# Efficient element-wise multiplication of a matrix and a vector in TensorFlow

## Question:

What would be the most efficient way to multiply (element-wise) a 2D tensor (matrix):

```
x11 x12 .. x1N
...
xM1 xM2 .. xMN
```

by a vertical vector:

```
w1
...
wN
```

to obtain a new matrix:

```
x11*w1 x12*w2 ... x1N*wN
...
xM1*w1 xM2*w2 ... xMN*wN
```

To give some context, we have `M`

data samples in a batch that can be processed in parallel, and each `N`

-element sample must be multiplied by weights `w`

stored in a variable to eventually pick the largest `Xij*wj`

for each row `i`

.

## Answers:

The simplest code to do this relies on the broadcasting behavior of `tf.multiply()`

^{*}, which is based on numpy’s broadcasting behavior:

```
x = tf.constant(5.0, shape=[5, 6])
w = tf.constant([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])
xw = tf.multiply(x, w)
max_in_rows = tf.reduce_max(xw, 1)
sess = tf.Session()
print sess.run(xw)
# ==> [[0.0, 5.0, 10.0, 15.0, 20.0, 25.0],
# [0.0, 5.0, 10.0, 15.0, 20.0, 25.0],
# [0.0, 5.0, 10.0, 15.0, 20.0, 25.0],
# [0.0, 5.0, 10.0, 15.0, 20.0, 25.0],
# [0.0, 5.0, 10.0, 15.0, 20.0, 25.0]]
print sess.run(max_in_rows)
# ==> [25.0, 25.0, 25.0, 25.0, 25.0]
```

^{*} In older versions of TensorFlow, `tf.multiply()`

was called `tf.mul()`

. You can also use the `*`

operator (i.e. `xw = x * w`

) to perform the same operation.