In my attached R function, I was wondering how to solve for mdes (suppose it is unknown) which is currently one of the input values IF everything else is known?
Is it also possible to solve for mdes and power (both currently input values) IF everything else is known?
foo <- function(A = 200, As = 15, B = 100,Bs = 10,iccmax = 0.15,mdes = .25,SD = 1.2,power = 80)
{
tail <- 2
alpha <- 5
inv_d <- function(mdes) {
c(mean_dif = 1, Vmax = 2/mdes^2)
}
SDr <- 1/SD
pars <- inv_d(mdes)
mean_dif <- pars[[1]]
Vmax <- pars[[2]]
zbeta <- qnorm((power/100))
zalpha <- qnorm(1-(alpha/(100*tail)))
maxvarmean_difhat <- (mean_dif / (zbeta + zalpha))**2
ntreat <- sqrt((A/As)*((1-iccmax)/iccmax))
ncont <- sqrt((B/Bs)*((1-iccmax)/iccmax))
costpertreatcluster <- A + (As*ntreat)
costperconcluster <- B + (Bs*ncont)
gtreat <- (sqrt(A*iccmax) + sqrt(As*(1-iccmax)))**2
gcon <- (sqrt(B*iccmax) + sqrt(Bs*(1-iccmax)))**2
pratio <- sqrt(gtreat/gcon)
budgetratio <- 99999
budgetratio <- ifelse( ((pratio <= SD) & (pratio >= SDr)), pratio**2, ifelse((pratio > SD), pratio*SD, pratio*SDr))
fraction <- budgetratio/(1 + budgetratio)
mmvnumer <- 99999
mmvnumer <- ifelse( ((pratio <= SD) & (pratio >= SDr)),
gcon*Vmax*(1+(pratio**2)),
ifelse((pratio > SD),
gcon*Vmax*(((pratio*SD)+1)**2/((SD**2)+1)),
gcon*Vmax*(((pratio*SDr)+1)**2/((SDr**2) + 1))) )
budget <- mmvnumer/maxvarmean_difhat
treatbudget <- fraction*budget
conbudget <- (1-fraction)*budget
ktreat <- treatbudget/costpertreatcluster
kcont <- conbudget/costperconcluster
ktreatrup <- ceiling(ktreat)
kcontrup <- ceiling(kcont)
ktreatplus <- ifelse(pmin(ktreatrup,kcontrup) < 8, ktreatrup + 3, ktreatrup + 2)
kcontplus <- ifelse(pmin(ktreatrup,kcontrup) < 8, kcontrup + 3, kcontrup + 2)
budgetplus <- (ktreatplus*costpertreatcluster) + (kcontplus*costperconcluster)
return(c(ncont = ncont, kcont = kcontplus,
ntreat = ntreat, ktreat = ktreatplus, budget = budgetplus))
}
#--------------------------------------------------------------------------------
# EXAMPLE OF USE:
foo()
ncont kcont ntreat ktreat budget
7.527727 73.000000 8.692270 62.000000 33279.051347
Define a function of one variable as
p0 = foo()
fn1 = function(x) sum((foo(mdes=x) - p0)^2)
and find a minimum that should be 0, and which corresponds to your mdes = 0.25 input!
optimize(fn1, c(0.0, 1.0))
## $minimum
## [1] 0.2497695
## $objective
## [1] 0
For two variables, this is more difficult, as the function has many local minima and is ill-defined outside certain regions. Applying optim() you will need well-chosen starting points.
