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fitModel2.R
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fitModel2.R
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# for fitting the model assuming the locking rate data product is tapered
fitModel2 = function(initParams=NULL, useMVNApprox=FALSE, gpsDat=slipDatCSZ,
G=NULL, fauxG=NULL, subDat=dr1, fault=csz, nKnots=5, normalizeTaper=TRUE,
dStar=21000, useGrad=FALSE, maxit=500, latRange=c(40, 50),
normalModel=FALSE, doHess=TRUE, corGPS=FALSE, finalFit=FALSE,
diffGPSTaper=FALSE, nKnotsGPS=nKnots, reltol=1e-8, anisotropic=FALSE,
useGradForHess=(finalFit && doHess && useGrad), verbose=TRUE,
nKnotsGamma=7, doGammaSpline=FALSE, nKnotsVar=5, doVarSpline=FALSE,
dStarGPS=dStar) {
##### Set up initial parameter guesses for the MLE optimization if necessary (OUTDATED INITIALIZATION)
# variance of a lognormal (x) is (exp(sigma^2) - 1) * exp(2mu + sigma^2)
# then sigma^2 = log(var(e^x)) - 2mu - log(e^(sigma^2) - 1)
# so sigma^2 \approx log(var(e^x)) - 2mu
# sigmaZetaInit = sqrt(log(var(dr1$subsidence)) - 2*muZetaInit)
if(is.null(initParams)) {
lambdaInit=2
if(!normalModel) {
muZetaInit = log(20)
phiInit = 250
sigmaZetaInit = 1
}
else {
muZetaInit = 20
phiInit = 175
sigmaZetaInit = sd(gpsDat$slip)*(muZetaInit/mean(gpsDat$slip))
}
# muXiInit = log(2.25) # based on plots from exploratory analysis
# initSplineParams = getInitialSplineEsts(muZetaInit, sigmaZetaInit, lambdaInit, nKnots=nKnots,
# normalizeTaper=normalizeTaper, dStar=dStar)
initSplineParams = getSplineEstsMomentMatch(muZetaInit, sigmaZetaInit, lambdaInit, corMatCSZ, nKnotsMean=nKnots,
nKnotsVar=nKnots, normalizeTaper=normalizeTaper, dStar=dStar,
normalModel=normalModel, useGrad=useGrad, fault=fault,
latRange=latRange, G=G, subDat=subDat)$betaHat
initParams = c(muZetaInit, sigmaZetaInit, initSplineParams)
# initialize with isotropic model even if we want to fit an anisotropic model eventually
if(anisotropic) {
initParams = c(muZetaInit, sigmaZetaInit, initSplineParams, 1)
}
initParams
}
# get input parameters
out = getInputPar(initParams, fault, gpsDat, nKnots, diffGPSTaper, nKnotsGPS, taperedGPSDat, anisotropic, normalModel, nKnotsVar, doVarSpline)
muZeta = out$muZeta
muVecCSZ = out$muVecCSZ
muVecGPS = out$muVecGPS
sigmaZeta = out$sigmaZeta
taperPar = out$taperPar
taperParGPS = out$taperParGPS
phiZeta = out$phiZeta
nuZeta = out$nuZeta
lambda0 = out$lambda0
alpha = out$alpha
varPar = out$varPar
parscale = out$parscale
parNames = out$parNames
# set spatial correlation smoothness
nuZeta = 3/2
##### calculate correlation matrices for Zeta in km (for CSZ grid and the GPS data)
# NOTE: only the upper triangle is computed for faster computation. This is
# sufficient for R's Cholesky decomposition
# since we only want the correlation matrix, set sigmaZeta to 1
# coords = cbind(csz$longitude, csz$latitude)
# corMatCSZ = stationary.cov(coords, Covariance="Matern", theta=phiZeta,
# onlyUpper=TRUE, Distance="rdist.earth",
# Dist.args=list(miles=FALSE), smoothness=nuZeta)
# don't compute the areally averaged covariance matrix: takes too long
# tmpParams = rep(1, 5)
# corMatCSZ = arealZetaCov(tmpParams, csz, nDown1=9, nStrike1=12)
# get Okada linear transformation matrix
if(is.null(G)) {
nx = 300
ny= 900
lonGrid = seq(lonRange[1], lonRange[2], l=nx)
latGrid = seq(latRange[1], latRange[2], l=ny)
G = okadaAll(fault, lonGrid, latGrid, cbind(subDat$Lon, subDat$Lat), slip=1, poisson=0.25)
}
if(is.null(fauxG))
fauxG = getFauxG()
##### calculate depths of the centers of the CSZ subfaults
cszDepths = getFaultCenters(fault)[,3]
##### compute distance matrices for fault and for gps data
coordsGPS = cbind(gpsDat$lon, gpsDat$lat)
coordsCSZ = cbind(fault$longitude, fault$latitude)
if(!anisotropic) {
distMatGPS = rdist.earth(coordsGPS, miles=FALSE)
distMatCSZ = rdist.earth(coordsCSZ, miles=FALSE)
squareStrikeDistCsz = NULL
squareDipDistCsz = NULL
squareStrikeDistGps = NULL
squareDipDistGps = NULL
} else {
distMatGPS = NULL
distMatCSZ = NULL
# the below code has bin commented out because the resulting covariances are not positive semi-definite
# ## under anisotropic model, we compute the along strike and along dip distances separately
# # fault geometry distances
# out = compute_subfault_distances(csz)
# squareStrikeDistCsz = out$Dstrike^2
# squareDipDistCsz = out$Ddip^2
#
# # gps data distances
# out = compute_dip_strike_distance_gps(slipDatCSZ, csz)
# squareStrikeDistGps = out$Dstrike^2
# squareDipDistGps = out$Ddip^2
### the below code is been commented out because the resulting transformation
### modified the original distances too much
# ## under anisotropic model, we compute the along strike and along dip distances separately
# # straighten fault and gps geometries
# faultGeomStraight = straightenFault3()
# cszStraight = divideFault2(faultGeomStraight)
# cszStraight$centerX = 0.5 * (cszStraight$topLeftX + cszStraight$topRightX)
# cszStraight$centerY = 0.5 * (cszStraight$topLeftY + cszStraight$bottomRightY)
# straightenedGpsCoords = calcStraightGpsCoords(faultGeomStraight, faultGeom, gpsDat)
#
# # convert from new, straightened coordinate system to kilometers
# topI = 13
# bottomI = 1
# originalDist = rdist.earth(faultGeom[c(topI, bottomI), 2:3], miles=FALSE)[1, 2]
# newDist = rdist(cbind(c(faultGeomStraight$topMiddleX[topI], faultGeomStraight$topMiddleX[bottomI]),
# c(faultGeomStraight$topMiddleY[topI], faultGeomStraight$topMiddleY[bottomI])))[1, 2]
# kmPerUnit = originalDist / newDist
#
# # calculate along strike and along dip squared distances in kilometers
# strikeCoords = cbind(0, cszStraight$centerY * kmPerUnit)
# dipCoords = cbind(cszStraight$centerX * kmPerUnit, 0)
# squareStrikeDistCsz = rdist(strikeCoords)^2
# squareDipDistCsz = rdist(dipCoords)^2
#
# # do the same for the gps data
# strikeCoords = cbind(0, straightenedGpsCoords[,2] * kmPerUnit)
# dipCoords = cbind(straightenedGpsCoords[,1] * kmPerUnit, 0)
# squareStrikeDistGps = rdist(strikeCoords)^2
# squareDipDistGps = rdist(dipCoords)^2
### Rather than training the fault, we redefine an axis to be the strike access in Euclidean space
### using a Lambert projection and PCA
out = straightenFaultLambert()
faultGeomStraight = out$fault
scale = out$scale
parameters = out$projPar
transformation = out$transformation
cszStraight = divideFault2(faultGeomStraight)
centers = getFaultCenters(csz)[,1:2]
newCenters = transformation(centers)
cszStraight$centerX = newCenters[,1]
cszStraight$centerY = newCenters[,2]
straightenedGpsCoords = transformation(cbind(gpsDat$lon, gpsDat$lat))
# calculate along strike and along dip squared distances in kilometers
strikeCoords = cbind(0, cszStraight$centerY)
dipCoords = cbind(cszStraight$centerX, 0)
squareStrikeDistCsz = rdist(strikeCoords)^2
squareDipDistCsz = rdist(dipCoords)^2
# do the same for the gps data
strikeCoords = cbind(0, straightenedGpsCoords[,2])
dipCoords = cbind(straightenedGpsCoords[,1], 0)
squareStrikeDistGps = rdist(strikeCoords)^2
squareDipDistGps = rdist(dipCoords)^2
}
##### Do optimization
optimTable <<- NULL # table to save likelihood optimization steps
if(is.null(reltol)) {
if(normalizeTaper)
reltol=1e-13
else
reltol=1e-8
}
# if(normalizeTaper)
# controls = list(fnscale = -1, reltol=reltol, parscale=c(2, 2, rep(1, length(initParams)-3-anisotropic), 25), maxit=maxit)
# else
# controls = list(fnscale = -1, reltol=reltol, parscale=c(2, 2, rep(1/21000, length(initParams)-3-anisotropic), 25), maxit=maxit)
# if(anisotropic)
# controls$parscale = c(controls$parscale, 2)
#
# if(finalFit) {
# controls$parscale = controls$parscale/25
# }
controls = list(fnscale = -1, reltol=reltol, parscale=parscale, maxit=maxit)
cszDepthsIn = cszDepths
corMatGPSIn = NULL
corMatCSZIn = NULL
corMatCSZLIn = NULL
gpsDatIn = gpsDat
nsimIn = 500 # this doens't matter since it's not used
dStarIn = dStar
normalizeTaperIn = normalizeTaper
useMVNApproxIn = TRUE
useASLApproxIn = FALSE
nKnotsIn = nKnots
GIn = G
subDatIn = subDat
faultIn = fault
useSubPriorIn = FALSE
useSlipPriorIn = FALSE
fauxGIn = fauxG
constrLambdaIn = FALSE
latRangeIn = latRange
normalModelIn = normalModel
taperedGPSDatIn = TRUE
distMatGPSIn = distMatGPS
distMatCSZIn = distMatCSZ
corGPSIn = corGPS
diffGPSTaperIn = diffGPSTaper
nKnotsGPSIn = nKnotsGPS
anisotropicIn = anisotropic
squareStrikeDistCszIn = squareStrikeDistCsz
squareDipDistCszIn = squareDipDistCsz
squareStrikeDistGpsIn = squareStrikeDistGps
squareDipDistGpsIn = squareDipDistGps
verboseIn = verbose
doGammaSplineIn = doGammaSpline
nKnotsGammaIn = nKnotsGamma
dStarGPSIn=dStarGPS
nKnotsVarIn=nKnotsVar
doVarSplineIn=doVarSpline
if(!useGrad)
opt = optim(initParams, fixedDataLogLik, control=controls, hessian=FALSE,
cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
gpsDat=gpsDatIn, nsim=nsimIn, nKnots=nKnotsIn,
useMVNApprox=useMVNApproxIn, G=GIn, subDat=subDatIn, fault=faultIn,
normalizeTaper=normalizeTaperIn, dStar=dStarIn, useASLApprox=useASLApproxIn,
useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
squareDipDistGps=squareDipDistGpsIn, verbose=verboseIn, doGammaSpline=doGammaSplineIn,
nKnotsGamma=nKnotsGammaIn, dStarGPS=dStarGPSIn, doVarSpline=doVarSplineIn,
nKnotsVar=nKnotsVarIn)
else {
lats=seq(latRange[1], latRange[2], l=100)
Xi = getSplineBasis(latRange=latRange, nKnots=nKnots, lats=lats)
if(diffGPSTaper) {
gpsTaperZeroMat = matrix(0, ncol=nKnotsGPS, nrow=100)
uiIn = cbind(0,0,-Xi, gpsTaperZeroMat, 0)
}
else
uiIn = cbind(0,0,-Xi, 0)
if(anisotropic)
uiIn = cbind(uiIn, 0)
opt = constrOptim(initParams, fixedDataLogLik, fixedDataLogLikGrad, control=controls, hessian=FALSE,
cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
gpsDat=gpsDatIn, nKnots=nKnotsIn,
useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
squareDipDistGps=squareDipDistGpsIn, verbose=verboseIn, doGammaSpline=doGammaSplineIn,
nKnotsGamma=nKnotsGammaIn, dStarGPS=dStarGPSIn, doVarSpline=doVarSplineIn,
nKnotsVar=nKnotsVarIn,
method="BFGS", ui=uiIn, ci=rep(-10, 100))
