# File to test commands in part 1 of Chapter 2  of MacAnova Users' Guide
# Version of 010731
# Set default configuration
startTime <- gettime(quiet:T,keep:T)
setoptions(default:T)
if (!isdefined(PI)){PI <- atan(1, radians:T);;}
if (!isdefined(DEGPERRAD)){DEGPERRAD <- 180/PI;;}
if (!isdefined(E)){E <- exp(1);;}
lockvars(DEGPERRAD, PI, E, silent:T)
PLATFORM <- vecread(string:VERSION,bywords:T)[5]
MACINTOSH <- PLATFORM == "(Mac" || PLATFORM == "(Macintosh" ||\
	PLATFORM == "(Power"
DOS <- PLATFORM == "(DOS" || PLATFORM == "(Win32s"
if (MACINTOSH || DOS){DATAPATH <- DATAPATHS <- HOME;;}
PATHSEP <- if (MACINTOSH){":"}else{"/"}
DATAFILE <- "macanova.dat"; MACROFILE <-  "macanova.mac"
MACROFILES <- vector("graphics.mac","regress.mac","design.mac",\
	"tser.mac", "arima.mac", "mulvar.mac", "math.mac", "macanova.mac")
setoptions(errors:20,dumbplot:T,height:25,width:80)
#2.  The Basics
#2.1 Getting Started
#2.2 Quitting
#2.3 Functions and macros
PI # PI is a predefined REAL variable
euler <- .577215664; euler # semi-colon used as separator
#2.5 Data types
untrue <- F; untrue
greetings <- "Hello!"
greetings # typing the variable name prints the variable
print("\"Hello\"") # inner double quotes are part of string
print("\\Hello\\") #backslash is escaped.
a <- NULL
#2.6 Shapes of variables - scalars, vectors, matrices, arrays
#2.7 Missing values
10 > ? # comparison of a REAL with a MISSING
ismissing(vector(1,?,3)) # 1 MISSING REAL
ismissing(vector("Hello","","World")) # "" treated as missing
anymissing(vector(1,?,5)) # one or more missing values
anymissing(vector(1,3,5)) # no missing values
anymissing(vector("Hello","","World?")) # "" treated as missing
#2.8 Introduction to MacAnova syntax
(3 + 4)*sqrt(2); 3+4*sqrt(2) # 2 commands separated by ';'
#2.8.1 Spaces and comments
 x <- 23 456.7  # embedded space in number is error.
des cribe(x) # embedded space in command name is error.
#2.8.2 Keywords
#2.8.3 Arithmetic expressions
vector(3 + 4, -7/8, 2*PI, 3^.5)
vector(19.3 %% 5,-19.3 %% 5)
vector((1+2)*3, 1+2*3)
vector(2^3*2, 2^(3*2))
vector((3 + 4)*sqrt(2), 3 + 4*sqrt(2))
vector(1,3,-2)^vector(1,2,3)#same as vector(1^1,3^2,(-2)^3)
vector(1,3,5)/2 # same as vector(1/2,3/2,5/2)
#2.8.4 Comparison operators and logical operators
vector(2 == 1, 3 != 3, 2 >= 5, 3 < 1, 2 == 2, 3 != 2)
vector(T == T, F < T, F != F)
vector("A" < "B", "Ab" <= "Ac", "Bb" > "ab")
vector(T || T, T || F, F || T, F || F, 3 < 5 && 5 < 10)
vector(!T, !F, !(3 < 2))
anytrue(log10(5) < 1 || sqrt(5) > 2) # sqrt(5) not computed
alltrue(log10(5) > 1 , sqrt(5) > 2) # sqrt(5) not computed
7 <= vector(4, 5, 6, 7, 8, 9)# compare 7 with several numbers
vector(T, F, F) || vector(F, F, T)
#2.8.5 Bit-wise operations on integers
25 %& 19 # 11001b AND 10011b
25 %| 19 # 11001b OR 10011b
25 %^ 19 # 11001b XOR 10011b
print(nsig:10, %!25) #COMPL(0000000000000000000000000011001b)
print(nsig:10, %! 0) #COMPL(0000000000000000000000000000000b)
nbits(vector(0,25,27)) # all values appropriate integers