Related
I have four high resolution rasters for a country. I have split each raster into tiles and done some other processing to them. I now want to apply a function to each cell, of each 'stack' of the raster tiles, to produce one set of output tiles. The function is a little complex. I have tried to synthesise some data below to reproduce my current approach. It works (ish) but I'm convinced that there's a better way to do this. To use parallel processing on my unix box, I simply swap mapply for mcmapply, but I haven't done that in the example below as I presume many will be working on Windows machines. I'd welcome ideas on my approach and particularly optimisation.
library("terra")
library("glue")
## Make some toy data
dir.create("temp_folder")
dir.create("result_folder")
x <- rast(ncols = 10, nrows = 10)
a <- rast(ncol = 100, nrow = 100)
some_values <- as.integer(runif(10000, min = 1, max = 100))
ind <- which(some_values %in% sample(some_values, 15))
some_values[ind] <- NA
values(a) <- some_values
a_tiles <- makeTiles(a, x, glue("temp_folder/tile_a_{1:100}.tif"), overwrite = TRUE)
b <- rast(ncol = 100, nrow = 100)
some_values <- as.integer(runif(10000, min = 1, max = 100))
ind <- which(some_values %in% sample(some_values, 15))
some_values[ind] <- NA
values(b) <- some_values
b_tiles <- makeTiles(b, x, glue("temp_folder/tile_b_{1:100}.tif"), overwrite = TRUE)
c <-rast(ncol = 100, nrow = 100)
some_values <- as.integer(runif(10000, min = 1, max = 100))
ind <- which(some_values %in% sample(some_values, 15))
some_values[ind] <- NA
values(c) <- some_values
c_tiles <- makeTiles(c, x, glue("temp_folder/tile_c_{1:100}.tif"), overwrite = TRUE)
d <- rast(ncol = 100, nrow = 100)
some_values <- as.integer(runif(10000, min = 1, max = 100))
ind <- which(some_values %in% sample(some_values, 15))
some_values[ind] <- NA
values(d) <- some_values
d_tiles <- makeTiles(d, x, glue("temp_folder/tile_d_{1:100}.tif"), overwrite = TRUE)
## Outer function so that this can be used in parallel ? But maybe this is a silly way to do it?
outer_function <- function(a_tiles, b_tiles, c_tiles, d_tiles, output_files) {
one_a_tile <- rast(unlist(a_tiles))
one_b_tile <- rast(unlist(b_tiles))
one_c_tile <- rast(unlist(c_tiles))
one_d_tile <- rast(unlist(d_tiles))
output_file <- output_files
# I replace any NAs with 0 as an NA will break my 'if' statement of the inner_function.
# I get Error in if (z["a"] <= z["b"]) { : missing value where TRUE/FALSE needed
one_a_tile[is.na(one_a_tile)] <- 0
one_b_tile[is.na(one_b_tile)] <- 0
one_c_tile[is.na(one_c_tile)] <- 0
one_d_tile[is.na(one_d_tile)] <- 0
z <- sds(one_a_tile, one_b_tile, one_c_tile, one_d_tile)
## Inner function that actually does the work I want doing
inner_function <- function(z) {
names(z) <- c('a', 'b', 'c', 'd')
if (z['a'] <= z['b']) {
y <- rowSums(cbind((z['c'] + z['a'] * 10),
(z['c'] + z['a'] * 20)))
}
if (z['a'] >= z['b']) {
y <- rowSums(cbind((z['c'] + z['a'] * 40),
(z['c'] + z['a'] * 10)))
}
if (z['a'] == z['b']) {
y <- rowSums(cbind((z['c'] + z['a'] * 60),
(z['c'] + z['a'] * 10)))
}
y <- ifelse(y == 0, NA, y)
return(y)
}
app(z,
inner_function,
filename = output_file,
overwrite = TRUE,
wopt = list(datatype = "INT4U"))
return(output_file)
}
results <- mapply(outer_function,
a_tiles = a_tiles,
b_tiles = b_tiles,
c_tiles = c_tiles,
d_tiles = d_tiles,
output_files = output_files <- glue("result_folder/result_tile_{1:length(d_tiles)}.tif"))
names(results) <- NULL
unlink("temp_folder", recursive = TRUE)
unlink("result_folder", recursive = TRUE)
I wrote down this function for MLE estimation and then I apply it for different settings of parameters.
Finally, I bind all results for an output.
But is not working i have problem with the output and also I need to organize the output like the attached image using R program.
enter image description here
could some one help me please?
