I have implemented ReLu derivative as:
def relu_derivative(x):
return (x>0)*np.ones(x.shape)
I also tried:
def relu_derivative(x):
x[x>=0]=1
x[x<0]=0
return x
Size of X=(3072,10000).
But it's taking much time to compute. Is there any other optimized solution?
Approach #1 : Using numexpr
When working with large data, we can use numexpr module that supports multi-core processing if the intended operations could be expressed as arithmetic ones. Here, one way would be -
(X>=0)+0
Thus, to solve our case, it would be -
import numexpr as ne
ne.evaluate('(X>=0)+0')
Approach #2 : Using NumPy views
Another trick would be to use views by viewing the mask of comparisons as an int array, like so -
(X>=0).view('i1')
On performance, it should be identical to creating X>=0.
Timings
Comparing all posted solutions on a random array -
In [14]: np.random.seed(0)
...: X = np.random.randn(3072,10000)
In [15]: # OP's soln-1
...: def relu_derivative_v1(x):
...: return (x>0)*np.ones(x.shape)
...:
...: # OP's soln-2
...: def relu_derivative_v2(x):
...: x[x>=0]=1
...: x[x<0]=0
...: return x
In [16]: %timeit ne.evaluate('(X>=0)+0')
10 loops, best of 3: 27.8 ms per loop
In [17]: %timeit (X>=0).view('i1')
100 loops, best of 3: 19.3 ms per loop
In [18]: %timeit relu_derivative_v1(X)
1 loop, best of 3: 269 ms per loop
In [19]: %timeit relu_derivative_v2(X)
1 loop, best of 3: 89.5 ms per loop
The numexpr based one was with 8 threads. Thus, with more number of threads available for compute, it should improve further. Related post on how to control multi-core functionality.
Approach #3 : Approach #1 + #2 -
Mix both of those for the most optimal one for large arrays -
In [27]: np.random.seed(0)
...: X = np.random.randn(3072,10000)
In [28]: %timeit ne.evaluate('X>=0').view('i1')
100 loops, best of 3: 14.7 ms per loop
Related
I'm relatively new to NumPy and often read that you should avoid to write loops. In many cases I understand how to deal with that, but at the moment I have the following code:
p = np.arange(15).reshape(5,3)
w = np.random.rand(5)
A = np.sum(w[i] * np.outer(p[i], p[i]) for i in range(len(p)))
Does anybody know if there is there a way to avoid the inner for loop?
Thanks in advance!
Approach #1 : With np.einsum -
np.einsum('ij,ik,i->jk',p,p,w)
Approach #2 : With broadcasting + np.tensordot -
np.tensordot(p[...,None]*p[:,None], w, axes=((0),(0)))
Approach #3 : With np.einsum + np.dot -
np.einsum('ij,i->ji',p,w).dot(p)
Runtime test
Set #1 :
In [653]: p = np.random.rand(50,30)
In [654]: w = np.random.rand(50)
In [655]: %timeit np.einsum('ij,ik,i->jk',p,p,w)
10000 loops, best of 3: 101 µs per loop
In [656]: %timeit np.tensordot(p[...,None]*p[:,None], w, axes=((0),(0)))
10000 loops, best of 3: 124 µs per loop
In [657]: %timeit np.einsum('ij,i->ji',p,w).dot(p)
100000 loops, best of 3: 9.07 µs per loop
Set #2 :
In [658]: p = np.random.rand(500,300)
In [659]: w = np.random.rand(500)
In [660]: %timeit np.einsum('ij,ik,i->jk',p,p,w)
10 loops, best of 3: 139 ms per loop
In [661]: %timeit np.einsum('ij,i->ji',p,w).dot(p)
1000 loops, best of 3: 1.01 ms per loop
The third approach just blew everything else!
Why Approach #3 is 10x-130x faster than Approach #1?
np.einsum is implemented in C. In the first approach, with those three strings there i,j,k in its string-notation, we would have three nested loops (in C of course). That's a lot of memory overhead there.
With the third approach, we are only getting into two strings i, j, hence two nested loops (in C again) and also leveraging BLAS based matrix-multiplication with that np.dot. These two factors are responsible for the amazing speedup with this one.
consider the array a
a = np.array([3, 3, np.nan, 3, 3, np.nan])
I could do
np.isnan(a).argmax()
But this requires finding all np.nan just to find the first.
Is there a more efficient way?
I've been trying to figure out if I can pass a parameter to np.argpartition such that np.nan get's sorted first as opposed to last.
EDIT regarding [dup].
There are several reasons this question is different.
