Re: [eigen] using views for symmetric matricies

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On 2018-03-08 17:38, Gael Guennebaud wrote:
2 - The line:

m4 = m1.selfadjointView<StrictlyLower>();

is invalid and should give you a compiler error (a static assert seems to
be missing in Eigen) because selfadjointView only accept Lower of Upper
parameters, no Strictly* nor Unit* stuff. If the diagonal of m1 is already
zero, then using Lower is fine.

I'm not sure if there are many applications for that, but having a selfadjointView with a zero diagonal might have some use cases.

What also could have some use cases is to have a skew-symmetric or skew-hermitian view on a matrix (i.e., "the other half" equals -A.transpose() or -A.adjoint())


I hope these two explanations answer your questions.


On Mon, Mar 5, 2018 at 7:39 PM, Smith, Louis <Louis_Smith@xxxxxxxxxxxxxxxxxx


I have a very basic question about views. Thanks in advance for being
understanding, I'm sure this a totally elementary problem that just shows
my lack of understanding, but this is the appropriate forum for getting
help with this library. Right?*

I'm trying to use views the way I perceive that they are being used in the quick
reference <>to,
for example, only compute and store half the entries in a symmetric matrix,
then have later operations view the matrix produced in this way as
symmetric. I'm working with things this way as a substitute for writing
nested for-loops where the inner loop's index is constrained to rolling
over only one of the triangles of the array I am either getting compile
time or runtime errors for all of it, with code that works if the
triangularView and selfadjointView statements I included are removed. The
question is how can I use views to only compute and store half of a
symmetric matrix, while still using the visitors and reductions that are
part of the Matrix class? Following are some examples I tried that do not

I use the following function to get a matrix of pairwise distances:
// takes a nxd data matrix, returns an nxn matrix containing pairwise
// use formula (a - b)^2 = a^2 + b^2 -2a*b.
MatrixXd pairwise_dists(const Ref<const MatrixXd>& data){
const VectorXd data_sq = data.rowwise().squaredNorm();
MatrixXd distances;
distances = data_sq.rowwise().replicate(data.rows())
+ data_sq.transpose().colwise().replicate(data.rows())
- 2.*data*data.transpose();
distances.diagonal().setZero(); // prevents nans from occurring along
distances = distances.cwiseSqrt();
return distances;

I would like to do something like:
// takes a nxd data matrix, returns an nxn matrix containing pairwise
// use formula (a - b)^2 = a^2 + b^2 -2a*b.
MatrixXd pairwise_dists(const Ref<const MatrixXd>& data){
const VectorXd data_sq = data.rowwise().squaredNorm();
MatrixXd distances;
distances.triangularView<StrictlyLower>() = data_sq.rowwise().replicate(
+ data_sq.transpose().colwise().replicate(data.rows())
- 2.*data*data.transpose();
distances = distances.cwiseSqrt();
return distances;

And then when I use this function later, for example in a reduction:
VectorXd rho = (-0.5*pairwise_dists(scdata)).array().exp().rowwise().sum

Would become something like:
VectorXd rho = (-0.5*pairwise_dists(scdata).selfadjointView<StrictlyLower,

Adding the triangular view statement to the function 'pairwise_dists'
compiles but gives a runtime error whenever the function is called by my
code, whereas using the 'selfadjointView' statement I give causes a compile
error. Changing the template parameters to only <StrictlyLower> or changing
both template parameters to <Lower> do not fix the issue.

Even in a toy example I seem to be having issues:
Matrix3f m0, m1, m2, m3, m4;
m2 << 1,2,3,
m3 << 1,0,1,

m0 = m2 + m3;
m1.triangularView<StrictlyLower>() = m2+m3;
cout << m0 << "\nNo triangular view\n";
cout << m1 << "\nS. Lower triangular view\n";
m4 = m1.selfadjointView<StrictlyLower>(); //+ m3;
cout << m4 << "\nself-adjoint lower view\n";

The above code will compile and run, but m4 is not a dense symmetric
matrix like I'd expect it to be. It has uninitialised values on the
diagonal and upper triangle, as though selfadjointView didn't do anything.

If I uncomment the addition operation on the line defining m4, the code no
longer compiles.

I hope this is enough information to germinate a response. Thanks in
advance for taking the time to read it.


*Sorry if this is not true. It really seems like many of the posts to this
mailing list are higher level discussions, comments on use, or bug reports,
so if there's a more correct place to mail basic use questions I'd happily
direct subsequent questions there.

 Dr.-Ing. Christoph Hertzberg

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