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## Copyright 2021 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.
# approximate \int_a^b f using Gauss-Legendre quadratures
@everywhere function integrate_legendre(f,a,b,weights)
out=0
for i in 1:length(weights[1])
out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)
end
return out
end
# \int f*g where g is sampled at the Legendre nodes
@everywhere function integrate_legendre_sampled(f,g,a,b,weights)
out=0
for i in 1:length(weights[1])
out+=(b-a)/2*weights[2][i]*f((b-a)/2*weights[1][i]+(b+a)/2)*g[i]
end
return out
end
# approximate \int_a^b f/sqrt((b-x)(x-a)) using Gauss-Chebyshev quadratures
@everywhere function integrate_chebyshev(f,a,b,N)
out=0
for i in 1:N
out=out+pi/N*f((b-a)/2*cos((2*i-1)/(2*N)*pi)+(b+a)/2)
end
return out
end
# approximate \int_0^\infty dr f(r)*exp(-a*r) using Gauss-Chebyshev quadratures
@everywhere function integrate_laguerre(f,a,weights_gL)
out=0.
for i in 1:length(weights_gL[1])
out+=1/a*f(weights_gL[1][i]/a)*weights_gL[2][i]
end
return out
end
# Hann window
@everywhere function hann(x,L)
if abs(x)<L/2
return cos(pi*x/L)^2
else
return 0.
end
end
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