Homework10.Rmd

---
title: "Homework 10- For Loops"
author: "Morgan Southgate"
date: "May 3, 2017"
output: html_document
---

## Number 1
### A function to calculate the number of zeroes in an atomic vector v
```{r}
zeroSum <- function(v=rep(-10:10,times=3)){
w <- vector(mode="numeric")
for (i in seq_along(v)){
  if(v[i]==0) w[i] <- 1 else
   w[i] <- 0
}
return(print(sum(w)))
}

zeroSum()
```

## Number 2
### Using subsetting rather than for loops to accomplish the same thing as in # 1
```{r}
v=rep(-10:10,times=3)

length(v[v==0])
```

##Number 3
### Code for the function maxDiff() which returns the maximum difference between all possible pairs of elements in an atomic vector 
```{r}

maxDiff <- function(x=rep(-5:5,each=1)) {
   diff <- c(dist(x))
  return(max(diff))
}

maxDiff()
```

# Number 4 
### Altering the maxDiff function to output the values and numbered positions of the maximally distant numbers in the atomic vector as the second and third elements in the output
### Based on code shared by Alex Burnham
```{r, echo=TRUE}

maxDiff1 <- function(x=rep(-5:5,each=1)){
  mat <- matrix(nrow=length(x),ncol=length(x))
  rownames(mat) <- x
  colnames(mat)<- x
    for (i in seq_along(x)){
    for (j in seq_along(x)){
     mat[i,j]<- x[i]-x[j]
    }
  }
  z <- c(mat)
  x <- which(mat==max(abs(mat)), arr.ind=TRUE)
  w<-colnames(mat)[x[1,1]]
  t<-rownames(mat)[x[1,2]]
  return(list(c(w,t),x,max(abs(z))))
  }
   
maxDiff1() 
```

## Number 5
### Making a function maxDiff2 which does the same thing as maxDiff1 but that works by storing a temporary variable that keeps track of differences and retains the largest 
### Based on code shared by Alex Looi
```{r}
 maxDiff2 <- function(x=rep(-10:10,by=1)){
  tempPairs =expand.grid(x,x)
  diffPairs = abs(tempPairs$Var1 - tempPairs$Var2)
  temp_max = 0
  for(v in 1:length(diffPairs)){
    
    if(temp_max <= diffPairs[v]){
      temp_max = diffPairs[v]
    }
  }
  return(temp_max)
}

maxDiff2()
```

## Number 6
### A function that takes as input two matrices and multiplies them together using the rules of matrix multiplication
### Based on code shared by Alex Looi
```{r}
matMult = function(m1=matrix(data=1:10,nrow=2,ncol=5),m2=t(m1)){
   m = matrix(0, nrow(m1), ncol(m2))
  if (nrow(m1) != ncol(m2)){
    cat("input matrices are not correct dimensions", "\n")
  } else {
    for (i in 1:nrow(m1)){
      for (j in 1:ncol(m2)){
        cell_val = sum(m1[i,]*m2[,j])
        m[i,j] = cell_val
      }
    }
  }
  return(m)
}

# test function with default parameter
matMult()

# compare results to those obtained by using the built-in R function
m1=matrix(data=1:10,nrow=2,ncol=5)
m2=t(m1)
m1%*%m2
```

## Number 7 
### A function that takes two integers representing the numbers of rows and columns in a matrix and returns a matrix of these dimensions in which the value of each cell is the product of the row number x column number. 
```{r}
matDims <- function(nr=sample(1:20,size=1),nc=sample(1:20,size=1)){
  mat = matrix(0,nr=nr,nc=nc)
  
 for (r in 1:nr){
      for (c in 1:nc){
      mat[r,c] = r*c
    }}
    return(mat)
}  

matDims()

```