set.seed(31)
y <- matrix(rnorm(50),
            10,
            5,
            dimnames=list(paste("g", 1:10, sep=""),
                          paste("t", 1:5, sep=""))
            )
 
# data needs to be in long format
# install reshape if necessary
#install.packages("reshape")
library(reshape)
yy <- melt(y)
 
ggplot(yy, aes(x=X1, y=X2, fill=value)) +
  geom_raster() +
  scale_fill_gradient2(midpoint=0, mid="grey70", limits=c(-2,2))

> sim.I <- function(x)  {  # this is a closure
+   function(u) exp(-(x*u)^2/2) * x
+ }
> 
> g <- sim.I(10) # function used to simulate I_10
> U <- runif(1e5)
> Ts <- g(U)
> mean(Ts)
[1] 1.245262
> 0.5 * sqrt(2*pi)
[1] 1.253314
> 

ctc

ctc

heatmap(...) function can draw a heatmap, it's usage is:

heatmap(x, Rowv=NULL, Colv=if(symm)"Rowv" else NULL,
        distfun = dist, hclustfun = hclust,
        reorderfun = function(d,w) reorder(d,w),
        add.expr, symm = FALSE, revC = identical(Colv, "Rowv"),
        scale=c("row", "column", "none"), na.rm = TRUE,
        margins = c(5, 5), ColSideColors, RowSideColors,
        cexRow = 0.2 + 1/log10(nr), cexCol = 0.2 + 1/log10(nc),
        labRow = NULL, labCol = NULL, main = NULL,
        xlab = NULL, ylab = NULL,
        keep.dendro = FALSE, verbose = getOption("verbose"), ...)


x: Numeric matrix
Rowv: Row dendrogram
Colv: Column dendrogram

curve(expr, from = NULL, to = NULL, n = 101, add = FALSE,
      type = "l", xname = "x", xlab = xname, ylab = NULL,
      log = NULL, xlim = NULL, ...)

expr

from_to

add

demo(plotmath)
par(mar = c(4, 4, 2, 0.1))
plot(rnorm(100), rnorm(100),
  xlab = expression(hat(mu)[0]), ylab = expression(alpha^beta),
  main = expression(paste("Plot of ", alpha^beta, " versus ", hat(mu)[0])))

par(mar = c(4, 4, 2, 0.1))
x_mean <- 1.5
x_sd <- 1.2
hist(rnorm(100, x_mean, x_sd),
  main = substitute(
    paste(X[i], " ~ N(", mu, "=", m, ", ", sigma^2, "=", s2, ")"),
    list(m = x_mean, s2 = x_sd^2)
  )
)

install.packages("rgl")

library(rgl)
data(volcano)
z <- 2 * volcano # Exaggerate the relief
x <- 10 * (1:nrow(z)) # 10 meter spacing (S to N)
y <- 10 * (1:ncol(z)) # 10 meter spacing (E to W)
zlim <- range(z)
zlen <- zlim[2] - zlim[1] + 1
colorlut <- terrain.colors(zlen,alpha=0) # height color lookup table
col <- colorlut[ z-zlim[1]+1 ] # assign colors to heights for each point
open3d()
rgl.surface(x, y, z, color=col, alpha=0.75, back="lines")

مشتق پذیر

 R

X0

h

R=x0+h

f<- function(x) {
  exp(2 * x) - x - 6
}


curve(f, col = 'blue', lty = 2, lwd = 2, xlim=c(-5,5), ylim=c(-5,5), ylab='f(x)')
abline(h=0)
abline(v=0)

newton <- function(f, tol=1E-12,x0=1,N=20) {

        h <- 0.001

        i <- 1; x1 <- x0

        p <- numeric(N)

        while (i<=N) {

                df.dx <- (f(x0+h)-f(x0))/h

                x1 <- (x0 - (f(x0)/df.dx))

                p[i] <- x1

                i <- i + 1

                if (abs(x1-x0) < tol) break

                x0 <- x1

        }

        return(p[1:(i-1)])

}

f <- function(x) {

  exp(2 * x) - x - 6

}

p <- newton(f, x0=1, N=20)

 p

> p <- newton(f, x0=1, N=10)

>  p

[1] 0.9717930 0.9708719 0.9708700 0.9708700 0.9708700 0.9708700

> 

> p <- newton(f, x0=1, N=20)

>  p

[1] 0.9717930 0.9708719 0.9708700 0.9708700 0.9708700 0.9708700

>