So I have a n x d matrix and an n x 1 vector. I'm trying to write a code to subtract every row in the matrix by the vector.
I currently have a for loop that iterates through and subtracts the i-th row in the matrix by the vector. Is there a way to simply subtract an entire matrix by the vector?
Thanks!
Current code:
for i in xrange( len( X1 ) ): X[i,:] = X1[i,:] - X2 This is where X1 is the matrix's i-th row and X2 is vector. Can I make it so that I don't need a for loop?
That works in numpy but only if the trailing axes have the same dimension. Here is an example of successfully subtracting a vector from a matrix:
In [27]: print m; m.shape [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] Out[27]: (4, 3) In [28]: print v; v.shape [0 1 2] Out[28]: (3,) In [29]: m - v Out[29]: array([[0, 0, 0], [3, 3, 3], [6, 6, 6], [9, 9, 9]]) This worked because the trailing axis of both had the same dimension (3).
In your case, the leading axes had the same dimension. Here is an example, using the same v as above, of how that can be fixed:
In [35]: print m; m.shape [[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] Out[35]: (3, 4) In [36]: (m.transpose() - v).transpose() Out[36]: array([[0, 1, 2, 3], [3, 4, 5, 6], [6, 7, 8, 9]]) The rules for broadcasting axes are explained in depth here.
m-v.transpose() would not work the same in general.
m - v[:, None]In addition to @John1024 answer, "transposing" a one-dimensional vector in numpy can be done like this:
In [1]: v = np.arange(3) In [2]: v Out[2]: array([0, 1, 2]) In [3]: v = v[:, np.newaxis] In [4]: v Out[4]: array([[0], [1], [2]]) From here, subtracting v from every column of m is trivial using broadcasting:
In [5]: print(m) [[ 0 1 2 3] [ 4 5 6 7] [ 8 9 10 11]] In [6]: m - v Out[6]: array([[0, 1, 2, 3], [3, 4, 5, 6], [6, 7, 8, 9]]) 
np.newaxis is None. They refer to the same object. At that point it's what the author considers to be more legible.If you were just creating the vector that gets subtracted, you can also create it with
column_vector = np.array([0,1,2], ndmin=2).T to get a column vector, which is only possible if it has dimension 2 or more.
One dimensional numpy arrays are always rows and cannot be transposed!
Then you can just do
each_column_of_matrix_minus_vector = matrix - column_vector to subtract column_vector from every column of matrix.