# use BFGS! (constraint makes lambdas not be able to be bigger than 10. Somehow that works...)
}
# test = fullDataLogLik(initParams, cszDepths=cszDepths, corMatGPS=corMatGPS, corMatCSZL=corMatCSZL,
# phiZeta=phiZeta, slipDatCSZ=slipDatCSZ)
# get results of optimization
muZetaMLE = opt$par[1]
sigmaZetaMLE = opt$par[2]
muZetaGPS = muZetaMLE
muZetaCSZ = muZetaMLE
if(length(opt$par) > 3 || (nKnots==1)) {
splinePar = opt$par[(length(opt$par)-(nKnots-1)-1):(length(opt$par) - 1)]
}
if(!anisotropic) {
phiMLE = opt$par[length(opt$par)]
alphaMLE = NA
}
else {
phiMLE = opt$par[length(opt$par) - 1]
alphaMLE = opt$par[length(opt$par)]
}
logLikMLE = opt$value
if(doHess) {
print("Calculating Hessian...")
# if(useGradForHess) {
# hess.args = list(eps=1e-7, d=0.0001, zero.tol=sqrt(.Machine$double.eps/7e-7), r=6, v=2, show.details=FALSE)
# hess = jacobian(fixedDataLogLikGrad, opt$par, method.args=hess.args,
# cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
# gpsDat=gpsDatIn, nKnots=nKnotsIn,
# useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
# fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
# useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
# constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
# taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
# corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
# anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
# squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
# squareDipDistGps=squareDipDistGpsIn, verbose=verboseIn)
# } else {
# hess.args = list(eps=1e-7, d=0.0001, zero.tol=sqrt(.Machine$double.eps/7e-7), r=6, v=2, show.details=FALSE)
# hess = hessian(fixedDataLogLik, opt$par, method.args=hess.args,
# cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
# gpsDat=gpsDatIn, nKnots=nKnotsIn,
# useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
# fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
# useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
# constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
# taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
# corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
# anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
# squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
# squareDipDistGps=squareDipDistGpsIn, verbose=verboseIn)
# # hess = opt$hessian
# }
hess.args = list(eps=1e-4, d=0.001, zero.tol=sqrt(.Machine$double.eps/7e-7), r=4, v=2, show.details=FALSE)
hess = jacobian(fixedDataLogLikGrad, opt$par, method.args=hess.args,
cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
gpsDat=gpsDatIn, nKnots=nKnotsIn,
useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
squareDipDistGps=squareDipDistGpsIn, doGammaSpline=doGammaSplineIn,
nKnotsGamma=nKnotsGammaIn, dStarGPS=dStarGPSIn, doVarSpline=doVarSplineIn,
nKnotsVar=nKnotsVarIn, verbose=FALSE)
# numeric hessian is numerically unstable
# hessNumeric = hessian(fixedDataLogLik, opt$par, method.args=hess.args,
# cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
# gpsDat=gpsDatIn, nKnots=nKnotsIn,
# useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
# fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
# useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
# constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
# taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
# corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
# anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
# squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
# squareDipDistGps=squareDipDistGpsIn, verbose=FALSE)
# hess = opt$hessian
}
else {
hess=NULL
}
# calculate gradient at optimum to make sure we're at a local maximum
print("Calculating Jacobian")
if(useGrad)
optGrad = fixedDataLogLikGrad(opt$par, cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
gpsDat=gpsDatIn, nKnots=nKnotsIn,
useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
squareDipDistGps=squareDipDistGpsIn, doGammaSpline=doGammaSplineIn,
nKnotsGamma=nKnotsGammaIn, dStarGPS=dStarGPSIn, doVarSpline=doVarSplineIn,
nKnotsVar=nKnotsVarIn)
else
optGrad = jacobian(fixedDataLogLik, opt$par, cszDepths=cszDepthsIn, corMatGPS=corMatGPSIn, corMatCSZL=corMatCSZLIn,
gpsDat=gpsDatIn, nKnots=nKnotsIn,
useMVNApprox=TRUE, G=GIn, subDat=subDatIn,
fault=faultIn, normalizeTaper=normalizeTaperIn, dStar=dStarIn,
useSubPrior=useSubPriorIn, useSlipPrior=useSlipPriorIn, fauxG=fauxGIn,
constrLambda=constrLambdaIn, latRange=latRangeIn, normalModel=normalModelIn,
taperedGPSDat=taperedGPSDatIn, distMatGPS=distMatGPSIn, distMatCSZ=distMatCSZIn,
corGPS=corGPSIn, diffGPSTaper=diffGPSTaperIn, nKnotsGPS=nKnotsGPSIn,
anisotropic=anisotropicIn, squareStrikeDistCsz=squareStrikeDistCszIn,
squareDipDistCsz=squareDipDistCszIn, squareStrikeDistGps=squareStrikeDistGpsIn,
squareDipDistGps=squareDipDistGpsIn, doGammaSpline=doGammaSplineIn,
nKnotsGamma=nKnotsGammaIn, dStarGPS=dStarGPSIn, doVarSpline=doVarSplineIn,
nKnotsVar=nKnotsVarIn)
# compute spline basis matrix for subsidence data
Xi = getSplineBasis(fault, nKnots=nKnots, latRange=latRange)
XiGPS1 = getSplineBasis(data.frame(list(latitude=gpsDat$lat)), nKnots=nKnots, latRange=latRange)
# now get lambdas
taperPar = opt$par[3:(length(opt$par)-1 - anisotropic)]
taperParGPS = taperPar[-(1:nKnots)]
taperPar = taperPar[1:nKnots]
lambda = Xi %*% taperPar
lambdaGPS = XiGPS1 %*% taperPar
if(diffGPSTaper) {
XiGPS2 = getSplineBasis(data.frame(list(latitude=gpsDat$lat)), nKnots=nKnotsGPS, latRange=latRange)
lambdaGPS = lambdaGPS - XiGPS2 %*% taperParGPS
}
# compute taper vector
tvec = taper(getFaultCenters(fault)[,3], lambda=lambda, alpha=2, normalize=normalizeTaper, dStar=dStar)
tvecGPS = taper(gpsDat$Depth, lambda=lambdaGPS, alpha=2, normalize=normalizeTaper, dStar=dStarGPS)