What should I fix and how can I print the results like the picture attached.
thank you in advance
rbssn<- function(n,alpha,beta)
{
if(!is.numeric(n)||!is.numeric(alpha)||!is.numeric(beta))
{stop("non-numeric argument to mathematical function")}
if(alpha<=0){ stop("alpha must be positive")}
if(beta<=0) { stop("beta must be positive") }
z <- rnorm(n,0,1)
r <- beta*((alpha*z*0.5)+sqrt((alpha*z*0.5)^2+1))^2
return(r)
}
#Function
mymle <- function(n,alpha,beta,rep)
{
theta=c(alpha,beta) # store starting values
#Tables
LHE=array(0, c(2,rep));
rownames(LHE)= c("MLE_alpha", "MLE_beta")
#Bias
bias= array(0, c(2,rep));
rownames(bias)= c("bias_alpha", "bias_beta")
#Simulation
set.seed(1)
#Loop
for(i in 1:rep){
myx <- exp(-rbssn(n, alpha, beta))
Score <- function(x) {
y <- numeric(2)
y[1] <- (-n/x[1])*(1+2/(x[1]^2)) - (1/(x[2]*x[1]^3))*sum(log(myx)) - (x[2]/(x[1]^3))*sum(1/log(myx))
y[2] <- -(n/(2*x[2])) + sum((1/(x[2]-log(myx)))) - (1/(2*(x[1]^2)*(x[2]^2)))*sum(log(myx)) + (1/(2*x[1]^2))*sum(1/(log(myx)))
y
}
Sin <- c(alpha,beta)
mle<- nleqslv(Sin, Score, control=list(btol=.01))[1]
LHE[i,]= mle
bias[i,]= c(mle[1]-theta[1], mle[2]-theta[2])
}
# end for i
#Format results
L <-round(apply(LHE, 1, mean), 3) # MLE of all the applied iterations
bs <-round(apply(bias,1, mean),3) # bias of all the applied iterations
row<- c(L, bs)
#Format a label
lab <- paste0('n= ',n,';',' alpha= ',alpha,';',' beta= ',beta)
row2 <- c(lab,row)
row2 <- as.data.frame(t(row2))
return(row2)
}
#Bind all
#Example 1
ex1 <- mymle(n = 20,alpha = 1,beta = 0.5,rep = 100)
ex2 <- mymle(n = 50,alpha = 2,beta = 0.5,rep = 100)
ex3 <- mymle(n = 100,alpha = 3,beta = 0.5,rep = 100)
#Example 2
ex4 <- mymle(n = 20,alpha = 0.5,beta = 0.5,rep = 100)
ex5 <- mymle(n = 50,alpha = 0.5,beta = 1,rep = 100)
ex6 <- mymle(n = 100,alpha = 0.5,beta = 1,rep = 100)
df <- rbind(ex1,ex2,ex3,ex4,ex5,ex6)
Any help will be appreciated.
I am writing code for producing a variogram. For validating my result, I checked with geoR::variog() but both variograms are different.
I tried to understand the code of variog() to see what happens under the hood but there are so many things happening that I can't seem to understand it. I, in my code, am using the parameters X-coordinate, Y-coordiante, data value, number of lags, minimum lag value, lag interval, azimuth (angle in degrees; 90 corresponds to vertical direction), angle tolerance (in degrees) and maximum bandwidth.
