# dot products

Discussion in 'Python' started by Rahul, Dec 19, 2004.

1. ### RahulGuest

HI.
I want to compute dot product of two vectors stored as lists a and b.a
and b are of the same length.

one simple way is
sum(a*b for i in range(len(a)))

another simple way is
ans=0.0
for i in range(len(a)):
ans=ans+a*b

But is there any other way which is faster than any of the above. (By
the way profiling them i found that the second is faster by about 30%.)
rahul

Rahul, Dec 19, 2004

2. ### Andrey TatarinovGuest

Rahul wrote:

> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.
>
> one simple way is
> sum(a*b for i in range(len(a)))
>

btw, imho the most "Pythonic" would be:

sum(i*j for (i,j) in zip(a,b))

Andrey Tatarinov, Dec 19, 2004

3. ### Nick CoghlanGuest

Rahul wrote:
> HI.
> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.
>
> one simple way is
> sum(a*b for i in range(len(a)))
>
> another simple way is
> ans=0.0
> for i in range(len(a)):
> ans=ans+a*b
>
> But is there any other way which is faster than any of the above.

Try:

sum(x * y for x, y in zip(a, b))

Between zip() (lockstep iteration over several sequences) and enumerate()
(iteration over a sequence, but also providing an index counter), it is rare
that you will want to use indexing notation in a generator expression.

> (By the way profiling them i found that the second is faster by about 30%.)

For short sequences, generator expressions may end up slightly slower than list
comprehensions or for loops, as the latter two do not involve the overhead of
setting up the generator and retrieving values from it. As the sequences
increase in length, generator expressions generally win in the end due to their
reduced memory impact.

Cheers,
Nick.

--
Nick Coghlan | | Brisbane, Australia
---------------------------------------------------------------
http://boredomandlaziness.skystorm.net

Nick Coghlan, Dec 19, 2004
4. ### Peter OttenGuest

Rahul wrote:

> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.
>
> one simple way is
> sum(a*b for i in range(len(a)))
>
> another simple way is
> ans=0.0
> for i in range(len(a)):
> ans=ans+a*b
>
> But is there any other way which is faster than any of the above. (By
> the way profiling them i found that the second is faster by about 30%.)

You could try

sigma = 0
for ai, bi in itertools.izip(a, b):
sigma += ai * bi

or

sum(itertools.starmap(operator.mul, itertools.izip(a, b)))

but if you are really concerned about number-crunching efficiency, use
Numarray.

Peter

Peter Otten, Dec 19, 2004
5. ### Steven BethardGuest

Rahul wrote:
> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.

.. >>> import numarray as na
.. >>> a, b = na.arange(5), na.arange(5, 10)
.. >>> na.dot(a, b)
.. 80

Steve

Steven Bethard, Dec 19, 2004
6. ### Raymond HettingerGuest

[Rahul].
> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.
>
> one simple way is
> sum(a*b for i in range(len(a)))
>
> another simple way is
> ans=0.0
> for i in range(len(a)):
> ans=ans+a*b
>
> But is there any other way which is faster than any of the above.

Yes:
from itertools import imap
from operator import mul
ans = sum(imap(mul, a, b))

In general:
* reduction functions like sum() do not need their arguments to
take time building a full list; instead, an iterator will do fine
* however, genexps are usually more readable than itertools solutions
* xrange() typically beats range()
* but indexing is rarely the way to go
* izip() typically beats zip()
* imap() can preclude the need for either izip() or zip()
* the timeit module settles these questions quickly

Here are the some timings for vectors of length 10 and 3 respectively

C:\pydev>python timedot.py 3
1.25333310984 sum(a*b for i in xrange(len(a)))
1.16825625639 sum(x*y for x,y in izip(a,b))
1.45373455807 sum(x*y for x,y in zip(a,b))
0.635497577901 sum(imap(mul, a, b))
0.85894416601 sum(map(mul, a, b))

C:\pydev>python timedot.py 10
2.19490353509 sum(a*b for i in xrange(len(a)))
2.01773998894 sum(x*y for x,y in izip(a,b))
2.44932533231 sum(x*y for x,y in zip(a,b))
1.24698871922 sum(imap(mul, a, b))
1.49768685362 sum(map(mul, a, b))

Raymond Hettinger

Raymond Hettinger, Dec 19, 2004
7. ### Fredrik LundhGuest

Raymond Hettinger wrote:

> * applying itertools instead of genexps can save the eval-loop overhead
> * however, genexps are usually more readable than itertools solutions

I'm still waiting for you to implement itertools as a parse-tree analyzer/code generator,
rather than an "bare" extension module.

