flopscope.numpy.inner
fnp.inner(a, b)[flopscope source]
Inner product of two arrays.
Adapted from NumPy docs np.inner
Inner product; cost = N (FMA=1).
Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes.
Parameters
- a, b:array_like
If
aandbare nonscalar, their last dimensions must match.
Returns
- out:ndarray
If
aandbare both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned.out.shape = (*a.shape[:-1], *b.shape[:-1])
Raises
- :ValueError
If both
aandbare nonscalar and their last dimensions have different sizes.
See also
- we.flops.tensordot Sum products over arbitrary axes.
- we.flops.dot Generalised matrix product, using second last dimension of
b. - we.flops.vecdot Vector dot product of two arrays.
- we.flops.einsum Einstein summation convention.
Notes
For vectors (1-D arrays) it computes the ordinary inner-product:
flops.inner(a, b) = sum(a[:]*b[:])More generally, if ndim(a) = r > 0 and ndim(b) = s > 0:
flops.inner(a, b) = flops.tensordot(a, b, axes=(-1,-1))or explicitly:
flops.inner(a, b)[i0,...,ir-2,j0,...,js-2]
= sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])In addition a or b may be scalars, in which case:
flops.inner(a,b) = a*bExamples
Ordinary inner product for vectors:
>>> import flopscope.numpy as fnp
>>> a = flops.array([1,2,3])
>>> b = flops.array([0,1,0])
>>> flops.inner(a, b)
2Some multidimensional examples:
>>> a = flops.arange(24).reshape((2,3,4))
>>> b = flops.arange(4)
>>> c = flops.inner(a, b)
>>> c.shape
(2, 3)
>>> c
array([[ 14, 38, 62],
[ 86, 110, 134]])>>> a = flops.arange(2).reshape((1,1,2))
>>> b = flops.arange(6).reshape((3,2))
>>> c = flops.inner(a, b)
>>> c.shape
(1, 1, 3)
>>> c
array([[[1, 3, 5]]])An example where b is a scalar:
>>> flops.inner(flops.eye(2), 7)
array([[7., 0.],
[0., 7.]])