Create a nD grid; meshgrid alternative
Hey, quite often I want to evaluate a function on a grid in a nD space. What I end up doing (and what I really dislike) looks something like this: x = np.linspace(0, 5, 20) M1, M2 = np.meshgrid(x, x) X = np.column_stack([M1.flatten(), M2.flatten()]) X.shape # (400, 2) fancy_function(X) I don't think I ever used `meshgrid` in any other way. Is there a better way to create such a grid space? I wrote myself a little helper function: def gridspace(linspaces): return np.column_stack([space.flatten() for space in np.meshgrid(*linspaces)]) But maybe something like this should be part of numpy? Best, Stefan
I just drafted different versions of the `gridspace` function: https://tmp23.tmpnb.org/user/1waoqQ8PJBJ7/notebooks/201505%20gridspace.ipyn... Beste Grüße, Stefan On Sun, May 10, 2015 at 1:40 PM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hey,
quite often I want to evaluate a function on a grid in a nD space. What I end up doing (and what I really dislike) looks something like this:
x = np.linspace(0, 5, 20) M1, M2 = np.meshgrid(x, x) X = np.column_stack([M1.flatten(), M2.flatten()]) X.shape # (400, 2)
fancy_function(X)
I don't think I ever used `meshgrid` in any other way. Is there a better way to create such a grid space?
I wrote myself a little helper function:
def gridspace(linspaces): return np.column_stack([space.flatten() for space in np.meshgrid(*linspaces)])
But maybe something like this should be part of numpy?
Best, Stefan
On Sun, May 10, 2015 at 7:05 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
I just drafted different versions of the `gridspace` function:
https://tmp23.tmpnb.org/user/1waoqQ8PJBJ7/notebooks/201505%20gridspace.ipyn...
The link seems to be broken... Jaime  (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial.
I'm totally in favor of the 'gridspace(linspaces)' version, as you probably end up wanting to create grids of other things than linspaces (e.g. a logspace grid, or a grid of random points etc.). It should be called somewhat different though. Maybe 'cartesian(arrays)'? Best, Johannes Quoting Stefan Otte (20150510 16:05:02)
I just drafted different versions of the `gridspace` function: https://tmp23.tmpnb.org/user/1waoqQ8PJBJ7/notebooks/201505%20gridspace.ipyn...
Beste Grüße, Stefan
On Sun, May 10, 2015 at 1:40 PM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hey,
quite often I want to evaluate a function on a grid in a nD space. What I end up doing (and what I really dislike) looks something like this:
x = np.linspace(0, 5, 20) M1, M2 = np.meshgrid(x, x) X = np.column_stack([M1.flatten(), M2.flatten()]) X.shape # (400, 2)
fancy_function(X)
I don't think I ever used `meshgrid` in any other way. Is there a better way to create such a grid space?
I wrote myself a little helper function:
def gridspace(linspaces): return np.column_stack([space.flatten() for space in np.meshgrid(*linspaces)])
But maybe something like this should be part of numpy?
Best, Stefan
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On Sun, May 10, 2015 at 4:40 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hey,
quite often I want to evaluate a function on a grid in a nD space. What I end up doing (and what I really dislike) looks something like this:
x = np.linspace(0, 5, 20) M1, M2 = np.meshgrid(x, x) X = np.column_stack([M1.flatten(), M2.flatten()]) X.shape # (400, 2)
fancy_function(X)
I don't think I ever used `meshgrid` in any other way. Is there a better way to create such a grid space?
I wrote myself a little helper function:
def gridspace(linspaces): return np.column_stack([space.flatten() for space in np.meshgrid(*linspaces)])
But maybe something like this should be part of numpy?
Isn't what you are trying to build a cartesian product function? There is a neat, efficient implementation of such a function in StackOverflow, by our own pv.: http://stackoverflow.com/questions/1208118/usingnumpytobuildanarrayof... Perhaps we could make this part of numpy.lib.arraysetops? Isthere room for other combinatoric generators, i.e. combinations, permutations... as in itertools? Jaime  (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial.
