Nothing
R/makeOscillatorySimModel-methods.R
In INSPEcT: Modeling RNA synthesis, processing and degradation with RNA-seq data
Defines functions
generateParamsShift
generateOscillatoryParams
#' @rdname makeOscillatorySimModel
#'
#' @description
#' This method allow the creation of synthesis, degradation and processing rates that generate
#' an oscillatory expression with a period of 24 hours. Two modes are available: one where
#' oscillations arise just by oscillations in the synthesis of the genes (oscillatoryk3=FALSE, default) and
#' another one where both synthesis and degradation rates oscillates (oscillatoryk3=TRUE). In this latter case,
#' the oscillations of the two rates can be coupled by a cetrain delay (parametrer k3delay).
#' After the creation of the synthetic rates, a dataset with noise and contamination added can be made by \code{\link{makeSimDataset}}.
#' @param object An object of class INSPEcT
#' @param nGenes A numeric with the number of synthtic genes to be created
#' @param oscillatoryk3 A logical that enables also degradation rate to oscillate
#' @param k3delay A numeric that set the delay between synthesis and degradation oscillations. When NULL, no coupling between the two oscillations is set.
#' @param na.rm A logical that set whether missing values in the real dataset should be removed
#' @param seed A numeric to obtain reproducible results
#' @return An object of class INSPEcT_model with synthetic rates
#' @seealso \code{\link{makeSimModel}}
#' @examples
#' nascentInspObj <- readRDS(system.file(package='INSPEcT', 'nascentInspObj.rds'))
#' simRates<-makeOscillatorySimModel(nascentInspObj, 1000, seed=1)
#' table(geneClass(simRates))
setMethod('makeOscillatorySimModel', 'INSPEcT', function(object
, nGenes
, oscillatoryk3=FALSE
, k3delay=NULL
, na.rm=TRUE
, seed=NULL)
{
checkINSPEcTObjectversion(object)
tpts <- object@tpts
if( !is.numeric(tpts) ) stop('makeSimModel: simulated data can be created only from time-course.')
#I remove genes without intronic signal
genesTmp <- which(apply(ratesFirstGuess(object, 'preMRNA'),1,function(r)all(is.finite(r))&all(r>0)))
concentrations <- list(
total=ratesFirstGuess(object, 'total')[genesTmp,]
, total_var=ratesFirstGuessVar(object, 'total')[genesTmp,]
, preMRNA=ratesFirstGuess(object, 'preMRNA')[genesTmp,]
, preMRNA_var=ratesFirstGuessVar(object, 'preMRNA')[genesTmp,]
)
rates <- list(
alpha=ratesFirstGuess(object, 'synthesis')[genesTmp,]
, alpha_var=ratesFirstGuessVar(object, 'synthesis')[genesTmp,]
, beta=ratesFirstGuess(object, 'degradation')[genesTmp,]
, gamma=ratesFirstGuess(object, 'processing')[genesTmp,]
)
if( !is.null(seed) ) set.seed(seed)
# read input
alpha <- rates$alpha
beta <- rates$beta
gamma <- rates$gamma
total <- concentrations$total
preMRNA <- concentrations$preMRNA
alpha_var <- rates$alpha_var
total_var <- concentrations$total_var
preMRNA_var <- concentrations$preMRNA_var
alphaFitVariance <- lm(formula = log(c(sqrt(alpha_var))) ~ log(c(alpha)))$coefficients
alphaFitVarianceLaw <- function(alpha)(exp(alphaFitVariance[[1]])*alpha^(alphaFitVariance[[2]]))^2
totalFitVariance <- lm(formula = log(c(sqrt(total_var))) ~ log(c(total)))$coefficients
totalFitVarianceLaw <- function(total)(exp(totalFitVariance[[1]])*total^(totalFitVariance[[2]]))^2
preFitVariance <- lm(formula = log(c(sqrt(preMRNA_var))) ~ log(c(preMRNA)))$coefficients
preFitVarianceLaw <- function(pre)(exp(preFitVariance[[1]])*pre^(preFitVariance[[2]]))^2
# sample initial timepoint
message('sampling means from rates distribution...')
