### Matrix Division in Eigen vs MATLAB

I am trying to find the equivalent of the opertaor in MATLAB:
 `` `` ``A = B/C``

where here A,B, and C are all square matrices with say ` N-by-N `.

So I have the following C++ code where I tried using Eigen but I am not getting correct results:
 ``1234567891011`` ``````Eigen::Matrix< double, (ny+1), (ny+1)> A; //same initialization for B and C for (int i = 0; i < ny+1; i++){ for (int j = 0; j < ny+1; j++){ C(j + (ny+1)*i) = cos(acos(ygl[j]) *(i)); B(0,j) = -1. * pow(-1,(j))*(pow(j,2));//replace 1st row with expression B((ny),j) = 1. * pow(j,2);//replace last row A(j + (ny+1)*i) = (B(j + (ny+1)*i))/(C(j + (ny+1)*i)); } } std::cout << A << "\n";``````

Is matrix division done just simply by / with Eigen like MATLAB or is there another way? Thanks
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there really is no such thing as matrix division.
matlab lets you do it and understands that you are using it as a convoluted way to write ax=b (rewritten improperly as x = b/a or b\a or whatever it is, my matlab is a few years behind me)

so in eigen you need to either do the underlying math by hand or use a solver depending on what you think division means. If you think a*b = c, then it may involve an inverse or pseudoinverse.
if you want the solution to a system, then you need to use whatever they provide for that.

I guess I can give an example in MATLAB.

This, in C++ is equivalent to ` x = A\b ` in MATLAB:
 ``12`` `````` x = A.colPivHouseholderQr().solve(b); ``````

But, I am looking for something equivalent to ` x = A/b ` in MATLAB. For example in MATLAB:
 ``1234567891011121314`` ``````A = 4 12 6 8 b = 6 12 14 8 >> A/b 1.1333 -0.2000 0.5333 0.2000 ``````

which is different from:
 ``1234`` ``````>> A\b 3.0000 0 -0.5000 1.0000``````

So I am trying to calculate ` x = A/b `, the first example.
I just solved my issue and the it's basically,
 ``12`` ``````X=A\B computes X=inv(A)*B. Y=A/B computes Y=A*inv(B)``````

so then in C++ with Eigen:
 `` `` ``x= A* B.inverse();``
 So I am trying to calculate x = A/b , the first example.

This duplicates the output in your first MATLAB example:
 ``12345678910`` ``````#include #include #include int main() { Eigen::Matrix2f A { { 4.f, 12.f }, { 6.f, 8.f } }; Eigen::Matrix2f B { { 6.f, 12.f }, { 14.f, 8.f } }; std::cout << B.transpose().colPivHouseholderQr().solve(A.transpose()).transpose(); }``````

Could be faster than computing the inverse matrix, but YMMV
Last edited on
@mbozzi
Thanks! This is pretty helpful actually.