SciTech-BigDataAIML-Tensorflow-Introduction to Tensors

https://tensorflow.google.cn/guide/tensor

Introduction to Tensors

• Tensors are multi-dimensional arrays with a uniform type(called a dtype). tf.dtypes included all supported dtypes.
  If you're familiar with NumPy, tensors are (kind of) like np.arrays.
• All tensors are immutable and only create a new one, just like Python numbers and strings: you can never update the contents of a tensor.

About shapes
Tensors have shapes. Some vocabulary:

• Shape: The length (number of elements) of each of the axes of a tensor.
• Rank: Number of tensor axes:
  • A scalar has rank 0,
  • a vector has rank 1,
  • a matrix is rank 2.
• Axis or Dimension: A particular dimension of a tensor.
• Size: The total number of items in the tensor, the product of the shape vector's elements.
• The base tf.Tensor class requires tensors to be "rectangular" --- that is, along each axis, every element is the same size.
  However, there are specialized types of tensors that can handle different shapes:
  • Ragged tensors (see RaggedTensor below)
  • Sparse tensors (see SparseTensor below)
    You can do math on tensors, including addition, element-wise multiplication, and matrix multiplication.

Note: Although you may see reference to a "tensor of two dimensions", a rank-2 tensor does not usually describe a 2D space.
Tensors and tf.TensorShape objects have convenient properties for accessing these:

a = tf.constant([ [1, 2], [3, 4] ])
b = tf.constant([ [1, 1], [1, 1] ]) # Could have also said `tf.ones([2,2], dtype=tf.int32)`

print(tf.add(a, b), "\n") # print(a + b, "\n") # element-wise addition
print(tf.multiply(a, b), "\n") # print(a * b, "\n") # element-wise multiplication
print(tf.matmul(a, b), "\n") # print(a @ b, "\n") # matrix multiplication