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I need help in storing the combinations of column vectors' values in a numpy array.
My problem consists of two column vectors, having size nx1 and mx1, with n=m, and finding n combinations.
I then vertical stacked these column vectors in a matrix, having size nx2.
I found the combinations with the itertools.combination function of python, but I struggle to store them in a numpy array, since itertools gives n rows of tuples.
The main example I found online is reported below:
import itertools
val = [1, 2, 3, 4]
com_set = itertools.combinations(val, 2)
for i in com_set:
print(i)
Output:
(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)
Now, in my case, I have two vectors, val and val1, different from each other.
And, I would need the output in a numpy array, possible a matrix, so I can apply the maximum likelihood estimation method on these values.
You are looking for itertools.product instead of itertools.combinations.
x = [1, 2, 3]
y = [4, 5, 6]
z = list(itertools.product(x, y))
# z = [(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)]
You can turn the result into a (n * n, 2) shaped array by simply passing the result to np.array:
result = np.array(z)
# array([[1, 4],
# [1, 5],
# [1, 6],
# [2, 4],
# [2, 5],
# [2, 6],
# [3, 4],
# [3, 5],
# [3, 6]])
Finally, you can also do this with numpy directly, albeit in a different order:
result = np.stack(np.meshgrid(x, y)).reshape(2, -1).T
# array([[1, 4],
# [2, 4],
# [3, 4],
# [1, 5],
# [2, 5],
# [3, 5],
# [1, 6],
# [2, 6],
# [3, 6]])
I've seen variations of this question asked a few times but so far haven't seen any answers that get to the heart of this general case. I have an n-dimensional array of shape [a, b, c, ...] . For some dimension x, I want to look at each sub-array and find the coordinates of the maximum.
For example, say b = 2, and that's the dimension I'm interested in. I want the coordinates of the maximum of [:, 0, :, ...] and [:, 1, :, ...] in the form a_max = [a_max_b0, a_max_b1], c_max = [c_max_b0, c_max_b1], etc.
I've tried to do this by reshaping my input matrix to a 2d array [b, a*c*d*...], using argmax along axis 0, and unraveling the indices, but the output coordinates don't wind up giving the maxima in my dataset. In this case, n = 3 and I'm interested in axis 1.
shape = gains_3d.shape
idx = gains_3d.reshape(shape[1], -1)
idx = idx.argmax(axis = 1)
a1, a2 = np.unravel_index(idx, [shape[0], shape[2]])
Obviously I could use a loop, but that's not very pythonic.
For a concrete example, I randomly generated a 4x2x3 array. I'm interested in axis 1, so the output should be two arrays of length 2.
testarray = np.array([[[0.17028444, 0.38504759, 0.64852725],
[0.8344524 , 0.54964746, 0.86628204]],
[[0.77089997, 0.25876277, 0.45092835],
[0.6119848 , 0.10096425, 0.627054 ]],
[[0.8466859 , 0.82011746, 0.51123959],
[0.26681694, 0.12952723, 0.94956865]],
[[0.28123628, 0.30465068, 0.29498136],
[0.6624998 , 0.42748154, 0.83362323]]])
testarray[:,0,:] is
array([[0.17028444, 0.38504759, 0.64852725],
[0.77089997, 0.25876277, 0.45092835],
[0.8466859 , 0.82011746, 0.51123959],
[0.28123628, 0.30465068, 0.29498136]])
, so the first element of the first output array will be 2, and the first element of the other will be 0, pointing to 0.8466859. The second elements of the two matrices will be 2 and 2, pointing to 0.94956865 of testarray[:,1,:]
