from __future__ import division
from CoolProp.CoolProp import Props, DerivTerms

def finite_diff(Output,Input1,Val1,Input2,Val2,Fluid,  index,deriv,order,type = 'centered',dx = 1e-3):
    def f(index, dx):
        if index == 1:
            return Props(Output,Input1,Val1+dx,Input2,Val2,Fluid)
        else:
            return Props(Output,Input1,Val1,Input2,Val2+dx,Fluid)
        
    if deriv == 1:
        if order == 1:
            return (f(index,dx)-f(index,0))/(dx)
        elif order == 2:
            return (f(index,dx)-f(index,-dx))/(2*dx)
        elif order == 4:
            return (f(index,-2*dx)-8*f(index,-dx)+8*f(index,dx)-f(index,2*dx))/(12*dx)
    elif deriv == 2:
        if order == 2:
            return (f(index,-dx)-2*f(index,0)+f(index,dx))/(dx**2)
        elif order == 4:
            return (-f(index,-2*dx)+16*f(index,-dx)-30*f(index,0)+16*f(index,dx)-f(index,2*dx))/(12*dx**2)
        else:
            raise ValueError
    else:
        raise ValueError

## fluid = 'Water'
## T = 647.74374374374372#647#Props(fluid,'Tcrit')+1
## rho = 322.32199999#358#Props(fluid,'rhocrit')+1
## H = Props('H','T',T,'D',rho,fluid)
## P = Props('P','T',T,'D',rho,fluid)
## print T,rho,H,P

fluid = 'R125'
T = 300
rho = 1.5
H = Props('H','T',T,'D',rho,fluid)
P = Props('P','T',T,'D',rho,fluid)
print T,rho,H,P

dpdT__rho = DerivTerms('dpdT|rho',T,rho,fluid)
dpdrho__T = DerivTerms('dpdrho|T',T,rho,fluid)
dhdT__rho = DerivTerms('dhdT|rho',T,rho,fluid)
dhdrho__T = DerivTerms('dhdrho|T',T,rho,fluid)
print '*******************************************'
print 'CHECKING DERIVATIVES FROM EOS'
print '*******************************************'
dpdT__rho_num = finite_diff('P','T',T,'D',rho,fluid,1,1,4)
print 'dpdT|rho'
print dpdT__rho
print dpdT__rho_num

dpdrho__T_num = finite_diff('P','T',T,'D',rho,fluid,2,1,4)
print 'dpdrho|T'
print dpdrho__T
print dpdrho__T_num

dhdT__rho_num = finite_diff('H','T',T,'D',rho,fluid,1,1,4)
print 'dhdT|rho'
print dhdT__rho
print dhdT__rho_num

dhdrho__T_num = finite_diff('H','T',T,'D',rho,fluid,2,1,4)
print 'dhdrho|T'
print dhdrho__T
print dhdrho__T_num
print
print '*******************************************'
print 'CHECKING HELMHOLTZ DERIVATIVES'
print '*******************************************'
dx = 1e-10
Tc = Props(fluid,'Tcrit')
rhoc = Props(fluid,'rhocrit')
delta = rho/rhoc
tau = Tc/T

def f(dx):
    rho = rhoc*(delta+dx)
    return DerivTerms('dphir_dDelta',T,rho,fluid)
print 'd2phir_dDelta2'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d2phir_dDelta2',T,rho,fluid)

def f(dx):
    rho = rhoc*(delta+dx)
    return DerivTerms('d2phir_dDelta2',T,rho,fluid)
print 'd3phir_dDelta3'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d3phir_dDelta3',T,rho,fluid)

def f(dx):
    rho = rhoc*(delta+dx)
    return DerivTerms('dphir_dTau',T,rho,fluid)
print 'd2phir_dDelta_dTau'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d2phir_dDelta_dTau',T,rho,fluid)

def f(dx):
    rho = rhoc*(delta+dx)
    return DerivTerms('d2phir_dTau2',T,rho,fluid)
print 'd3phir_dDelta_dTau2'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d3phir_dDelta_dTau2',T,rho,fluid)

