Best way to compute length of arbitrary dimension vector?

[Gabriel]

Well, the subject says it almost all: I'd like to write a small Vector
class for arbitrary-dimensional vectors.

I am wondering what would be the most efficient and/or most elegant
way to compute the length of such a Vector?

Right now, I've got

def length(self): # x.length() = || x ||
total = 0.0
for k in range(len(self._coords)):
d = self._coords[k]
total += d*d
return sqrt(total)

However, that seems a bit awkward to me (at least in Python ;-) ).

I know there is the reduce() function, but I can't seem to find a way
to apply that to the case here (at least, not without jumping through
too many hoops).

I have also googled a bit, but found nothing really elegant.

Any ideas?

Best regards,
Gabriel.

 

[Chris Rebert]

Well, the subject says it almost all: I'd like to write a small Vector
class for arbitrary-dimensional vectors.

I am wondering what would be the most efficient and/or most elegant
way to compute the length of such a Vector?

Right now, I've got

 def length(self):                                                                                     # x.length() = || x ||
   total = 0.0
   for k in range(len(self._coords)):
     d = self._coords[k]
     total += d*d
   return sqrt(total)

However, that seems a bit awkward to me (at least in Python ;-) ).

I know there is the reduce() function, but I can't seem to find a way
to apply that to the case here (at least, not without jumping through
too many hoops).

I have also googled a bit, but found nothing really elegant.

Any ideas?

def length(self):
return sqrt(sum(coord*coord for coord in self._coords))

Cheers,
Chris

 

[Peter Otten]

Well, the subject says it almost all: I'd like to write a small Vector
class for arbitrary-dimensional vectors.

I am wondering what would be the most efficient and/or most elegant
way to compute the length of such a Vector?

Right now, I've got

def length(self): # x.length() = || x ||
total = 0.0
for k in range(len(self._coords)):
d = self._coords[k]
total += d*d
return sqrt(total)

However, that seems a bit awkward to me (at least in Python ;-) ).

I know there is the reduce() function, but I can't seem to find a way
to apply that to the case here (at least, not without jumping through
too many hoops).

I have also googled a bit, but found nothing really elegant.

.... def __init__(self, *coords):
.... self._coords = coords
.... def __abs__(self):
.... return math.sqrt(sum(x*x for x in self._coords))
....5.0

 

[Gabriel]

Thanks a lot to both of you, Chris & Peter!

(I knew the solution would be simple ... ;-) )

 

[Gabriel Genellina]

... def __init__(self, *coords):
... self._coords = coords
... def __abs__(self):
... return math.sqrt(sum(x*x for x in self._coords))
...
5.0

Using math.fsum instead of sum may improve accuracy, specially when
len(coords)≫2

py> import math
py>
py> def f1(*args):
.... return math.sqrt(sum(x*x for x in args))
....
py> def f2(*args):
.... return math.sqrt(math.fsum(x*x for x in args))
....
py> pi=math.pi
py> args=[pi]*16
py> abs(f1(*args)/4 - pi)
4.4408920985006262e-16
py> abs(f2(*args)/4 - pi)
0.0

 

[Gabriel]

py> def f2(*args):

...   return math.sqrt(math.fsum(x*x for x in args))

Wow! Thanks a million - I didn't now about math.fsum!

Best regards,
Gabriel.

 

[Ian Kelly]

import math

length = math.hypot(z, math.hypot(x, y))

One line and fast.

The dimension is arbitrary, though, so:

length = reduce(math.hypot, self._coords, 0)

Cheers,
Ian

 

[Gabriel]

The dimension is arbitrary, though, so:

length = reduce(math.hypot, self._coords, 0)

Thanks, I was going to ask Algis that same question.

But still, is this solution really faster or better than the one using
list comprehension and the expression 'x*x'?
It seems to me that the above solution (using hypot) involves repeated
square roots (with subsequent squaring).

Best regards,
Gabriel.

 

[Ian Kelly]

But still, is this solution really faster or better than the one using
list comprehension and the expression 'x*x'?

No, not really.

c:\python32\python -m timeit -s "coords = list(range(100))" -s "from math import hypot" -s "from functools import reduce" "reduce(hypot, coords, 0)"

10000 loops, best of 3: 53.2 usec per loop

c:\python32\python -m timeit -s "coords = list(range(100))" -s "from math import sqrt, fsum" "sqrt(fsum(x*x for x in coords))"

10000 loops, best of 3: 32 usec per loop

c:\python32\python -m timeit -s "coords = list(range(100))" -s "from math import sqrt" "sqrt(sum(x*x for x in coords))"

100000 loops, best of 3: 14.4 usec per loop

 

[Robert Kern]

Thanks, I was going to ask Algis that same question.

But still, is this solution really faster or better than the one using
list comprehension and the expression 'x*x'?
It seems to me that the above solution (using hypot) involves repeated
square roots (with subsequent squaring).

It also means that the floating point numbers stay roughly the same size, so you
will lose less precision as the number of elements goes up. I don't expect the
number of elements will be large enough to matter, though.

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco