In my last question, Ilmari Karonen suggested that I solve the Laplace equation in discrete mode. I use the grid and four nearest neighbors at each node to calculate the unknown height.

So the system that requires a solution can be written as a matrix:

A(matrix nxn) * U(vector n, unknown) = b(vector n, settled).

Last night I browsed online about C++ linear algebra. My choice is Armadillo

std::map<std::pair<float,float>,float> b;
std::map<std::pair<float,float>,float> U;
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if(g/*grid*/->getNode(r,c)->status == TO_COMPUTE){
          U.insert(std::make_pair(std::make_pair(r,c),g->getNode(r,c)->y));
          /*right*/ if(g->getNode(r+1,c)->status == SETTLED) b.at(std::make_pair(r,c)) += g >getNode(r+1,c)->y;
          /*left */ if(g->getNode(r-1,c)->status == SETTLED) b.at(std::make_pair(r,c)) += g->getNode(r-1,c)->y;
          /*down */ if(g->getNode(r,c+1)->status == SETTLED) b.at(std::make_pair(r,c)) += g->getNode(r,c+1)->y;
          /*up   */ if(g->getNode(r,c-1)->status == SETTLED) b.at(std::make_pair(r,c)) += g->getNode(r,c-1)->y;
        }

Then I guess I have to get the size of “U” to create arma::vec and use std::iterator to parse the entire map to transfer the value in my arma::vec. So I’m wondering how to grow arma::vec I’m looking for something like std::vector::p ush_back() and then I’ll replace my std::map. Also, How do I get the size of arma::vec?

Note 1: The picture shows the outline and the point where I will calculate the value, the grid of unknown values is at y=0, the current outline is at y=-0.2 and the upper outline is at y=0.8

Note 2: WHEN MY SMALL (LINUX) PROGRAM IS READY, I WILL POST THE CODE ON MY BITBUCKET AS A VERY SMALL EXAMPLE OF USING THE DISCRETE LAPLACE OPERATOR

Update

November 26, 2013:

You can get a link to the code here

Check out Armadillo’s documentation X.n_elem gets the length of vector X. To resize the vector while preserving the data, use .resize(). .insert_rows() or .insert_cols() .

Note that resizing objects in performance-critical loops, whether Armadillo matrix/vector or std::vector, is inefficient. It is better to calculate the correct size beforehand.