That question and answers addressed equality of values. This is in regards to isnan.
Those answers all suffer from the same issue my answer faces. Note, I provided a perfectly valid answer but highlighted it's inefficiency. I'm looking to fix the inefficiency.
EDIT regarding second [dup].
Still addressing equality and question/answers are old and very possibly outdated.
It might also be worth to look into numba.jit; without it, the vectorized version will likely beat a straight-forward pure-Python search in most scenarios, but after compiling the code, the ordinary search will take the lead, at least in my testing:
In [63]: a = np.array([np.nan if i % 10000 == 9999 else 3 for i in range(100000)])
In [70]: %paste
import numba
def naive(a):
for i in range(len(a)):
if np.isnan(a[i]):
return i
def short(a):
return np.isnan(a).argmax()
#numba.jit
def naive_jit(a):
for i in range(len(a)):
if np.isnan(a[i]):
return i
#numba.jit
def short_jit(a):
return np.isnan(a).argmax()
## -- End pasted text --
In [71]: %timeit naive(a)
100 loops, best of 3: 7.22 ms per loop
In [72]: %timeit short(a)
The slowest run took 4.59 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 37.7 µs per loop
In [73]: %timeit naive_jit(a)
The slowest run took 6821.16 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 6.79 µs per loop
In [74]: %timeit short_jit(a)
The slowest run took 395.51 times longer than the fastest. This could mean that an intermediate result is being cached.
10000 loops, best of 3: 144 µs per loop
Edit: As pointed out by #hpaulj in their answer, numpy actually ships with an optimized short-circuited search whose performance is comparable with the JITted search above:
In [26]: %paste
def plain(a):
return a.argmax()
#numba.jit
def plain_jit(a):
return a.argmax()
## -- End pasted text --
In [35]: %timeit naive(a)
100 loops, best of 3: 7.13 ms per loop
In [36]: %timeit plain(a)
The slowest run took 4.37 times longer than the fastest. This could mean that an intermediate result is being cached.
100000 loops, best of 3: 7.04 µs per loop
In [37]: %timeit naive_jit(a)
100000 loops, best of 3: 6.91 µs per loop
In [38]: %timeit plain_jit(a)
10000 loops, best of 3: 125 µs per loop
I'll nominate
a.argmax()
With #fuglede's test array:
In [1]: a = np.array([np.nan if i % 10000 == 9999 else 3 for i in range(100000)])
In [2]: np.isnan(a).argmax()
Out[2]: 9999
In [3]: np.argmax(a)
Out[3]: 9999
In [4]: a.argmax()
Out[4]: 9999
In [5]: timeit a.argmax()
The slowest run took 29.94 ....
10000 loops, best of 3: 20.3 µs per loop
In [6]: timeit np.isnan(a).argmax()
The slowest run took 7.82 ...
1000 loops, best of 3: 462 µs per loop
I don't have numba installed, so can compare that. But my speedup relative to short is greater than #fuglede's 6x.
I'm testing in Py3, which accepts <np.nan, while Py2 raises a runtime warning. But the code search suggests this isn't dependent on that comparison.
/numpy/core/src/multiarray/calculation.c PyArray_ArgMax plays with axes (moving the one of interest to the end), and delegates the action to arg_func = PyArray_DESCR(ap)->f->argmax, a function that depends on the dtype.
In numpy/core/src/multiarray/arraytypes.c.src it looks like BOOL_argmax short circuits, returning as soon as it encounters a True.
for (; i < n; i++) {
if (ip[i]) {
*max_ind = i;
return 0;
}
}
And #fname#_argmax also short circuits on maximal nan. np.nan is 'maximal' in argmin as well.
#if #isfloat#
if (#isnan#(mp)) {
/* nan encountered; it's maximal */
return 0;
}
#endif
Comments from experienced c coders are welcomed, but it appears to me that at least for np.nan, a plain argmax will be as fast you we can get.
Playing with the 9999 in generating a shows that the a.argmax time depends on that value, consistent with short circuiting.
Here is a pythonic approach using itertools.takewhile():
from itertools import takewhile
sum(1 for _ in takewhile(np.isfinite, a))
Benchmark with generator_expression_within_next approach: 1
In [118]: a = np.repeat(a, 10000)
In [120]: %timeit next(i for i, j in enumerate(a) if np.isnan(j))
100 loops, best of 3: 12.4 ms per loop
In [121]: %timeit sum(1 for _ in takewhile(np.isfinite, a))
100 loops, best of 3: 11.5 ms per loop
But still (by far) slower than numpy approach:
In [119]: %timeit np.isnan(a).argmax()
100000 loops, best of 3: 16.8 µs per loop
1. The problem with this approach is using enumerate function. Which returns an enumerate object from the numpy array first (which is an iterator like object) and calling the generator function and next attribute of the iterator will take time.