def f(dx):
    T = Tc/(tau+dx)
    return DerivTerms('d2phir_dDelta2',T,rho,fluid)
print 'd3phir_dDelta2_dTau'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d3phir_dDelta2_dTau',T,rho,fluid)

def f(dx):
    T = Tc/(tau+dx)
    return DerivTerms('dphir_dTau',T,rho,fluid)
print 'd2phir_dTau2'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d2phir_dTau2',T,rho,fluid)

def f(dx):
    T = Tc/(tau+dx)
    return DerivTerms('d2phir_dTau2',T,rho,fluid)
print 'd3phir_dTau3'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d3phir_dTau3',T,rho,fluid)

def f(dx):
    T = Tc/(tau+dx)
    return DerivTerms('dphi0_dTau',T,rho,fluid)
print 'd2phi0_dTau2'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d2phi0_dTau2',T,rho,fluid)

def f(dx):
    T = Tc/(tau+dx)
    return DerivTerms('d2phi0_dTau2',T,rho,fluid)
print 'd3phi0_dTau3'
print (f(-2*dx)-8*f(-dx)+8*f(dx)-f(2*dx))/(12*dx)
print DerivTerms('d3phi0_dTau3',T,rho,fluid)
print
print '*******************************************'
print 'CHECKING FIRST DERIVATIVES OF PROPERTIES'
print '*******************************************'

A = dpdT__rho*dhdrho__T-dpdrho__T*dhdT__rho

dT_dh_num = finite_diff('T','H',H,'P',P,fluid,1,1,4)
dT_dh = 1/Props('C','T',T,'D',rho,fluid)
print 'dTdh|p'
print dT_dh
print dT_dh_num

dT_dp_num = finite_diff('T','H',H,'P',P,fluid,2,1,4)
dT_dp = 1/A*dhdrho__T
print 'dTdp|h'
print dT_dp
print dT_dp_num

drho_dh_num = finite_diff('D','H',H,'P',P,fluid,1,1,4)
drho_dh = 1/A*dpdT__rho
print 'drhodh|p'
print drho_dh_num
print drho_dh_num

drho_dp_num = finite_diff('D','H',H,'P',P,fluid,2,1,4)
drho_dp = -1/A*dhdT__rho
print 'drhodp|h'
print drho_dp
print drho_dp_num

ds_dh_num = finite_diff('S','H',H,'P',P,fluid,1,1,4)
ds_dh = 1/T
print 'dsdh|p'
print ds_dh
print ds_dh_num

ds_dp_num = finite_diff('S','H',H,'P',P,fluid,2,1,4)
ds_dp = -1/(T*rho)
print 'dsdp|h'
print ds_dp
print ds_dp_num


print 
print '*******************************************'
print 'CHECKING SECOND DERIVATIVES OF PROPERTIES'
print '*******************************************'

## d2T_dh2_num = finite_diff('T','H',H,'P',P,fluid,1,2,4)
## d2T_dh2 = 1/Props('C','T',T,'D',rho,fluid)
## print 'dTdh|p'
## print dT_dh
## print dT_dh_num

d2s_dh2 = -(1/T/T)*dT_dh
d2s_dh2_num = finite_diff('S','H',H,'P',P,fluid,1,2,4,dx = 10)
print 'd2sdh2|p'
print d2s_dh2
print d2s_dh2_num

d2s_dp2 = 1/(T**2*rho)*dT_dp+1/(T*rho**2)*drho_dp
d2s_dp2_num = finite_diff('S','H',H,'P',P,fluid,2,2,4,dx = 10)
print 'd2sdp2|h'
print d2s_dp2
print d2s_dp2_num

d2s_dhdp = -(1/T/T)*dT_dp
d2s_dhdp_num = finite_diff('S','H',H,'P',P,fluid,1,2,4)
print 'd2s_dhdp'
print d2s_dhdp
print d2s_dhdp_num

## d2s_dhdp = -(1/T/T)*dT_dp
## print d2s_dhdp
## d2s_dhdp = 1/(T**2*rho)*dT_dh+1/(T*rho**2)*drho_dh
## print d2s_dhdp