Exercises on matrix operations in TensorFlow 1.4

11/12/2019 admin TENSORFLOW 0

EN111220192126

Exercises on matrix operations in TensorFlow 1.4

Practice makes perfect

In [1]:
import pandas as pd
import tensorflow as tf
import matplotlib.pyplot as plt



















Exercise 1. Please define a tensor: constant = vector [1, 2, 3] in format int16


image.png
















$ begin{bmatrix}

1 \

2 \

3

end{bmatrix}$












In [2]:








vector1 = tf.constant ([1,3,5], tf.int16)
print(vector1)





















Tensor("Const:0", shape=(3,), dtype=int16)





















Exercise 2. Please define a tensor: constant = matrix [1, 2, 3, 4] in format int16


image2.png
















$begin{bmatrix}

1 & 2 \

3 & 4

end{bmatrix}$












In [3]:








matrix1 = tf.constant ([[1, 2],[3, 4]], tf.int16)
print (matrix1)





















Tensor("Const_1:0", shape=(2, 2), dtype=int16)





















Exercise 3. Please define a tensor: constant = matrix [1, 2, 3, 4, 5, 6] in format int16


image3.png
















$begin{bmatrix}

1 & 2 \

3 & 4 \

5 & 6

end{bmatrix}$












In [4]:








matrix2 = tf.constant ([[[1, 2],  [3, 4], [5, 6]]], tf.int16)
print (matrix2)





















Tensor("Const_2:0", shape=(1, 3, 2), dtype=int16)

















In [5]:








matrix2.shape

















Out[5]:




TensorShape([Dimension(1), Dimension(3), Dimension(2)])




















Exercise 4. Create a tensor in the form of a vector of a specific shape 5, filled with zeros


image4.png
















$begin{bmatrix}

0 \

0 \

0 \

0 \

0

end{bmatrix}$












In [6]:








kot = tf.zeros(5)
print(kot)
kot.shape





















Tensor("zeros:0", shape=(5,), dtype=float32)









Out[6]:




TensorShape([Dimension(5)])




















Exercise 5. Create a tensor in the form of a matrix with a specific 4×4 shape, filled with only ones


image5.png
















$begin{bmatrix}

1 & 1 & 1 & 1\

1 & 1 & 1 & 1\

1 & 1 & 1 & 1\

1 & 1 & 1 & 1

end{bmatrix}$












In [7]:








fok = tf.ones ([4, 4])
print(fok)
fok.shape





















Tensor("ones:0", shape=(4, 4), dtype=float32)









Out[7]:




TensorShape([Dimension(4), Dimension(4)])




















Exercise 6. Matrix adding


image6.png
















$ begin{eqnarray}

nonumber

begin{bmatrix}

2 & 5\

4 & 5\

end{bmatrix}

&=&

begin{bmatrix}

1 & 3\

2 & 4\

end{bmatrix}+

begin{bmatrix}

1 & 2\

2 & 1\

end{bmatrix}

end{eqnarray} $
















To add two matrices, their dimensions must be equal. That is, the number of rows and the number of columns of the first and second matrices must be equal.












In [8]:








matrix3 = tf.constant ([[[1, 3], [2, 4]]], tf.int16)
matrix4 = tf.constant ([[[1, 2], [2, 1]]], tf.int16)

















In [9]:








PZU = tf.add(matrix3, matrix4)

















In [10]:








sess = tf.Session()
print(sess.run(PZU))





















[[[2 5]
  [4 5]]]





















Exercise 7. Matrix subtraction


image7.png
















$ begin{eqnarray}


nonumber

begin{bmatrix}

0 & 1\

0 & 3\

end{bmatrix}

&=&

begin{bmatrix}

1 & 3\

2 & 4\

end{bmatrix}-

begin{bmatrix}

1 & 2\

2 & 1\

end{bmatrix}

end{eqnarray} $
















To subtract two matrices their dimensions must be equal. That is, the number of rows and the number of columns of the first and second matrices must be equal.