Let's first try to get a clear idea of what you are trying to do:
Sample 3d array:
In [136]: arr = np.random.randint(0,10,(2,3,4))
In [137]: arr
Out[137]:
array([[[1, 7, 6, 2],
[1, 5, 7, 1],
[2, 2, 5, *6*]],
[[*9*, 1, 2, 9],
[2, *9*, 3, 9],
[0, 2, 0, 6]]])
After fiddling around a bit I came up with this iteration, showing the coordinates for each middle dimension, and the max value
In [151]: [(i,np.unravel_index(np.argmax(arr[:,i,:]),(2,4)),np.max(arr[:,i,:])) for i in range
...: (3)]
Out[151]: [(0, (1, 0), 9), (1, (1, 1), 9), (2, (0, 3), 6)]
I can move the unravel outside the iteration:
In [153]: np.unravel_index([np.argmax(arr[:,i,:]) for i in range(3)],(2,4))
Out[153]: (array([1, 1, 0]), array([0, 1, 3]))
Your reshape approach does avoid this loop:
In [154]: arr1 = arr.transpose(1,0,2) # move our axis first
In [155]: arr1 = arr1.reshape(3,-1)
In [156]: arr1
Out[156]:
array([[1, 7, 6, 2, 9, 1, 2, 9],
[1, 5, 7, 1, 2, 9, 3, 9],
[2, 2, 5, 6, 0, 2, 0, 6]])
In [158]: np.argmax(arr1,axis=1)
Out[158]: array([4, 5, 3])
In [159]: np.unravel_index(_,(2,4))
Out[159]: (array([1, 1, 0]), array([0, 1, 3]))
max and argmax take only one axis value, where as you want the equivalent of taking the max along all but one axis. Some ufunc takes a axis tuple, but these do not. The transpose and reshape may be the only way.
In [163]: np.max(arr1,axis=1)
Out[163]: array([9, 9, 6])
Now,i have a 3D(c) array and a 2D(b) array,i want to make a new 3D(d) array, so what shall I do? :
c=np.array([[[1, 2, 3],[2, 3, 4]],[[1, 2, 3],[2, 3, 4]]])
c.shape
(2, 2, 3)
a=np.array([[1, 2, 3],[2, 3, 4]])
a.shape
(2, 3)
d=np.array([[[1, 2, 3],[2, 3, 4]],[[1, 2, 3],[2, 3, 4]],[[1,2,3],[1,2,3]]])
d.shape
(3, 2, 3)
You first need to reshape one of them, then you can use vstack or dstack depends on which one you want to use. For example I use dstack:
c = c.reshape((2, 3, 2))
np.dstack((c, a)).shape
i solved it.
b.reshape(1,2,3), then d=np.vstack((c,b))
What would be the best way of broadcasting two arrays together when a simple call to np.broadcast_to() would fail?
Consider the following example:
import numpy as np
arr1 = np.arange(2 * 3 * 4 * 5 * 6).reshape((2, 3, 4, 5, 6))
arr2 = np.arange(3 * 5).reshape((3, 5))
arr1 + arr2
# ValueError: operands could not be broadcast together with shapes (2,3,4,5,6) (3,5)
arr2_ = np.broadcast_to(arr2, arr1.shape)
# ValueError: operands could not be broadcast together with remapped shapes
arr2_ = arr2.reshape((1, 3, 1, 5, 1))
arr1 + arr2
# now this works because the singletons trigger the automatic broadcast
This only work if I manually select a shape for which automatic broadcasting is going to work.
What would be the most efficient way of doing this automatically?
Is there an alternative way other than reshape on a cleverly constructed broadcastable shape?
Note the relation to np.squeeze(): this would perform the inverse operation by removing singletons. So what I need is some sort of np.squeeze() inverse.
The official documentation (as of NumPy 1.13.0 suggests that the inverse of np.squeeze() is np.expand_dim(), but this is not nearly as flexible as I'd need it to be, and actually np.expand_dim() is roughly equivalent to np.reshape(array, shape + (1,)) or array[:, None].
