options(repos=c(CRAN="http://mirrors.ustc.edu.cn/CRAN/"))
#multivariate descriptive statistics 

#measure of location

iris.a<-iris[,1:4]
sapply(iris.a,mean)
sapply(iris.a,median)
sapply(iris.a,IQR)
sapply(iris.a,summary)


#means and variances par group
iris.set<-iris[iris$Species=="setosa",1:4]
sapply(iris.set,mean)
sapply(iris.set,var)

printMeanAndSdByGroup <- function(variables,groupvariable)
  {
     # find the names of the variables
     variablenames <- c(names(groupvariable),names(as.data.frame(variables)))
     # within each group, find the mean of each variable
     means <- aggregate(as.matrix(variables) ~ groupvariable, FUN = mean)
     print(paste("Means:"))
     print(means)
     # within each group, find the standard deviation of each variable:
     sds <- aggregate(as.matrix(variables) ~ groupvariable, FUN = sd)
     print(paste("Standard deviations:"))
     print(sds)
     # within each group, find the number of samples:
     samplesizes <- aggregate(as.matrix(variables) ~ groupvariable, FUN = length)
     print(paste("Sample sizes:"))
     print(samplesizes)
  }

printMeanAndSdByGroup(iris[,1:4],iris[,5])


#Covariance and Correlation Matrices
cov(iris.a)
cor(iris.a)
cor.test(iris[,1],iris[,2])

mosthighlycorrelated <- function(mydataframe,numtoreport=ncol(mydataframe))
  {   
     # find the correlations
     cormatrix <- cor(mydataframe)
     # set the correlations on the diagonal or lower triangle to zero,
     # so they will not be reported as the highest ones:
     diag(cormatrix) <- 0
     cormatrix[lower.tri(cormatrix)] <- 0
     # flatten the matrix into a dataframe for easy sorting
     fm <- as.data.frame(as.table(cormatrix))
     # assign human-friendly names
     names(fm) <- c("First.Variable", "Second.Variable","Correlation")
     # sort and print the top n correlations
     head(fm[order(abs(fm$Correlation),decreasing=T),],n=numtoreport)
  }

mosthighlycorrelated(iris.a)
mosthighlycorrelated(iris.a,2)

#shape
install.packages("moments")
library(moments)
sapply(iris.a,skewness)
sapply(iris.a,kurtosis)


#standardize variables
stand.iris<-scale(iris.a)
apply(stand.iris,2,mean)
apply(stand.iris,2,var)



#distance
dist.iris<-dist(iris.a)
dist.man.iris<-dist(iris.a,method='manhattan')

dst <- data.matrix(dist.iris)
n<-nrow(dst)
image(1:n, 1:n, dst)