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Change mat.Vector to []float64

When composing a ode.Rhs it is cumbersome to extract the components of x mat.Vector. Change everything to plain []float64; everything but the mat.Matrix in ExplicitRungeKutta.

Refactor ExplicitRungeKutta

  • A should be of size l-1 x l-1 instead of l x l, since the diagonal elements are always zero.
  • Consider c of size l-1, since its first component is always zero as well.
  • Consider b of size l-1, as its components must sum up to 1. What effect does this have on the numerics due to potential different rounding in the skipped (last) component?

Side effect

When benchmarking Euler's method as a Runge-Kutta method, it would be fine to use an uninitialized var aa mat.Matrix instead of

aa := mat.NewDense(1, 1, []float64{0})

as its values are never accessed. This already works right now. After the refactor, it would be mandatory, since aa must be of size 0 x 0.

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