This issue is also related to the keepdims keyword accepted by e.g. sum:
import numpy as np
arr1 = np.arange(2 * 3 * 4 * 5 * 6).reshape((2, 3, 4, 5, 6))
# not using `keepdims`
arr2 = np.sum(arr1, (0, 2, 4))
arr2.shape
# : (3, 5)
arr1 + arr2
# ValueError: operands could not be broadcast together with shapes (2,3,4,5,6) (3,5)
# now using `keepdims`
arr2 = np.sum(arr1, (0, 2, 4), keepdims=True)
arr2.shape
# : (1, 3, 1, 5, 1)
arr1 + arr2
# now this works because it has the correct shape
EDIT: Obviously, in cases where np.newaxis or keepdims mechanisms are an appropriate choice, there would be no need for a unsqueeze() function.
Yet, there are use-cases where none of these is an option.
For example, consider the case of the weighted average as implemented in numpy.average() over an arbitrary number of dimensions specified by axis.
Right now the weights parameter must have the same shape as the input.
However, weights there is no need specify the weights over the non-reduced dimensions as they are just repeating and the NumPy's broadcasting mechanism would appropriately take care of them.
So if we would like to have such a functionality, we would need to code something like (where some consistency checks are just omitted for simplicity):
def weighted_average(arr, weights=None, axis=None):
if weights is not None and weights.shape != arr.shape:
weights = unsqueeze(weights, ...)
weights = np.zeros_like(arr) + weights
result = np.sum(arr * weights, axis=axis)
result /= np.sum(weights, axis=axis)
return result
or, equivalently:
def weighted_average(arr, weights=None, axis=None):
if weights is not None and weights.shape != arr.shape:
weights = unsqueeze(weights, ...)
weights = np.zeros_like(arr) + weights
return np.average(arr, weights, axis)
In either of the two, it is not possible to replace unsqueeze() with weights[:, np.newaxis]-like statements because we do not know beforehand where the new axis will be needed, nor we can use the keepdims feature of sum because the code will fail at arr * weights.
This case could be relatively nicely handled if np.expand_dims() would support an iterable of ints for its axis parameter, but as of NumPy 1.13.0 does not.
My way of achieving this is by defining the following unsqueezing() function to handle cases where this can be done automatically and giving a warning when the inputs could be ambiguous (e.g. when some source elements of the source shape may match multiple elements of the target shape):
def unsqueezing(
source_shape,
target_shape):
"""
Generate a broadcasting-compatible shape.
The resulting shape contains *singletons* (i.e. `1`) for non-matching dims.
Assumes all elements of the source shape are contained in the target shape
(excepts for singletons) in the correct order.
Warning! The generated shape may not be unique if some of the elements
from the source shape are present multiple timesin the target shape.
Args:
source_shape (Sequence): The source shape.
target_shape (Sequence): The target shape.
Returns:
shape (tuple): The broadcast-safe shape.
Raises:
ValueError: if elements of `source_shape` are not in `target_shape`.
Examples:
For non-repeating elements, `unsqueezing()` is always well-defined:
>>> unsqueezing((2, 3), (2, 3, 4))
(2, 3, 1)
>>> unsqueezing((3, 4), (2, 3, 4))
(1, 3, 4)
>>> unsqueezing((3, 5), (2, 3, 4, 5, 6))
(1, 3, 1, 5, 1)
>>> unsqueezing((1, 3, 5, 1), (2, 3, 4, 5, 6))
(1, 3, 1, 5, 1)
If there is nothing to unsqueeze, the `source_shape` is returned:
>>> unsqueezing((1, 3, 1, 5, 1), (2, 3, 4, 5, 6))
(1, 3, 1, 5, 1)
>>> unsqueezing((2, 3), (2, 3))
(2, 3)
If some elements in `source_shape` are repeating in `target_shape`,
a user warning will be issued:
>>> unsqueezing((2, 2), (2, 2, 2, 2, 2))
(2, 2, 1, 1, 1)
>>> unsqueezing((2, 2), (2, 3, 2, 2, 2))
(2, 1, 2, 1, 1)
If some elements of `source_shape` are not presente in `target_shape`,
an error is raised.
>>> unsqueezing((2, 3), (2, 2, 2, 2, 2))
Traceback (most recent call last):
...