##### get conditional MLE of muXi
# Calculate the standard error vector of xi. Derivation from week 08_30_17.Rmd presentation.
# Transformation from additive error to multiplicative lognormal model with asympototic
# median and variance matching.
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
# estimate muXi MLE with inverse variance weighting
x = log(gpsDat$slip)
ci = 1/sigmaXi^2
ci = ci/sum(ci)
if(doGammaSpline) {
ys = x- log(muZetaMLE) - log(tvecGPS)
X = getSplineBasis(data.frame(list(latitude=gpsDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
logModel = lm(ys~X-1, weights=ci)
gammaEstGps = exp(X %*% logModel$coefficients)
gammaCoefs = logModel$coefficients
gammaBasis = X
gammaEst = list(gammaEstGps=gammaEstGps, gammaCoefs=gammaCoefs, gammaBasis=gammaBasis)
MLEs = c(NA, opt$par[1:2], 0.25, NA, opt$par[-c(1:2)])
# plot gamma estimate
sortI=sort(gpsDat$lat, index.return=TRUE)$ix
plot(exp(ys), gpsDat$lat, pch=".", xlab=TeX("$\\gamma$"), ylab="Latitude", main=TeX("Estimate of $\\gamma$"))
lines(gammaEstGps[sortI], gpsDat$lat[sortI], col="blue")
quilt.plot(gpsDat$lon, gpsDat$lat, exp(ys), xlab="Longitude", ylab="Latitude", main=TeX("Estimate of $\\gamma$"))
map("world", "Canada", add=TRUE)
world(add=TRUE)
# plot of years between earthquakes
plot(1000/exp(ys), gpsDat$lat, pch=".", xlab="Time (Years)", ylab="Latitude", main="Estimate of Time Between Earthquakes")
lines(1000/gammaEstGps[sortI], gpsDat$lat[sortI], col="blue")
ticks = c(seq(0, 1000, by=100), seq(1500, max(pretty(1000/exp(ys), n=20)), by=500))
quilt.plot(gpsDat$lon, gpsDat$lat, log10(1000/exp(ys)), xlab="Longitude", ylab="Latitude", main="Estimate of Years Between Earthquakes",
add.legend=FALSE)
image.plot(add=TRUE, zlim=range(log10(1000/exp(ys))), nlevel=64, legend.only=TRUE, horizontal=FALSE, axis.args=list( at=log10(ticks), labels=ticks))
map("world", "Canada", add=TRUE)
world(add=TRUE)
}
else {
gammaEst = exp(sum((x- log(muZetaMLE) - log(tvecGPS))*ci))
# params is in order: lambda, muZeta, sigmaZeta, lambda0, gamma, splineParams, phi
MLEs = c(NA, opt$par[1:2], 0.25, gammaEst, opt$par[-c(1:2)])
}
# compute final anisotropy distances if necessary
if(anisotropic) {
strikeDistGps = (1 / alphaMLE) * sqrt(squareStrikeDistGps)
dipDistGps = alphaMLE * sqrt(squareDipDistGps)
strikeDistCsz = (1 / alphaMLE) * sqrt(squareStrikeDistCsz)
dipDistCsz = alphaMLE * sqrt(squareDipDistCsz)
} else {
strikeDistGps = NULL
dipDistGps = NULL
strikeDistCsz = NULL
dipDistCsz = NULL
}
# Return results
return(list(MLEs=MLEs, muZetaMLE=muZetaMLE, sigmaZetaMLE=sigmaZetaMLE, lambdaMLE=NA,
gammaEst=gammaEst, logLikMLE=logLikMLE, splineParMLE=splinePar, phiMLE=phiMLE,
alphaMLE=alphaMLE, hess=hess, optimTable=optimTable,
tvec=tvec, tvecGPS=tvecGPS, optPar=opt$par, optGrad=optGrad,
strikeDistGps = strikeDistGps, dipDistGps = dipDistGps,
strikeDistCsz = strikeDistCsz, dipDistCsz = dipDistCsz))
}
# compute derivative of Matern correlation matrix with respect to phi (assuming 3/2 smoothness)
corrGrad = function(distMat, phiZeta, corMat,
anisotropic=FALSE, alpha=NULL, squareDistMatStrike=NULL, squareDistMatDip=NULL) {
# distMat * (-1/phiZeta^2 + 1/(-phiZeta^2+(-phiZeta)*distMat)) * corMat
if(!anisotropic)
distMat^2/phiZeta^3 * exp(-distMat/phiZeta)
else {
## an anisotropic case, compute derivative with respect to phi and alpha
# derivative with respect to phi
dphi = distMat^2/phiZeta^3 * exp(-distMat/phiZeta)
# derivative with respect to alpha
numerator = alpha * squareDistMatStrike - alpha^(-3) * squareDistMatDip
denominator = distMat
# dalpha = (1 - 1 / phiZeta) * corMat * (numerator / denominator)
dalpha = (1 / (phiZeta + distMat) - 1 / phiZeta) * corMat * (numerator / denominator)
diag(dalpha) = 0
list(dphi=dphi, dalpha=dalpha)
}
}
# compute the derivative of the expectation of muX
meanXGrad = function(muZeta, nPar, tvecGPS, tGrad, gpsDat=slipDatCSZ, normalModel=FALSE,
