numpy matrix vector multiplication
arrays, matrix, numpy, python, vector
Solution
Simplest solution
Use `numpy.dot` or `a.dot(b)`. See the documentation here.
>>> a = np.array([[ 5, 1 ,3],
[ 1, 1 ,1],
[ 1, 2 ,1]])
>>> b = np.array([1, 2, 3])
>>> print a.dot(b)
array([16, 6, 8])
This occurs because numpy arrays are not matrices, and the standard operations `*, +, -, /` work element-wise on arrays.
Note that while you can use `numpy.matrix` (as of early 2021) where `*` will be treated like standard matrix multiplication, `numpy.matrix` is deprecated and may be removed in future releases.. See the note in its documentation (reproduced below):
It is no longer recommended to use this class, even for linear algebra. Instead use regular arrays. The class may be removed in the future.
Thanks @HopeKing.
Other Solutions
Also know there are other options:
As noted below, if using python3.5+ and numpy v1.10+, the `@` operator works as you'd expect:
>>> print(a @ b)
array([16, 6, 8])
If you want overkill, you can use `numpy.einsum`. The documentation will give you a flavor for how it works, but honestly, I didn't fully understand how to use it until reading this answer and just playing around with it on my own.
>>> np.einsum('ji,i->j', a, b)
array([16, 6, 8])
As of mid 2016 (numpy 1.10.1), you can try the experimental `numpy.matmul`, which works like `numpy.dot` with two major exceptions: no scalar multiplication but it works with stacks of matrices.
>>> np.matmul(a, b)
array([16, 6, 8])
`numpy.inner` functions the same way as `numpy.dot` for matrix-vector multiplication but behaves differently for matrix-matrix and tensor multiplication (see Wikipedia regarding the differences between the inner product and dot product in general or see this SO answer regarding numpy's implementations).
>>> np.inner(a, b)
array([16, 6, 8])
# Beware using for matrix-matrix multiplication though!
>>> b = a.T
>>> np.dot(a, b)
array([[35, 9, 10],
[ 9, 3, 4],
[10, 4, 6]])
>>> np.inner(a, b)
array([[29, 12, 19],
[ 7, 4, 5],
[ 8, 5, 6]])
If you have multiple 2D arrays to `dot` together, you may consider the `np.linalg.multi_dot` function, which simplifies the syntax of many nested `np.dot`s. Note that this only works with 2D arrays (i.e. not for matrix-vector multiplication).
>>> np.dot(np.dot(a, a.T), a).dot(a.T)
array([[1406, 382, 446],
[ 382, 106, 126],
[ 446, 126, 152]])
>>> np.linalg.multi_dot((a, a.T, a, a.T))
array([[1406, 382, 446],
[ 382, 106, 126],
[ 446, 126, 152]])
Rarer options for edge cases
If you have tensors (arrays of dimension greater than or equal to one), you can use `numpy.tensordot` with the optional argument `axes=1`:
>>> np.tensordot(a, b, axes=1)
array([16, 6, 8])
Don't use `numpy.vdot` if you have a matrix of complex numbers, as the matrix will be flattened to a 1D array, then it will try to find the complex conjugate dot product between your flattened matrix and vector (which will fail due to a size mismatch `n*m` vs `n`).
Problem
When I multiply two `numpy` arrays of sizes (n x n)*(n x 1), I get a matrix of size (n x n). Following normal matrix multiplication rules, an (n x 1) vector is expected, but I simply cannot find any information about how this is done in Python's Numpy module. The thing is that I don't want to implement it manually to preserve the speed of the program. Example code is shown below: ``` a = np.array([[5, 1, 3], [1, 1, 1], [1, 2, 1]]) b = np.array([1, 2, 3]) print a*b >> [[5 2 9] [1 2 3] [1 4 3]] ``` What I want is: ``` print a*b >> [16 6 8] ```