def MCMC_PSPVP(MCMC_List):
MCMCInit=MCMC_List
L = int(MCPAR[1])
Stepnumber= int(MCPAR[2])
SampleMatrix=np.zeros([Stepnumber,L+1])
SampleMatrix[0,:]=MCMCInit
Move = np.zeros([L+1])
ChiPrior = MCMCInit[L]
for step in np.arange(1,Stepnumber,1):
Temp = SampleMatrix[step-1,:]
print(Temp)
for p in range(L-3):
StepControl = MCPAR[5]+MCPAR[6]*np.random.random_sample()
Move[p] = (FITPARUB[p]-FITPARLB[p])/StepControl*(np.random.random_sample()-0.5) # need out of bounds check
Temp=Temp+Move
SimPost=SimInt_PSPVP(Temp)
ChiPost=np.sum(CD.Misfit(Intensity,SimPost))
if ChiPost < ChiPrior:
SampleMatrix[step,0:L]=Temp[0:L]
SampleMatrix[step,L]=ChiPost
else:
MoveProb = np.exp(-0.5*np.power(ChiPost-ChiPrior,2))
if np.random.random_sample() < MoveProb:
SampleMatrix[step,0:L]=Temp[0:L]
SampleMatrix[step,L]=ChiPost
else:
SampleMatrix[step,:]=SampleMatrix[step-1,:]
return SampleMatrix
def MCMCInit_ID1(FITPAR,FITPARLB,FITPARUB,MCPAR):
MCMCInit=np.zeros([int(MCPAR[0]),int(MCPAR[1])+1])
for i in range(int(MCPAR[0])):
if i <MCPAR[3]: #reversed from matlab code assigns all chains below randomnumber as random chains
for c in range(int(MCPAR[1])):
MCMCInit[i,c]=FITPARLB[c]+(FITPARUB[c]-FITPARLB[c])*np.random.random_sample()
(SimInt,Amplitude)=SimInt_ID1(MCMCInit[i,:])
C=np.sum(CD.Misfit(Intensity2,SimInt))
MCMCInit[i,int(MCPAR[1])]=C
else:
MCMCInit[i,0:int(MCPAR[1])]=FITPAR
(SimInt,Amplitude)=SimInt_ID1(MCMCInit[i,:])
C=np.sum(CD.Misfit(Intensity2,SimInt))
MCMCInit[i,int(MCPAR[1])]=C
return MCMCInit
def MCMC_LAM1(MCMC_List):
MCMCInit = MCMC_List
L = int(MCPAR[1])
Stepnumber = int(MCPAR[2])
SampledMatrix = np.zeros([Stepnumber, L + 1])
SampledMatrix[0, :] = MCMCInit
Move = np.zeros([L + 1])
ChiPrior = MCMCInit[L]
for step in np.arange(1, Stepnumber, 1):
Temp = SampledMatrix[step - 1, :].copy()
for p in range(L - 1):
StepControl = MCPAR[5] + MCPAR[6] * np.random.random_sample()
Move[p] = (FITPARUB[p] - FITPARLB[p]) / StepControl * (
np.random.random_sample() - 0.5) # need out of bounds check
Temp[p] = Temp[p] + Move[p]
if Temp[p] < FITPARLB[p]:
Temp[p] = FITPARLB[p] + (FITPARUB[p] - FITPARLB[p]) / 1000
elif Temp[p] > FITPARUB[p]:
Temp[p] = FITPARUB[p] - (FITPARUB[p] - FITPARLB[p]) / 1000
SimPost = SimInt_LAM1(Temp)
ChiPost = np.sum(CD.Misfit(Intensity, SimPost))
if ChiPost < ChiPrior:
SampledMatrix[step, 0:L] = Temp[0:L]
SampledMatrix[step, L] = ChiPost
ChiPrior = ChiPost
else:
MoveProb = np.exp(-0.5 * np.power(ChiPost - ChiPrior, 2))
