[R] exponent confusion

[(Ted Harding)]

On 22-Feb-06 tom wright wrote:
> please excuse me if this ones a basic error
> 
>> y<-c(-0.7,-0.6,-0.5)
>> -0.7^1.22
> [1] -0.6471718
> 
>> y^1.22
> [1] NaN NaN NaN
> 
> am I missing something important in my basic math?

Ummm, not sure ... it depends where the explanation fits in.
It's certainly important, but whether it's "basic math" is
another question. And you're certainly missing it!

See

?Syntax

which outputs (initally)

 The following unary and binary operators are defined.  They are
     listed in precedence groups, from highest to lowest.

       '[ [['             indexing
       '::'               name space/variable name separator
       '$ @'              component / slot extraction
       '^'                exponentiation (right to left)
       '- +'              unary minus and plus
       ':'                sequence operator
       '%any%'            special operators
       '* /'              multiply, divide
       '+ -'              (binary) add, subtract
       '< > <= >= == !='  ordering and comparison
       '!'                negation
       '&  &&'            and
       '| ||'             or
       '~'                as in formulae
       '-> ->>'           rightwards assignment
       '='                assignment (right to left)
       '<- <<-'           assignment (right to left)
       '?'                help (unary and binary)

     Within an expression operators of equal precedence are evaluated
     from left to right except where indicated.

Therefore the binary unary operator "^" has precedence over the
unary (sign) operator "-" .

Hence your expression

  -0.7^1.22

is evaluated as

  -(0.7^1.22)

i.e. first do 0.7^1.22, then apply "-".

On the other hand, once you have created

  y<-c(-0.7,-0.6,-0.5)

then each element is already a negative number before you do
anything with it. Hence

  y^1.22 = c( (-0.7)^1.22, (-0.6)^1.22, (-0.5)^1.22 )
         = c(NaN, NaN, NaN)

As an alternative example, unary "-" has precedence over
binary "+" or "-", so that -2+3 is not -(2+3) = 5 but
(-2) + 3 (first apply unary "-", then do binary "+").

Computer languages always embody precedence rules such
as the above to resolve ambiguites in expressions such
as "-a^b" written without parenetheses; but then, in order
to get what you want you need to know the rules in order
to write such expressions correctly.

When in doubt use paraentheses!

A case which has often trapped  people in R (see many
places in the r-help archive) is a sequence expression
such as

  a<-1
  b<-10
  (a:b-1)

which for many is an optical illusion tempting them to
think it is a:(b-1) whereas is is in fact (a:b)-1, i.e.

  0, 1, 2, 3, 4, 5, 6, 7, 8, 9

and not

  1, 2, 3, 4, 5, 6, 7, 8, 9

(see the precedences of binary "-" and the sequence
operator ":" above -- i.e. first do ":" and then the
binary "-").

In cases like this it really is worth while writing
the parantheses:

  (a:b)-1   or   a:(b-1)

according to which you mean, since (a:b-1) really is
visually deceptive.

Best wishes,
Ted.

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Date: 22-Feb-06                                       Time: 16:59:17
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