##------------------------------------------------------------##
##            Script for Session 8: Writing Packages          ##
##                         John Fox                           ##
##  Introduction to the R Statistical Computing Environment   ##
##                ICPSR Summer Program                        ##
##                         2010                               ##
##------------------------------------------------------------##


  # Functions for a simple matrix-algebra package

source(
  "http://socserv.socsci.mcmaster.ca/jfox/Courses/R-course/matrixDemos.R")

objects()

# some examples

A <- matrix(c(1,2,3,4,5,6,7,8,10), 3, 3) # a nonsingular matrix
A
RREF(A) # the reduced row-echelon form of A

b <- 1:3
RREF(A, b)  # solving the matrix equation Ax = b

RREF(A, diag(3)) # inverting A

B <- matrix(1:9, 3, 3) # a singular matrix
B
RREF(B)

RREF(B, b)

RREF(B, diag(3))

Ginv(A, fractions=TRUE)  # a generalized inverse of A = inverse of A
round(Ginv(A) %*% A, 6)  # check

Ginv(B, fractions=TRUE)  # a generalized inverse of B
B %*% Ginv(B) %*% B   # check

C <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
cholesky(C)
cholesky(C) %*% t(cholesky(C))  # check

    # Create the package "skeleton"

objects()
remove(A, b, B, C)
objects()

setwd("c:/temp") # make a mess in the temp directory

package.skeleton("matrixDemos")

# to check package (at OS prompt): R CMD check matrixDemos
# to install package (at OS prompt): R CMD INSTALL matrixDemos