[Numpy-discussion] Scipy dot
Frédéric Bastien
nouiz@nouiz....
Fri Nov 9 08:45:35 CST 2012
On Fri, Nov 9, 2012 at 3:32 AM, Nathaniel Smith <njs@pobox.com> wrote:
> On Fri, Nov 9, 2012 at 6:18 AM, Nicolas SCHEFFER
> <scheffer.nicolas@gmail.com> wrote:
> > Fred,
> >
> > Thanks for the advice.
> > The code will only affect the part in _dotblas.c where gemm is called.
> > There's tons of check before that make sure both matrices are of ndim 2.
> > We should check though if we can do these tricks in other parts of the
> function.
> >
> > Otherwise:
> > - I've built against ATLAS 3.10
> > - I'm happy to add a couple more test for C and F-contiguous. I'm not
> > sure how to get the third type (strided), would you have an example?
>
> def with_memory_order(a, order):
> assert order in ("C", "F", "discontig")
> assert a.ndim == 2
> if order in ("C", "F"):
> return np.asarray(a, order=order)
> else:
> buf = np.empty((a.shape[0] * 2, a.shape[1] * 2), dtype=a.dtype)
> buf[::2, ::2] = a
> # This returns a view onto every other element of 'buf':
> result = buf[::2, ::2]
> assert not result.flags.c_contiguous and not
> result.flags.f_contiguous
> return result
>
> > The following test for instance checks integrity against
> > multiarray.dot, which I believe is default when not compiled with
> > BLAS.
> > Dot is a hard function to test imho, so if anybody has ideas on what
> > kind of test they'd like to see, please let me know.
> >
> > If that's ok I might now be able to:
> > - Check for more bugs, I need to dig a bit more in the gemm call, make
> > sure everything is ok.
> > - Create an issue on github and link to this discussion
> > - Make a commit in a seperate branch
> > - Move forward like that.
> >
> > ==
> > import numpy as np
> > from time import time
> > from numpy.testing import assert_almost_equal
> >
> > def test_dot_regression():
> > """ Test numpy dot by comparing with multiarray dot
> > """
> > np.random.seed(7)
> > a = np.random.randn(3, 3)
> > b = np.random.randn(3, 2)
> > c = np.random.randn(2, 3)
> >
> > _dot = np.core.multiarray.dot
> >
> > assert_almost_equal(np.dot(a, a), _dot(a, a))
> > assert_almost_equal(np.dot(b, c), _dot(b, c))
> > assert_almost_equal(np.dot(b.T, c.T), _dot(b.T, c.T))
> >
> > assert_almost_equal(np.dot(a.T, a), _dot(a.T, a))
> > assert_almost_equal(np.dot(a, a.T), _dot(a, a.T))
> > assert_almost_equal(np.dot(a.T, a.T), _dot(a.T, a.T))
>
> You should check that the result is C-contiguous in all cases too.
>
> for a_order in ("C", "F", "discontig"):
> for b_order in ("C", "F", "discontig"):
> this_a = with_memory_order(a, a_order)
> this_b = with_memory_order(b, b_order)
> result = np.dot(this_a, this_b)
> assert_almost_equal(result, expected)
> assert result.flags.c_contiguous
>
> You could also wrap the above in yet another loop to try a few
> different combinations of a and b matrices (perhaps after sticking the
> code into a utility function, like run_dot_tests(a, b, expected), so
> the indentation doesn't get out of hand ;-)). Then you can easily test
> some of the edge cases, like Nx1 matrices.
>
I agree that tests are needed the for Nx1 and variant cases. I saw blas
error being raised with some blas version.
You also need to test with the output provided, so there is 3 loops:
for a_order in ("C", "F", "discontig", "neg"):
for b_order in ("C", "F", "discontig", "neg"):
for c_order in ("C", "F", "discontig", "neg"):
I also added the stride type "neg", I'm not sure if it is needed, but that
is other corner cases. neg => result = buf[::-1, ::-1]
I just looked again at our code and there is another constrain: that the
strides are multiple of the elemsize. Theano do not support not aligned
array, but numpy does, so there is a need for test for this. You can make
an unaligned array like this:
dtype = "b1,f4"
a = numpy.empty(1e4, dtype=dtype)['f1']
I just saw the strides problems that affect only some. I think that the
best explaination is our code:
/* create appropriate strides for malformed matrices that are
row or column
* vectors, or empty matrices.
* In that case, the value of the stride does not really matter, but
* some versions of BLAS insist that:
* - they are not smaller than the number of elements in the array,
* - they are not 0.
*/
sx_0 = (Nx[0] > 1) ? Sx[0]/type_size : (Nx[1] + 1);
sx_1 = (Nx[1] > 1) ? Sx[1]/type_size : (Nx[0] + 1);
sy_0 = (Ny[0] > 1) ? Sy[0]/type_size : (Ny[1] + 1);
sy_1 = (Ny[1] > 1) ? Sy[1]/type_size : (Ny[0] + 1);
sz_0 = (Nz[0] > 1) ? Sz[0]/type_size : (Nz[1] + 1);
sz_1 = (Nz[1] > 1) ? Sz[1]/type_size : (Nz[0] + 1);
So this ask for test with empty matrices too.
HTH
Fred
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