</F>

Fredrik Lundh, Dec 19, 2004
8. ### RahulGuest

Raymond Hettinger wrote:
> [Rahul].
> > I want to compute dot product of two vectors stored as lists a and

b.a
> > and b are of the same length.
> >
> > one simple way is
> > sum(a*b for i in range(len(a)))
> >
> > another simple way is
> > ans=0.0
> > for i in range(len(a)):
> > ans=ans+a*b
> >
> > But is there any other way which is faster than any of the above.

>
> Yes:
> from itertools import imap
> from operator import mul
> ans = sum(imap(mul, a, b))
>
> In general:
> * reduction functions like sum() do not need their arguments to
> take time building a full list; instead, an iterator will do fine
> * applying itertools instead of genexps can save the eval-loop

> * however, genexps are usually more readable than itertools solutions
> * xrange() typically beats range()
> * but indexing is rarely the way to go
> * izip() typically beats zip()
> * imap() can preclude the need for either izip() or zip()
> * the timeit module settles these questions quickly
>
> Here are the some timings for vectors of length 10 and 3 respectively
>
> C:\pydev>python timedot.py 3
> 1.25333310984 sum(a*b for i in xrange(len(a)))
> 1.16825625639 sum(x*y for x,y in izip(a,b))
> 1.45373455807 sum(x*y for x,y in zip(a,b))
> 0.635497577901 sum(imap(mul, a, b))
> 0.85894416601 sum(map(mul, a, b))
>
> C:\pydev>python timedot.py 10
> 2.19490353509 sum(a*b for i in xrange(len(a)))
> 2.01773998894 sum(x*y for x,y in izip(a,b))
> 2.44932533231 sum(x*y for x,y in zip(a,b))
> 1.24698871922 sum(imap(mul, a, b))
> 1.49768685362 sum(map(mul, a, b))
>
>
>
> Raymond Hettinger

Thanks all of you guys for enlightening me. Python is truly elegant.

Rahul, Dec 20, 2004
9. ### Bengt RichterGuest

On 19 Dec 2004 03:04:15 -0800, "Rahul" <> wrote:

>HI.
>I want to compute dot product of two vectors stored as lists a and b.a
>and b are of the same length.
>
>one simple way is
>sum(a*b for i in range(len(a)))
>
>another simple way is
>ans=0.0
>for i in range(len(a)):
>ans=ans+a*b
>
>But is there any other way which is faster than any of the above. (By
>the way profiling them i found that the second is faster by about 30%.)
>rahul
>

Don't know about the timing, but another way:

>>> import operator
>>> a, b = range(5), range(5,10)
>>> sum(map(operator.mul, a, b))

80

Checking...

>>> class OpShow(object):

... def __init__(self): self.tot = 0
... def __call__(self, x, y):
... prod = x*y
... self.tot += prod
... print '%3s * %-3s => %s (tot %s)' %(x, y, prod, self.tot)
... return prod
...
>>> sum(map(OpShow(), a, b))

0 * 5 => 0 (tot 0)
1 * 6 => 6 (tot 6)
2 * 7 => 14 (tot 20)
3 * 8 => 24 (tot 44)
4 * 9 => 36 (tot 80)
80

