ProgrammingAssignment2/cachematrix.R at master · yychiang/ProgrammingAssignment2 · GitHub

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## Put comments here that give an overall description of what your
## functions do
## Two functions are defined below: "makeCacheMatrix" and "cacheSolve"
## The first function is a function with four functions ("methods") in it. They are
## "set", "get", "setinverse", and "getinverse".
## Normally, we do not call "setinverse" directly.
## The following is a usage example:

# > hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
# > h8 <- hilbert(8); h8
          # [,1]      [,2]      [,3]       [,4]       [,5]       [,6]       [,7]       [,8]
# [1,] 1.0000000 0.5000000 0.3333333 0.25000000 0.20000000 0.16666667 0.14285714 0.12500000
# [2,] 0.5000000 0.3333333 0.2500000 0.20000000 0.16666667 0.14285714 0.12500000 0.11111111
# [3,] 0.3333333 0.2500000 0.2000000 0.16666667 0.14285714 0.12500000 0.11111111 0.10000000
# [4,] 0.2500000 0.2000000 0.1666667 0.14285714 0.12500000 0.11111111 0.10000000 0.09090909
# [5,] 0.2000000 0.1666667 0.1428571 0.12500000 0.11111111 0.10000000 0.09090909 0.08333333
# [6,] 0.1666667 0.1428571 0.1250000 0.11111111 0.10000000 0.09090909 0.08333333 0.07692308
# [7,] 0.1428571 0.1250000 0.1111111 0.10000000 0.09090909 0.08333333 0.07692308 0.07142857
# [8,] 0.1250000 0.1111111 0.1000000 0.09090909 0.08333333 0.07692308 0.07142857 0.06666667
# > a<-makeCacheMatrix(h8)
# > a$get()
          # [,1]      [,2]      [,3]       [,4]       [,5]       [,6]       [,7]       [,8]
# [1,] 1.0000000 0.5000000 0.3333333 0.25000000 0.20000000 0.16666667 0.14285714 0.12500000
# [2,] 0.5000000 0.3333333 0.2500000 0.20000000 0.16666667 0.14285714 0.12500000 0.11111111
# [3,] 0.3333333 0.2500000 0.2000000 0.16666667 0.14285714 0.12500000 0.11111111 0.10000000
# [4,] 0.2500000 0.2000000 0.1666667 0.14285714 0.12500000 0.11111111 0.10000000 0.09090909
# [5,] 0.2000000 0.1666667 0.1428571 0.12500000 0.11111111 0.10000000 0.09090909 0.08333333
# [6,] 0.1666667 0.1428571 0.1250000 0.11111111 0.10000000 0.09090909 0.08333333 0.07692308
# [7,] 0.1428571 0.1250000 0.1111111 0.10000000 0.09090909 0.08333333 0.07692308 0.07142857
# [8,] 0.1250000 0.1111111 0.1000000 0.09090909 0.08333333 0.07692308 0.07142857 0.06666667
# > cacheSolve(a)
        # [,1]      [,2]       [,3]       [,4]        [,5]        [,6]        [,7]       [,8]
# [1,]      64     -2016      20160     -92400      221760     -288288      192192     -51480
# [2,]   -2016     84672    -952560    4656960   -11642400    15567552   -10594584    2882880
# [3,]   20160   -952560   11430720  -58212000   149688000  -204324119   141261119  -38918880
# [4,]  -92400   4656960  -58212000  304919999  -800414996  1109908794  -776936155  216215998
# [5,]  221760 -11642400  149688000 -800414996  2134439987 -2996753738  2118916783 -594593995
# [6,] -288288  15567552 -204324119 1109908793 -2996753738  4249941661 -3030050996  856215352
# [7,]  192192 -10594584  141261119 -776936154  2118916782 -3030050996  2175421226 -618377753
# [8,]  -51480   2882880  -38918880  216215998  -594593995   856215351  -618377753  176679358
# > cacheSolve(a)
# getting cached data
        # [,1]      [,2]       [,3]       [,4]        [,5]        [,6]        [,7]       [,8]
# [1,]      64     -2016      20160     -92400      221760     -288288      192192     -51480
# [2,]   -2016     84672    -952560    4656960   -11642400    15567552   -10594584    2882880
# [3,]   20160   -952560   11430720  -58212000   149688000  -204324119   141261119  -38918880
# [4,]  -92400   4656960  -58212000  304919999  -800414996  1109908794  -776936155  216215998
# [5,]  221760 -11642400  149688000 -800414996  2134439987 -2996753738  2118916783 -594593995
# [6,] -288288  15567552 -204324119 1109908793 -2996753738  4249941661 -3030050996  856215352
# [7,]  192192 -10594584  141261119 -776936154  2118916782 -3030050996  2175421226 -618377753
# [8,]  -51480   2882880  -38918880  216215998  -594593995   856215351  -618377753  176679358
# > sh8 <- a$getinverse()
# > round(sh8 %*% h8)
     # [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
# [1,]    1    0    0    0    0    0    0    0
# [2,]    0    1    0    0    0    0    0    0
# [3,]    0    0    1    0    0    0    0    0
# [4,]    0    0    0    1    0    0    0    0
# [5,]    0    0    0    0    1    0    0    0
# [6,]    0    0    0    0    0    1    0    0
# [7,]    0    0    0    0    0    0    1    0
# [8,]    0    0    0    0    0    0    0    1
# >

## Write a short comment describing this function

makeCacheMatrix <- function(x = matrix()) {
	invx <- NULL ## invx : the inverse of x
	set <- function(y) {
			x <<- y
			invx <<- NULL
	}
	get <- function() x
	setinverse <- function(inverse) invx <<- inverse
	getinverse <- function() invx
	list(set = set, get = get,
		 setinverse = setinverse,
		 getinverse = getinverse)

}


## Write a short comment describing this function
## First, fetch the inverse of x by " x$getinverse()"
## if the fetched value is null, means the matrix x just setted before,
## then the inverse should be computed.
## Otherwise, the inverse need not be computed again, and directly return the cached value.

cacheSolve <- function(x, ...) {
    ## Return a matrix that is the inverse of 'x'
	invx <- x$getinverse()
	if(!is.null(invx)) {
			message("getting cached data")
			return(invx)
	}
	data <- x$get()
	invx <- solve(data, ...)
	x$setinverse(invx)
	invx
}