When looking for the first match in various scenarios, we could iterate through and look for the first match and exit out on the first match rather than going/processing the entire array. So, we would have an approach using Python's next function , like so -
next((i for i, val in enumerate(a) if np.isnan(val)))
Sample runs -
In [192]: a = np.array([3, 3, np.nan, 3, 3, np.nan])
In [193]: next((i for i, val in enumerate(a) if np.isnan(val)))
Out[193]: 2
In [194]: a[2] = 10
In [195]: next((i for i, val in enumerate(a) if np.isnan(val)))
Out[195]: 5
Consider the following two functions, which essentially multiply every number in a small sequence with every number in a larger sequence to build up a 2D array, and then doubles all the values in the array. noloop() uses direct multiplication of 2D numpy arrays and returns the result, whereas loop() uses a for loop to iterate over arr1 and gradually build up an output array.
import numpy as np
arr1 = np.random.rand(100, 1)
arr2 = np.random.rand(1, 100000)
def noloop():
return (arr1*arr2)*2
def loop():
out = np.empty((arr1.size, arr2.size))
for i in range(arr1.size):
tmp = (arr1[i]*arr2)*2
out[i] = tmp.reshape(tmp.size)
return out
I expected noloop to be much faster even for a small number of iterations, but for the array sizes above, loop is actually faster:
>>> %timeit noloop()
10 loops, best of 3: 64.7 ms per loop
>>> %timeit loop()
10 loops, best of 3: 41.6 ms per loop
And interestingly, if I remove *2 in both functions, noloop is faster, but only slightly:
>>> %timeit noloop()
10 loops, best of 3: 29.4 ms per loop
>>> %timeit loop()
10 loops, best of 3: 34.4 ms per loop
Is there a good explanation for these results, and is there a notably faster way to perform the same task?
I wasn't able to reproduce your results, but I did find that I could get substantial speed up (factor of 2) using numpy.multiply. By using the out argument you can take advantage of the fact that the memory is already allocated and eliminate the copying of tmp to out.
def out_loop():
out = np.empty((arr1.size, arr2.size))
for i in range(arr1.size):
np.multiply(arr1[i], arr2, out=out[i].reshape((1, arr2.size)))
out[i] *= 2
return out
Results on my machine:
In [32]: %timeit out_loop()
100 loops, best of 3: 17.7 ms per loop
In [33]: %timeit loop()
10 loops, best of 3: 28.3 ms per loop
Edit to add: I don't think the numba benchmarks are fair, notes below
I'm trying to benchmark different approaches to numerically processing data for the following use case:
Fairly big dataset (100,000+ records)
100+ lines of fairly simple code (z = x + y)
Don't need to sort or index
In other words, the full generality of series and dataframes is not needed, although they are included here b/c they are still convenient ways to encapsulate the data and there is often pre- or post-processing that does require the generality of pandas over numpy arrays.
Question: Based on this use case, are the following benchmarks appropriate and if not, how can I improve them?
# importing pandas, numpy, Series, DataFrame in standard way
from numba import jit
nobs = 10000
nlines = 100
def proc_df():
df = DataFrame({ 'x': np.random.randn(nobs),
'y': np.random.randn(nobs) })
for i in range(nlines):
df['z'] = df.x + df.y
return df.z
def proc_ser():
x = Series(np.random.randn(nobs))
y = Series(np.random.randn(nobs))
for i in range(nlines):
z = x + y
return z
def proc_arr():
x = np.random.randn(nobs)
y = np.random.randn(nobs)
for i in range(nlines):
z = x + y
return z
#jit
def proc_numba():
xx = np.random.randn(nobs)
yy = np.random.randn(nobs)
zz = np.zeros(nobs)
for j in range(nobs):
x, y = xx[j], yy[j]
for i in range(nlines):
z = x + y
zz[j] = z
return zz
Results (Win 7, 3 year old Xeon workstation (quad-core). Standard and recent anaconda distribution or very close.)
