19cjl/figs/numerical.fig/simpleq/tools.jl

21 lines
471 B
Julia

# \Phi(x)=2*(1-sqrt(1-x))/x
function Phi(x)
if abs(x)>1e-5
return 2*(1-sqrt(1-x))/x
else
return 1+x/4+x^2/8+5*x^3/64+7*x^4/128+21*x^5/512
end
end
# \partial\Phi
function dPhi(x)
#if abs(x-1)<1e-5
# @printf(stderr,"warning: dPhi is singular at 1, and evaluating it at (% .8e+i% .8e)\n",real(x),imag(x))
#end
if abs(x)>1e-5
return 1/(sqrt(1-x)*x)-2*(1-sqrt(1-x))/x^2
else
return 1/4+x/4+15*x^2/64+7*x^3/32+105*x^4/512+99*x^5/512
end
end