taperedGPSDat=FALSE, anisotropic=FALSE, doGammaSpline=FALSE, nKnotsGamma=7) {
##### get conditional MLE of muXi
# Calculate the standard error vector of xi. Derivation from week 08_30_17.Rmd presentation.
# Transformation from additive error to multiplicative lognormal model with asympototic
# median and variance matching.
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
# estimate muXi MLE with inverse variance weighting
x = log(gpsDat$slip)
ci = 1/sigmaXi^2
ci = ci/sum(ci)
if(normalModel) {
x = gpsDat$slip
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
ci = 1/sigmaXi^2
ci = ci/sum(ci)
if(doGammaSpline) {
# first compute gamma estimates
ys = log(x)- log(muZeta) - log(tvecGPS)
X = getSplineBasis(data.frame(list(latitude=gpsDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
logModel = lm(ys~X-1, weights=ci)
muXi = X %*% logModel$coefficients
gammaEst = exp(muXi)
# now compute the gradients of gamma estimates
W = diag(ci)
H = solve(t(X) %*% W %*% X, t(X) %*% W)
tempMat = sweep(X %*% H, 1, -gammaEst, "*")
dGammaMu = rowSums(tempMat) * (1 / muZeta)
dGammaBeta = sweep(tempMat, 2, 1 / tvecGPS, "*") %*% tGrad
} else {
muXi = sum((log(x)- log(muZeta) - log(tvecGPS))*ci)
gammaEst = exp(muXi)
}
}
# compute gradient of mu_X:
ExpXGrad = array(0, dim=c(length(x), nPar))
if(taperedGPSDat) {
if(!normalModel) {
ExpXGrad[,1] = 1
if(taperedGPSDat)
ExpXGrad[,3:(nPar-1 - anisotropic)] = 1/tGrad
}
else {
if(doGammaSpline) {
ExpXGrad[,3:(nPar-1 - anisotropic)] = sweep(tGrad, 1, gammaEst * muZeta, "*") + sweep(dGammaBeta, 1, tvecGPS * muZeta, "*")
} else {
# ExpXGrad[,3:(nPar-1)] = gammaEst * muZeta * tGrad + outer(c(tvecGPS * muZeta), c(gammaEst * matrix(ci*tvecGPS, nrow=1) %*% tGrad))
ExpXGrad[,3:(nPar-1 - anisotropic)] = muZeta * gammaEst * (tvecGPS %*% matrix(-ci/tvecGPS, nrow=1) + diag(nrow=length(tvecGPS))) %*% tGrad
}
}
}
else {
# do nothing, since gradient is 0
}
ExpXGrad
}
# compute the derivative of the covariance matrix of X
covXGrad = function(muZeta, sigmaZeta, tvecGPS, tGrad, corMatGPS, nPar, distMatGPS=NULL,
phiZeta=NULL, gpsDat=slipDatCSZ, normalModel=FALSE, taperedGPSDat=FALSE,
corGPS=FALSE, anisotropic=FALSE, alpha=1, squareDistMatStrike=NULL,
squareDistMatDip=NULL, doGammaSpline=FALSE, nKnotsGamma=7) {
##### get conditional MLE of muXi
# Calculate the standard error vector of xi. Derivation from week 08_30_17.Rmd presentation.
# Transformation from additive error to multiplicative lognormal model with asympototic
# median and variance matching.
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
# estimate muXi MLE with inverse variance weighting
x = log(gpsDat$slip)
ci = 1/sigmaXi^2
ci = ci/sum(ci)
if(normalModel) {
x = gpsDat$slip
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
ci = 1/sigmaXi^2
ci = ci/sum(ci)
if(doGammaSpline) {
ys = log(x) - log(muZeta) - log(tvecGPS)
X = getSplineBasis(data.frame(list(latitude=gpsDat$lat)), nKnots=nKnotsGamma, latRange=latRange)
logModel = lm(ys~X-1, weights=ci)
muXi = X %*% logModel$coefficients
gammaEst = exp(muXi)
# now compute the gradients of gamma estimates
W = diag(ci)
H = solve(t(X) %*% W %*% X, t(X) %*% W)
tempMat = sweep(X %*% H, 1, -gammaEst, "*")
dGammaMu = rowSums(tempMat) * (1 / muZeta)
dGammaBeta = sweep(tempMat, 2, 1 / tvecGPS, "*") %*% tGrad
} else {
muXi = sum((log(x)- log(muZeta) - log(tvecGPS))*ci)
gammaEst = exp(muXi)
}
