Periodic spline

SplinePP( degree, ncells)

• degree : degree of 1d spline
• poly_coeffs : poly_coeffs[i,j] coefficient of $x^{deg+1-j}$ for ith B-spline function size= (degree+1, degree+1)
• poly_coeffs_fp : poly_coeffs[i,j] coefficient of $x^{deg+1-j}$ for ith B-spline function size= (degree+1, degree+1)
• ncells : number of gridcells
• scratch_b : scratch data for b_to_pp-converting
• scratch_p : scratch data for b_to_pp-converting

b_to_pp( SplinePP, ncells, b_coeffs)

Convert 1d spline in B form to spline in pp form with periodic boundary conditions

b_to_pp_1d_cell( self, b_coeffs, pp_coeffs )

Convert 1d spline in B form in a cell to spline in pp form with periodic boundary conditions

• spline : arbitrary degree 1d spline
• b_coeffs(self%degree+1) : coefficients of spline in B-form
• pp_coeffs(self%degree+1) : coefficients of spline in pp-form

b_to_pp_2d!( pp, spl1, spl2, b)

Convert 2d spline in B form to spline in pp form

• n_cells(2) : number of gridcells
• b_coeffs : coefficients of spline in B-form
• pp_coeffs : coefficients of spline in pp-form

b_to_pp_2d_cell(spline1, spline2, b_coeffs, pp_coeffs, i, j)

Convert 2d spline in B form in a cell to spline in pp form with periodic boundary conditions

• spline1 : arbitrary degree 1d spline
• spline2 : arbitrary degree 1d spline
• n_cells(2) : number of gridcells
• bcoeffs(ncells(1)*n_cells(2)) : coefficients of spline in B-form
• ppcoeffs((spline1.degree+1)*(spline2.degree+1),ncells(1)*n_cells(2)) : coefficients of spline in pp-form

horner_1d(degree, pp_coeffs, x, index)

Perform a 1d Horner schema on the pp_coeffs at index

horner_2d(degrees, pp_coeffs, position, indices, ncells)

Perform a 2d hornerschema on the pp_coeffs at the indices

• degree : degree of the spline
• pp_coeffs : coefficients of spline in pp-form
• position(2) : point at which we evaluate our spline
• indices(2) : indices of cell in which is x
• ncells(2) : number of gridcells
• res : value of the splinefunction at position

horner_m_2d!(val, spl1, spl2, degree, x)

Perform two times a 1d hornerschema on the poly_coeffs

• val : array of values
• degree : degree of the spline
• x : point at which we evaluate our spline

horner_primitive_1d(val, degree, pp_coeffs, x)

Perform a 1d Horner schema on the pp_coeffs evaluate at x