In [1251]: %timeit proc_df()
10 loops, best of 3: 46.6 ms per loop
In [1252]: %timeit proc_ser()
100 loops, best of 3: 15.8 ms per loop
In [1253]: %timeit proc_arr()
100 loops, best of 3: 2.02 ms per loop
In [1254]: %timeit proc_numba()
1000 loops, best of 3: 1.04 ms per loop # may not be valid result (see note below)
Edit to add (response to jeff) alternate results from passing df/series/array into functions rather than creating them inside of functions (i.e. move the code lines containing 'randn' from inside function to outside function):
10 loops, best of 3: 45.1 ms per loop
100 loops, best of 3: 15.1 ms per loop
1000 loops, best of 3: 1.07 ms per loop
100000 loops, best of 3: 17.9 µs per loop # may not be valid result (see note below)
Note on numba results: I think the numba compiler must be optimizing on the for loop and reducing the for loop to a single iteration. I don't know that but it's the only explanation I can come up as it couldn't be 50x faster than numpy, right? Followup question here: Why is numba faster than numpy here?
Well, you are not really timing the same things here (or rather, you are timing different aspects).
E.g.
In [6]: x = Series(np.random.randn(nobs))
In [7]: y = Series(np.random.randn(nobs))
In [8]: %timeit x + y
10000 loops, best of 3: 131 µs per loop
In [9]: %timeit Series(np.random.randn(nobs)) + Series(np.random.randn(nobs))
1000 loops, best of 3: 1.33 ms per loop
So [8] times the actual operation, while [9] includes the overhead for the series creation (and the random number generation) PLUS the actual operation
Another example is proc_ser vs proc_df. The proc_df includes the overhead of assignement of a particular column in the DataFrame (which is actually different for an initial creation and subsequent reassignement).
So create the structure (you can time that too, but that is a separate issue). Perform the exact same operation and time them.
Further you say that you don't need alignment. Pandas gives you this by default (and no really easy way to turn it off, though its just a simple check if they are already aligned). While in numba you need to 'manually' align them.
Following up on #Jeff answer. The code can be further optimized.
nobs = 10000
x = pd.Series(np.random.randn(nobs))
y = pd.Series(np.random.randn(nobs))
%timeit proc_ser()
%timeit x + y
%timeit x.values + y.values
100 loops, best of 3: 11.8 ms per loop
10000 loops, best of 3: 107 µs per loop
100000 loops, best of 3: 12.3 µs per loop
I'm looking for the fastest way to check for the occurrence of NaN (np.nan) in a NumPy array X. np.isnan(X) is out of the question, since it builds a boolean array of shape X.shape, which is potentially gigantic.
I tried np.nan in X, but that seems not to work because np.nan != np.nan. Is there a fast and memory-efficient way to do this at all?
(To those who would ask "how gigantic": I can't tell. This is input validation for library code.)
Ray's solution is good. However, on my machine it is about 2.5x faster to use numpy.sum in place of numpy.min:
In [13]: %timeit np.isnan(np.min(x))
1000 loops, best of 3: 244 us per loop
In [14]: %timeit np.isnan(np.sum(x))
10000 loops, best of 3: 97.3 us per loop
Unlike min, sum doesn't require branching, which on modern hardware tends to be pretty expensive. This is probably the reason why sum is faster.
edit The above test was performed with a single NaN right in the middle of the array.
It is interesting to note that min is slower in the presence of NaNs than in their absence. It also seems to get slower as NaNs get closer to the start of the array. On the other hand, sum's throughput seems constant regardless of whether there are NaNs and where they're located:
In [40]: x = np.random.rand(100000)
In [41]: %timeit np.isnan(np.min(x))
10000 loops, best of 3: 153 us per loop
In [42]: %timeit np.isnan(np.sum(x))
10000 loops, best of 3: 95.9 us per loop
In [43]: x[50000] = np.nan
In [44]: %timeit np.isnan(np.min(x))
1000 loops, best of 3: 239 us per loop
In [45]: %timeit np.isnan(np.sum(x))
10000 loops, best of 3: 95.8 us per loop
In [46]: x[0] = np.nan
In [47]: %timeit np.isnan(np.min(x))
1000 loops, best of 3: 326 us per loop
In [48]: %timeit np.isnan(np.sum(x))
10000 loops, best of 3: 95.9 us per loop
I think np.isnan(np.min(X)) should do what you want.
There are two general approaches here:
Check each array item for nan and take any.
Apply some cumulative operation that preserves nans (like sum) and check its result.