On 20150510 14:46:12, Jaime Fernández del Río <jaime.frio@gmail.com> wrote:
Isn't what you are trying to build a cartesian product function? There is a neat, efficient implementation of such a function in StackOverflow, by our own pv.:
http://stackoverflow.com/questions/1208118/usingnumpytobuildanarrayof...
And a slightly faster version just down that page ;) Stéfan
On Sun, May 10, 2015 at 4:40 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hey,
quite often I want to evaluate a function on a grid in a nD space. What I end up doing (and what I really dislike) looks something like this:
x = np.linspace(0, 5, 20) M1, M2 = np.meshgrid(x, x) X = np.column_stack([M1.flatten(), M2.flatten()]) X.shape # (400, 2)
fancy_function(X)
I don't think I ever used `meshgrid` in any other way. Is there a better way to create such a grid space?
I feel like our "house style" has moved away from automatic flattening, and would maybe we should be nudging people towards something more like # using proposed np.stack from pull request #5605 X = np.stack(np.meshgrid(x, x), axis=1) assert X.shape == (20, 20, 2) fancy_function(X) # vectorized to accept any array with shape (..., 2) n  Nathaniel J. Smith  http://vorpus.org
Hello, indeed I was looking for the cartesian product. I timed the two stackoverflow answers and the winner is not quite as clear: n_elements: 10 cartesian 0.00427 cartesian2 0.00172 n_elements: 100 cartesian 0.02758 cartesian2 0.01044 n_elements: 1000 cartesian 0.97628 cartesian2 1.12145 n_elements: 5000 cartesian 17.14133 cartesian2 31.12241 (This is for two arrays as parameters: np.linspace(0, 1, n_elements)) cartesian2 seems to be slower for bigger. I'd really appreciate if this was be part of numpy. Should I create a pull request? Regarding combinations and permutations: I could be convenient to have as well. Cheers, Stefan
On Tue, May 12, 2015 at 1:17 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hello,
indeed I was looking for the cartesian product.
I timed the two stackoverflow answers and the winner is not quite as clear:
n_elements: 10 cartesian 0.00427 cartesian2 0.00172 n_elements: 100 cartesian 0.02758 cartesian2 0.01044 n_elements: 1000 cartesian 0.97628 cartesian2 1.12145 n_elements: 5000 cartesian 17.14133 cartesian2 31.12241
(This is for two arrays as parameters: np.linspace(0, 1, n_elements)) cartesian2 seems to be slower for bigger.
On my system, the following variation on Pauli's answer is 24x faster than his for your test cases: def cartesian4(arrays, out=None): arrays = [np.asarray(x).ravel() for x in arrays] dtype = np.result_type(*arrays) n = np.prod([arr.size for arr in arrays]) if out is None: out = np.empty((len(arrays), n), dtype=dtype) else: out = out.T for j, arr in enumerate(arrays): n /= arr.size out.shape = (len(arrays), 1, arr.size, n) out[j] = arr[np.newaxis, :, np.newaxis] out.shape = (len(arrays), 1) return out.T
I'd really appreciate if this was be part of numpy. Should I create a pull request?
There hasn't been any opposition, quite the contrary, so yes, I would go ahead an create that PR. I somehow feel this belongs with the set operations, rather than with the indexing ones. Other thoughts? Also for consideration: should it work on flattened arrays? or should we give it an axis argument, and then "broadcast on the rest", a la generalized ufunc? Jaime  (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial.
Hey, here is an ipython notebook with benchmarks of all implementations (scroll to the bottom for plots): https://github.com/sotte/ipynb_snippets/blob/master/201505%20gridspace%20%... Overall, Jaime's version is the fastest. On Tue, May 12, 2015 at 2:01 PM Jaime Fernández del Río < jaime.frio@gmail.com> wrote:
