Powermanifold

[bahu....@gmail.com]

If M = productmanifold(struct( 'X', spherefactory(n), 'Y', euclideanfactory(n, r) )) and
N=powermanifold(M,m), how do we address the 2*m components of N for cost() etc.?

[Nicolas Boumal]

Hello,

Points on a product manifold are structures. Points on a power manifold are cells. Here is an example:

n = 5; r = 3; m = 10;

M = productmanifold(struct( 'X', spherefactory(n), 'Y', euclideanfactory(n, r) ));

N = powermanifold(M,m);

P = N.rand()

% P is a point on N. It is a cell containing m entries. Each entry of this cell is a structure with fields X and Y. For exaple, the X property (unit vector) of the 4th entrty can be accessed via:

P{4}.X

Hope this helps.

Cheers,

Nicolas

[bahu....@gmail.com]

Yes, that helps. Thanks!

[chenzhe...@gmail.com]

Hi Nicolas,

Do you mean that the inputs and outputs of egrad(a) and ehess(a,u) (a is the point in object function, u is the input variable of hessian) are also address in cells?

Best
Zhengyu

[Nicolas Boumal]

Yes, these functions take as input points and vector on the manifold being used (in problem.M). So, if that manifold comes from a call to powermanifold or productmanifold, the points and vectors are represented as cells or structures.

Cheers,

Nicolas