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Glas :[glas] arithmetic operations |
From: Karl Meerbergen (Karl.Meerbergen_at_[hidden])
Date: 2005-10-27 06:52:51
Hello,
I would like to discuss the syntax of arithmetic operations on
vectors/matrices (collections).
Matlab allows exp(v), sin(v), cos(v) etc on vectors (matrices) and the
result is a vector (matrix) where the function is applied on each entry.
Fortran95 goes one step further uses operations for scalars (+, *, -, /,
abs, conj, ...) on vectors (matrices) where the result is a vector
(matrix) whose elements are the result of the scalar operation on the
respective elements of the argument collections.
E.g. v * w is a new vector (or vector expression) where each entry is
the product of the two corresponding entries in v and w. Operations that
require interaction between elements of a vector (matrix) have specific
function names, e.g sum(v) computes the sum of the elements of v, e.g.
sum(abs(v)) is the 1-norm, and max(abs(v)) the inf-norm.
I like this approach because it induces operations from the value_type
to the collection.
It also opens some possibilities that we have not thought of.
For example, x = v * w * z
is equivalent to a loop over all elements of x where the corresponding
elements of v, w, and z are multiplied.
sum(v*w) is the same as dot(v,w), and also sum(v*w*z) makes sense.
It does not imply we have to forget about the function dot() or norm_1()
v<w would then be a collection of bool. And (v<w) && (x>=z) also is a
collection of bool.
But what is v==w? If we are consistent, it also is a collection of bool.
In order to test equality we should have to write min_elt(v==w) or
perhaps better and(v==w). There is no loss of efficiency with the
traditional v==w. This is all a matter of dispatching function calls.
I quite like this approach, because the collection inherits operations
from the value_type in a very intuitive way. (I repeat myself, so I
really like it, don't I ;-) )
What is your opinion?
Karl