pao_elem_derivative_2 is called on scalars inside a loop

[tkoskela]

The second hotspot shown in profiling in #197 is

CONQUEST-release/src/PAO_grid_transform_module.f90

Lines 394 to 400 in 4162a3c

	do m1=-l1,l1
	call pao_elem_derivative_2(direction,the_species,l1,acz,m1,x,y,z,val)
	if(position+(count1-1)*n_pts_in_block > gridfunctions(pao_fns)%size) &
	call cq_abort('single_pao_to_grad: position error ', &
	position, gridfunctions(pao_fns)%size)
	gridfunctions(pao_fns)%griddata(position+(count1-1)*n_pts_in_block) = val
	count1 = count1+1

Disregarding the if statement, which we can remove, It looks like the main issue is pao_elem_derivative_2 (and all functions it calls) are called on scalar arguments, but the call is being made from inside a loop nest. To speed this up, the loop nest should be moved to the bottom of the call chain, which would allow vectorization and get rid of a lot of function calling overheads.

[davidbowler]

This will take a very great deal of work: the code is deeply nested and forked based on lots of different variables; simply moving the nest down is not obviously possible. Really we'd need a full refactoring of the code; probably a good thing, but will require careful maths/physics preparation before coding.