How to multiply each column of a matrix by a vector element-wise in Theano?

Question

I have a Theano dvector with 100 elements. I also have a matrix with 5 columns and 100 rows (in other words each column contains 100 elements).

Now I need to apply an element-wise multiplication of each column by the vector. What is a correct way to do it in Theano?

Should I create a new matrix by repeating my vector 5 times and transposing it and then multiply two matrices of the same shape element-wise?

ADDED

I have learned that in numpy, to achieve the desired behavior, I just need to declare my vector as a 2D array with one column. In other words I need to replace a "row"-vector by a "column"-vectors (or I need to write the values vertically, instead of horizontally). In this case numpy will broadcast the vector (column) as desired (each column of my matrix will be multiplied by my vector element wise). However, it looks like Theano does not inherit this behavior of numpy:

X = T.dmatrix('X')

w = np.array([
    [10.0, 0.0, 0.0, 0.0, 0.0], 
    [0.0, 10.0, 0.0, 0.0, 0.0], 
    [0.0, 0.0, 10.0, 0.0, 0.0]
    ], dtype=th.config.floatX)
w = np.transpose(w)

W = th.shared(w, name='W', borrow=True)

R = W + X

f = th.function([X], R)

x = np.array([[1.0], [2.0], [3.0], [4.0], [5.0]])
print f(x)

This is the error that I get:

ValueError: Input dimension mis-match. (input[0].shape[1] = 3, input[1].shape[1] = 1)
Apply node that caused the error: Elemwise{add,no_inplace}(W, X)
Toposort index: 0
Inputs types: [TensorType(float64, matrix), TensorType(float64, matrix)]
Inputs shapes: [(5, 3), (5, 1)]
Inputs strides: [(8, 40), (8, 8)]

By the way, the code works if I define x in the following way:

x = np.array([[1.0, 1.0, 1.0], [2.0, 2.0, 2.0], [3.0, 3.0, 3.0], [4.0, 4.0, 4.0], [5.0, 5.0, 5.0]])

Answer 1

The "native" solution that I have found is to use theano.tensor.extra_ops.repeat operation. In more details, I need to use

Xr = T.extra_ops.repeat(X, 3, axis=1)

This operation will repeat the column-vector 3 times. So, as a result we will get a matrix with 3 (identical) columns and this matrix can be multiplied (or summed up) with the W matrix element wise.