behaviour, i.e. probably a crash).
NB Matrix views do not make copies, so be careful with
temporaries! Look at these examples (val is a RingElem):
// OK
const vector<RingElem> v(3, val);
MatrixView MV = RowMat(v); // MV reads/writes in the vector v
// NO this compiles, but the vector disappears after the ";"!!
ConstMatrixView MVGhost = RowMat(vector<RingElem>(3, val));
// OK NewDenseMat makes a copy of the vector before it disappears
matrix M = NewDenseMat(RowMat(vector<RingElem>(3, val)));
NB no entry is writable
ZeroMat(R, r, c) -- constant r-by-c zero matrix over R
IdentityMat(R, n) -- constant n-by-n identity matrix over R
You can view a std::vector<RingElem>, all of whose entries belong to the
same ring, as a matrix in three ways:
ColMat(v) -- view a vector<RingElem> v as a column matrix
RowMat(v) -- view a vector<RingElem> v as a row matrix
DiagMat(v) -- view a vector<RingElem> v as a diagonal matrix
(NB: only the diagonal entries are writable)
MatByRows(r,c, v) -- view a vector<RingElem> v as an rxc matrix
where the entries of v are row 1, then row 2, and so on.
MatByCols(r,c, v) -- view a vector<RingElem> v as an rxc matrix
where the entries of v are col 1, then col 2, and so on.
transpose(M) -- transposed view of the matrix M
submat(M, rows, cols)-- submatrix view into M; the
rows and columns visible in the submatrix
are those specified in the (std::vector<long>) arguments rows
and cols; repeated indices are not allowed.
The following pseudo-constructors assemble several matrices into a bigger one;
the argument matrices must all have the same BaseRing. Be careful about
passing temporaries to these functions: they only make references to the
submatrices A, B etc
ConcatVer(A, B) -- matrix view with the rows of A above those of B
| A |
| B |
ConcatHor(A, B) -- matrix view with the cols of A before those of B
| A | B |
ConcatDiag(A,B) -- block diagonal matrix view
| A | 0 |
| 0 | B |
ConcatAntiDiag(A,B) -- block antidiagonal matrix view
| 0 | A |
| B | 0 |
BlockMat(A, B, C, D) -- block matrix view
| A | B |
| C | D |
NB the boundaries of the four submatrices must be aligned.
Most of the implementations are quite straightforward; the tricky part was getting the design of the abstract classes right (well, I hope it is right now). Below are a few comments on some less obvious aspects of the implementations.
Note: it is a mathematical fact that the determinant of the 0x0 matrix is 1.
ZeroMatImpl and IdentityMatImpl are both derived from
MatrixViewBase rather than ConstMatrixViewBase as one might
naturally expect. The main reason for this is to simplify the
implementation of BlockMat. I wanted to be lazy and
implement ConcatDiag and ConcatAntidiag using BlockMat;
while this may not be the best implementation, it is a natural
approach and should certainly work as one might reasonably expect.
However, the pseudo-ctor BlockMat has just two signatures: if any
one of the submatrices is const then whole result becomes const.
I didn't want to implement sixteen different signatures for
BlockMat, and the easy way out seemed to be to make
ZeroMatImpl and IdentityMatImpl non-const. As a consequence
there are a number of useless member functions in ZeroMatImpl
and IdentityMatImpl. I believe this compromise is reasonable. It
seemed reasonable to allow ZeroMatImpl::myAssignZero to succeed.
There is a small problem with creating a matrix from an empty std::vector
because there is no indication of what the base ring should be. I have
chosen to throw an error if one tries to create a matrix view from an empty
vector (in RowMat, ColMat and DiagMat).
The routines which access the (i,j) entry in a BlockMat are messy.
I could not see an elegant way to make them simpler (or to avoid repeating
similar structure in several places in the code). See Bugs about implementing
BlockMat in terms of ConcatVer and ConcatHor.
There is an appalling amount of code duplication in the implementations. I do not yet see a good way of reducing this. I hope someone will sooner or later find an elegant way to avoid the duplication. Maybe a diagonal abstract class for ZeroMatImpl, IdentityMatImpl, DiagMatImpl, ConstDiagMatImpl?
It is a great nuisance to have to implement two very similar classes: one for the const case, and the other for the non-const case. Is there a better way?
Add ColMat, RowMat and DiagMat for a free module element?
Should submatrix allow repeated row/col indices? It could lead to
some some funny behaviour (e.g. setting one entry may change other
entries), so perhaps it would be better to forbid it? Currently, it
is forbidden.
The pseudo-ctor for submatrix ought to accept begin/end iterators instead
of insisting that the caller put the indices in std::vectors.
Should there be a more general version of BlockMat which allows
non-aligned borders? BlockMat could be eliminated and replaced by
suitable calls to ConcatVer and ConcatHor.
Tensor product of two matrices: we implement it as a DenseMatrix instead of MatrixView because the latter would give no practical advantage and hide the cost of accessing the entries.
2014
FilledMat
2011
IsSymmetric, IsAntiSymmetric, IsDiagonal, operator==
FilledMat
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