#
if( na.rm == TRUE ) {
beta[beta <= 0] <- NA
gamma[gamma <= 0] <- NA
}
alphaVals <- sample(alpha, nGenes, replace=TRUE)
betaVals <- 2^sampleNormQuantile(
values_subject=log2(alphaVals)
, dist_subject=log2(alpha)
, dist_object=log2(beta)
, na.rm=na.rm)
gammaVals <- 2^sampleNormQuantile(
values_subject=log2(betaVals)
, dist_subject=log2(beta)
, dist_object=log2(gamma)
, na.rm=na.rm)
if( !oscillatoryk3 ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
betaParams <- generateOscillatoryParams(tpts, betaVals , probs=c(oscillatory=.0))
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
} else if( oscillatoryk3 & !is.null(k3delay) ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
osc_ix <- which(sapply(alphaParams, '[[', 'type') == 'oscillatory')
amplitude <- sapply(alphaParams[osc_ix], '[[', 'params')[3,]
alpha_shift <- sapply(alphaParams[osc_ix], '[[', 'params')[4,]
betaParams <- generateParamsShift(tpts, betaVals, osc_ix, amplitude, alpha_shift+k3delay)
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
} else if( oscillatoryk3 & is.null(k3delay) ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
betaParams <- generateOscillatoryParams(tpts, betaVals, probs=c(oscillatory=.5))
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
}
paramSpecs <- lapply(1:nGenes,
function(i)
list(alpha=alphaParams[[i]]
, beta=betaParams[[i]]
, gamma=gammaParams[[i]]))
out <- lapply(1:nGenes, function(i){
tryCatch(
.makeModel(tpts, paramSpecs[[i]]),error=function(e){cbind(time=rep(NaN,length(tpts))
,preMRNA=rep(NaN,length(tpts))
,total=rep(NaN,length(tpts))
,alpha=rep(NaN,length(tpts))
,beta=rep(NaN,length(tpts))
,gamma=rep(NaN,length(tpts)))})})
okGenes <- which(sapply(out,function(i)all(is.finite(unlist(i)))))
out <- out[okGenes]
paramSpecs <- paramSpecs[okGenes]
cleanDataSet <- list(
tpts = tpts
, concentrations = list(
total=t(sapply(out, function(x) x$total))
, total_var=rep(1,nGenes)
, preMRNA=t(sapply(out, function(x) x$preMRNA))
, preMRNA_var=rep(1,nGenes)
)
, rates = list(
alpha=t(sapply(out, function(x) x$alpha))
, alpha_var=rep(1,nGenes)
, beta=t(sapply(out, function(x) x$beta))
, gamma=t(sapply(out, function(x) x$gamma))
)
)
alphaSim_noisevar <- t(apply(cleanDataSet$rates$alpha,1,function(x)alphaFitVarianceLaw(x)))
totalSim_noisevar <- t(apply(cleanDataSet$concentrations$total,1,function(x)totalFitVarianceLaw(x)))
preSim_noisevar <- t(apply(cleanDataSet$concentrations$preMRNA,1,function(x)preFitVarianceLaw(x)))
# select genes whose noise evaluation succeded
okGenes <- which(
apply(alphaSim_noisevar,1,function(r)all(is.finite(r))) &
apply(totalSim_noisevar,1,function(r)all(is.finite(r))) &
apply(preSim_noisevar,1,function(r)all(is.finite(r)))
)
paramSpecs <- paramSpecs[okGenes]
alphaSim_noisevar <- alphaSim_noisevar[okGenes,]
totalSim_noisevar <- totalSim_noisevar[okGenes,]
preSim_noisevar <- preSim_noisevar[okGenes,]
# add params specification
simulatedFC <- list(
alpha=apply(cleanDataSet$rates$alpha[okGenes, ], 1,
function(x) diff(log2(range(x))))
, beta=apply(cleanDataSet$rates$beta[okGenes, ], 1,
function(x) diff(log2(range(x))))
, gamma=apply(cleanDataSet$rates$gamma[okGenes, ], 1,
function(x) diff(log2(range(x))))
)
noiseVar <- list(
alpha=alphaSim_noisevar
, total=totalSim_noisevar
, pre=preSim_noisevar
)
# arrange simdataSpecs form .makeSimData
paramSpecs <- lapply(paramSpecs, function(x) list(x))
#
newObject <- new('INSPEcT_model')
newObject@ratesSpecs <- paramSpecs
newObject@params$sim$flag <- TRUE
newObject@params$sim$foldchange <- simulatedFC
newObject@params$sim$noiseVar <- noiseVar
newObject@params$sim$noiseFunctions <- list(alpha = alphaFitVarianceLaw, preMRNA = preFitVarianceLaw, total = totalFitVarianceLaw)
newObject@params$tpts <- tpts
if(length(out$paramSpecs)>nGenes){return(newObject[1:nGenes])} #Return only the required number of genes or less
return(newObject)
})
generateOscillatoryParams <- function(tpts
, sampled_val
, probs=c(oscillatory=.5))
