What does this numpy code snippet do?

Question

float(multiply(colVec1,colVec2).T * (matrix*matrix[i,:].T)) + c 

I am new to Python and numpy and I am trying to understand what the code snippet above does.

The multiply().T part performs an element-by-element multiplication and then does a transpose, and so the result becomes a row vector.

I am trying to understand what matrix[i,:] does. Does it create a sub-matrix by picking just the i'th row vector or does it create a sub-matrix from the i'th row vector all the way to the end of the matrix?

The * performs a dot-product which is then converted to a float using float().

Answer 1

Yes, matrix[i, :] will give you the i:th row of matrix since the : means "pick all in this dimension".

And no, A * B is not the dot product between A and B, it is the element-wise product of A and B. To get the dot product you would use any of

A.dot(B)
np.dot(A, B)
A @ B           # Python 3.5+ only

The above is true as long as you use the np.ndarray class, which you did if you created your matrices/arrays using np.array, np.eye, np.zeros, etc. There is also a np.matrix class where the multiplication operator * is actually the dot product, but it is strongly adviced to never use it since it tends to create confusion when mixed with the normal array type.

So what is going on in the expression?

Lets's break it down to parts.

multiply(colVec1,colVec2).T will create the transpose of the element-wise product of colVec1 and colVec2.

matrix*matrix[i,:].T is the element-wise product between matrix and the transpose of the i:th row of matrix. Due to numpys broadcasting rules this is actually the same as multiplying (elementwise) each row of matrix with its i:th row.

What we can see now is that both these expressions will create a matrix/array and not a scalar. Therefore the call to float() will fail, as it expects a 1-element array or scalar.

My verdict is that someone has either been using the np.matrix class, or has interpreted the use of * wrong.