On Sun, May 10, 2015 at 7:05 AM, Stefan Otte wrote:

I just drafted different versions of the `gridspace` function:

https://tmp23.tmpnb.org/user/1waoqQ8PJBJ7/notebooks/2015-05%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.

On Sun, May 10, 2015 at 4:40 AM, Stefan Otte wrote:

Hey,

quite often I want to evaluate a function on a grid in a n-D 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 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 2-4x 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, 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 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/2015-05%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 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 2-4x 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. _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion