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- hum1wei24(x, y)
- Complex error function combining Humlicek's and Weideman's rational approximations:
|x|+y>15: Humlicek (JQSRT, 1982) rational approximation for region I;
else: J.A.C. Weideman (SIAM-NA 1994); equation (38.I) and table I.
F. Schreier, JQSRT 112, pp. 1010-1025, 2011: doi: 10.1016/j.jqsrt.2010.12.010
- hum1zpf16m(x, y, s=15.0)
- Complex error function w(z)=w(x+iy) combining Humlicek's rational approximations:
|x|+y>15: Humlicek (JQSRT, 1982) rational approximation for region I;
else: Humlicek (JQSRT, 1979) rational approximation with n=16 and delta=y0=1.31183
Version using a mask and np.place; two real arguments x,y.
- hum2wei32(x, y)
- Complex error function combining Humlicek's and Weideman's rational approximations:
|x|+y>10.0: Humlicek (JQSRT, 1982) rational approximation for region II;
else: J.A.C. Weideman (SIAM-NA 1994); equation (38.I) and table I.
F. Schreier, JQSRT 112, pp. 1010-1025, 2011: doi: 10.1016/j.jqsrt.2010.12.010
- hum2zpf16m(x, y, s=10.0)
- Complex error function w(z)=w(x+iy) combining Humlicek's rational approximations:
|x|+y>10: Humlicek (JQSRT, 1982) rational approximation for region II;
else: Humlicek (JQSRT, 1979) rational approximation with n=16 and delta=y0=1.31183
Version using a mask and np.place; two real arguments x,y.
- weideman24a(x, y)
- Complex error function using Weideman's rational approximation:
J.A.C. Weideman (SIAM-NA 1994); equation (38.I) for N=24 and table I.
Maximum relative error: 2.6e-1 for 0<x<25 and 1e-8<y<1e2
2.6e-3 for 0<x<25 and 1e-6<y<1e2
2.6e-5 for 0<x<25 and 1e-4<y<1e2.
- weideman32a(x, y)
- Complex error function using Weideman's rational approximation:
J.A.C. Weideman (SIAM-NA 1994); equation (38.I) for N=32 and table I.
Maximum relative error: 2.6e-4 for 0<x<25 and 1e-8<y<1e2
2.6e-6 for 0<x<25 and 1e-6<y<1e2.
- zpf16h(x, y)
- Humlicek (JQSRT 1979) complex probability function for n=16 and delta=1.31183.
Generalization described in MNRAS 479(3), 3068-3075, 2018, doi: 10.1093/mnras/sty1680
Optimized rational approximation with Horner scheme (applicable for all z=x+iy).
- zpf16p(x, y)
- Humlicek (JQSRT 1979) complex probability function for n=16 and delta=1.31183.
Generalization described in MNRAS 479(3), 3068-3075, 2018, doi: 10.1093/mnras/sty1680
Optimized rational approximation using numpy.poly1d (applicable for all z=x+iy).
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