While the first approach is certainly the cleanest, the heavy optimization of some of the cumulative operations (particularly the ones that are executed in BLAS, like dot) can make those quite fast. Note that dot, like some other BLAS operations, are multithreaded under certain conditions. This explains the difference in speed between different machines.
import numpy as np
import perfplot
def min(a):
return np.isnan(np.min(a))
def sum(a):
return np.isnan(np.sum(a))
def dot(a):
return np.isnan(np.dot(a, a))
def any(a):
return np.any(np.isnan(a))
def einsum(a):
return np.isnan(np.einsum("i->", a))
b = perfplot.bench(
setup=np.random.rand,
kernels=[min, sum, dot, any, einsum],
n_range=[2 ** k for k in range(25)],
xlabel="len(a)",
)
b.save("out.png")
b.show()
Even there exist an accepted answer, I'll like to demonstrate the following (with Python 2.7.2 and Numpy 1.6.0 on Vista):
In []: x= rand(1e5)
In []: %timeit isnan(x.min())
10000 loops, best of 3: 200 us per loop
In []: %timeit isnan(x.sum())
10000 loops, best of 3: 169 us per loop
In []: %timeit isnan(dot(x, x))
10000 loops, best of 3: 134 us per loop
In []: x[5e4]= NaN
In []: %timeit isnan(x.min())
100 loops, best of 3: 4.47 ms per loop
In []: %timeit isnan(x.sum())
100 loops, best of 3: 6.44 ms per loop
In []: %timeit isnan(dot(x, x))
10000 loops, best of 3: 138 us per loop
Thus, the really efficient way might be heavily dependent on the operating system. Anyway dot(.) based seems to be the most stable one.
If you're comfortable with numba it allows to create a fast short-circuit (stops as soon as a NaN is found) function:
import numba as nb
import math
#nb.njit
def anynan(array):
array = array.ravel()
for i in range(array.size):
if math.isnan(array[i]):
return True
return False
If there is no NaN the function might actually be slower than np.min, I think that's because np.min uses multiprocessing for large arrays:
import numpy as np
array = np.random.random(2000000)
%timeit anynan(array) # 100 loops, best of 3: 2.21 ms per loop
%timeit np.isnan(array.sum()) # 100 loops, best of 3: 4.45 ms per loop
%timeit np.isnan(array.min()) # 1000 loops, best of 3: 1.64 ms per loop
But in case there is a NaN in the array, especially if it's position is at low indices, then it's much faster:
array = np.random.random(2000000)
array[100] = np.nan
%timeit anynan(array) # 1000000 loops, best of 3: 1.93 µs per loop
%timeit np.isnan(array.sum()) # 100 loops, best of 3: 4.57 ms per loop
%timeit np.isnan(array.min()) # 1000 loops, best of 3: 1.65 ms per loop
Similar results may be achieved with Cython or a C extension, these are a bit more complicated (or easily avaiable as bottleneck.anynan) but ultimatly do the same as my anynan function.
use .any()
if numpy.isnan(myarray).any()
numpy.isfinite maybe better than isnan for checking
if not np.isfinite(prop).all()
Related to this is the question of how to find the first occurrence of NaN. This is the fastest way to handle that that I know of:
index = next((i for (i,n) in enumerate(iterable) if n!=n), None)
Adding to #nico-schlömer and #mseifert 's answers, I computed the performance of a numba-test has_nan with early stops, compared to some of the functions that will parse the full array.
On my machine, for an array without nans, the break-even happens for ~10^4 elements.
import perfplot
import numpy as np
import numba
import math
def min(a):
return np.isnan(np.min(a))
def dot(a):
return np.isnan(np.dot(a, a))
def einsum(a):
return np.isnan(np.einsum("i->", a))
#numba.njit
def has_nan(a):
for i in range(a.size - 1):
if math.isnan(a[i]):
return True
return False
def array_with_missing_values(n, p):
""" Return array of size n, p : nans ( % of array length )
Ex : n=1e6, p=1 : 1e4 nan assigned at random positions """
a = np.random.rand(n)
p = np.random.randint(0, len(a), int(p*len(a)/100))
a[p] = np.nan
return a
#%%
perfplot.show(
setup=lambda n: array_with_missing_values(n, 0),
kernels=[min, dot, has_nan],
n_range=[2 ** k for k in range(20)],
logx=True,
logy=True,
xlabel="len(a)",
)
What happens if the array has nans ? I investigated the impact of the nan-coverage of the array.
For arrays of length 1,000,000, has_nan becomes a better option is there are ~10^-3 % nans (so ~10 nans) in the array.
#%%
N = 1000000 # 100000
perfplot.show(
setup=lambda p: array_with_missing_values(N, p),
kernels=[min, dot, has_nan],
n_range=np.array([2 ** k for k in range(20)]) / 2**20 * 0.01,
logy=True,
xlabel=f"% of nan in array (N = {N})",
)
If in your application most arrays have nan and you're looking for ones without, then has_nan is the best approach.
Else; dot seems to be the best option.