Regards,
Bengt Richter

Bengt Richter, Dec 20, 2004
10. ### John LentonGuest

On Sun, Dec 19, 2004 at 03:04:15AM -0800, Rahul wrote:
> HI.
> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length.
>
> one simple way is
> sum(a*b for i in range(len(a)))
>
> another simple way is
> ans=0.0
> for i in range(len(a)):
> ans=ans+a*b
>
> But is there any other way which is faster than any of the above. (By
> the way profiling them i found that the second is faster by about 30%.)
> rahul

some numbers to confirm my previous reply:

1
zip: 0.00115 (1.00)
range: 0.00108 (0.94)
array: 0.00075 (0.65)
10
zip: 0.00306 (1.00)
range: 0.00288 (0.94)
array: 0.00074 (0.24)
100
zip: 0.02195 (1.00)
range: 0.02035 (0.93)
array: 0.00079 (0.04)
1000
zip: 0.21016 (1.00)
range: 0.19930 (0.95)
array: 0.00130 (0.01)
10000
zip: 4.98902 (1.00)
range: 2.70843 (0.54)
array: 0.01405 (0.00)

(the integers are the number of elements in a random array of floats;
'zip' refers to

sum([x*y for (x,y) in zip(a,b)])

'range', to

sum([a*b for i in range(len(a))])

and 'array' makes a and b Numeric's 'array' objects, with atlas
tuned for the system's processor (in this case a pentium3)). The code
in this case is simply

Numeric.dot(a, b)

The advantage of atlas on systems with sse2 should be even greater.

--
John Lenton () -- Random fortune:
El deseo nos fuerza a amar lo que nos hará sufrir.
-- Marcel Proust. (1871-1922) Escritor francÃ©s.

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John Lenton, Dec 20, 2004
11. ### Raymond HettingerGuest

[Rahul].
> > I want to compute dot product of two vectors stored as lists a and b.a
> > and b are of the same length.
> >
> > one simple way is
> > sum(a*b for i in range(len(a)))
> >
> > another simple way is
> > ans=0.0
> > for i in range(len(a)):
> > ans=ans+a*b
> >
> > But is there any other way which is faster than any of the above.

>
> Yes:
> from itertools import imap
> from operator import mul
> ans = sum(imap(mul, a, b))

Doh! We all missed it.

If your vector length is known in advance (and it often is in some apps), the
simplest and fastest approach is:

a[0]*b[0] + a[1]*b[1] + a[2]*b[2]

C:\pydev>python timedot.py 3
0.32 sec: a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
1.38 sec: sum(a*b for i in xrange(len(a)))
1.32 sec: sum(x*y for x,y in izip(a,b))
1.62 sec: sum(x*y for x,y in zip(a,b))
0.75 sec: sum(imap(mul, a, b))
1.04 sec: sum(map(mul, a, b))

Raymond Hettinger

Raymond Hettinger, Dec 21, 2004
12. ### Alan G IsaacGuest

[Rahul].
> I want to compute dot product of two vectors stored as lists a and b.a
> and b are of the same length

from scipy import dot
ans=dot(a,b)

This times faster than the alternatives I have seen mentioned so far,
given scipy.

Cheers,
Alan Isaac

Alan G Isaac, Dec 21, 2004
13. ### Alan G IsaacGuest

"Alan G Isaac" <> wrote in message
news:...
> This times faster than the alternatives I have seen mentioned so far,
> given scipy.

Actually, since I am new to 'timeit', I probably should check that
I am not overlooking something. Especially since I see an order
of magnitude difference in performance. Does the code below
give the right comparisons?

Thanks,
Alan Isaac

#-------------------------------------------------------------
import timeit
env1='''
from operator import mul
from itertools import imap
def innerprod(x,y):
return sum(imap(mul,x,y))
from scipy import rand
x=rand(50); y=rand(50)
'''
env2='''
from operator import mul
from itertools import imap
from scipy import rand
x=rand(50); y=rand(50)
'''
env3='''
from scipy import rand,dot
x=rand(50); y=rand(50)
'''
t1=timeit.Timer("innerprod(x,y)",env1)
t2=timeit.Timer("sum(imap(mul,x,y))",env2)
t3=timeit.Timer("dot(x,y)",env3)
trials=1000