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priors.f90
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priors.f90
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module priors
use utils1
contains
!=======================================================================
! Prior distribution functions: r is a uniform deviate from the unit
!
!
! Uniform[0:1] -> Delta[x1]
function DeltaFunctionPrior(r,x1,x2)
implicit none
double precision r,x1,x2,DeltaFunctionPrior
DeltaFunctionPrior=x1
end function DeltaFunctionPrior
!=======================================================================
! Uniform[0:1] -> Uniform[x1:x2]
function UniformPrior(r,x1,x2)
implicit none
double precision r,x1,x2,UniformPrior
UniformPrior=x1+r*(x2-x1)
end function UniformPrior
!=======================================================================
! Uniform[0:1] -> LogUniform[x1:x2]
function LogPrior(r,x1,x2)
implicit none
double precision r,x1,x2,LogPrior
double precision lx1,lx2
if (r.le.0.0d0) then
LogPrior=-1.0d32
else
lx1=dlog10(x1)
lx2=dlog10(x2)
LogPrior=10.d0**(lx1+r*(lx2-lx1))
endif
end function LogPrior
!=======================================================================
! Uniform[0:1] -> Sin[x1:x2] (angles in degrees):
function SinPrior(r,x1,x2)
implicit none
double precision r,x1,x2,SinPrior
real cx1,cx2,deg2rad
parameter(deg2rad=0.017453292)
cx1=cos(x1*deg2rad)
cx2=cos(x2*deg2rad)
SinPrior=1.d0*acos(cx1+r*(cx2-cx1))
end function SinPrior
!=======================================================================
! Uniform[0:1] -> Cauchy[mean=x0,FWHM=2*gamma]
function CauchyPrior(r,x0,gamma)
implicit none
double precision r,x0,gamma,CauchyPrior
real Pi
parameter(Pi=3.141592654)
CauchyPrior=x0+gamma*tan(Pi*(r-0.5))
end function CauchyPrior
!=======================================================================
! Uniform[0:1] -> Gaussian[mean=mu,variance=sigma**2]
function GaussianPrior(r,mu,sigma)
implicit none
double precision r,mu,sigma,GaussianPrior
double precision SqrtTwo
parameter(SqrtTwo=1.414213562d0)
if (r.le.1.0d-16.or.(1.0d0-r).le.1.0d-16) then
GaussianPrior=-1.0d32
else
GaussianPrior=mu+sigma*SqrtTwo*dierfc(2.d0*(1.d0-r))
endif
end function GaussianPrior
!=======================================================================
! Uniform[0:1] -> LogNormal[mode=a,width parameter=sigma]
function LogNormalPrior(r,a,sigma)
implicit none
double precision r,a,sigma,LogNormalPrior
double precision SqrtTwo,bracket
parameter(SqrtTwo=1.414213562d0)
bracket=sigma*sigma+sigma*SqrtTwo*dierfc(2.d0*r)
LogNormalPrior=a*dexp(bracket)
end function LogNormalPrior
!=======================================================================
! Inverse of complimentary error function in double precision
function dierfc(y)
implicit none
double precision y,dierfc
double precision qa,qb,qc,qd,q0,q1,q2,q3,q4,pa,pb,p0,p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15,p16,p17,p18
double precision p19,p20,p21,p22,x,z,w,u,s,t
double precision infinity
parameter (infinity=5.0d0)
parameter (qa=9.16461398268964d-01, &
qb=2.31729200323405d-01, &
qc=4.88826640273108d-01, &
qd=1.24610454613712d-01, &
q0=4.99999303439796d-01, &
q1=1.16065025341614d-01, &
q2=1.50689047360223d-01, &
q3=2.69999308670029d-01, &
q4=-7.28846765585675d-02)
parameter (pa=3.97886080735226000d+00, &
pb=1.20782237635245222d-01, &
p0=2.44044510593190935d-01, &
p1=4.34397492331430115d-01, &
p2=6.86265948274097816d-01, &
p3=9.56464974744799006d-01, &
p4=1.16374581931560831d+00, &
p5=1.21448730779995237d+00, &
p6=1.05375024970847138d+00, &
p7=7.13657635868730364d-01, &
p8=3.16847638520135944d-01, &
p9=1.47297938331485121d-02, &
p10=-1.05872177941595488d-01, &
p11=-7.43424357241784861d-02)
parameter (p12=2.20995927012179067d-03, &
p13=3.46494207789099922d-02, &
p14=1.42961988697898018d-02, &
p15=-1.18598117047771104d-02, &
p16=-1.12749169332504870d-02, &
p17=3.39721910367775861d-03, &
p18=6.85649426074558612d-03, &
p19=-7.71708358954120939d-04, &
p20=-3.51287146129100025d-03, &
p21=1.05739299623423047d-04, &
p22=1.12648096188977922d-03)
if (y==0.0) then
dierfc=infinity
return
endif
z=y
if (y .gt. 1) z=2-y
w=qa-log(z)
u=sqrt(w)
s=(qc+log(u))/w
t=1/(u+qb)
x=u*(1-s*(0.5d0+s*qd))-((((q4*t+q3)*t+q2)*t+q1)*t+q0)*t
t=pa/(pa+x)
u=t-0.5d0
s=(((((((((p22*u+p21)*u+p20)*u+p19)*u+p18)*u+p17)*u+p16)*u+p15)*u+p14)*u+p13)*u+p12
s=((((((((((((s*u+p11)*u+p10)*u+p9)*u+p8)*u+p7)*u+p6)*u+p5)*u+p4)*u+p3)*u+p2) &
*u+p1)*u+p0)*t-z*exp(x*x-pb)
x=x+s*(1+x*s)
if (y .gt. 1) x=-x
dierfc=x
end function dierfc
!=======================================================================
end module priors