if np.random.random_sample() < MoveProb:
SampledMatrix[step, 0:L] = Temp[0:L]
SampledMatrix[step, L] = ChiPost
ChiPrior = ChiPost
else:
SampledMatrix[step, :] = SampledMatrix[step - 1, :]
AcceptanceNumber = 0
Acceptancetotal = len(SampledMatrix[:, 1])
for i in np.arange(1, len(SampledMatrix[:, 1]), 1):
if SampledMatrix[i, 0] != SampledMatrix[i - 1, 0]:
AcceptanceNumber = AcceptanceNumber + 1
AcceptanceProbability = AcceptanceNumber / Acceptancetotal
print(AcceptanceProbability)
ReSampledMatrix = np.zeros(
[int(MCPAR[2]) / int(MCPAR[4]),
len(SampledMatrix[1, :])])
c = -1
for i in np.arange(0, len(SampledMatrix[:, 1]), MCPAR[4]):
c = c + 1
ReSampledMatrix[c, :] = SampledMatrix[i, :]
return (ReSampledMatrix)
def MCMC_ID1(MCMC_List):
MCMCInit = MCMC_List
L = int(MCPAR[1])
Stepnumber = int(MCPAR[2])
SampledMatrixI = np.zeros([Stepnumber, L + 1])
SampledMatrixI[0, :] = MCMCInit
Move = np.zeros([L + 1])
ChiPrior = MCMCInit[L]
for step in np.arange(1, Stepnumber, 1):
Temp = SampledMatrixI[step - 1, :].copy()
for p in range(L - 1):
StepControl = MCPAR[5] + MCPAR[6] * np.random.random_sample()
Move[p] = (FITPARUB[p] - FITPARLB[p]) / StepControl * (
np.random.random_sample() - 0.5) # need out of bounds check
Temp[p] = Temp[p] + Move[p]
if Temp[p] < FITPARLB[p]:
Temp[p] = FITPARLB[p] + (FITPARUB[p] - FITPARLB[p]) / 1000
elif Temp[p] > FITPARUB[p]:
Temp[p] = FITPARUB[p] - (FITPARUB[p] - FITPARLB[p]) / 1000
(SimPost, AmpPost) = SimInt_ID1(Temp)
ChiPost = np.sum(CD.Misfit(Intensity2, SimPost))
if ChiPost < ChiPrior:
SampledMatrixI[step, 0:L] = Temp[0:L]
SampledMatrixI[step, L] = ChiPost
ChiPrior = ChiPost
else:
MoveProb = np.exp(-0.5 * np.power(ChiPost - ChiPrior, 2))
if np.random.random_sample() < MoveProb:
SampledMatrixI[step, 0:L] = Temp[0:L]
SampledMatrixI[step, L] = ChiPost
ChiPrior = ChiPost
else:
SampledMatrixI[step, :] = SampledMatrixI[step - 1, :]
ReSampledMatrixI = np.zeros(
[int(MCPAR[2]) / int(MCPAR[4]),
len(SampledMatrixI[1, :])])
c = -1
for i in np.arange(0, len(SampledMatrixI[:, 1]), MCPAR[4]):
c = c + 1
ReSampledMatrixI[c, :] = SampledMatrixI[i, :]
(UNCT_Param) = Uncertainty1T(ReSampledMatrixI)
return (UNCT_Param) #ReSampledMatrixI
def MCMCInit_PSPVPUniform(FITPAR,FITPARLB,FITPARUB,MCPAR):
MCMCInit=np.zeros([int(MCPAR[0]),int(MCPAR[1])+1])
for i in range(int(MCPAR[1])-3):
if FITPARUB[i]==FITPARLB[i]:
MCMCInit[:,i]=FITPAR[i]
else:
A= np.arange(FITPARLB[i],FITPARUB[i]+0.0001,(FITPARUB[i]-FITPARLB[i])/(int(MCPAR[0])-1))
