Hi,

is it in Eigen possible to somehow do arithmetic operations on matrices with different shape as in Numpy (there called broadcasting)?

I would like to do
x-y
with x(3,8) and y(3,1) and would like Eigen to substract y for each row of x. So basicly a rowwise/colwise arithmetic opration.

BTW: Nice library!

Thanks
Roland

Fun coincidence, this is exactly the subject of one of the most recent threads,
question-on-cwiseb ... 47094.html
the answer is to use replicate() that is available in the development version (trunk). No good solution is available in 2.0.

i'm starting to wonder -- perhaps it's worth adding also operators +,-,+=,-= to PartialRedux, allowing m.rowwise()+v ....?

bjacob wrote:i'm starting to wonder -- perhaps it's worth adding also operators +,-,+=,-= to PartialRedux, allowing m.rowwise()+v ....?

yes this is something I wanted to do after implementing Replicate, but 1) I wanted to have some feedbacks on Replicate before using it more seriously, 2) lack of time !

To have numpy-like broadcasting would be fantastic, indeed, as it enables to write operations such as A = A-mean(A) easily. (Btw, isn't mean missing from PartialRedux?)

However, wouldn't it be more logical to add it to .cwise() rather than row/colwise? In an example such as:

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A.cwise() *= w;


from the dimensions of w (1xN or Nx1) it should clear whether the operation is meant row- or columnwise.

In numpy, dimensions of length 1 are implicitly broadcast up to match, i.e., if A is 5x1x6 and B is 5x3x1, A+B is 5x3x6. With this semantics, an outer product (i.e., x*x^T) could be performed simply by writing

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MatrixXf P = u.cwise() * v.transpose();


Well, cwise means coefficient-wise, it wasn't intended as a generic prefix for all array operations, and I think that asking the user to write explicitly rowwise or colwise can actually make the code more explicit.

Dear Benoit,

I see your point. Would with rowwise/colwise an outer product still be possible? Such as:

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A = u.rowwise() * v.transpose().colwise();


why would you need a special product for that ? simply do:

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A = u * v.transpose();


OK, that was a bad example What about an outer sum:

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A = u.rowwise() + v.transpose().colwise();


I don't remember exactly what outer sums are used for, but A has always rank 2 with some special properties.

marton wrote:OK, that was a bad example What about an outer sum:

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A = u.rowwise() + v.transpose().colwise();


I don't remember exactly what outer sums are used for, but A has always rank 2 with some special properties.

With the proposed change (not yet implemented), if A is a matrix and v is a vector, so that v.transpose() is a row-vector, then you could just do

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A = u.rowwise() + v.transpose();


bjacob wrote:

marton wrote:OK, that was a bad example What about an outer sum:

Code: Select all

A = u.rowwise() + v.transpose().colwise();


I don't remember exactly what outer sums are used for, but A has always rank 2 with some special properties.

With the proposed change (not yet implemented), if A is a matrix and v is a vector, so that v.transpose() is a row-vector, then you could just do

Code: Select all

A = u.rowwise() + v.transpose();


This will work only if u is a matrix. If u is a column vector, then you either have to explicitly "replicate" one of the vector, or extend eigen to add a outerSum() function doing the proper calls to replicate.

If we want to handle that example more nicely we would have to add the notion of "automatic size" (via an enum like Dynamic) so that an expression could have no specific size. This would also allows to define size-less constants (Identity, Ones, Zero, etc.). However, this would require deep changes in Eigen, and I don't see any pertinent use cases for that, so it's not worth it.

ggael wrote:

bjacob wrote:

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A = u.rowwise() + v.transpose();


This will work only if u is a matrix. If u is a column vector, then you either have to explicitly "replicate" one of the vector, or extend eigen to add a outerSum() function doing the proper calls to replicate.

Ah right, i had misunderstood what he wanted -- i mixed up u and A.

I mentioned this a month ago, but I think Stata's mata matrix language has a very elegant and consistent set of rules for what they they call colon operators. They are like elementwise operators, but allow other obviously conformable operations. They call it C-conformability. The help files gives lots of nice examples:

http://www.stata.com/help.cgi?m2_op_colon

The basic idea is to do elementwise operations, but match on one dimension of the matrix. So a 1x2 row vector can be added to a 10x2 matrix.

I think it is a good idea to enforce some standards. For instance, not allow 1x3 to be added to a 3x1. It makes sense to force a transpose here. This ensures there is no ambiguity for something like a 2x1 and a 2x2 matrix. 2x1+2x2 should add column wise, whereas 1x2 +2x2 should add row wise.

I understand replicate is another option, but its definitely doesn't seem as elegant.

Thoughts?

I've just added a few rowwise/colwise operators: +, -, +=, and -= so that you can write:

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Vector3f v;
Matrix3f a, b;
a = b.colwise() + v;

ggael wrote:I've just added a few rowwise/colwise operators: +, -, +=, and -= so that you can write:

Code: Select all

Vector3f v;
Matrix3f a, b;
a = b.colwise() + v;

Thank you !!

ggael wrote:I've just added a few rowwise/colwise operators: +, -, +=, and -= so that you can write:

Code: Select all

Vector3f v;
Matrix3f a, b;
a = b.colwise() + v;

Wow, great! What about *, /, *= and /=? Wouldn't they make sense, too? To normalize a list of vectors to unit length, for example...