Declaring Operations

Now we must learn about the other operations we can add to a TensorFlow graph.

Getting ready

Besides the standard arithmetic operations, TensorFlow provides us with more operations that we should be aware of. We need to know how to use them before proceeding. Again, we can create a graph session by running the following code:

import tensorflow as tf
sess = tf.Session()

How to do it…

TensorFlow has the standard operations on tensors: add(), sub(), mul(), and div(). Note that all of these operations in this section will evaluate the inputs element-wise unless specified otherwise:

1. TensorFlow provides some variations of div() and relevant functions.
2. It is worth mentioning that div() returns the same type as the inputs. This means it really returns the floor of the division (akin to Python 2) if the inputs are integers. To return the Python 3 version, which casts integers into floats before dividing and always returning a float, TensorFlow provides the function truediv() function, as shown as follows:

   print(sess.run(tf.div(3,4)))
   0
   print(sess.run(tf.truediv(3,4)))
   0.75

3. If we have floats and want an integer division, we can use the function floordiv(). Note that this will still return a float, but rounded down to the nearest integer. The function is shown as follows:

   print(sess.run(tf.floordiv(3.0,4.0)))
   0.0

4. Another important function is mod(). This function returns the remainder after the division. It is shown as follows:

   print(sess.run(tf.mod(22.0, 5.0)))
   2.0-

5. The cross-product between two tensors is achieved by the cross() function. Remember that the cross-product is only defined for two three-dimensional vectors, so it only accepts two three-dimensional tensors. The function is shown as follows:

   print(sess.run(tf.cross([1., 0., 0.], [0., 1., 0.])))
   [ 0.  0.  1.0]

6. Here is a compact list of the more common math functions. All of these functions operate elementwise.

   abs()	Absolute value of one input tensor
   ceil()	Ceiling function of one input tensor
   cos()	Cosine function of one input tensor
   exp()	Base e exponential of one input tensor
   floor()	Floor function of one input tensor
   inv()	Multiplicative inverse (1/x) of one input tensor
   log()	Natural logarithm of one input tensor
   maximum()	Element-wise max of two tensors
   minimum()	Element-wise min of two tensors
   neg()	Negative of one input tensor
   pow()	The first tensor raised to the second tensor element-wise
   round()	Rounds one input tensor
   rsqrt()	One over the square root of one tensor
   sign()	Returns -1, 0, or 1, depending on the sign of the tensor
   sin()	Sine function of one input tensor
   sqrt()	Square root of one input tensor
   square()	Square of one input tensor

7. Specialty mathematical functions: There are some special math functions that get used in machine learning that are worth mentioning and TensorFlow has built in functions for them. Again, these functions operate element-wise, unless specified otherwise:

   digamma()	Psi function, the derivative of the lgamma() function
   erf()	Gaussian error function, element-wise, of one tensor
   erfc()	Complimentary error function of one tensor
   igamma()	Lower regularized incomplete gamma function
   igammac()	Upper regularized incomplete gamma function
   lbeta()	Natural logarithm of the absolute value of the beta function
   lgamma()	Natural logarithm of the absolute value of the gamma function
   squared_difference()	Computes the square of the differences between two tensors

How it works…

It is important to know what functions are available to us to add to our computational graphs. Mostly, we will be concerned with the preceding functions. We can also generate many different custom functions as compositions of the preceding functions, as follows:

# Tangent function (tan(pi/4)=1)
print(sess.run(tf.div(tf.sin(3.1416/4.), tf.cos(3.1416/4.))))
1.0

There's more…

If we wish to add other operations to our graphs that are not listed here, we must create our own from the preceding functions. Here is an example of an operation not listed previously that we can add to our graph. We choose to add a custom polynomial function, :

def custom_polynomial(value):
    return(tf.sub(3 * tf.square(value), value) + 10)
print(sess.run(custom_polynomial(11)))
362