# given a vector of absolute values and a vector of log2foldchanges
# create parametric functions (either constant, sigmoidal or impulse,
# according to probs) and evaluate them at tpts.
{
nGenes <- length(sampled_val)
#
n_constant <- round(nGenes * (1 - probs['oscillatory']))
# initialize
params <- as.list(rep(NA,nGenes))
# constant: choose the one with the lower absoulute fold change to be
# constant
constant_idx <- 1:nGenes %in% sample(1:nGenes, n_constant)
if( any(constant_idx) )
{
params[constant_idx] <- lapply(sampled_val[constant_idx],
function(val)
list(type='constant', fun=constantModelP , params=val, df=1)
)
}
generateOscillatoryParamsFun <- function(tpts, sampled_val)
# Given an absolute value and a value of log2fold change sample a set
# of parameters for the impulse function.
{
n <- length(sampled_val)
sampled_freqs <- pi/12
initial_values <- sampled_val
amplitude <- runif(n, .05, .4)
x_shift <- runif(n, min(tpts), max(tpts))
oscillatorypars <- cbind(
sampled_freqs
, initial_values
, amplitude
, x_shift
)
return(oscillatorypars)
}
# sigmoid
oscillatory_idx <- !constant_idx
if( any(oscillatory_idx) ) {
params[oscillatory_idx] <- lapply(
which(oscillatory_idx)
, function(i) list(
type='oscillatory'
, fun=oscillatoryModelP
, params=generateOscillatoryParamsFun(
tpts
, sampled_val[i]
)
, df=4
)
)
}
return(params)
}
generateParamsShift <- function(tpts
, sampled_val
, oscillatory_idx
, amplitude
, x_shift)
# given a vector of absolute values and a vector of log2foldchanges
# create parametric functions (either constant, sigmoidal or impulse,
# according to probs) and evaluate them at tpts.
{
nGenes <- length(sampled_val)
# initialize
params <- as.list(rep(NA,nGenes))
# constant: choose the one with the lower absoulute fold change to be
# constant
constant_idx <- ! (1:nGenes %in% oscillatory_idx)
if( any(constant_idx) )
{
params[constant_idx] <- lapply(sampled_val[constant_idx],
function(val)
list(type='constant', fun=constantModelP , params=val, df=1)
)
}
generateOscillatoryParamsShiftFun <- function(tpts, sampled_val, amplitude, x_shift)
# Given an absolute value and a value of log2fold change sample a set
# of parameters for the impulse function.
{
n <- length(sampled_val)
sampled_freqs <- pi/12
initial_values <- sampled_val
# amplitude <- runif(n, .05, .4)
oscillatorypars <- cbind(
sampled_freqs
, initial_values
, amplitude
, x_shift
)
return(oscillatorypars)
}
# sigmoid
if( any(oscillatory_idx) ) {
params[oscillatory_idx] <- lapply(
seq_along(oscillatory_idx)
, function(i) list(
type='oscillatory'
, fun=oscillatoryModelP
, params=generateOscillatoryParamsShiftFun(
tpts
, sampled_val[oscillatory_idx[i]]
, amplitude[i]
, x_shift[i]
)
, df=4
)
)
}
return(params)
}
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INSPEcT documentation built on Nov. 8, 2020, 6:49 p.m.