In [11]:








PZU = tf.subtract(matrix3, matrix4)

















In [12]:








sess = tf.Session()
print(sess.run(PZU))





















[[[0 1]
  [0 3]]]





















Exercise 8. Multiply the matrix by a number


image8.png
















$ begin{eqnarray}


nonumber

begin{bmatrix}

5 & 10 \

15 & 20 \

end{bmatrix}

&=&

begin{bmatrix}

1 & 2 \

3 & 4 \

end{bmatrix}*

end{eqnarray}$ 5












In [13]:








matrix1 = tf.constant ([[1, 2],[3, 4]], tf.int16)

















In [14]:








FOK = tf.multiply (matrix1, 5)

















In [15]:








sess = tf.Session()
print(sess.run(FOK))





















[[ 5 10]
 [15 20]]





















Exercise 9. Multiply the matrix by a number TensorFlow


image9.png
















$ begin{eqnarray}


nonumber

begin{bmatrix}

10 & 35 & 20\

25 & 10 & 5\

30 & 15 & 20\

end{bmatrix}

&=&

begin{bmatrix}

2 & 7 & 4\

5 & 2 & 1\

6 & 3 & 4\

end{bmatrix}*

end{eqnarray}$ 5












In [16]:








matrix5 = tf.constant ([[2,7,4],[5,2,1],[6,3,4]], tf.int16)

















In [17]:








ZHP = tf.multiply (matrix1, 5)

















In [18]:








sess = tf.Session()
print(sess.run(ZHP))





















[[ 5 10]
 [15 20]]





















Exercise 10. Multiply the matrix by a matrix TensorFlow


Matrix multiplication is not alternating.


image11.png
















$ begin{eqnarray}


nonumber

begin{bmatrix}

33 & 40\

86 & 66\

end{bmatrix}

&=&

begin{bmatrix}

1 & 4 & 6\

8 & 2 & 4\

end{bmatrix}*

begin{bmatrix}

9 & 6\

3 & 7\

2 & 1\

end{bmatrix}

end{eqnarray} $
















image.png












In [19]:








matrix6 = tf.constant([[1,4,6],[8,2,4]],tf.int32)
matrix7 = tf.constant([[9,6],[3,7],[2,1]],tf.int32)

KPU = tf.matmul(matrix6,matrix7)

















In [20]:








sess = tf.Session()
print(sess.run(KPU))





















[[33 40]
 [86 66]]





















Exercise 11. Multiply the matrix by a matrix TensorFlow


Matrix multiplication is not alternating.
















image.png












In [21]:








KPU = tf.matmul(matrix7,matrix6)

















In [22]:








sess = tf.Session()
print(sess.run(KPU))





















[[57 48 78]
 [59 26 46]
 [10 10 16]]





















Exercise 11. Multiplication of C⋅D square matrices
















image.png












In [23]:








matrix8 = tf.constant([[5,6,1],[8,7,9],[1,5,2]],tf.int32)
matrix9 = tf.constant([[4,6,7],[2,5,1],[0,3,9]],tf.int32)

















In [24]:








PKS = tf.matmul(matrix8,matrix9)

















In [25]:








sess = tf.Session()
print(sess.run(PKS))





















[[ 32  63  50]
 [ 46 110 144]
 [ 14  37  30]]





















Exercise 11.Transpose the matrix


image12.png
















$A=begin{bmatrix}

1 & 3 & 9 \

7 & 2 & 5 \

end{bmatrix}$


$A^T=begin{bmatrix}

1 & 7 \

3 & 2 \

9 & 5 \

end{bmatrix}$












In [26]:








x = tf.constant([[1, 3, 9], [7, 2, 5]])
GAP = tf.transpose(x)

















In [27]:








sess = tf.Session()
print(sess.run(GAP))





















[[1 7]
 [3 2]
 [9 5]]





