ValueError: Target shape must contain all source shape elements\
(in correct order). (2, 3) -> (2, 2, 2, 2, 2)
>>> unsqueezing((5, 3), (2, 3, 4, 5, 6))
Traceback (most recent call last):
...
ValueError: Target shape must contain all source shape elements\
(in correct order). (5, 3) -> (2, 3, 4, 5, 6)
"""
shape = []
j = 0
for i, dim in enumerate(target_shape):
if j < len(source_shape):
shape.append(dim if dim == source_shape[j] else 1)
if i + 1 < len(target_shape) and dim == source_shape[j] \
and dim != 1 and dim in target_shape[i + 1:]:
text = ('Multiple positions (e.g. {} and {})'
' for source shape element {}.'.format(
i, target_shape[i + 1:].index(dim) + (i + 1), dim))
warnings.warn(text)
if dim == source_shape[j] or source_shape[j] == 1:
j += 1
else:
shape.append(1)
if j < len(source_shape):
raise ValueError(
'Target shape must contain all source shape elements'
' (in correct order). {} -> {}'.format(source_shape, target_shape))
return tuple(shape)
This can be used to define unsqueeze() as a more flexible inverse of np.squeeze() compared to np.expand_dims() which can only append one singleton at a time:
def unsqueeze(
arr,
axis=None,
shape=None,
reverse=False):
"""
Add singletons to the shape of an array to broadcast-match a given shape.
In some sense, this function implements the inverse of `numpy.squeeze()`.
Args:
arr (np.ndarray): The input array.
axis (int|Iterable|None): Axis or axes in which to operate.
If None, a valid set axis is generated from `shape` when this is
defined and the shape can be matched by `unsqueezing()`.
If int or Iterable, specified how singletons are added.
This depends on the value of `reverse`.
If `shape` is not None, the `axis` and `shape` parameters must be
consistent.
Values must be in the range [-(ndim+1), ndim+1]
At least one of `axis` and `shape` must be specified.
shape (int|Iterable|None): The target shape.
If None, no safety checks are performed.
If int, this is interpreted as the number of dimensions of the
output array.
If Iterable, the result must be broadcastable to an array with the
specified shape.
If `axis` is not None, the `axis` and `shape` parameters must be
consistent.
At least one of `axis` and `shape` must be specified.
reverse (bool): Interpret `axis` parameter as its complementary.
If True, the dims of the input array are placed at the positions
indicated by `axis`, and singletons are placed everywherelse and
the `axis` length must be equal to the number of dimensions of the
input array; the `shape` parameter cannot be `None`.
If False, the singletons are added at the position(s) specified by
`axis`.
If `axis` is None, `reverse` has no effect.
Returns:
arr (np.ndarray): The reshaped array.
Raises:
ValueError: if the `arr` shape cannot be reshaped correctly.
Examples:
Let's define some input array `arr`:
>>> arr = np.arange(2 * 3 * 4).reshape((2, 3, 4))
>>> arr.shape
(2, 3, 4)
A call to `unsqueeze()` can be reversed by `np.squeeze()`:
>>> arr_ = unsqueeze(arr, (0, 2, 4))
>>> arr_.shape
(1, 2, 1, 3, 1, 4)
>>> arr = np.squeeze(arr_, (0, 2, 4))
>>> arr.shape
(2, 3, 4)
The order of the axes does not matter:
>>> arr_ = unsqueeze(arr, (0, 4, 2))
>>> arr_.shape
(1, 2, 1, 3, 1, 4)
If `shape` is an int, `axis` must be consistent with it:
>>> arr_ = unsqueeze(arr, (0, 2, 4), 6)
>>> arr_.shape
(1, 2, 1, 3, 1, 4)
>>> arr_ = unsqueeze(arr, (0, 2, 4), 7)
Traceback (most recent call last):
...