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Defines functions generateParamsShift generateOscillatoryParams
#' @rdname makeOscillatorySimModel
#'
#' @description
#' This method allow the creation of synthesis, degradation and processing rates that generate
#' an oscillatory expression with a period of 24 hours. Two modes are available: one where
#' oscillations arise just by oscillations in the synthesis of the genes (oscillatoryk3=FALSE, default) and
#' another one where both synthesis and degradation rates oscillates (oscillatoryk3=TRUE). In this latter case,
#' the oscillations of the two rates can be coupled by a cetrain delay (parametrer k3delay).
#' After the creation of the synthetic rates, a dataset with noise and contamination added can be made by \code{\link{makeSimDataset}}.
#' @param object An object of class INSPEcT
#' @param nGenes A numeric with the number of synthtic genes to be created
#' @param oscillatoryk3 A logical that enables also degradation rate to oscillate
#' @param k3delay A numeric that set the delay between synthesis and degradation oscillations. When NULL, no coupling between the two oscillations is set.
#' @param na.rm A logical that set whether missing values in the real dataset should be removed
#' @param seed A numeric to obtain reproducible results
#' @return An object of class INSPEcT_model with synthetic rates
#' @seealso \code{\link{makeSimModel}}
#' @examples
#' nascentInspObj <- readRDS(system.file(package='INSPEcT', 'nascentInspObj.rds'))
#' simRates<-makeOscillatorySimModel(nascentInspObj, 1000, seed=1)
#' table(geneClass(simRates))
setMethod('makeOscillatorySimModel', 'INSPEcT', function(object
, nGenes
, oscillatoryk3=FALSE
, k3delay=NULL
, na.rm=TRUE
, seed=NULL)
{
checkINSPEcTObjectversion(object)
tpts <- object@tpts
if( !is.numeric(tpts) ) stop('makeSimModel: simulated data can be created only from time-course.')
#I remove genes without intronic signal
genesTmp <- which(apply(ratesFirstGuess(object, 'preMRNA'),1,function(r)all(is.finite(r))&all(r>0)))
concentrations <- list(
total=ratesFirstGuess(object, 'total')[genesTmp,]
, total_var=ratesFirstGuessVar(object, 'total')[genesTmp,]
, preMRNA=ratesFirstGuess(object, 'preMRNA')[genesTmp,]
, preMRNA_var=ratesFirstGuessVar(object, 'preMRNA')[genesTmp,]
)
rates <- list(
alpha=ratesFirstGuess(object, 'synthesis')[genesTmp,]
, alpha_var=ratesFirstGuessVar(object, 'synthesis')[genesTmp,]
, beta=ratesFirstGuess(object, 'degradation')[genesTmp,]
, gamma=ratesFirstGuess(object, 'processing')[genesTmp,]
)
if( !is.null(seed) ) set.seed(seed)
# read input
alpha <- rates$alpha
beta <- rates$beta
gamma <- rates$gamma
total <- concentrations$total
preMRNA <- concentrations$preMRNA
alpha_var <- rates$alpha_var
total_var <- concentrations$total_var
preMRNA_var <- concentrations$preMRNA_var
alphaFitVariance <- lm(formula = log(c(sqrt(alpha_var))) ~ log(c(alpha)))$coefficients
alphaFitVarianceLaw <- function(alpha)(exp(alphaFitVariance[[1]])*alpha^(alphaFitVariance[[2]]))^2
totalFitVariance <- lm(formula = log(c(sqrt(total_var))) ~ log(c(total)))$coefficients
totalFitVarianceLaw <- function(total)(exp(totalFitVariance[[1]])*total^(totalFitVariance[[2]]))^2
preFitVariance <- lm(formula = log(c(sqrt(preMRNA_var))) ~ log(c(preMRNA)))$coefficients
preFitVarianceLaw <- function(pre)(exp(preFitVariance[[1]])*pre^(preFitVariance[[2]]))^2
# sample initial timepoint
message('sampling means from rates distribution...')