Exercise 12. Determinant of the matrix
















image.png
















$A = begin{bmatrix}

1 & 2 \

3 & 4

end{bmatrix}$


$|A| = (1*4)-(3*2)= -2$












In [28]:








matrix1 = tf.constant ([[1, 2],[3, 4]], tf.float32)

















In [29]:








PKO = tf.matrix_determinant(matrix1)

















In [30]:








sess = tf.Session()
print(sess.run(PKO))





















-2.0





















Exercise 13. Diagonal matrix


Diagonal matrix – a matrix, usually square [a], whose all coefficients lying outside the main diagonal (main diagonal) are zero. In other words, it is an upper- and lower-triangular matrix at the same time.












In [31]:








PPS = tf.diag([1.2, 1.5, 1.0, 7.1, 2, 8.3])

















In [32]:








sess = tf.Session()
print(sess.run(PPS))





















[[1.2 0.  0.  0.  0.  0. ]
 [0.  1.5 0.  0.  0.  0. ]
 [0.  0.  1.  0.  0.  0. ]
 [0.  0.  0.  7.1 0.  0. ]
 [0.  0.  0.  0.  2.  0. ]
 [0.  0.  0.  0.  0.  8.3]]





















Exercise 14. Outputs random values from a truncated normal distribution


https://docs.w3cub.com/tensorflow~python/tf/truncated_normal/


The generated values follow a normal distribution with specified mean and standard deviation, except that values whose magnitude is more than 2 standard deviations from the mean are dropped and re-picked.












In [33]:








ABC = tf.truncated_normal([2, 3])

















In [34]:








sess = tf.Session()
print(sess.run(ABC))





















[[ 0.05371307  1.4564506  -1.7267214 ]
 [-1.7192566   1.5986782   0.91717476]]

















In [35]:








print(ABC.shape)





















(2, 3)





















Random values for the mean: 7 and standard deviation: 2. Generate matrix: 3 by 5, the values should be in the format: float32.












In [39]:








KSU = tf.truncated_normal([3,5],mean=7,stddev=2.0,dtype=tf.float32)
sess = tf.Session()





















Exercise 15. Creates a tensor filled with a scalar value.


This operation creates a tensor of shape dims and fills it with value.

https://docs.w3cub.com/tensorflow~python/tf/fill/












In [40]:








print(sess.run(tf.fill([4,2],4)))





















[[4 4]
 [4 4]
 [4 4]
 [4 4]]





















Macierz 4×2 wypełniona wartościami 4
















Exercise 16. Outputs random values from a uniform distribution.


The generated values follow a uniform distribution in the range [minval, maxval). The lower bound minval is included in the range, while the upper bound maxval is excluded.


https://docs.w3cub.com/tensorflow~python/tf/random_uniform/












In [41]:








GAD = tf.random_uniform([3,7], minval=4, maxval=8, dtype=tf.float32)

















In [42]:








sess = tf.Session()
print(sess.run(GAD))





















[[5.8656416 4.652042  4.3458786 5.7581544 6.0479655 6.6700726 6.035503 ]
 [5.729369  7.1762366 6.052859  6.8669724 6.278867  5.959975  7.3483486]
 [7.441143  7.3443627 6.4590683 5.6526484 5.656465  4.5448027 5.9519987]]





















Exercise 17. Transforming the matrix into a Tensorflow matrix


We have some kind of matrix and we want to include it in the tensorflow model.












In [43]:








import numpy as np
KAT = np.array([[1., 2., 3.],[-3., -7., -1.],[0., 5., -2.]])
KAT

















Out[43]:




array([[ 1.,  2.,  3.],
       [-3., -7., -1.],
       [ 0.,  5., -2.]])
















In [44]:








DOK = tf.convert_to_tensor(KAT)

















In [45]:








sess = tf.Session()
print(sess.run(DOK))





















[[ 1.  2.  3.]
 [-3. -7. -1.]
 [ 0.  5. -2.]]