variogram = function(xcor, ycor, data, nlag, minlag, laginv, azm, atol, maxbandw){
dl <- length(data)
lowangle <- azm - atol
upangle <- azm + atol
gamlag <- integer(nlag)
n <- integer(nlag)
dist <- pairdist(xcor, ycor)
maxd <- max(dist)
llag <- seq(minlag, minlag + (nlag-1) * laginv, by = laginv)
hlag <- llag + laginv
for(i in 1:dl){
for(j in i:dl){
if(i != j){
if(xcor[j]- xcor[i] == 0)
theta <- 90
else
theta <- 180/pi * atan((ycor[j] - ycor[i])/(xcor[j] - xcor[i]))
for(k in 1:nlag){
d <- dist[j, i]
b <- abs(d * sin(theta - azm))
if((llag[k] <= d & d < hlag[k]) & (lowangle <= theta & theta < upangle) & (b <= maxbandw)){
gamlag[k] <- gamlag[k] + (data[i] - data[j])^2;
n[k] <- n[k] + 1
}
}
}
}
}
gamlag <- ifelse(n == 0, NA, gamlag/(2*n))
tmp <- data.frame("lag" = llag, "gamma" = gamlag)
return(tmp)
}
function call for the above code
ideal_variogram_2 <- variogram(data3[,1], data3[,2], data3[,3], 18, 0, 0.025, 90, 45, 1000000)
ideal_variogram_2 <- na.omit(ideal_variogram_2)
plot(ideal_variogram_2$lag, ideal_variogram_2$gamma, main = "Using my code")
function call for variog()
geodata1 <- as.geodata(data3, coords.col = 1:2, data.col = 3)
ideal_variogram_1 <- variog(geodata1, coords = geodata1$coords, data = geodata1$data, option = "bin", uvec = seq(0, 0.45, by = 0.025), direction = pi/2, tolerance = pi/4)
df <- data.frame(u = ideal_variogram_1$u, v = ideal_variogram_1$v)
plot(df$u, df$v, main = "Using variog()")
The 2 variograms that I got are at the following link:
Variogram
I put together a function to identify outliers. It takes a dataframe and then shows plots of the data with lines to indicate potential outliers. It'll give a table with outliers marked, too.
But, it is SLOOOW. The problem is it takes a really long time for the plots to load.
I was curious if you might have advice on how to speed this up.
Related: Is the default plotting system faster than ggplot?
I'll start with the dependencies
#These next four functions are not mine. They're used in GetOutliers()
ExtractDetails <- function(x, down, up){
outClass <- rep("N", length(x))
indexLo <- which(x < down)
indexHi <- which(x > up)
outClass[indexLo] <- "L"
outClass[indexHi] <- "U"
index <- union(indexLo, indexHi)
values <- x[index]
outClass <- outClass[index]
nOut <- length(index)
maxNom <- max(x[which(x <= up)])
minNom <- min(x[which(x >= down)])
outList <- list(nOut = nOut, lowLim = down,
upLim = up, minNom = minNom,
maxNom = maxNom, index = index,
values = values,
outClass = outClass)
return(outList)
}
Hampel <- function(x, t = 3){
#
mu <- median(x, na.rm = TRUE)
sig <- mad(x, na.rm = TRUE)
if (sig == 0){
message("Hampel identifer implosion: MAD scale estimate is zero")
}
up<-mu+t*sig
down<-mu-t*sig
out <- list(up = up, down = down)
return(out)
}
ThreeSigma <- function(x, t = 3){
#
mu <- mean(x, na.rm = TRUE)
sig <- sd(x, na.rm = TRUE)
if (sig == 0){
message("All non-missing x-values are identical")
}
up<-mu+t* sig
down<-mu-t * sig
out <- list(up = up, down = down)
return(out)
}
BoxplotRule <- function(x, t = 1.5){
#
xL <- quantile(x, na.rm = TRUE, probs = 0.25, names = FALSE)
xU <- quantile(x, na.rm = TRUE, probs = 0.75, names = FALSE)
Q<-xU-xL
if(Q==0){
message("Boxplot rule implosion: interquartile distance is zero")
}
up<-xU+t*Q
down<-xU-t*Q
out <- list(up = up, down = down)
return(out)
}
FindOutliers <- function(x, t3 = 3, tH = 3, tb = 1.5){
threeLims <- ThreeSigma(x, t = t3)
HampLims <- Hampel(x, t = tH)
boxLims <- BoxplotRule(x, t = tb)