#
if( na.rm == TRUE ) {
beta[beta <= 0] <- NA
gamma[gamma <= 0] <- NA
}
alphaVals <- sample(alpha, nGenes, replace=TRUE)
betaVals <- 2^sampleNormQuantile(
values_subject=log2(alphaVals)
, dist_subject=log2(alpha)
, dist_object=log2(beta)
, na.rm=na.rm)
gammaVals <- 2^sampleNormQuantile(
values_subject=log2(betaVals)
, dist_subject=log2(beta)
, dist_object=log2(gamma)
, na.rm=na.rm)
if( !oscillatoryk3 ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
betaParams <- generateOscillatoryParams(tpts, betaVals , probs=c(oscillatory=.0))
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
} else if( oscillatoryk3 & !is.null(k3delay) ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
osc_ix <- which(sapply(alphaParams, '[[', 'type') == 'oscillatory')
amplitude <- sapply(alphaParams[osc_ix], '[[', 'params')[3,]
alpha_shift <- sapply(alphaParams[osc_ix], '[[', 'params')[4,]
betaParams <- generateParamsShift(tpts, betaVals, osc_ix, amplitude, alpha_shift+k3delay)
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
} else if( oscillatoryk3 & is.null(k3delay) ) {
alphaParams <- generateOscillatoryParams(tpts, alphaVals, probs=c(oscillatory=.5))
betaParams <- generateOscillatoryParams(tpts, betaVals, probs=c(oscillatory=.5))
gammaParams <- generateOscillatoryParams(tpts, gammaVals, probs=c(oscillatory=.0))
}
paramSpecs <- lapply(1:nGenes,
function(i)
list(alpha=alphaParams[[i]]
, beta=betaParams[[i]]
, gamma=gammaParams[[i]]))
out <- lapply(1:nGenes, function(i){
tryCatch(
.makeModel(tpts, paramSpecs[[i]]),error=function(e){cbind(time=rep(NaN,length(tpts))
,preMRNA=rep(NaN,length(tpts))
,total=rep(NaN,length(tpts))
,alpha=rep(NaN,length(tpts))
,beta=rep(NaN,length(tpts))
,gamma=rep(NaN,length(tpts)))})})
okGenes <- which(sapply(out,function(i)all(is.finite(unlist(i)))))
out <- out[okGenes]
paramSpecs <- paramSpecs[okGenes]
cleanDataSet <- list(
tpts = tpts
, concentrations = list(
total=t(sapply(out, function(x) x$total))
, total_var=rep(1,nGenes)
, preMRNA=t(sapply(out, function(x) x$preMRNA))
, preMRNA_var=rep(1,nGenes)
)
, rates = list(
alpha=t(sapply(out, function(x) x$alpha))
, alpha_var=rep(1,nGenes)
, beta=t(sapply(out, function(x) x$beta))
, gamma=t(sapply(out, function(x) x$gamma))
)
)
alphaSim_noisevar <- t(apply(cleanDataSet$rates$alpha,1,function(x)alphaFitVarianceLaw(x)))
totalSim_noisevar <- t(apply(cleanDataSet$concentrations$total,1,function(x)totalFitVarianceLaw(x)))
preSim_noisevar <- t(apply(cleanDataSet$concentrations$preMRNA,1,function(x)preFitVarianceLaw(x)))
# select genes whose noise evaluation succeded
okGenes <- which(
apply(alphaSim_noisevar,1,function(r)all(is.finite(r))) &
apply(totalSim_noisevar,1,function(r)all(is.finite(r))) &
apply(preSim_noisevar,1,function(r)all(is.finite(r)))
)
paramSpecs <- paramSpecs[okGenes]
alphaSim_noisevar <- alphaSim_noisevar[okGenes,]
totalSim_noisevar <- totalSim_noisevar[okGenes,]
preSim_noisevar <- preSim_noisevar[okGenes,]
# add params specification
simulatedFC <- list(
alpha=apply(cleanDataSet$rates$alpha[okGenes, ], 1,
function(x) diff(log2(range(x))))
, beta=apply(cleanDataSet$rates$beta[okGenes, ], 1,
function(x) diff(log2(range(x))))
, gamma=apply(cleanDataSet$rates$gamma[okGenes, ], 1,
function(x) diff(log2(range(x))))
)
noiseVar <- list(
alpha=alphaSim_noisevar
, total=totalSim_noisevar
, pre=preSim_noisevar
)
# arrange simdataSpecs form .makeSimData
paramSpecs <- lapply(paramSpecs, function(x) list(x))
#
newObject <- new('INSPEcT_model')
newObject@ratesSpecs <- paramSpecs
newObject@params$sim$flag <- TRUE
newObject@params$sim$foldchange <- simulatedFC
newObject@params$sim$noiseVar <- noiseVar
newObject@params$sim$noiseFunctions <- list(alpha = alphaFitVarianceLaw, preMRNA = preFitVarianceLaw, total = totalFitVarianceLaw)
newObject@params$tpts <- tpts
if(length(out$paramSpecs)>nGenes){return(newObject[1:nGenes])} #Return only the required number of genes or less
return(newObject)
})
generateOscillatoryParams <- function(tpts
, sampled_val
, probs=c(oscillatory=.5))
