[Numpy-discussion] Creating a sine wave with exponential decay

Stanley Seibert sseibert at anaconda.com
Tue Jul 23 14:38:01 EDT 2019

(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:

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

On Tue, Jul 23, 2019 at 10:38 AM Hameer Abbasi <einstein.edison at gmail.com>

> 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 <https://aka.ms/o0ukef>
> ------------------------------
> *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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