n <- length(x)
nMiss <- length(which(is.na(x)))
threeList <- ExtractDetails(x, threeLims$down, threeLims$up)
HampList <- ExtractDetails(x, HampLims$down, HampLims$up)
boxList <- ExtractDetails(x, boxLims$down, boxLims$up)
sumFrame <- data.frame(method = "ThreeSigma", n = n,
nMiss = nMiss, nOut = threeList$nOut,
lowLim = threeList$lowLim,
upLim = threeList$upLim,
minNom = threeList$minNom,
maxNom = threeList$maxNom)
upFrame <- data.frame(method = "Hampel", n = n,
nMiss = nMiss, nOut = HampList$nOut,
lowLim = HampList$lowLim,
upLim = HampList$upLim,
minNom = HampList$minNom,
maxNom = HampList$maxNom)
sumFrame <- rbind.data.frame(sumFrame, upFrame)
upFrame <- data.frame(method = "BoxplotRule", n = n,
nMiss = nMiss, nOut = boxList$nOut,
lowLim = boxList$lowLim,
upLim = boxList$upLim,
minNom = boxList$minNom,
maxNom = boxList$maxNom)
sumFrame <- rbind.data.frame(sumFrame, upFrame)
threeFrame <- data.frame(index = threeList$index,
values = threeList$values,
type = threeList$outClass)
HampFrame <- data.frame(index = HampList$index,
values = HampList$values,
type = HampList$outClass)
boxFrame <- data.frame(index = boxList$index,
values = boxList$values,
type = boxList$outClass)
outList <- list(summary = sumFrame, threeSigma = threeFrame,
Hampel = HampFrame, boxplotRule = boxFrame)
return(outList)
}
#strip non-numeric variables out of a dataframe
num_vars <- function(df){
X <- which(sapply(df, is.numeric))
num_vars <- df[names(X)]
return(num_vars)
}
This is the function
GetOutliers <- function(df){
library('dplyr')
library('ggplot2')
#strip out the non-numeric columns
df_out <- num_vars(df)
#initialize the data frame
df_out$Hampel <- NA
df_out$threeSigma <- NA
df_out$boxplotRule <- NA
df_out_id <- df_out
#identify outliers for each column
for (i in 1:length(names(num_vars(df)))){
#find the outliers
Outs <- FindOutliers(df_out[[i]])
OutsSum <- Outs$summary
#re-enter the outlier status
df_out$Hampel <- NA
df_out$threeSigma <- NA
df_out$boxplotRule <- NA
ifelse(is.na(Outs$Hampel), print(), df_out[unlist(Outs$Hampel[1]),]$Hampel <- TRUE)
ifelse(is.na(Outs$threeSigma), print(), df_out[unlist(Outs$threeSigma[1]),]$threeSigma <- TRUE)
ifelse(is.na(Outs$boxplotRule), print(), df_out[unlist(Outs$boxplotRule[1]),]$boxplotRule <- TRUE)
#visualize the outliers and print outlier information
Temp <- df_out
A <- colnames(Temp)[i]
AA <- paste(A,"Index")
colnames(Temp)[i] <- 'curr_column'
#table with outlier status
X <- arrange(subset(Temp,Hampel == TRUE | boxplotRule == TRUE | threeSigma == TRUE), desc(curr_column))
#scatterplot with labels
Y <- ggplot(Temp,aes(seq_along(curr_column),curr_column)) + geom_point() +
geom_hline(yintercept=OutsSum$lowLim[1],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$lowLim[2],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$lowLim[3],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[1],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[2],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[3],linetype = 'dashed') +
geom_text(aes(40,OutsSum$lowLim[1],label="ThreeSigma Lower",vjust=-1)) +
geom_text(aes(40,OutsSum$lowLim[2],label="Hampel Lower",vjust=-1)) +
geom_text(aes(40,OutsSum$lowLim[3],label="Boxplot Lower",vjust=-1)) +
geom_text(aes(40,OutsSum$upLim[1],label="ThreeSigma Upper",vjust=-1)) +
geom_text(aes(40,OutsSum$upLim[2],label="Hampel Upper",vjust=-1)) +
geom_text(aes(40,OutsSum$upLim[3],label="Boxplot Upper",vjust=-1)) +
xlab(AA) + ylab(A)
#scatterplot without labels