nbits(vector(4294967270,4294967295,?)) # 1 MISSING value
nbits(vector(1/3,-1,5000000000)) # all improper values
#2.8.6 Mathematical functions
abs(3-5)+log10(10)+sqrt(25) # 2+1+5
vector(round(-3.2), floor(-3.2), ceiling(-3.2))
DEGPERRAD*vector(atan(1,sqrt(3)),atan(-1,-sqrt(3)))#degrees
vector(round(PI,2), round(10000*PI,-2))
x <- y <- 1e154; vector(hypot(x,y),sqrt(x^2+y^2))
x <- y <- 1e-165; vector(hypot(x,y),sqrt(x^2+y^2))
a <- vector(2.30753, .27061); b <- vector(1,.99229, .04481)
tt <-  sqrt(-2*log(.05));tt-rational(tt,a,b) # upper 5%
tt <-  sqrt(-2*log(.01));tt-rational(tt,a,b) # upper 1%
log(vector("height","weight"))
atan("height","distance")
round("score",2) # or round("score","2")
#2.8.7 Assignment of values to variables
x <- 6; x # Assign 6 to variable x and display the value
department <- "Applied Statistics"; true <- T
y <- (x <- 6) + 8; u <- w <- x + 10; vector(x,y,u,w)
3*5
x <- 3*5 # no output because assignment
x
_pi <- PI; twopi <- 2*_pi
_pi # nothing printed because "invisible"
twopi # not "invisible"
#2.8.8 Arithmetic assignment operators
a <- 17; b <- 5; c <- 3
a <-/ 2; b <-+ 1; c <-^ 2; vector(a,b,c) # 17/2, b+1, c^2
#2.8.9 print(), write(), list(), listbrief() and delete()
x <- 1/6; y <- 1/14; print(x,y,x+y,"Hello")
print("This string is the only argument to print")
write(x,y) # default is 9 significant digits
x <- 5; y <- 6; z <- vector("A","B")
list(x,y,z) # full information
listbrief(x, y, yy) # NOTE: yy has not been previously defined
listbrief("y*") # list all variables whose names start with 'y'
listbrief("*x") # list all variables whose names end with 'x'
listbrief("????plot")#list all 8 letters names ending with plot
listbrief(real:T)
list(nrows:2,char:T) # all CHARACTER variables with 2 rows
az <- 5; _z <- 10 # _z is "invisible"
@z <- 5; listbrief("*z") # only az and z are listed
@z<-5; listbrief("*z",invisible:T)
zvars <- listbrief("*z",keep:T) # or list ("*z",keep:T)
zvars
delete(E, PI)
if (isfunction(islocked)){
	delete(E, PI, lockedok:T)
}
#2.8.10 Vectors - vector(), enter and enterchars
a <- matrix(run(10),2)
print(a,vector(a)) # a is 2 by 5; vector(a) is a 10-vector
data <- vector(146,140,152,112,\
	labels:vector("Tom","Dick","Harry","Elizabeth")); data
z <- vector(1,7,4,9,6); length(z)
nrows(z)
enter(1 7 4 -1 6)
labels <- enterchars(gender height weight "strength"); labels
#2.8.11 Using subscripts with vectors
z <- vector(1,7,4,9,6); z
z[] # Note empty set of subscripts
vector(z,-z)#Note second line of output starts with subscript 6
z[4]
z[vector(1,1,2,2,4,5,3)] # positive subscripts can be repeated
z > 4
z[z > 4] # use of logical subscript
z[vector(-1,-5)]# negative subscripts
a <- z[NULL] ; list(a) # NULL subscript returns NULL
z[4] <- 11 ; z # change element 4 of z
z[vector(1,3)] <- vector(17,19); z # change elements 1 and 3
z[-1] <- 13; z # change all except z[1] to 13
z[10] # error, 10 is too big
z[vector(-1,-2,-1)] # error
nullvar <- z[vector(F,F,F,F,F)]; list(nullvar) # none selected
nullvar <- z[-run(5)]; list(nullvar) # none selected