sigmaXi = gpsDat$slipErr
}
# compute gradient of Sigma_X:
SigmaGrad = array(0, dim = c(length(x), length(x), nPar))
if(!normalModel) {
SigmaGrad[,,2] = 2*sigmaZeta*corMatGPS
if(taperedGPSDat) {
SigmaGrad[,,nPar] = sigmaZeta^2 * corrGrad(distMatGPS, phiZeta, corMatGPS,
anisotropic, alpha, squareDistMatStrike, squareDistMatDip)
}
}
else {
if(!doGammaSpline)
dGammaEstDMu = -gammaEst/muZeta
if(!taperedGPSDat) {
if(doGammaSpline)
stop("Fitting gamma spline while assuming the gps data is not tapered is not yet supported")
SigmaGrad[,,1] = 2*gammaEst*sigmaZeta^2*corMatGPS * dGammaEstDMu
SigmaGrad[,,2] = 2*gammaEst^2*sigmaZeta*corMatGPS
}
else {
if(!doGammaSpline) {
SigmaGrad[,,1] = 2*gammaEst* sweep(sweep(sigmaZeta^2*corMatGPS, 1, tvecGPS, "*"), 2, tvecGPS, "*") * dGammaEstDMu
SigmaGrad[,,2] = 2*gammaEst^2*sigmaZeta*sweep(sweep(corMatGPS, 1, tvecGPS, "*"), 2, tvecGPS, "*")
}
else {
SigmaGrad[,,1] = sweep(sweep(sigmaZeta^2*corMatGPS, 1, tvecGPS * dGammaMu, "*"), 2, tvecGPS * gammaEst, "*")
SigmaGrad[,,1] = SigmaGrad[,,1] + t(SigmaGrad[,,1])
SigmaGrad[,,2] = 2*sigmaZeta*sweep(sweep(corMatGPS, 1, tvecGPS * gammaEst, "*"), 2, tvecGPS * gammaEst, "*")
}
# use the taper gradient to compute the rest of the covariance gradient
nKnotsTot = ncol(tGrad)
for(i in 1:nKnotsTot) {
if(!doGammaSpline) {
pt1 = c(-sigmaZeta^2*2*gammaEst^2*(matrix(ci/tvecGPS, nrow=1)%*%matrix(tGrad[,nKnotsTot-i+1], ncol=1))) * sweep(sweep(corMatGPS, 1, tvecGPS, "*"), 2, tvecGPS, "*")
# tmp = sweep(sweep(sigmaZeta^2 * corMatGPS, 1, tGrad[,nKnotsTot-i+1], "*"), 2, tvecGPS, "*")
# pt2 = gammaEst^2 * (tmp + t(tmp))
tmp = tGrad[,nKnotsTot-i+1] %*% matrix(tvecGPS, nrow=1)
pt2 = gammaEst^2 * corMatGPS * sigmaZeta^2 * (tmp + t(tmp))
SigmaGrad[,,nPar-i - anisotropic] = pt1 + pt2
}
else {
gradVec = dGammaBeta[,nKnotsTot-i+1] * tvecGPS + gammaEst * tGrad[,nKnotsTot-i+1]
tmp = sweep(sweep(corMatGPS, 1, gradVec, "*"), 2, tvecGPS * gammaEst, "*")
SigmaGrad[,,nPar-i - anisotropic] = sigmaZeta^2 * (tmp + t(tmp))
}
}
if(!anisotropic) {
CGrad = corrGrad(distMatGPS, phiZeta, corMatGPS,
anisotropic, alpha, squareDistMatStrike, squareDistMatDip)
if(!doGammaSpline)
SigmaGrad[,,nPar] = sigmaZeta^2 * gammaEst^2 * sweep(sweep(CGrad, 1, tvecGPS, "*"), 2, tvecGPS, "*")
else
SigmaGrad[,,nPar] = sigmaZeta^2 * sweep(sweep(CGrad, 1, tvecGPS * gammaEst, "*"), 2, tvecGPS * gammaEst, "*")
if(corGPS) {
extraBit = sweep(sweep(CGrad, 1, sigmaXi, "*"), 2, sigmaXi, "*")
SigmaGrad[,,nPar] = SigmaGrad[,,nPar] + extraBit
}
}
else {
out = corrGrad(distMatGPS, phiZeta, corMatGPS,
anisotropic, alpha, squareDistMatStrike, squareDistMatDip)
CGrad = out$dphi
alphaGrad = out$dalpha
if(!doGammaSpline) {
SigmaGrad[,,nPar - 1] = sigmaZeta^2 * gammaEst^2 * sweep(sweep(CGrad, 1, tvecGPS, "*"), 2, tvecGPS, "*")
SigmaGrad[,,nPar] = sigmaZeta^2 * gammaEst^2 * sweep(sweep(alphaGrad, 1, tvecGPS, "*"), 2, tvecGPS, "*")
}
else {
SigmaGrad[,,nPar - 1] = sigmaZeta^2 * sweep(sweep(CGrad, 1, tvecGPS * gammaEst, "*"), 2, tvecGPS * gammaEst, "*")
SigmaGrad[,,nPar] = sigmaZeta^2 * sweep(sweep(alphaGrad, 1, tvecGPS * gammaEst, "*"), 2, tvecGPS * gammaEst, "*")
}
if(corGPS) {
# if we assume the same correlation structure in the measurement error of xi, we must account for this
extraBitPhi = sweep(sweep(CGrad, 1, sigmaXi, "*"), 2, sigmaXi, "*")
extraBitAlpha = sweep(sweep(alphaGrad, 1, sigmaXi, "*"), 2, sigmaXi, "*")
