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quickstart.j
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quickstart.j
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# load a source file
load("file.j")
# defining and changing scalar and array variables
x = 3
x = [1 2 3] # set x to a 1x3 row vector
x = [1, 2, 3] # set x to a 1d vector (implicitly treated as a column)
A = [1 2 3 4; 5 6 7 8; 9 10 11 12];
# set A to a 3x4 matrix, semicolon hides output at the prompt.
# inside a source file no output is the default.
x[2] = 7 # change x to [1 7 3]
A[2,1] = 0 # chage A[2,1] to 0
# matrix constructors
rand(n) # uniform random n-element 1d vector
randn(m,n) # normal random mxn matrix
# same for ones, zeros
diag(A) # diagonal of matrix
diagm(x) # construct a diagonal matrix from a vector
# cell arrays
c = {1, 2, 3} # 1d
c = {1 2; A x} # 2d
# solving linear equations
(L,U,P) = lu(A)
# function definitions, loops
# 1. long form (for multiple statements)
function f1(x, y, n)
s = 0
for i=1:n
s += x
end
while n < y < x # (n<y) && (y<x)
n *= 2
end
s+n # value of last expression is returned; "return s+n" also works
end
# example of returning multiple values
# return (gcd(a,b),x,y) such that ax+by == gcd(a,b)
function gcdx(a, b)
if b == 0
(a, 1, 0)
else
m = a % b
k = div((a-m), b) # div is integer division
(g, x, y) = gcdx(b, m)
(g, y, x-k*y)
end
end
# 2. short form (for a single expression)
f(x) = 2x-1
# 3. anonymous functions
map(x->x+1, {1,2,3}) # gives {2,3,4}. "x->x+1" is a 1-argument function
()->2 # zero-argument anonymous function
(x,y)->3y-x # two-argument anonymous function
# conditional within an expression
fib(n) = n < 2 ? n : fib(n-1) + fib(n-2)
# multiple statements on a line
x = 1; a = 2; b = x
"string"
'A' # character
# pascal's triangle symmetric matrix using a comprehension
S(n) = [nCr(i+j-2,i-1) | i=1:n,j=1:n]