nullvar <- z[z > 20] <- 20; z # no change is made
list(nullvar) # result of z[z > 20] <- 20 is NULL
z[z > 20] <- run(2) # right hand side is not scalar or NULL
rep(3,5) # 5 copies of 3
run(4) # numbers 1 through 4
run(3,5)
run(3,4.6,.5) # can replace 4.6 by any x, 4.5 <= x < 5
run(1,-1/3,-1/3)
#2.8.13 Matrices and matrix()
x <- matrix(run(6),3); x # 3 divides 6 = length(run(6))
matrix(run(7),3) # 3 does not divide 7 = length(run(7))
list(x) # x has 3 rows and 2 columns
vector(nrows(x),ncols(x),length(x)) # x as above
data <- matrix(vector(17,19,23, 146,112,140),3,\
	labels:structure(vector("Tom","Betty","Dick"),\
	vector("Age","Weight"))); data
#2.8.14 Using subscripts with matrices
x[3,1]   # Note the two subscripts (1,1) at the left
x[,2] # Select column 2 of x, getting a column vector
x[run(2),2] # Select rows 1 and 2 and column 2 of x
x[-run(2),]  # Note 2 subscripts in output for this row vector
vector(x[-run(2),])# Note this ordinary vector has 1 subscript
x[,1] <- -vector(7,8,9); x # change column 1 of x
nullvar <- x[-run(3),] <- 6 ; x # no change, NULL result
list(nullvar)
x[,run(2) < 0] <- run(2)# non-scalar assigned, nothing selected
#2.8.15 Arrays - array()
a <- array(run(8),vector(2,2,2)); a # create a 2 by 2 by 2
matrix(run(6),3)[3,,,] # extra 2 empty subscripts are ignored
matrix(run(6),3)[3,,1,] # extra subscript 1 and empty subscript
matrix(run(6),3)[3,,,1]
a[1,,1] <- 10; a # change a[1,1,1] and a[1,2,1] to 10
a[1,-run(2),1] <- 12; a # no change made
length(a)
print(dim(run(5)),dim(matrix(run(10),2)),\
dim(array(run(24),vector(2,3,4))))
vector(ndims(run(5)),ndims(matrix(run(10),2)),\
ndims(array(run(24),vector(2,3,4))))
#2.8.16 Structures - structure()
temperatures <- structure(Saturday:vector(65,71,75,86,91,93,\
89,78,69,59),Sunday:vector(61,73,85,83,81),\
Monday:vector(51,65,71,78,83,84,85,84,81,75,69,64,59,49))
trees <- structure(info:"Made up data on 6 trees",\
  varnames:vector("Species","DBH"),\
  data:matrix(vector(1,1,1,2,2,2,5.6,4.5,8.9,7.3,9.9,11.3),6))
temperatures
trees
temperatures$Sunday # or temperatures[2]
trees[3][run(2),] # or trees$data[run(2),]
trees[run(2)] # or trees[-3], extract first two components
nullvar <- trees[-run(3)]; list(nullvar) #or trees[rep(F,3)]
vector(temperatures)
temperatures <- structure(Saturday:vector(65,71,75,86,91,93,\
89,78,69,59),Sunday:vector(61,73,85,83,81),\
Monday:vector(51,65,71,78,83,84,85,84,81,75,69,64,59,49))
trees <- structure(info:"Made up data on 6 trees",\
  varnames:vector("Species","DBH"),\
  data:matrix(vector(1,1,1,2,2,2,5.6,4.5,8.9,7.3,9.9,11.3),6))
#2.8.17 Matrix subscripts
a <- matrix(vector(11,21,31,12,22,32,13,23,33,14,24,34),3);a
i <- matrix(vector(1,2,3, 1,2,3),3);i
a[i] # same as diag(a); see Sec. 2.10.6
i <- matrix(vector(1,2,3, 4,3,2),3); i
a[i] # anti-diagonal elements of a
vector(a[1,4],a[2,3],a[3,2]) # same thing
#2.9 Help - help() and usage()
help()
usage(makecols)
help(makecols)
#2.9.1 Using the help() wild card characters - "*" and "?"