R=np.random.rand(int(MCPAR[0]))
ind=R.argsort()
A=A[ind]
MCMCInit[:,i]=A
MCMCInit[:,int(MCPAR[1])-3:int(MCPAR[1])]=FITPAR[int(MCPAR[1])-3:int(MCPAR[1])]
for i in range(int(MCPAR[0])):
SimInt=SimInt_PSPVP(MCMCInit[i,:])
C=np.sum(CD.Misfit(Intensity,SimInt))
MCMCInit[i,int(MCPAR[1])]=C
return MCMCInit
SLD[2, 0] = SLD1
SLD[3, 0] = SLD1
Coord = CD.ID1CoordAssign(TPAR, SLD, Trapnumber, Pitch)
#CDp.plotID1(Coord,Trapnumber,Pitch)
(FITPAR, FITPARLB, FITPARUB) = CD.PBA_ID1(TPAR, SPAR, Trapnumber)
R = np.random.normal(0, 0.225, [len(Qx[:, 0]), len(Qx[0, :])])
(Intensity, Amplitude) = SimInt_ID1(FITPAR)
N = (1 / (np.power(Intensity, 0.5))) * Intensity # Generates noise
N = N * R
Intensity2 = Intensity + R
# Applies Noise
C = CD.Misfit(Intensity, Intensity2)
Chi2 = np.sum((C))
MCPAR = np.zeros([7])
MCPAR[0] = 1 # Chainnumber
MCPAR[1] = len(FITPAR)
MCPAR[2] = 5000 #stepnumber
MCPAR[3] = 0 #randomchains
MCPAR[4] = 20 # Resampleinterval
MCPAR[5] = 100 # stepbase
MCPAR[6] = 100 # steplength
MCMCInitial = MCMCInit_ID1(FITPAR, FITPARLB, FITPARUB, MCPAR)
Acceptprob = 0
while Acceptprob < 0.3 or Acceptprob > 0.45:
L = int(MCPAR[1])
SLD[2, 0] = SLD1
SLD[3, 0] = SLD1
Coord = CD.ID1CoordAssign(TPAR, SLD, Trapnumber, Pitch)
#CDp.plotID1(Coord,Trapnumber,Pitch)
(FITPAR, FITPARLB, FITPARUB) = CD.PBA_ID1(TPAR, SPAR, Trapnumber)
R = np.random.normal(0, 0.225, [len(Qx[:, 0]), len(Qx[0, :])])
(Intensity, Amplitude) = SimInt_ID1(FITPAR)
N = (1 / (np.power(Intensity, 0.5))) * Intensity # Generates noise
N = N * R
Intensity2 = Intensity + R
# Applies Noise
C = CD.Misfit(Intensity, Intensity2)
Chi2 = np.sum((C))
MCPAR = np.zeros([7])
MCPAR[0] = 6 # Chainnumber
MCPAR[1] = len(FITPAR)
MCPAR[2] = 1000 #stepnumber
MCPAR[3] = 0 #randomchains
MCPAR[4] = 20 # Resampleinterval
MCPAR[5] = 350 # stepbase
MCPAR[6] = 350 # steplength
# MCMCInitial=MCMCInit_ID1(FITPAR,FITPARLB,FITPARUB,MCPAR)
# Acceptprob=0;
# while Acceptprob < 0.3 or Acceptprob > 0.45:
# L = int(MCPAR[1])
Move = np.zeros([L + 1])
ChiPrior = MCMCInitial[0, L]
for step in np.arange(1, Stepnumber, 1):
Temp = SampledMatrix[step - 1, :].copy()
for p in range(L - 1):
StepControl = MCPAR[5] + MCPAR[6] * np.random.random_sample()
Move[p] = (FITPARUB[p] - FITPARLB[p]) / StepControl * (
np.random.random_sample() - 0.5) # need out of bounds check
Temp[p] = Temp[p] + Move[p]
if Temp[p] < FITPARLB[p]:
Temp[p] = FITPARLB[p] + (FITPARUB[p] - FITPARLB[p]) / 1000
elif Temp[p] > FITPARUB[p]:
