Implemented makeCacheMatrix and cacheSolve functions for Programming Assignment 2

Author: davidbody

cachematrix.R

@@ -1,15 +1,83 @@
-## Put comments here that give an overall description of what your
-## functions do
+## This pair of functions demonstrates the use of R's lexical scoping
+## to create a function closure that caches the result of computing
+## the inverse of a matrix.
+##
+## For example, suppose the matrix to be computed is m:
+##
+## > m <- matrix(c(4, 2, 7, 6), nrow=2, ncol=2)
+## > m
+##      [,1] [,2]
+## [1,]    4    7
+## [2,]    2    6
+##
+## We first create the function closure by passing m to
+## makeCacheMatrix, storing the result in cache.m:
+##
+## > cache.m <- makeCacheMatrix(m)
+##
+## Then we compute the inverse of m by passing cache.m to cacheSolve:
+##
+## > inv1 <- cacheSolve(cache.m)
+## > inv1
+##      [,1] [,2]
+## [1,]  0.6 -0.7
+## [2,] -0.2  0.4
+##
+## If we calculate the inverse a second time, the cached result is
+## returned:
+##
+## > inv2 <- cacheSolve(cache.m)
+## getting cached data
+## > inv2
+##      [,1] [,2]
+## [1,]  0.6 -0.7
+## [2,] -0.2  0.4
+##
 
-## Write a short comment describing this function
 
-makeCacheMatrix <- function(x = matrix()) {
+## makeCacheMatrix creates an environment (closure) for caching the
+## inverse of a matrix.
+##
+## The argument x is the matrix to be inverted.
+##
+## makeCacheMatrix returns a list of functions:
+##
+##   setm - sets the matrix and clears any cached inverse
+##   getm - gets the matrix
+##   getinv - gets the inverse
+##   setinv - sets the inverse
 
+makeCacheMatrix <- function(x = matrix()) {
+        inv <- NULL
+        setm <- function(y) {
+                m <<- y
+                inv <<- NULL
+        }
+        getm <- function() m
+        setinv <- function(inverse) inv <<- inverse
+        getinv <- function() inv
+        list(setm = setm, getm = getm, setinv = setinv, getinv = getinv)
 }
 
 
-## Write a short comment describing this function
+## cacheSolve returns the inverse of a matrix.
+##
+## The argument x is the list of functions returned by
+## makeCacheMatrix for the matrix to be inverted.
+##
+## If the inverse has already been computed, cacheSolve
+## returns a cached copy of the inverse.
+##
+## Note: It is assumed that the matrix is always invertible.
 
 cacheSolve <- function(x, ...) {
-        ## Return a matrix that is the inverse of 'x'
+        inv <- x$getinv()
+        if(!is.null(inv)) {
+                message("getting cached data")
+                return(inv)
+        }
+        mat <- x$getm()
+        inv <- solve(mat, ...)
+        x$setinv(inv)
+        inv
 }