Method backSub

JSAT/src/jsat/linear/LUPDecomposition.java:254–275

Solves for the vector x such that U x = y @param U an upper triangular matrix @param y a vector whos length is equal to the rows in U @return x such that U x = y

(Matrix U, Vec y)

     * @return x such that U x = y
     */
    public static Vec backSub(Matrix U, Vec y)
    {
        if (y.length() != U.rows())
            throw new ArithmeticException("Vector and matrix sizes do not agree");

        Vec x = y instanceof SparseVector ? new SparseVector(U.cols()) : new DenseVector(U.cols());
        
        final int start = Math.min(U.rows(), U.cols())-1;

        for (int i = start; i >= 0; i--)
        {
            double x_i = y.get(i);
            for (int j = i + 1; j <= start; j++)
                x_i -= U.get(i, j) * x.get(j);
            x_i /= U.get(i, i);
            if(Double.isInfinite(x_i))//Occurs when U_(i,i) = 0
                x_i = 0;
            x.set(i, x_i);
        }

        return x;
    }

    /**
     * Solves for the matrix x such that U x = y