coordinates_derivatives.h

// Description: Derivatives of coordinate conversions

#ifndef PASTELMATH_COORDINATES_DERIVATES_H
#define PASTELMATH_COORDINATES_DERIVATES_H

#include "pastel/sys/vector.h"
#include "pastel/math/matrix.h"

namespace Pastel
{

    //! Derivative of the cartesianToSpherical function.
    template <typename Real, integer N>
    Matrix<Real> cartesianToSphericalDerivative(
        const Vector<Real, N>& cartesian);

    //! Derivative of the sphericalToCartesian function.
    template <typename Real, integer N>
    Matrix<Real> sphericalToCartesianDerivative(
        const Vector<Real, N>& cartesian);

    //! Partial derivatives of the sphericalToCartesian function.
    /*!
   Preconditions:
   allGreaterEqual(index, 0)

   Let f : R^n -> R^n : f(r, alpha_1, ..., alpha_{n - 1})
   where f = sphericalToCartesian.
   
   Using multi-index notation, this function computes df / d(index).
   In other words, 

   d^|index|f / ((dr_0)^index[0] (dalpha_1)^index[1] ... (dalpha_(n-1))^index[n - 1])
   where
   |index| = sum(index)
   */
    template <typename Real, integer N>
    Vector<Real, N> sphericalToCartesianDerivative(
        const Vector<Real, N>& spherical, 
        const Vector<integer, N>& index);

}

#include "pastel/math/coordinate/coordinates_derivatives.hpp"

#endif