;
;  the idea is that you copy and paste these into your idl session 
;  to see what happens.
;  You can do all at once (but I do not recommend it) by doing 
;  IDL> @maths
; (after you've copied maths.pro to your directory)


;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;  +           floating point and integer arithmetic                     +
;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

;
; floating point (note the "," to separate commands from values and keywords)
x = 2.
y = 3.
print,' x = ',x,' y = ',y,' x/y=', x/y

; idl does not does not require explicit variable
; declaration (unlike fortran or c). x=2. will assume
; that x is a floating point variable (single precision), since 2. is
; (note the dot)

; integer
x = 2
y = 3
print,' x = ',x,' y = ',y,' x/y=', x/y

;
; Unexpected? Since 2 and 3 are integers, so are x and y, hence 2/3 -> 0.
; Needles to say, this is the root of many an error!
; Try using the index to find which variable types exist, for example
; do ?data types
; you can also use strings
string1 = 'Hello '
string2 = 'World!'
print,string1+string2

; Functions
; Most standard arithmetic functions exist, for example
print,' sqrt(-1) = ',sqrt(complex(-1,0))
print,' atan(-1)/Pi = ',atan(-1)/!PI

; short integers: another source of errors.
; try this
i = 1
print,' Integers: i = ',i,' i+1 = ',i+1
; Good! But now try this:
i = 32767
print,' Integers: i = ',i,' i+1 = ',i+1
; BAD! By default, integers in idl are short, i.e. they
; have values ranging between -32768:32767
; The following gives you what you intended (note the ell in 32767l)
i =32767l
print,' Long integers: i = ',i,' i+1 = ',i+1
; I most often make an error involving sort integers when using i as
; the index in a loop, or, when addressing an element in a vector.


;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;  +           Vectors and matrices                                      +
;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;  A great advange of idl is that all functions work on vectors/arrays
;  as well.
; 
; Notice the [] brackets for defing a vector,and the () for a function
x = float([1,2,3,4,5])
print,' vector x = ',x
print,' x^2   = ',x^2
print,' 1/x =   ',1./x

; another commonly made mistake:
print,' x[1] = ',x[1]

; idl indexes like C: zero based. Thus
print,' x[0] = ',x[0]

; This difference with Fortran is an important source of error when
; tanslating idl programmes to F90

; some more nice stuff
print,' min(x) = ',min(x)
print,' max(x) = ',max(x)
print,' sum of all x = ',total(x)
print,' reverse(x) = ',reverse(x)
print,'   shift x by one ',shift(x,-1)
print,' statistics of x : ',moment(x)
; use ?moment to find which moments are computed

; you can enquire about a variable using help:
help,x

; 
y = replicate(2.,n_elements(x))
print,' x = ',x
print,' y = ',y
print,' y^x = ',y^x

;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;  +           operations on vectors                                     +
;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

; generate nran random numbers with a given seed.
; (uniformly spaced in ]0,1[ )
nran   = 5
myseed = - 1234
x = randomu(myseed,nran)
; setting the seed guarantees you get the same sequence everytime
; randomu(seed,nran) (without declaring seed) gives a different
; sequence everytime.
print,nran,' random numbers '
print,' x = ',x
index = sort(x)
xs    = x[index]
print,'   sorting x : ',xs
print,'   where is x > 0.5: ',where(x gt 0.5)
print,'       and its values are :',x[where(x gt 0.5)]


; the "where" statement is *very* powerful, I use it *very* often
; Note that you find the indices also this way
index_where_x_gt_onehalf = where(x gt 0.5)
print,' x = ',x
print,' x is gt 1/2 at indices :',where(x gt 0.5)
; what happens if no indices qualify?
index = where(x gt 1)
print,' index where x > 1 = ',index




;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;  +           simple loops                                              +
;  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

;  idl has 
;    -- do loops
for i=0,2 do print,' i = ',i
;    -- while loops
i = 0
while (i lt 10) do begin print,' i = ',i & i = i + 1 
;    -- if/else/endif  
;    -- case             (see the index and try them)
;    -- repeat until
;    -- many others