---------------
#  Aufgabe 1  #
---------------

# 1a)

n = 40
m = 200
c = rep(1,n)                                  

# 1b)

a = runif(n*m)
A = matrix(a,ncol=n,nrow=m)
b = runif(m,min=n/2-sqrt(n),max=n/2+sqrt(n))

# 1c)

require(linprog)
res = solveLP(c,b,A,TRUE)
res

# 1d)

names(res)
res$opt                 # maxF
res$iter2               # numbers of iterations 
                        # in Simplex Algorithm
res$solution            # x_max such that F(x_max) = maxF

# 1e)

calctimes = rep(0,100)
iterations = rep(0,100)
maxF = rep(0,100)

for(i in 1:100)
{
    calctime = Sys.time()
    a = runif(n*m)
    A = matrix(a,ncol=n,nrow=m)
    b = runif(m,min=n/2-sqrt(n),max=n/2+sqrt(n))
    res = solveLP(c,b,A,TRUE)
    calctimes[i] = Sys.time() - calctime
    iterations[i] = res$iter2
    maxF[i] = res$opt
}

plot(calctimes,ylim=c(0,1))
plot(iterations, ylim=c(0,100))
plot(iterations,calctimes,main="n = 40, m = 200")
plot(maxF,ylim=c(0,60),main="n = 40, m = 200")


# 1f)

nn = seq(from=10,to=100,by=10)
nn
mm = seq(from=200,to=400,by=20)
mm
calctimes = matrix(0,ncol=10,nrow=11)
iterations = matrix(0,ncol=10,nrow=11)
maxF = matrix(0,ncol=10,nrow=11)
bincoeff = matrix(0,ncol=10,nrow=11)

totaltime = Sys.time()
for(n in nn)
{
  for(m in mm)
  {
    calctime = Sys.time()
    a = runif(n*m)
    A = matrix(a,ncol=n,nrow=m)
    b = runif(m,min=n/2-sqrt(n),max=n/2+sqrt(n))
    c = rep(1,n)
    res = solveLP(c,b,A,TRUE)
    i = m/20 - 9
    j = n/10
    calctimes[i,j] = Sys.time() - calctime
    iterations[i,j] = res$iter2
    maxF[i,j] = res$opt
    bincoeff[i,j] = choose(n+m,m)
  }
}
totaltime = Sys.time() - totaltime 
totaltime

# let's take a quick look:
calctimes
iterations
bincoeff

# plots:
require(plot3D)

persp3D(mm,nn,calctimes)
persp3D(mm,nn,calctimes,xlab="m",ylab="n",zlab="calctimes")

persp3D(mm,nn,iterations)
persp3D(mm,nn,iterations,xlab="m",ylab="n",zlab="iterations")

persp3D(mm,nn,maxF)
persp3D(mm,nn,maxF,xlab="m",ylab="n",zlab="maxF")

persp3D(mm,nn,bincoeff)





# we want to write the pictures into a png-file which will be 
# automatically created in the working directory. The working 
# directory can be set with this command:

setwd("C:/Users/detlef/HSRM/Vorlesungen/SS2017/LinOpt")

# if the following command is executed, pictures will be sent 
# to a file and are not shown on the screen:

png()      

# now invoke plot-commands to generate the pictures;
# once this has been done, type

dev.off()

# then the pictures can be found as Rplot001.png, Rplot002.png, ... 
# in your working directory