Prepared by Sanasam Ranbir Singh
How to define tensors?
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Import TensorFlow module
For using tensorflow, we would need to import the tensorflow module first as follows.
import tensorflow as tf # tensorflow is imported as object tf
print("The version is " + tf.__version__) # print the version. I have used 2.xTypes of Tensors
Four Types
> 1. Constant
> 2. Variable
> 3. Placeholder
> 4. SparseTensor
In today's lesson, we will define tensor using constant tensor type. Other types of tensors, we will discuss in the subsequent lessons.
Constant Tensor
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A Constant tensor is created using tf.constant() method. As the name suggest, once created, the value of constant type tensor can not be changed.
Syntex
> tf.constant ( value, dtype=None, shape=None, name='Const')
Attributes:
> value: A constant value (or list) of output type dtype.
> dtype: The type of the elements of the resulting tensor.
> shape: Optional dimensions of resulting tensor.
> name: Optional name for the tensor.
Return
> It returns a Constant Tensor
Data Types
Define a Scalar Tensor
A scalar tensor stores a scalar value wich can be a number, a string, a boolean value.
It has no direction associated with it. That means,
- Rank (dimension) = 0
- Shape = 0
Some examples of scalar tensors are defined below.
x = tf.constant(5) # Integer value
print(x)tf.Tensor(5, shape=(), dtype=int32)
x = tf.constant(5.0)
print(x)x = tf.constant("Tensor Definition")
print(x)x = tf.constant(True)
print(x)Vector Tensor (1 Dimensional Tensor)
It has data with only one direction i.e., coordinate space. The following figure defines four data points in one direction, which can be realized by a vector of [1,3,6,8].
All the data points lies in a the same direction, it means,
- Rank (dimention)= 1
- Shape = $n$; $n$ is the number of the elements in the vector.
It defines vectors such as vector of,
> - Integers: [1, 2, 3]
> - Rank=1, Shape=3
> - Floats: [2.0, 4.0, 6.0, 8.0]
> - Rank=1, Shape=4
> - String: ["Tom", "John", "Sally"]
> - Rank=1, Shape=3
1D tensor is a vector of 0D Tensors. Few examples are defined below.
x = tf.constant([2, 4, 6]) # A Rank 1 tensor of shape 3 with integer values.
print(x)tf.Tensor([2 4 6], shape=(3,), dtype=int32)
x = tf.constant([2.0, 4.0, 6.0, 8.0]) # A Rank 1 tensor of shape 4 with real values.
print(x)tf.Tensor([2. 4. 6. 8.], shape=(4,), dtype=float32)
x = tf.constant(["Tom", "John", "Sally"]) # A Rank 1 tensor of shape 4 with string values.
print(x)tf.Tensor([b'Tom' b'John' b'Sally'], shape=(3,), dtype=string)
Matrix Tensor (2 Dimensional Tensor)
Rank = 2, shape = ($n$,$m$); $n$ and $m$ are positive natural numbers
2D tensor is a vector of 1D tensor
y = tf.constant([[1, 2, 3, 4],[5,6,7,8]])
print(y)3 Dimensional Tensor
Rank = 3, shape = ($l$,$n$,$m$); $l$, $n$ and $m$ are positive natural numbers
3D tensor is a vector of 2D tensor
y = tf.constant([[[1, 2, 3, 4],[5,6,7,8]],[[1, 2, 3, 4],[5,6,7,8]],[[1, 2, 3, 4],[5,6,7,8]]])
print(y)Generalization
We can define a tensor $x$ of dimension $k$ with the shape ($n_{k}$,$n_{k-1}$, $n_{k-2}$,$n_{k-3}$,...,$n_{1}$)
> as a vector with $n_{k}$ number of $k-1$ Dimemsional tensors of shape ($n_{k-1}$, $n_{k-2}$,$n_{k-3}$,...,$n_{1}$)
Recursively, a tensor of dimension $k-1$ shape ($n_{k-1}$, $n_{k-2}$,$n_{k-3}$,...,$n_{1}$) can be defined
> asas a vector with $n_{k-1}$ number of $k-2$ Dimemsional tensors of shape ($n_{k-2}$,$n_{k-3}$,...,$n_{1}$), and so on...
Summary
- Rank/Degree of a tensor defines the number of associated dirctions or dimenssions.
y = tf.constant([[1, 2, 3, 4],[5,6,7,8]])
tf.rank(y)- Shape of a tensor defines the number of element in each of the dirctions or dimenssions.
y = tf.constant([[1, 2, 3, 4],[5,6,7,8]])
tf.shape(y)- The value of a tensor can be printed as
y = tf.constant([[1, 2, 3, 4],[5,6,7,8]])
tf.print(y)