A MatrixView
offers a means to view one or more
existing objects as though they were a matrix
:
MatrixView
changes;
MatrixView
then the objects change;
MatrixView
may become invalid (and using it could lead to the
dreaded undefined behaviour, i.e. probably a crash).
NB The 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
byc
zero matrix over R
IdentityMat(R, n)
 constant n
byn
identity matrix over R
FilledMat(R, r, c, val)
 constant r
byc
matrix over R
filled with val (a RingElem
, long,
BigInt
, or BigRat
)
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)
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 arguments rows
and cols
(which are of type std::vector
)
The following pseudoconstructors assemble several matrices into a bigger one;
the argument matrices must all have the same BaseRing
.
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
views. 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 pseudoctor 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
nonconst. 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 nonconst 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 pseudoctor 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
nonaligned 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.
2011
IsSymmetric
, IsAntiSymmetric
, IsDiagonal
, operator==
FilledMat