Temp[p] = FITPARUB[p] - (FITPARUB[p] - FITPARLB[p]) / 1000
(SimPost) = SimInt_LAM1(Temp)
ChiPost = np.sum(CD.Misfit(Intensity, SimPost))
if ChiPost < ChiPrior:
SampledMatrix[step, 0:L] = Temp[0:L]
SampledMatrix[step, L] = ChiPost
ChiPrior = ChiPost
else:
MoveProb = np.exp(-0.5 * np.power(ChiPost - ChiPrior, 2))
if np.random.random_sample() < MoveProb:
SampledMatrix[step, 0:L] = Temp[0:L]
SampledMatrix[step, L] = ChiPost
ChiPrior = ChiPost
else:
SampledMatrix[step, :] = SampledMatrix[step - 1, :]
AcceptanceNumber = 0
Acceptancetotal = len(SampledMatrix[:, 1])
Offset = FITPAR[T * 5:T * 5 + 7]
SPAR = FITPAR[T * 5 + 7:T * 5 + 11]
Coord = CD.PSPVPCoord(Spline, MCoord, Trapnumber, Disc, Pitch, Offset)
F1 = CD.FreeFormTrapezoid(Coord[:, :, 0], Qx, Qz, Disc + 1)
F2 = CD.FreeFormTrapezoid(Coord[:, :, 1], Qx, Qz, Disc + 1)
F3 = CD.FreeFormTrapezoid(Coord[:, :, 2], Qx, Qz, Disc + 1)
F4 = CD.FreeFormTrapezoid(Coord[:, :, 3], Qx, Qz, Disc + 1)
F5 = CD.FreeFormTrapezoid(Coord[:, :, 4], Qx, Qz, Disc + 1)
F6 = CD.FreeFormTrapezoid(Coord[:, :, 5], Qx, Qz, Disc + 1)
F7 = CD.FreeFormTrapezoid(Coord[:, :, 6], Qx, Qz, Disc + 1)
F8 = CD.FreeFormTrapezoid(Coord[:, :, 7], Qx, Qz, Disc + 1)
Formfactor = (F1 + F2 + F3 + F4 + F5 + F6 + F7 + F8)
M = np.power(
np.exp(-1 * (np.power(Qx, 2) + np.power(Qz, 2)) *
np.power(SPAR[0], 2)), 0.5)
Formfactor = Formfactor * M
SimInt = np.power(abs(Formfactor), 2) * SPAR[1] + SPAR[2]
return SimInt
(FITPAR, FITPARLB, FITPARUB) = CD.PSPVP_PB(Offset, Spline, SPAR, Trapnumber,
Disc)
F2 = np.zeros([len(FITPAR) + 1])
F2[0:len(FITPAR)] = FITPAR
Sim = SimInt_PSPVP(F2)
C = np.sum(CD.Misfit(Intensity, Sim))
plt.semilogy(Qz[:, 4], Intensity[:, 4], '.')
plt.semilogy(Qz[:, 4], Sim[:, 4])
ppar[2,0]=0.5; ppar[2,1]=0.2; ppar[2,2]=0; Pitch = 135.7; DW = 1.5 I0 = 0.005 Bk = 33.4 SPAR=np.zeros([4,1]) SPAR[0,0]=DW; SPAR[1,0]=I0; SPAR[2,0]=Bk;SPAR[3,0]=Pitch Coord=CD.SCNCoordAssign(tpar,Trapnumber,X1,X2,X3,Pitch) SimInt = CD.SCNIntensitySim(Coord,Qx,Qz,Trapnumber,DW,I0,Bk) Coordp=CD.SCNParabolaCoord(tpar,ppar,Discretization,Trapnumber, X1, X2, Pitch) SimIntp = CD.SCNIntensitySim(Coordp,Qx,Qz,Trapnumber+Discretization-1,DW,I0,Bk) CD.PlotQzCut(Qz,SimIntp,Intensity,26) Chi2=CD.Misfit(Intensity,SimInt) C=Chi2.sum() #%% [a, b, c,d,e,f,g,h]=CD.ParBoundSCN(tpar,ppar,SPAR,X) #%% MCPAR=np.zeros[4,1] MCPAR[0,0] = 10 # Chainnumber MCPAR[1,0] = len(FITPAR) MCPAR[1,0] = 10 #stepnumber MCPAR[2,0] = 0 #randomchains