ValueError: Incompatible `[0, 2, 4]` axis and `7` shape for array of\
shape (2, 3, 4)
It is possible to reverse the meaning to `axis` to add singletons
everywhere except where specified (but requires `shape` to be defined
and the length of `axis` must match the array dims):
>>> arr_ = unsqueeze(arr, (0, 2, 4), 10, True)
>>> arr_.shape
(2, 1, 3, 1, 4, 1, 1, 1, 1, 1)
>>> arr_ = unsqueeze(arr, (0, 2, 4), reverse=True)
Traceback (most recent call last):
...
ValueError: When `reverse` is True, `shape` cannot be None.
>>> arr_ = unsqueeze(arr, (0, 2), 10, True)
Traceback (most recent call last):
...
ValueError: When `reverse` is True, the length of axis (2) must match\
the num of dims of array (3).
Axes values must be valid:
>>> arr_ = unsqueeze(arr, 0)
>>> arr_.shape
(1, 2, 3, 4)
>>> arr_ = unsqueeze(arr, 3)
>>> arr_.shape
(2, 3, 4, 1)
>>> arr_ = unsqueeze(arr, -1)
>>> arr_.shape
(2, 3, 4, 1)
>>> arr_ = unsqueeze(arr, -4)
>>> arr_.shape
(1, 2, 3, 4)
>>> arr_ = unsqueeze(arr, 10)
Traceback (most recent call last):
...
ValueError: Axis (10,) out of range.
If `shape` is specified, `axis` can be omitted (USE WITH CARE!) or its
value is used for addiotional safety checks:
>>> arr_ = unsqueeze(arr, shape=(2, 3, 4, 5, 6))
>>> arr_.shape
(2, 3, 4, 1, 1)
>>> arr_ = unsqueeze(
... arr, (3, 6, 8), (2, 5, 3, 2, 7, 2, 3, 2, 4, 5, 6), True)
>>> arr_.shape
(1, 1, 1, 2, 1, 1, 3, 1, 4, 1, 1)
>>> arr_ = unsqueeze(
... arr, (3, 7, 8), (2, 5, 3, 2, 7, 2, 3, 2, 4, 5, 6), True)
Traceback (most recent call last):
...
ValueError: New shape [1, 1, 1, 2, 1, 1, 1, 3, 4, 1, 1] cannot be\
broadcasted to shape (2, 5, 3, 2, 7, 2, 3, 2, 4, 5, 6)
>>> arr = unsqueeze(arr, shape=(2, 5, 3, 7, 2, 4, 5, 6))
>>> arr.shape
(2, 1, 3, 1, 1, 4, 1, 1)
>>> arr = np.squeeze(arr)
>>> arr.shape
(2, 3, 4)
>>> arr = unsqueeze(arr, shape=(5, 3, 7, 2, 4, 5, 6))
Traceback (most recent call last):
...
ValueError: Target shape must contain all source shape elements\
(in correct order). (2, 3, 4) -> (5, 3, 7, 2, 4, 5, 6)
The behavior is consistent with other NumPy functions and the
`keepdims` mechanism:
>>> axis = (0, 2, 4)
>>> arr1 = np.arange(2 * 3 * 4 * 5 * 6).reshape((2, 3, 4, 5, 6))
>>> arr2 = np.sum(arr1, axis, keepdims=True)
>>> arr2.shape
(1, 3, 1, 5, 1)
>>> arr3 = np.sum(arr1, axis)
>>> arr3.shape
(3, 5)
>>> arr3 = unsqueeze(arr3, axis)
>>> arr3.shape
(1, 3, 1, 5, 1)
>>> np.all(arr2 == arr3)
True
"""
# calculate `new_shape`
if axis is None and shape is None:
raise ValueError(
'At least one of `axis` and `shape` parameters must be specified.')
elif axis is None and shape is not None:
new_shape = unsqueezing(arr.shape, shape)
elif axis is not None:
if isinstance(axis, int):
axis = (axis,)
# calculate the dim of the result
if shape is not None:
if isinstance(shape, int):
ndim = shape
else: # shape is a sequence
ndim = len(shape)
elif not reverse:
ndim = len(axis) + arr.ndim
else:
raise ValueError('When `reverse` is True, `shape` cannot be None.')
