Resolve matrix differential equation with sparse matrix and ojAlgo

Question

I am developping a java evolution tool with ojAlgo, and I try to resolve the following equation :

where A is a sparse matrix (for now the dimension of the matrix is 2000 x 2000, it will be scaled later on), A is not symmetric and use only real values.

I made some researchs and I tried to find the way to resolve this equation (using SparseStore) on github wiki/javadoc but I didn't find a way to do it. Can you help me find methods/class I should use ? Thank you

score 1 · Accepted Answer · answered Mar 28 '18 at 07:42

1

There is no direct/specific method to solve differential equations in ojAlgo. You have to know how to do it (using pen and paper) then ojAlgo can help you perform the calculations.

The main problem here is finding the eigenpairs, right?

    Eigenvalue<Double> evd = Eigenvalue.PRIMITIVE.make(matrix);

    evd.decompose(matrix);

    Array1D<ComplexNumber> values = evd.getEigenvalues();
    MatrixStore<ComplexNumber> vectors = evd.getEigenvectors();
    Eigenpair pair = evd.getEigenpair(0); // One of the pairs

answered Mar 28 '18 at 07:42

apete

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This is exactly what I wanted, Thank you so much ! – Johann MARTINET Mar 28 '18 at 07:51
To be effecient you should reuse the evd instances, and if the original matrix is only changed by scaling then perhaps you should avoid recalculating the EvD altogether. – apete Mar 28 '18 at 08:23
I will try this, thank you. I will probably open another question afterwards! – Johann MARTINET Mar 28 '18 at 08:29
Just a little question : Is there a way to print on console or write in a file a matrix when its dimension are higher than 50x50 (limit in MatrixUtils.toString method) ? – Johann MARTINET Mar 28 '18 at 08:36
BasicLogger.debug("",matrix); – apete Mar 28 '18 at 09:31

Resolve matrix differential equation with sparse matrix and ojAlgo

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