[Numpy-discussion] Creating a sine wave with exponential decay
Ram Rachum
ram at rachum.com
Fri Jul 26 07:09:13 EDT 2019
Thanks for your answers and insight, everybody!
On Fri, Jul 26, 2019 at 9:07 AM Francesc Alted <faltet at gmail.com> wrote:
> Hi Juan,
>
> With the time I have grown to appreciate the simplicity of strings for
> representing the expressions that numexpr is designed to tackle. Having
> said that, PEP 523 looks intriguing indeed. As always, PRs are welcome!
>
> Francesc
>
> El dj., 25 jul. 2019, 4.29, Juan Nunez-Iglesias <jni at fastmail.com> va
> escriure:
>
>> Hi Francesc,
>>
>> Those numbers are really eye-popping! But the formatting of the code as a
>> string still bugs me a lot. Asking this as a totally naive user, do you
>> know whether PEP523 <https://www.python.org/dev/peps/pep-0523/> (adding
>> a frame evaluation API) would allow numexpr to have a more Pythonic syntax?
>> eg.
>>
>> with numexpr:
>> y = np.sin(x) * np.exp(newfactor * x)
>>
>> ?
>>
>> Juan.
>>
>>
>> On 24 Jul 2019, at 6:39 pm, Francesc Alted <faltet at gmail.com> wrote:
>>
>> (disclosure: I have been a long time maintainer of numexpr)
>>
>> An important thing to be noted is that, besides avoiding creating big
>> temporaries, numexpr has support for multi-threading out of the box and
>> Intel VML for optimal evaluation times on Intel CPUs. For choosing your
>> best bet, there is no replacement for experimentation:
>>
>> https://gist.github.com/FrancescAlted/203be8a44d02566f31dae11a22c179f3
>>
>> I have no time now to check for memory consumption, but you can expect
>> numexpr and Numba consuming barely the same amount of memory. Performance
>> wise things are quite different, but this is probably due to my
>> inexperience with Numba (in particular, paralellism does not seem to work
>> for this example in Numba 0.45, but I am not sure why).
>>
>> Cheers!
>>
>>
>> Probably numba has this too, but my attempts to use parallelism failed
>>
>> Missatge de Sebastian Berg <sebastian at sipsolutions.net> del dia dc., 24
>> de jul. 2019 a les 1:32:
>>
>>> On Tue, 2019-07-23 at 13:38 -0500, Stanley Seibert wrote:
>>> > (Full disclosure: I work on Numba...)
>>> >
>>> > Just to note, the NumPy implementation will allocate (and free) more
>>> > than 2 arrays to compute that expression. It has to allocate the
>>> > result array for each operation as Python executes. That expression
>>> > is equivalent to:
>>> >
>>>
>>> That is mostly true, although – as Hameer mentioned – on many platforms
>>> (gcc compiler is needed I think) a bit of magic happens.
>>>
>>> If an array is temporary, the operation is replaced with an in-place
>>> operation for most python operators calls. For example:
>>> `-abs(arr1 * arr2 / arr3 - arr4)`
>>> should only create a single new array and keep reusing it in many
>>> cases[0]. You would achieve similar things with `arr1 *= arr2`
>>> manually.
>>>
>>> Another thing is that numpy will cache some arrays, so that the
>>> allocation cost itself may be avoided in many cases.
>>>
>>> NumPy does no "loop fusing", i.e. each operation is finished before the
>>> next is started. In many cases, with simple math loop fusing can give a
>>> very good speedup (which is wher Numba or numexpr come in). Larger
>>> speedups are likely if you have large arrays and very simple math
>>> (addition). [1]
>>>
>>> As Stanley noted, you probably should not worry too much about it. You
>>> have `exp`/`sin` in there, which are slow by nature. You can try, but
>>> it is likely that you simply cannot gain much speed there.
>>>
>>> Best,
>>>
>>> Sebastian
>>>
>>>
>>> [0] It requires that the shapes all match and that the result arrays
>>> are obviously temporary.
>>> [1] For small arrays overheads may be avoided using tools such as
>>> numba, which can help a lot as well. If you want to use multiple
>>> threads for a specific function that may also be worth a look.
>>>
>>> > s1 = newfactor * x
>>> > s2 = np.exp(s1)
>>> > s3 = np.sin(x)
>>> > y = s3 * s2
>>> >
>>> > However, memory allocation is still pretty fast compared to special
>>> > math functions (exp and sin), which dominate that calculation. I
>>> > find this expression takes around 20 milliseconds for a million
>>> > elements on my older laptop, so that might be negligible in your
>>> > program execution time unless you need to recreate this decaying
>>> > exponential thousands of times. Tools like Numba or numexpr will be
>>> > useful to fuse loops so you only do one allocation, but they aren't
>>> > necessary unless this becomes the bottleneck in your code.
>>> >
>>> > If you are getting started with NumPy, I would suggest not worrying
>>> > about these issues too much, and focus on making good use of arrays,
>>> > NumPy array functions, and array expressions in your code. If you
>>> > have to write for loops (if there is no good way to do the operation
>>> > with existing NumPy functions), I would reach for something like
>>> > Numba, and if you want to speed up complex array expressions, both
>>> > Numba and Numexpr will do a good job.
>>> >
>>> >
>>> > On Tue, Jul 23, 2019 at 10:38 AM Hameer Abbasi <
>>> > einstein.edison at gmail.com> wrote:
>>> > > Hi Ram,
>>> > >
>>> > > No, NumPy doesn’t have a way. And it newer versions, it probably
>>> > > won’t create two arrays if all the dtypes match, it’ll do some
>>> > > magic to re use the existing ones, although it will use multiple
>>> > > loops instead of just one.
>>> > >
>>> > > You might want to look into NumExpr or Numba if you want an
>>> > > efficient implementation.
>>> > >
>>> > > Get Outlook for iOS
>>> > >
>>> > > From: NumPy-Discussion <
>>> > > numpy-discussion-bounces+einstein.edison=gmail.com at python.org> on
>>> > > behalf of Ram Rachum <ram at rachum.com>
>>> > > Sent: Tuesday, July 23, 2019 7:29 pm
>>> > > To: numpy-discussion at python.org
>>> > > Subject: [Numpy-discussion] Creating a sine wave with exponential
>>> > > decay
>>> > >
>>> > > Hi everyone! Total Numpy newbie here.
>>> > >
>>> > > I'd like to create an array with a million numbers, that has a sine
>>> > > wave with exponential decay on the amplitude.
>>> > >
>>> > > In other words, I want the value of each cell n to be sin(n)
>>> > > * 2 ** (-n * factor).
>>> > >
>>> > > What would be the most efficient way to do that?
>>> > >
>>> > > Someone suggested I do something like this:
>>> > >
>>> > > y = np.sin(x) * np.exp(newfactor * x)
>>> > > But this would create 2 arrays, wouldn't it? Isn't that wasteful?
>>> > > Does Numpy provide an efficient way of doing that without creating
>>> > > a redundant array?
>>> > >
>>> > >
>>> > >
>>> > > Thanks for your help,
>>> > >
>>> > > Ram Rachum.
>>> > >
>>> > > _______________________________________________
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>>> > > NumPy-Discussion at python.org
>>> > > https://mail.python.org/mailman/listinfo/numpy-discussion
>>> >
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>>
>>
>> --
>> Francesc Alted
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