Programming Assignment 2

ProgrammingAssignment2.Rproj

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+Version: 1.0
+
+RestoreWorkspace: Default
+SaveWorkspace: Default
+AlwaysSaveHistory: Default
+
+EnableCodeIndexing: Yes
+UseSpacesForTab: Yes
+NumSpacesForTab: 2
+Encoding: UTF-8
+
+RnwWeave: Sweave
+LaTeX: pdfLaTeX

cachematrix.R

@@ -1,120 +1,35 @@
-## some instructions for testing your makeCacheMatrix and cacheSolve functions
+R session:
 
-This is from this post: "Simple test matrices for the lexical scoping programming assignment"
+# makeCacheMatrix 
+# creates a special "matrix" object that can cache its inverse 
 
-https://www.coursera.org/learn/r-programming/discussions/weeks/3/threads/ePlO1eMdEeahzg7_4P4Vvg
+makeCacheMatrix <- function(x = matrix()) {
+      inv <- NULL
+      set <- function(y) {
+            x <<- y 
+            inv <<- NULL
+      }
+      get <- function() x
+      setInverse <- function(inverse) inv <<- inverse
+      getInverse <- function() inv
+      list(set=set, get=get, 
+           setInverse=setInverse, 
+           getInverse=getInverse)
+      }
 
 
-R session:
 
-> # Matrices for testing the R functions 
-> # makeCacheMatrix and cacheSolve
-> # in the Coursera R Programming Course
-> #
-> # First, 
-> # If you haven't read Leonard Greski's invaluable
-> # [TIPS] Demystifying makeVector()  Post
-> # be sure to do so.
-> #
-> # A simple matrix m1 with a simple matrix inverse n1
-> # Define
-> m1 <- matrix(c(1/2, -1/4, -1, 3/4), nrow = 2, ncol = 2)
-> m1
-      [,1]  [,2]
-[1,]  0.50 -1.00
-[2,] -0.25  0.75
-> 
-> # You can use m1 to test your 
-> # makeCacheMatrix and cacheSolve functions.
-> # Since the grading is done on the correctness of your 
-> # makeCacheMatrix and cacheSolve functions and your 
-> # comments on how they work, using this (or some other)   
-> # test matrix to check your code 
-> # before submitting it 
-> # is OK relative to the Coursera Honor Code.
-> # (Checking code with test cases is always a good idea.)
-> #
-> # m1 was constructed (using very simple linear algebra, so
-> # no references are given, almost surely the examples
-> # in this post have been given many times before) 
-> # to have a simple marrix inverse, call it n1.
-> # This means  m1 %*% n1 (%*% is matrix multiply in R) 
-> # is the 2 row by 2 column Identity matrix I2
-> I2 <- matrix(c(1,0,0,1), nrow = 2, ncol = 2)
-> I2
-     [,1] [,2]
-[1,]    1    0
-[2,]    0    1
-> 
-> # And so (by linear algebra) n1 %*% m1 is also equal I2.
-> # (If n1 is the inverse of m1 then m1 is the inverse of n1.)
-> # With m1 defined as above, n1 ( the inverse of m1) is
-> n1 <- matrix(c(6,2,8,4), nrow = 2, ncol = 2)
-> n1
-     [,1] [,2]
-[1,]    6    8
-[2,]    2    4
-> 
-> # Checks:
-> m1 %*% n1
-     [,1] [,2]
-[1,]    1    0
-[2,]    0    1
-> 
-> n1 %*% m1
-     [,1] [,2]
-[1,]    1    0
-[2,]    0    1
-> 
-> solve(m1)
-     [,1] [,2]
-[1,]    6    8
-[2,]    2    4
-> 
-> solve(n1)
-      [,1]  [,2]
-[1,]  0.50 -1.00
-[2,] -0.25  0.75
-> 
-> # So if you have programmed your functions 
-> # correctly (in the file cachematrix.R),
-> # (that, and your comments-explanation of how they work
-> # are what you are graded on)
-> # and sourced cachematrix.R so they are 
-> # available in your R session workspace, then doing 
-> #
-> myMatrix_object <- makeCacheMatrix(m1)
-> 
-> # and then
-> # cacheSolve(myMatrix_object)
-> 
-> # should return exactly the matrix n1
-> cacheSolve(myMatrix_object)
-     [,1] [,2]
-[1,]    6    8
-[2,]    2    4
-> 
-> # calling cacheSolve again should retrieve (not recalculate)
-> # n1
-> cacheSolve(myMatrix_object)
-getting cached data
-     [,1] [,2]
-[1,]    6    8
-[2,]    2    4
-> 
-> # you can use the set function to "put in" a new matrix.
-> # For example n2
-> n2 <- matrix(c(5/8, -1/8, -7/8, 3/8), nrow = 2, ncol = 2)
-> myMatrix_object$set(n2)
-> # and obtain its matrix inverse by
-> cacheSolve(myMatrix_object)
-     [,1] [,2]
-[1,]    3    7
-[2,]    1    5
-> 
-> cacheSolve(myMatrix_object)
-getting cached data
-     [,1] [,2]
-[1,]    3    7
-[2,]    1    5
-> 
+# cacheSolve
+# computes the inverse of the special "matrix" returned by makeCachematrix 
+
+cacheSolve <- function(x, ...) {
+inv <- x$getInverse()
+      if(!is.null(inv)){
+            message("getting cached data")
+            return(inv)
+      }
+      matrix <- x$get()
+      inv <- solve(matrix)
+      x$setInverse(inv)
+      inv
+}