# given a vector of absolute values and a vector of log2foldchanges
# create parametric functions (either constant, sigmoidal or impulse,
# according to probs) and evaluate them at tpts.
{
nGenes <- length(sampled_val)
#
n_constant <- round(nGenes * (1 - probs['oscillatory']))
# initialize
params <- as.list(rep(NA,nGenes))
# constant: choose the one with the lower absoulute fold change to be
# constant
constant_idx <- 1:nGenes %in% sample(1:nGenes, n_constant)
if( any(constant_idx) )
{
params[constant_idx] <- lapply(sampled_val[constant_idx],
function(val)
list(type='constant', fun=constantModelP , params=val, df=1)
)
}
generateOscillatoryParamsFun <- function(tpts, sampled_val)
# Given an absolute value and a value of log2fold change sample a set
# of parameters for the impulse function.
{
n <- length(sampled_val)
sampled_freqs <- pi/12
initial_values <- sampled_val
amplitude <- runif(n, .05, .4)
x_shift <- runif(n, min(tpts), max(tpts))
oscillatorypars <- cbind(
sampled_freqs
, initial_values
, amplitude
, x_shift
)
return(oscillatorypars)
}
# sigmoid
oscillatory_idx <- !constant_idx
if( any(oscillatory_idx) ) {
params[oscillatory_idx] <- lapply(
which(oscillatory_idx)
, function(i) list(
type='oscillatory'
, fun=oscillatoryModelP
, params=generateOscillatoryParamsFun(
tpts
, sampled_val[i]
)
, df=4
)
)
}
return(params)
}
generateParamsShift <- function(tpts
, sampled_val
, oscillatory_idx
, amplitude
, x_shift)
# given a vector of absolute values and a vector of log2foldchanges
# create parametric functions (either constant, sigmoidal or impulse,
# according to probs) and evaluate them at tpts.
{
nGenes <- length(sampled_val)
# initialize
params <- as.list(rep(NA,nGenes))
# constant: choose the one with the lower absoulute fold change to be
# constant
constant_idx <- ! (1:nGenes %in% oscillatory_idx)
if( any(constant_idx) )
{
params[constant_idx] <- lapply(sampled_val[constant_idx],
function(val)
list(type='constant', fun=constantModelP , params=val, df=1)
)
}
generateOscillatoryParamsShiftFun <- function(tpts, sampled_val, amplitude, x_shift)
# Given an absolute value and a value of log2fold change sample a set
# of parameters for the impulse function.
{
n <- length(sampled_val)
sampled_freqs <- pi/12
initial_values <- sampled_val
# amplitude <- runif(n, .05, .4)
oscillatorypars <- cbind(
sampled_freqs
, initial_values
, amplitude
, x_shift
)
return(oscillatorypars)
}
# sigmoid
if( any(oscillatory_idx) ) {
params[oscillatory_idx] <- lapply(
seq_along(oscillatory_idx)
, function(i) list(
type='oscillatory'
, fun=oscillatoryModelP
, params=generateOscillatoryParamsShiftFun(
tpts
, sampled_val[oscillatory_idx[i]]
, amplitude[i]
, x_shift[i]
)
, df=4
)
)
}
return(params)
}
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