help("res*") # find all topics starting with "res"
help("*plot*") # find all topics containing "plot"
help("*pl?t") # like *plot but also lists split
help("c*o*e")
help("???????????") # all topics with 11 letter names
#2.9.2 Using help() index keys
help(key:"?") # get list of all keys
#2.9.3 Getting help on macros - macrousage()
macrousage(boxcox,readcols)
#2.10 Operations with vectors, matrices, arrays and structures
#2.10.1 Transformations
sqrt(vector(2,4,7))
log10(matrix(run(6),2))
sqrt(temperatures)
#2.10.2 Arithmetic with vectors, matrices and arrays
x <- matrix(run(6),3); x
x*5  # Rule (ii), op = '+' ; 5*x would yield the same
2^x  #  Rule (ii), op = '^'
x + vector(6,5,4,3,2,1) #length of vector != number of rows of x
vector(x) + vector(1,1,2,2,3,3)# Rule (i), op = '+'
x <= 4 # Rule (ii), op = '<=' (Sec. 2.8.4)
x + vector(1,3,5) # Rule (iii), op = '+'
x == matrix(vector(2,4),1)#Rule (iv), op = '==' (Sec. 2.8.4)
run(3)  %& vector(1, 2)'#Rule (v), op = '%&' (Sec. 2.8.5)
#2.10.3 Matrix transposition
print(x, transposex:x')
#2.10.4 Matrix multiplication
y <- matrix(vector(1,3,2,4),2);x <- matrix(vector(4,1,2,3),2)
print(x,y)
print(x %*% y, x %c% y, x %C% y) # all three products
matrix(run(4),2) %*% rep(10,5)
#2.10.5  Matrix inversion and linear equation solving
a <- matrix(run(4),2); ainv <- solve(a)
print(a, ainv)
a %*% ainv # should be the identity matrix
solve(matrix(vector(1,2, 2,4),2))
solve(matrix(vector(27.7,7.4,2.6,23.5,23.8,23.4),3))#3 by 2 arg
b <- matrix(vector(5,-7,1, 2),2); b
x <- a %\% b
print(x, aTimesx:a %*% x)
solve(a, b)
c <- vector(1, 1)'; x <- c %/% a
print(x, xTimesa:x %*% a)
rsolve(a,c)
#2.10.6  Other matrix functions - det(), trace(), hconcat(), vconcat(), diag(), dmat(),
# nrows(), ncols(), select(), reverse()
b <- matrix(vector(2891,1851,1302,2139),2); b
det(b) # b[1,1]*b[2,2] - b[1,2]*b[2,1] 
det(b,mantexp:T) # base 10 mantissa and exponent form
trace(b) # b[1,1] + b[2,2]
a1 <- matrix(run(6),3);a2 <- vector(1,0,-1);a3 <- matrix(rep(1,6),3)
print(a1,a2,a3)
hconcat(a1,a2,a3)
vconcat(a1,a3)
diag(a1) # same as vector(a1[1,1],a1[2,2])
select(vector(1,3),a1') # or vector(a1'[vector(1,3),])
select(vector(T,F,F),a1) # same as select(vector(2,1,1),a1)
b <- matrix(run(9)^2,3); b
diag(b)
dmat(diag(b))
dmat(2,7)
reverse(matrix(run(12),3)) # reverses order of rows
asciisave("chkpnt2a.sav") # make sure all variables created are savable
restore("chkpnt2a.sav")
print(paste("Total time =",gettime(quiet:T,keep:T) - startTime))