# check that axis is properly constructed
if any([ax < -ndim - 1 or ax > ndim + 1 for ax in axis]):
raise ValueError('Axis {} out of range.'.format(axis))
# normalize axis using `ndim`
axis = sorted([ax % ndim for ax in axis])
# manage reverse mode
if reverse:
if len(axis) == arr.ndim:
axis = [i for i in range(ndim) if i not in axis]
else:
raise ValueError(
'When `reverse` is True, the length of axis ({})'
' must match the num of dims of array ({}).'.format(
len(axis), arr.ndim))
elif len(axis) + arr.ndim != ndim:
raise ValueError(
'Incompatible `{}` axis and `{}` shape'
' for array of shape {}'.format(axis, shape, arr.shape))
# generate the new shape from axis, ndim and shape
new_shape = []
i, j = 0, 0
for l in range(ndim):
if i < len(axis) and l == axis[i] or j >= arr.ndim:
new_shape.append(1)
i += 1
else:
new_shape.append(arr.shape[j])
j += 1
# check that `new_shape` is consistent with `shape`
if shape is not None:
if isinstance(shape, int):
if len(new_shape) != ndim:
raise ValueError(
'Length of new shape {} does not match '
'expected length ({}).'.format(len(new_shape), ndim))
else:
if not all([new_dim == 1 or new_dim == dim
for new_dim, dim in zip(new_shape, shape)]):
raise ValueError(
'New shape {} cannot be broadcasted to shape {}'.format(
new_shape, shape))
return arr.reshape(new_shape)
Using these, one can write:
import numpy as np
arr1 = np.arange(2 * 3 * 4 * 5 * 6).reshape((2, 3, 4, 5, 6))
arr2 = np.arange(3 * 5).reshape((3, 5))
arr3 = unsqueeze(arr2, (0, 2, 4))
arr1 + arr3
# now this works because it has the correct shape
arr3 = unsqueeze(arr2, shape=arr1.shape)
arr1 + arr3
# this also works because the shape can be expanded unambiguously
So dynamic broadcast can now happen, and this is consistent with the behavior of keepdims:
import numpy as np
axis = (0, 2, 4)
arr1 = np.arange(2 * 3 * 4 * 5 * 6).reshape((2, 3, 4, 5, 6))
arr2 = np.sum(arr1, axis, keepdims=True)
arr3 = np.sum(arr1, axis)
arr3 = unsqueeze(arr3, axis)
np.all(arr2 == arr3)
# : True
Effectively, this extends np.expand_dims() to handle more complex scenarios.
Improvements over this code are obviously more than welcome.
I am trying to take the dot product between three numpy arrays. However, I am struggling with wrapping my head around this.
The problem is as follows:
I have two (4,) shaped numpy arrays a and b respectively, as well as a numpy array with shape (4, 4, 3), c.
import numpy as np
a = np.array([0, 1, 2, 3])
b = np.array([[[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
[[2, 2, 2], [2, 2, 2], [2, 2, 2], [2, 2, 2]],
[[3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3]],
[[4, 4, 4], [4, 4, 4], [4, 4, 4], [4, 4, 4]]])
c = np.array([4, 5, 6, 7])
I want to compute the dot product in such a way that my result is a 3-tuple. That is, first dot a with b and then dotting with c, taking transposes if needed. In other words, I want to compute the dot product between a, b and c as if c was of shape (4, 4), but I want a 3-tuple as result.
I have tried:
Reshaping a and c, and then computing the dot product:
a = np.reshape(a, (4, 1))
c = np.reshape(c, (4, 1))
tmp = np.dot(a.T, b) # now has shape (1, 4, 3)
result = np.dot(tmp, c)
Ideally, I should now have:
print(result.shape)
>> (1, 1, 3)
but I get the error
ValueError: shapes (1,4,3) and (4,1) not aligned: 3 (dim 2) != 4 (dim 0)
I have also tried using the tensordot function from numpy, but without luck.
