the Faddeeva function

the scaled complementary error function

the error function of complex arguments

the imaginary error function

the complementary error function

the Dawson function

Faddeeva_w(z, relerr = 0)

erfcx(z, relerr = 0)

erf(z, relerr = 0)

erfi(z, relerr = 0)

erfc(z, relerr = 0)

Dawson(z, relerr = 0)

Arguments

z
complex vector
relerr
double, requested error

Value

complex vector

Functions

  • Faddeeva_w: compute w(z) = exp(-z^2) erfc(-iz)

  • erfcx: compute erfcx(z) = exp(z^2) erfc(z)

  • erf: compute erf(z)

  • erfi: compute erfi(z) = -i erf(iz)

  • erfc: compute erfc(z) = 1 - erf(z)

  • Dawson: compute Dawson(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z)

Examples

Faddeeva_w(1:10 + 1i)
#> [1] 0.30474421+0.20821894i 0.14023958+0.22221344i 0.06531778+0.17391832i #> [4] 0.03628146+0.13583895i 0.02300313+0.11033283i 0.01588513+0.09262875i #> [7] 0.01162996+0.07973206i 0.00888366+0.06995041i 0.00700798+0.06228848i #> [10] 0.00566994+0.05612965i
erfcx(1:10 + 1i)
#> [1] 0.30474421-0.20821894i 0.21849262-0.09299781i 0.16426114-0.05019714i #> [4] 0.12988816-0.03077886i 0.10679774-0.02060409i 0.09042061-0.01468696i #> [7] 0.07827740-0.01096897i 0.06894724-0.00849054i 0.06156985-0.00676006i #> [10] 0.05559832-0.00550608i
erf(1:10 + 1i)
#> [1] 1.3161513+0.1904535i 1.0036063-0.0112590i 0.9999424+0.0000008i #> [4] 1.0000000+0.0000000i 1.0000000-0.0000000i 1.0000000-0.0000000i #> [7] 1.0000000+0.0000000i 1.0000000-0.0000000i 1.0000000-0.0000000i #> [10] 1.0000000+0.0000000i
erfi(1:10 + 1i)
#> [1] 1.904535e-01+1.316151e+00i -5.049144e+00-5.366436e-01i #> [3] 4.433889e+02-3.308154e+02i 5.273182e+04+4.565923e+05i #> [5] -2.783777e+09-1.078693e+09i 1.104525e+14-1.000882e+14i #> [7] 1.573367e+19+5.430456e+19i -1.595241e+26-2.667998e+25i #> [9] 1.987267e+33-2.848176e+33i 2.777023e+41+4.838652e+41i
erfc(1:10 + 1i)
#> [1] -3.161513e-01-1.904535e-01i -3.606343e-03+1.125901e-02i #> [3] 5.761387e-05-7.717956e-07i -1.509630e-08-3.794033e-08i #> [5] -2.959777e-12+2.846018e-12i 5.307800e-17+2.277635e-17i #> [7] -2.316003e-25-1.126479e-22i -2.771994e-29+1.219870e-29i #> [9] 8.254004e-37+7.539657e-37i 1.786012e-45-5.359995e-45i
Dawson(1:10 + 1i)
#> [1] 0.99037309-0.63887305i 0.16353941-0.15312458i 0.15404802-0.05760092i #> [4] 0.12038440-0.03215364i 0.09777993-0.02038600i 0.08209009-0.01407783i #> [7] 0.07066069-0.01030679i 0.06199194-0.00787294i 0.05520173-0.00621066i #> [10] 0.04974360-0.00502486i