Z <- ggplot(Temp,aes(seq_along(curr_column),curr_column)) + geom_point() +
geom_hline(yintercept=OutsSum$lowLim[1],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$lowLim[2],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$lowLim[3],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[1],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[2],linetype = 'dashed') +
geom_hline(yintercept=OutsSum$upLim[3],linetype = 'dashed') +
xlab(AA) + ylab(A)
U <- ggplot(Temp,aes(curr_column)) + geom_density() + xlab(A)
print(A)
print(X)
print(OutsSum)
print(Z)
print(Y)
print(U)
#mark the extreme outliers, the rest are reasonable outliers
A <- colnames(df_out_id[i])
Q <- as.numeric(readline(prompt="Enter the index for final Extreme value on the upper limit (if none, enter 0): "))
W <- as.numeric(readline(prompt="Enter the index for first Extreme value on the lower limit (if none, enter 0): "))
col <- df_out_id[i]
df_out_id[i] <- sapply(col[[1]], function(x){
if(Q>1 & x %in% X$curr_column[1:Q]) return('Extreme')
if(W>1 & x %in% X$curr_column[W:length(X$curr_column)]) return('Extreme')
else if (x %in% X$curr_column[Q+1:length(X$curr_column)]) return('Reasonable')
else return('Non-Outlier')
})
}
#return a dataframe with outlier status, excluding the outlier ID columns
summary(df_out_id)
return(df_out_id[1:(length(names(df_out_id))-3)])
}
Example
library('ISLR')
data(Carseats)
GetOutliers(Carseats)
It'll show you the outliers for each numeric variable.
It'll plot the variable density and then a scatterplot with identifier lines
It will also accept input so you can mark some outliers as reasonable and other as extreme
I need little help. I try to do plot with ggplot package. When I want to make plot, depends of more than 1 factor (for example here: plot changes when średnia1 and odchylenie1 change):
alpha = 0.05
N = 100
sample_l = 10
srednia1 = seq(-7, 7, by = 1)
odchylenie1 = seq(1, 10, by = 1)
srednia2 = 2
odchylenie2 = 2
prob = 0.7
params = expand.grid(sample_l, srednia1, odchylenie1, srednia2, odchylenie2, prob)
str(params)
names(params) = c("dlugość", "średnia1", "odchylenie1", "średnia2", "odchyelnie2", "prawdopodobienstwo")
set.seed(100)
now <- Sys.time()
powers <- sapply(1:nrow(params), function(p){
l <- params[p, 1]
par_1 <- c(params[p, 2],params[p, 3])
par_2 <- c(params[p, 4], params[p, 5])
p <- params[p,6]
p_sim <-sapply(rep(l, N), function(x){
my_sample <- rmix(l,"norm", par_1, "norm", par_2, p)
shapiro.test(my_sample)$p.value
})
mean(p_sim < alpha)
})
Sys.time() - now
power_df <- bind_cols(params, power = powers)
power_df %>% ggplot(aes(x = średnia1,
y = power,
col = factor(odchylenie1))) +
geom_line()
it work perfect, but now, when I want to make plot only depends of 1 factor - prob something goes wrong. I have error : Error: Aesthetics must be either length 1 or the same as the data (150): x, y. Here is a code:
alpha = 0.05
N = 100
sample_l = 10
srednia1 = 2
odchylenie1 = 2
srednia2 = 1
odchylenie2 = 1
prob = seq(0.1,0.9,by=0.1)
set.seed(100)
now <- Sys.time()
powers <- sapply(1:nrow(params), function(p){
l <- params[p, 1]
par_1 <- c(params[p, 2],params[p, 3])
par_2 <- c(params[p, 4], params[p, 5])
p <- params[p,6]
p_sim <-sapply(rep(l, N), function(x){
my_sample <- rmix(l,"norm", par_1, "norm", par_2, p)
shapiro.test(my_sample)$p.value
})
mean(p_sim < alpha)
})
Sys.time() - now
power_df <- bind_cols(params, power = powers)
power_df %>% ggplot(aes(x = prob, y = power)) + geom_line()
PLEASE HELP ME :(