The basic dot(A,B) rule is: last axis of A with the 2nd to the last of B
In [965]: a.shape
Out[965]: (4,)
In [966]: b.shape
Out[966]: (4, 4, 3)
a (and c) is 1d. It's (4,) can dot with the 2nd (4) of b with:
In [967]: np.dot(a,b).shape
Out[967]: (4, 3)
Using c in the same on the output produces a (3,) array
In [968]: np.dot(c, np.dot(a,b))
Out[968]: array([360, 360, 360])
This combination may be clearer with the equivalent einsum:
In [971]: np.einsum('i,jik,j->k',a,b,c)
Out[971]: array([360, 360, 360])
But what if we want a to act on the 1st axis of b? With einsum that's easy to do:
In [972]: np.einsum('i,ijk,j->k',a,b,c)
Out[972]: array([440, 440, 440])
To do the same with the dot, we could just switch a and c:
In [973]: np.dot(a, np.dot(c,b))
Out[973]: array([440, 440, 440])
Or transpose axes of b:
In [974]: np.dot(c, np.dot(a,b.transpose(1,0,2)))
Out[974]: array([440, 440, 440])
This transposition question would be clearer if a and c had different lengths. e.g. A (2,) and (4,) with a (2,4,3) or (4,2,3).
In
tmp = np.dot(a.T, b) # now has shape (1, 4, 3)
you have a (1,4a) dotted with (4,4a,3). The result is (1,4,3). I added the a to identify when axes were combined.
To apply the (4,1) c, we have to do the same transpose:
In [977]: np.dot(c[:,None].T, np.dot(a[:,None].T, b))
Out[977]: array([[[360, 360, 360]]])
In [978]: _.shape
Out[978]: (1, 1, 3)
np.dot(c[None,:], np.dot(a[None,:], b)) would do the same without the transposes.
I was hoping numpy would automagically distribute over the last axis. That is, that the dot product would run over the two first axes, if that makes sense.
Given the dot rule that I cited at the start this does not make sense. But if we transpose b so the (3) axis is first, it can 'carry that along', using the last and 2nd to the last.
In [986]: b.transpose(2,0,1).shape
Out[986]: (3, 4, 4)
In [987]: np.dot(a, b.transpose(2,0,1)).shape
Out[987]: (3, 4)
In [988]: np.dot(np.dot(a, b.transpose(2,0,1)),c)
Out[988]: array([440, 440, 440])
(4a).(3, 4a, 4c) -> (3, 4c)
(3, 4c). (4c) -> 3
Not automagical but does the job:
np.einsum('i,ijk,j->k',a,b,c)
# array([440, 440, 440])
This computes d of shape (3,) such that d_k = sum_{ij} a_i b_{ijk} c_j.
You are multiplying (1,4,3) matrix by (4,1) matrix so it is impossible because you have 3 pages of (1,4) matrices in b. If you want to do multiplication of each page of matrix b by c just multiply each page separately.
a = np.array([0, 1, 2, 3])
b = np.array([[[1, 1, 1], [1, 1, 1], [1, 1, 1], [1, 1, 1]],
[[2, 2, 2], [2, 2, 2], [2, 2, 2], [2, 2, 2]],
[[3, 3, 3], [3, 3, 3], [3, 3, 3], [3, 3, 3]],
[[4, 4, 4], [4, 4, 4], [4, 4, 4], [4, 4, 4]]])
c = np.array([4, 5, 6, 7])
a = np.reshape(a, (4, 1))
c = np.reshape(c, (4, 1))
tmp = np.dot(a.T, b) # now has shape (1, 4, 3)
result = np.dot(tmp[:,:,0], c)
for i in range(1,3):
result = np.dstack((result, np.dot(tmp[:,:,i], c)))
print np.shape(result)
So you have result of size (1,1,3)