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## Copyright 2021-2023 Ian Jauslin
##
## Licensed under the Apache License, Version 2.0 (the "License");
## you may not use this file except in compliance with the License.
## You may obtain a copy of the License at
##
## http://www.apache.org/licenses/LICENSE-2.0
##
## Unless required by applicable law or agreed to in writing, software
## distributed under the License is distributed on an "AS IS" BASIS,
## WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
## See the License for the specific language governing permissions and
## limitations under the License.
# \Phi(x)=2*(1-sqrt(1-x))/x
@everywhere function Phi(
x::Float64
)
if abs(x)>1e-5
return 2*(1-sqrt(abs(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
@everywhere function dPhi(
x::Float64
)
#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(abs(1-x))*x)*(1-x>=0 ? 1 : -1)-2*(1-sqrt(abs(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
# apply Phi to every element of a vector
@everywhere function dotPhi(
v::Array{Float64,1}
)
out=zeros(Float64,length(v))
for i in 1:length(v)
out[i]=Phi(v[i])
end
return out
end
@everywhere function dotdPhi(
v::Array{Float64,1}
)
out=zeros(Float64,length(v))
for i in 1:length(v)
out[i]=dPhi(v[i])
end
return out
end
@everywhere function sinc(x::Float64)
return (x == 0 ? 1 : sin(x)/x)
end
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