SigmaGrad[,,nPar - 1] = SigmaGrad[,,nPar - 1] + extraBitPhi
SigmaGrad[,,nPar] = SigmaGrad[,,nPar] + extraBitAlpha
}
}
}
}
SigmaGrad
}
# compute gamma estimate from model fit assuming a normal model
computeGammaEst = function(modelFit, gpsDat, tvecGPS=modelFit$tvecGPS) {
muZeta = modelFit$muZetaMLE
# Calculate the standard error vector of xi. Derivation from week 08_30_17.Rmd presentation.
# Transformation from additive error to multiplicative lognormal model with asympototic
# median and variance matching.
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
# estimate muXi MLE with inverse variance weighting
x = gpsDat$slip
sigmaXi = sqrt(log(.5*(sqrt(4*gpsDat$slipErr^2/gpsDat$slip^2 + 1) + 1)))
ci = 1/sigmaXi^2
ci = ci/sum(ci)
muXi = sum((log(x)- log(muZeta) - log(tvecGPS))*ci)
gammaEst = exp(muXi)
return(gammaEst)
}
# parametricBootstrap = function(optParams, useMVNApprox=FALSE, gpsDat=slipDatCSZ,
# G=NULL, fauxG=NULL, subDat=dr1, fault=csz, nKnots=5, normalizeTaper=TRUE,
# dStar=21000, useGrad=FALSE, maxit=500, latRange=c(40, 50),
# normalModel=FALSE, doHess=TRUE, corGPS=FALSE, finalFit=FALSE,
# diffGPSTaper=FALSE, nKnotsGPS=nKnots, reltol=1e-8, anisotropic=FALSE,
# useGradForHess=(finalFit && doHess && useGrad), verbose=TRUE) {
#
# ##### Set up initial parameter guesses for the MLE optimization if necessary
# # variance of a lognormal (x) is (exp(sigma^2) - 1) * exp(2mu + sigma^2)
# # then sigma^2 = log(var(e^x)) - 2mu - log(e^(sigma^2) - 1)
# # so sigma^2 \approx log(var(e^x)) - 2mu
# # sigmaZetaInit = sqrt(log(var(dr1$subsidence)) - 2*muZetaInit)
# if(is.null(optParams)) {
# lambdaInit=2
# if(!normalModel) {
# muZetaInit = log(20)
# phiInit = 250
# sigmaZetaInit = 1
# }
# else {
# muZetaInit = 20
# phiInit = 175
# sigmaZetaInit = sd(gpsDat$slip)*(muZetaInit/mean(gpsDat$slip))
# }
#
# # muXiInit = log(2.25) # based on plots from exploratory analysis
# # initSplineParams = getInitialSplineEsts(muZetaInit, sigmaZetaInit, lambdaInit, nKnots=nKnots,
# # normalizeTaper=normalizeTaper, dStar=dStar)
# initSplineParams = getSplineEstsMomentMatch(muZetaInit, sigmaZetaInit, lambdaInit, corMatCSZ, nKnotsMean=nKnots,
# nKnotsVar=nKnots, normalizeTaper=normalizeTaper, dStar=dStar,
# normalModel=normalModel, useGrad=useGrad, fault=fault,
# latRange=latRange, G=G, subDat=subDat)$betaHat
# optParams = c(muZetaInit, sigmaZetaInit, initSplineParams)
#
# # initialize with isotropic model even if we want to fit an anisotropic model eventually
# if(anisotropic) {
# optParams = c(muZetaInit, sigmaZetaInit, initSplineParams, 1)
# }
#
# optParams
# }
#
# # set spatial correlation smoothness
# nuZeta = 3/2
#
# ##### calculate correlation matrices for Zeta in km (for CSZ grid and the GPS data)
# # NOTE: only the upper triangle is computed for faster computation. This is
# # sufficient for R's Cholesky decomposition
# # since we only want the correlation matrix, set sigmaZeta to 1
# # coords = cbind(csz$longitude, csz$latitude)
# # corMatCSZ = stationary.cov(coords, Covariance="Matern", theta=phiZeta,
# # onlyUpper=TRUE, Distance="rdist.earth",
# # Dist.args=list(miles=FALSE), smoothness=nuZeta)
# # don't compute the areally averaged covariance matrix: takes too long
# # tmpParams = rep(1, 5)
# # corMatCSZ = arealZetaCov(tmpParams, csz, nDown1=9, nStrike1=12)
#
# # get Okada linear transformation matrix
# if(is.null(G)) {
# nx = 300
# ny= 900
# lonGrid = seq(lonRange[1], lonRange[2], l=nx)
# latGrid = seq(latRange[1], latRange[2], l=ny)
# G = okadaAll(fault, lonGrid, latGrid, cbind(subDat$Lon, subDat$Lat), slip=1, poisson=0.25)
# }
# if(is.null(fauxG))
# fauxG = getFauxG()
#
# ##### calculate depths of the centers of the CSZ subfaults
# cszDepths = getFaultCenters(fault)[,3]
#
# ##### compute distance matrices for fault and for gps data
# coordsGPS = cbind(gpsDat$lon, gpsDat$lat)
# coordsCSZ = cbind(fault$longitude, fault$latitude)
# if(!anisotropic) {
# distMatGPS = rdist.earth(coordsGPS, miles=FALSE)
# distMatCSZ = rdist.earth(coordsCSZ, miles=FALSE)
# squareStrikeDistCsz = NULL
# squareDipDistCsz = NULL
# squareStrikeDistGps = NULL
# squareDipDistGps = NULL
# } else {
# distMatGPS = NULL
# distMatCSZ = NULL
#
# # the below code has bin commented out because the resulting covariances are not positive semi-definite
# # ## under anisotropic model, we compute the along strike and along dip distances separately
# # # fault geometry distances
# # out = compute_subfault_distances(csz)
# # squareStrikeDistCsz = out$Dstrike^2
# # squareDipDistCsz = out$Ddip^2
# #
# # # gps data distances
# # out = compute_dip_strike_distance_gps(slipDatCSZ, csz)
# # squareStrikeDistGps = out$Dstrike^2
# # squareDipDistGps = out$Ddip^2
#
# ### the below code is been commented out because the resulting transformation
# ### modified the original distances too much
# # ## under anisotropic model, we compute the along strike and along dip distances separately
# # # straighten fault and gps geometries
# # faultGeomStraight = straightenFault3()
# # cszStraight = divideFault2(faultGeomStraight)
# # cszStraight$centerX = 0.5 * (cszStraight$topLeftX + cszStraight$topRightX)
# # cszStraight$centerY = 0.5 * (cszStraight$topLeftY + cszStraight$bottomRightY)
# # straightenedGpsCoords = calcStraightGpsCoords(faultGeomStraight, faultGeom, gpsDat)
# #
# # # convert from new, straightened coordinate system to kilometers
# # topI = 13
# # bottomI = 1
# # originalDist = rdist.earth(faultGeom[c(topI, bottomI), 2:3], miles=FALSE)[1, 2]
# # newDist = rdist(cbind(c(faultGeomStraight$topMiddleX[topI], faultGeomStraight$topMiddleX[bottomI]),
# # c(faultGeomStraight$topMiddleY[topI], faultGeomStraight$topMiddleY[bottomI])))[1, 2]
# # kmPerUnit = originalDist / newDist
# #
# # # calculate along strike and along dip squared distances in kilometers
# # strikeCoords = cbind(0, cszStraight$centerY * kmPerUnit)
# # dipCoords = cbind(cszStraight$centerX * kmPerUnit, 0)
# # squareStrikeDistCsz = rdist(strikeCoords)^2
# # squareDipDistCsz = rdist(dipCoords)^2
# #
# # # do the same for the gps data
# # strikeCoords = cbind(0, straightenedGpsCoords[,2] * kmPerUnit)
# # dipCoords = cbind(straightenedGpsCoords[,1] * kmPerUnit, 0)
# # squareStrikeDistGps = rdist(strikeCoords)^2
# # squareDipDistGps = rdist(dipCoords)^2
#
# ### Rather than training the fault, we redefine an axis to be the strike access in Euclidean space
# ### using a Lambert projection and PCA
# out = straightenFaultLambert()
# faultGeomStraight = out$fault
# scale = out$scale
# parameters = out$projPar
# transformation = out$transformation
#
# cszStraight = divideFault2(faultGeomStraight)
# centers = getFaultCenters(csz)[,1:2]
# newCenters = transformation(centers)
# cszStraight$centerX = newCenters[,1]
# cszStraight$centerY = newCenters[,2]
# straightenedGpsCoords = transformation(cbind(gpsDat$lon, gpsDat$lat))
#
# # calculate along strike and along dip squared distances in kilometers
# strikeCoords = cbind(0, cszStraight$centerY)
# dipCoords = cbind(cszStraight$centerX, 0)
# squareStrikeDistCsz = rdist(strikeCoords)^2
# squareDipDistCsz = rdist(dipCoords)^2
#
# # do the same for the gps data
# strikeCoords = cbind(0, straightenedGpsCoords[,2] * alpha)
# dipCoords = cbind(straightenedGpsCoords[,1] / alpha, 0)
# squareStrikeDistGps = rdist(strikeCoords)^2
# squareDipDistGps = rdist(dipCoords)^2
# }
#
# # set inputs to the data simulation function
# cszDepthsIn = cszDepths
# corMatGPSIn = NULL
# corMatCSZIn = NULL
# corMatCSZLIn = NULL
# gpsDatIn = gpsDat
# nsimIn = 500 # this doens't matter since it's not used
# dStarIn = dStar
# normalizeTaperIn = normalizeTaper
# useMVNApproxIn = TRUE
# useASLApproxIn = FALSE
# nKnotsIn = nKnots
# GIn = G
# subDatIn = subDat
# faultIn = fault
# useSubPriorIn = FALSE
# useSlipPriorIn = FALSE
# fauxGIn = fauxG
# constrLambdaIn = FALSE
# latRangeIn = latRange
# normalModelIn = normalModel
# taperedGPSDatIn = TRUE
# distMatGPSIn = distMatGPS
# distMatCSZIn = distMatCSZ
# corGPSIn = corGPS
# diffGPSTaperIn = diffGPSTaper
# nKnotsGPSIn = nKnotsGPS
# anisotropicIn = anisotropic
# squareStrikeDistCszIn = squareStrikeDistCsz
# squareDipDistCszIn = squareDipDistCsz
# squareStrikeDistGpsIn = squareStrikeDistGps
# squareDipDistGpsIn = squareDipDistGps
# verboseIn = verbose
# }
#
# generateSimulatedDataSets = function(nsim=100, params, cszDepths, corMatGPS=NULL, corMatCSZL=NULL, gpsDat=slipDatCSZ,
# subDat=dr1, fault=csz, useMVNApprox=FALSE, verbose=TRUE, muZeta=NULL,
# G=NULL, nKnots=5, normalizeTaper=TRUE, dStar=21000, useASLApprox=FALSE,
# useSubPrior=FALSE, useSlipPrior=FALSE, fauxG=NULL, constrLambda=TRUE, latRange=c(40,50),
# normalModel=FALSE, taperedGPSDat=FALSE, distMatGPS=NULL, distMatCSZ=NULL,
# corGPS=FALSE, diffGPSTaper=FALSE, nKnotsGPS=nKnots, anisotropic=FALSE,
# squareStrikeDistCsz=NULL, squareDipDistCsz=NULL, squareStrikeDistGps=NULL,
# squareDipDistGps=NULL) {
# ##### get parameters
# alpha = 1
# if(!taperedGPSDat) {
# tvec=NULL
# if(length(params) <= 3 && (nKnots != 1)) {
# vecLambda=FALSE
# if(is.null(muZeta)) {
# lambda = params[1]
# muZeta = params[2]
# sigmaZeta = params[3]
# muZetaGPS = muZeta
# muZetaCSZ = muZeta
# vecMu=FALSE
# }
# else {
# lambda = params[1]
# sigmaZeta = params[2]
# muZetaGPS = muZeta[1:nrow(gpsDat)]
# muZetaCSZ = muZeta[(nrow(gpsDat)+1):length(muZeta)]
# vecMu=TRUE
# }
# }
# if(length(params) > 3 || (nKnots == 1)) {
# vecLambda=TRUE
# if(is.null(muZeta)) {
# muZeta = params[1]
# sigmaZeta = params[2]
# splinePar = params[-c(1:2)]
# tvec = getTaperSpline(splinePar, nKnots=nKnots, normalize=normalizeTaper, dStar=dStar, latRange=latRange, fault=fault)
# Xi = getSplineBasis(fault, nKnots=nKnots, latRange=latRange)
# lambda = Xi %*% splinePar # lambda is only used for checking if lambda < 0
# muZetaGPS = muZeta
# muZetaCSZ = muZeta
# vecMu=FALSE
# }
# else {
# stop("Code not yet written for spline taper fit along with vector muZeta")
# }
# }
# else
# tvec = taper(cszDepths, lambda=lambda, dStar=dStar, normalize=normalizeTaper)
# }
# else {
# ## if the GPS data is considered tapered
# # in this case the parameter vector is the same as otherwise, except it has an additional
# # scale parameter, phi, at the end.
#
# tvec=NULL
# if(length(params) <= 3 && (nKnots != 1)) {
# vecLambda=FALSE
# if(is.null(muZeta)) {
# lambda = params[1]
# muZeta = params[2]
# sigmaZeta = params[3]
# muZetaGPS = muZeta
# muZetaCSZ = muZeta
# vecMu=FALSE
# }
# else {
# lambda = params[1]
# sigmaZeta = params[2]
# muZetaGPS = muZeta[1:nrow(gpsDat)]
# muZetaCSZ = muZeta[(nrow(gpsDat)+1):length(muZeta)]
# vecMu=TRUE
# }
# }
# if(length(params) > 3 || (nKnots == 1)) {
# vecLambda=TRUE
# if(is.null(muZeta)) {
# muZeta = params[1]
# sigmaZeta = params[2]
# if(!anisotropic)
# splinePar = params[-c(1:2, length(params))]
# else
# splinePar = params[-c(1:2, length(params) - 1, length(params))]
# if(diffGPSTaper) {
# splineParGPS = splinePar[-(1:nKnots)]
# splinePar = splinePar[1:nKnots]
# }
# tvec = getTaperSpline(splinePar, nKnots=nKnots, normalize=normalizeTaper, dStar=dStar, latRange=latRange, fault=fault)