Parabolic Cylinder Functions C++ Version

This project is a faster version of MATLAB code original from E. Cojocaru. Parabolic Cylinder Functions (https://www.mathworks.com/matlabcentral/fileexchange/22620-parabolic-cylinder-functions)

Features:

• The API is similar to original functions, such as val = pwlx(a,x); -> val = pcf_mex(a,x,'pwlx');
• The MATLAB toolbox only support scalar inputs, pcf_mex now support 1D array of size (1,n) or (n,1), return value will have size(n,1).
• Intel compiler, OPENMP， AVX2 or AVX512 are utilized to speed up the calculation.
• Add two useful functions for bortfeld function
• Apple Silicon supported (Rosseta2(R2022a) and Native(R2022a beta) Matlab)

What's inside the box

• pcf_mex(a,x,'pu') Compute parabolic cylinder function U(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'dpu') Compute derivative of parabolic cylinder function U(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'pulx') Compute parabolic cylinder function U(a,x) for large argument x (|x| >> |a| and |a| moderate)
• pcf_mex(a,x,'dpulx') Compute parabolic derivative of cylinder function U(a,x) for large argument x (|x| >> |a| and |a| moderate)
• pcf_mex(a,x,'pd') Compute parabolic cylinder function D(a,x) = U(-a-0.5,x), s.t. |a|<5 and |x|<5 (used in bortfeld function)
• pcf_mex(a,x,'dpd') Compute parabolic derivative of cylinder function D(a,x) = U(-a-0.5,x), s.t. |a|<5 and |x|<5 (used in bortfeld function)
• pcf_mex(a,x,'pv') Compute parabolic cylinder function V(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'dpv') Compute derivative of parabolic cylinder function V(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'pvlx') Compute parabolic cylinder function V(a,x) for large argument x (|x| >> |a| and |a| moderate)
• pcf_mex(a,x,'dpvlx') Compute parabolic derivative of cylinder function V(a,x) for large argument x (|x| >> |a| and |a| moderate)
• pcf_mex(a,x,'pw') Compute parabolic cylinder function W(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'dpw') Compute derivative of parabolic cylinder function W(a,x), s.t. abs(a)<5 and abs(x)<5
• pcf_mex(a,x,'pwlx') Compute parabolic cylinder function W(a,x) for large argument x (|x| >> |a| and |a| moderate)
• pcf_mex(a,x,'dpwlx') Compute parabolic derivative of cylinder function W(a,x) for large argument x (|x| >> |a| and |a| moderate)

Speed benchmark

I tested it with simple benchmark : pcf_mex(-1,linspace(4,5,1e6),'pwlx'), unit is seconds % 0.7554 Apple M1 pro(8core) + openmp (Matlab2022a beta Native)

% 1.8453 Apple M1 pro(8core) + openmp (Matlab2022a Rosseta2)

% 0.3994 intel compiler 2021 + openmp + avx2

% 1.0733 vs + openmp + avx2

% 1.0858 vs + openmp

% 9.7933 vs

% 4.476539 original + parfor

% 32.521651 original

The first one is compiled with Visual Studio + Intel OneAPI, intel compiler 2021 is much more faster.

"omp.h" not found at M1 Mac

refer to my answer: https://www.mathworks.com/matlabcentral/answers/1761950-m1-mac-compile-mex-file-with-openmp