AMDG On 11/24/2011 06:25 AM, Janek Kozicki wrote:
Hi, I wrote a short function that integrates Huyghens spherical wave for diffraction. (This is a single slit experiment btw).
I have some questions, marked with (*)
double integral( const quantity<length> x // x - position where light intensity is calculated , const quantity<length> R // R - distance from slit to screen , const quantity<length> D // D - slit width , const quantity<length> lambda // lambda - wavelength , double steps // steps - number of integration steps // (*) ) { complex<double> i(0,1); complex<double> a(0); static const double pi = 3.14159265358979323846; // (**) quantity<wavenumber,complex<double> > k=2*pi/lambda; quantity<length> d=-0.5*D; // d - position on the slit quantity<length> dd=D/steps; // dd - width of integral step // integrate from -d to d: exp(i*k*r)/r for( ; d<= 0.5*D ; d+=dd ) { quantity<length> r=sqrt(pow<2>(R)+pow<2>(x-d)); a += (dd*exp(i*k*r)/r).value(); // (***) } return pow<2>(abs(a)); }
(*) it should be `int steps` but if I write it this way I get a compilation error here: quantity<length> dd=D/steps; // dd - width of integral step That looks like a conversion problem.
Try D/double(steps). Matthias, I seem to recall that the reason we disabled generic multiplication was that it was causing ambiguities with user defined types. Do you think it would be a good idea to enable arithmetic with any built-in arithmetic type?
(**) why do I need to define pi ? I expected to find it somewhere, but I couldn't.
Try boost::math?
(***) it seems strange that I need to take .value() here. The result is dimensionless, why can't it directly convert to complex<double> ? There is a risk that .value() would be expressed in millimeters or angstroms or whatever (maybe depending on dd), and then .value() would return a wrongly scaled number?
This is an idiosyncrasy of overload resolution. std::complex::operator+= is a template, so an implicit conversion doesn't work. The template argument can't be deduced.
Another question, why this works:
quantity<length> wavelength ( 632.8 *nano*meters);
and this does not?
quantity<length> wavelength = 632.8 *nano*meters;
Of course I know about extra copying, and waste of CPU resources on execution, when compiler isn't able to optimize this away (and usually it is able to do that). But why the heck this simple assignment can't work?
This isn't assignment. It's copy construction and requires an implicit conversion which is forbidden.
PS: I am attaching a short test version of this program, it's in polish, but I hope you don't mind.
best regards and thanks in advance for your help
In Christ, Steven Watanabe