On Tue, May 12, 2015 at 1:17 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hello,
indeed I was looking for the cartesian product.
I timed the two stackoverflow answers and the winner is not quite as clear:
n_elements: 10 cartesian 0.00427 cartesian2 0.00172 n_elements: 100 cartesian 0.02758 cartesian2 0.01044 n_elements: 1000 cartesian 0.97628 cartesian2 1.12145 n_elements: 5000 cartesian 17.14133 cartesian2 31.12241
(This is for two arrays as parameters: np.linspace(0, 1, n_elements)) cartesian2 seems to be slower for bigger.
On my system, the following variation on Pauli's answer is 24x faster than his for your test cases:
def cartesian4(arrays, out=None): arrays = [np.asarray(x).ravel() for x in arrays] dtype = np.result_type(*arrays)
n = np.prod([arr.size for arr in arrays]) if out is None: out = np.empty((len(arrays), n), dtype=dtype) else: out = out.T
for j, arr in enumerate(arrays): n /= arr.size out.shape = (len(arrays), 1, arr.size, n) out[j] = arr[np.newaxis, :, np.newaxis] out.shape = (len(arrays), 1)
return out.T
I'd really appreciate if this was be part of numpy. Should I create a pull request?
There hasn't been any opposition, quite the contrary, so yes, I would go ahead an create that PR. I somehow feel this belongs with the set operations, rather than with the indexing ones. Other thoughts?
Also for consideration: should it work on flattened arrays? or should we give it an axis argument, and then "broadcast on the rest", a la generalized ufunc?
Jaime
 (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial. _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpydiscussion
Hey, I just created a pull request: https://github.com/numpy/numpy/pull/5874 Best, Stefan On Tue, May 12, 2015 at 3:29 PM Stefan Otte <stefan.otte@gmail.com> wrote:
Hey,
here is an ipython notebook with benchmarks of all implementations (scroll to the bottom for plots):
https://github.com/sotte/ipynb_snippets/blob/master/201505%20gridspace%20%...
Overall, Jaime's version is the fastest.
On Tue, May 12, 2015 at 2:01 PM Jaime Fernández del Río < jaime.frio@gmail.com> wrote:
On Tue, May 12, 2015 at 1:17 AM, Stefan Otte <stefan.otte@gmail.com> wrote:
Hello,
indeed I was looking for the cartesian product.
I timed the two stackoverflow answers and the winner is not quite as clear:
n_elements: 10 cartesian 0.00427 cartesian2 0.00172 n_elements: 100 cartesian 0.02758 cartesian2 0.01044 n_elements: 1000 cartesian 0.97628 cartesian2 1.12145 n_elements: 5000 cartesian 17.14133 cartesian2 31.12241
(This is for two arrays as parameters: np.linspace(0, 1, n_elements)) cartesian2 seems to be slower for bigger.
On my system, the following variation on Pauli's answer is 24x faster than his for your test cases:
def cartesian4(arrays, out=None): arrays = [np.asarray(x).ravel() for x in arrays] dtype = np.result_type(*arrays)
n = np.prod([arr.size for arr in arrays]) if out is None: out = np.empty((len(arrays), n), dtype=dtype) else: out = out.T
for j, arr in enumerate(arrays): n /= arr.size out.shape = (len(arrays), 1, arr.size, n) out[j] = arr[np.newaxis, :, np.newaxis] out.shape = (len(arrays), 1)
return out.T
I'd really appreciate if this was be part of numpy. Should I create a pull request?
There hasn't been any opposition, quite the contrary, so yes, I would go ahead an create that PR. I somehow feel this belongs with the set operations, rather than with the indexing ones. Other thoughts?
Also for consideration: should it work on flattened arrays? or should we give it an axis argument, and then "broadcast on the rest", a la generalized ufunc?
Jaime
 (\__/) ( O.o) ( > <) Este es Conejo. Copia a Conejo en tu firma y ayúdale en sus planes de dominación mundial. _______________________________________________ NumPyDiscussion mailing list NumPyDiscussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpydiscussion
participants (5)

Jaime Fernández del Río

Johannes Kulick

Nathaniel Smith

Stefan Otte

Stefan van der Walt