[PYTHON MATRIX-SIG] Array comparisons, and determinants

[Geoffrey Furnish]

Konrad Hinsen writes:
 > > Inequalities are often generalised to work for vectors and matrices.  For
 > > example, x>=0 where x is a vector means x[i]>=0 for every i.
 > 
 > With such a definition, you could have an x for which both x > 0 and
 > x <=0 0 are false. But the __cmp__ function has to decide cleanly
 > between equal, greater, and less - there is nothing in between.

And Tim Hochberg writes:
 > The problem is that __cmp__ can only validly return an integer. Notice
 > that for your first example that am array might be neither >=0 nor <0
 > ([1,-1] comes to mind), so there's really no valid value to return.

The original poster's request has a utility which I think is being
missed.  The goal of expecting x >= 0 (or any other operator) to mean
x[i] >= 0 for every i, is not to get back a truth value, it is to get
back a boolean mask.  Data parallel languages of many stripes and
colors have historically allowed constructs like

<array declaration a, b, c>

where( a > 0) b = c

if (a > 0) b = c        (means the same thing)

a = b > c		(creates a "vector mask")

x = a * <complex function>	(selects complex function only for
				elements where b > c)

I do not yet know if I can think of a reason why I would want to do
exactly this in Python, but that is what the request means to me.
Seen in this light, it is of absolutely no consequence whether x =
[1,-1], or any other curious arrangement of elements, since the goal
is not to get back a single boolean for use in a scalar conditional,
but a vector mask for use in array expressions.

-- 
Geoffrey Furnish		email: furnish@llnl.gov
LLNL X/ICF			phone: 510-424-4227	fax: 510-423-6172

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