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Delete Book4_Ch04_Python_Codes directory
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Iris Series: Visualize Math -- From Arithmetic Basics to Machine Learning
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_01.py
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import numpy as np
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# 2d matrix
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A_matrix = np.matrix([[2,4],
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[6,8]])
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print(A_matrix.shape)
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print(type(A_matrix))
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# 1d array
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A_1d = np.array([2,4])
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print(A_1d.shape)
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print(type(A_1d))
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# 2d array
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A_2d = np.array([[2,4],
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[6,8]])
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print(A_2d.shape)
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print(type(A_2d))
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# 3d array
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A1 = [[2,4],
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[6,8]]
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A2 = [[1,3],
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[5,7]]
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A3 = [[1,0],
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[0,1]]
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A_3d = np.array([A1,A2,A3])
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print(A_3d.shape)
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print(type(A_3d))
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@@ -1,21 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_02.py
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import numpy as np
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A = np.matrix([[1,2,3],
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[4,5,6],
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[7,8,9]])
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# extract diagonal elements
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a = np.diag(A)
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# construct a diagonal matrix
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A_diag = np.diag(a)
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@@ -1,24 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_03.py
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import numpy as np
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# define matrix
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A = np.matrix([[1, 2], [3, 4]])
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B = np.matrix([[2, 6], [4, 8]])
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# matrix addition
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A_plus_B = np.add(A,B)
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A_plus_B_2 = A + B
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# matrix subtraction
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A_minus_B = np.subtract(A,B)
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A_minus_B_2 = A - B
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@@ -1,19 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_04.py
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import numpy as np
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k = 2
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X = [[1,2],
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[3,4]]
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# scalar multiplication
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k_times_X = np.dot(k,X)
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k_times_X_2 = k*np.matrix(X)
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@@ -1,41 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_05.py
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import numpy as np
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# define matrix
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A = np.matrix([[1, 2],
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[3, 4],
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[5, 6]])
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# scaler
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k = 2;
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# column vector c
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c = np.array([[3],
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[2],
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[1]])
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# row vector r
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r = np.array([[2,1]])
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# broadcasting principles
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# matrix A plus scalar k
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A_plus_k = A + k
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# matrix A plus column vector c
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A_plus_a = A + c
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# matrix A plus row vector r
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A_plus_r = A + r
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# column vector c plus row vector r
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c_plus_r = c + r
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@@ -1,21 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_06.py
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import numpy as np
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A = np.array([[1, 2],
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[3, 4]])
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B = np.array([[2, 4],
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[1, 3]])
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# matrix multiplication
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A_times_B = np.matmul(A, B)
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A_times_B_2 = A@B
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@@ -1,32 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_07.py
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import numpy as np
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A = np.array([[1, 2]])
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B = np.array([[5, 6],
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[8, 9]])
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print(A*B)
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A = np.array([[1, 2]])
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B = np.matrix([[5, 6],
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[8, 9]])
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print(A*B)
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A = np.matrix([[1, 2]])
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B = np.matrix([[5, 6],
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[8, 9]])
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print(A*B)
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@@ -1,20 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_08.py
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from numpy.linalg import matrix_power as pw
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A = np.array([[1., 2.],
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[3., 4.]])
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# matrix inverse
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A_3 = pw(A,3)
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A_3_v3 = A@A@A
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# piecewise power
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A_3_piecewise = A**3
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_09.py
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import numpy as np
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A = np.matrix([[1,3],
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[2,4]])
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print(A**2)
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B = np.array([[1,3],
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[2,4]])
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print(B**2)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_10.py
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import numpy as np
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A = np.array([[1, 2],
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[3, 4],
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[5, 6]])
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# matrix transpose
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A_T = A.transpose()
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A_T_2 = A.T
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_11.py
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from numpy.linalg import inv
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A = np.array([[1., 2.],
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[3., 4.]])
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# matrix inverse
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A_inverse = inv(A)
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A_times_A_inv = A@A_inverse
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_12.py
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import numpy as np
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A = np.matrix([[1, 2],
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[3, 4]])
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print(A.I)
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B = np.array([[1, 2],
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[3, 4]])
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print(B.I)
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_13.py
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import numpy as np
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A = np.array([[1, -1, 0],
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[3, 2, 4],
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[-2, 0, 3]])
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# calculate trace of A
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tr_A = np.trace(A)
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@@ -1,21 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_14.py
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import numpy as np
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A = np.array([[1,2],
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[3,4]])
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B = np.array([[5,6],
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[7,8]])
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# Hadamard product
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A_times_B_piecewise = np.multiply(A,B)
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A_times_B_piecewise_V2 = A*B
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@@ -1,16 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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# Bk4_Ch4_15.py
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import numpy as np
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A = np.array([[4, 2],
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[1, 3]])
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# calculate determinant of A
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det_A = np.linalg.det(A)
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@@ -1,129 +0,0 @@
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###############
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# Authored by Weisheng Jiang
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# Book 4 | From Basic Arithmetic to Machine Learning
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# Published and copyrighted by Tsinghua University Press
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# Beijing, China, 2022
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###############
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import plotly.graph_objects as go
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import numpy as np
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from plotly.subplots import make_subplots
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import streamlit as st
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def bmatrix(a):
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"""Returns a LaTeX bmatrix
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:a: numpy array
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:returns: LaTeX bmatrix as a string
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"""
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if len(a.shape) > 2:
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raise ValueError('bmatrix can at most display two dimensions')
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lines = str(a).replace('[', '').replace(']', '').splitlines()
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rv = [r'\begin{bmatrix}']
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rv += [' ' + ' & '.join(l.split()) + r'\\' for l in lines]
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rv += [r'\end{bmatrix}']
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return '\n'.join(rv)
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n = m = 20
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fig = make_subplots(rows=1, cols=2, horizontal_spacing=0.035)
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xv = []
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yv = []
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for k in range(-n, n+1):
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xv.extend([k, k, np.nan])
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yv.extend([-m, m, np.nan])
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lw= 1 #line_width
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fig.add_trace(go.Scatter(x=xv, y=yv, mode="lines", line_width=lw,
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line_color = 'red'), 1, 1)
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#set up the lists of horizontal line x and y-end coordinates
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xh=[]
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yh=[]
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for k in range(-m, m+1):
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xh.extend([-m, m, np.nan])
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yh.extend([k, k, np.nan])
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fig.add_trace(go.Scatter(x=xh, y=yh, mode="lines", line_width=lw,
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line_color = 'blue'), 1, 1)
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with st.sidebar:
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st.latex(r'''
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A = \begin{bmatrix}
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a & b\\
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c & d
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\end{bmatrix}''')
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a = st.slider('a',-2.0, 2.0, step = 0.1, value = 1.0)
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b = st.slider('b',-2.0, 2.0, step = 0.1, value = 0.0)
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c = st.slider('c',-2.0, 2.0, step = 0.1, value = 0.0)
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d = st.slider('c',-2.0, 2.0, step = 0.1, value = 1.0)
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theta = np.pi/6
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A = np.array([[a, b],
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[c, d]], dtype=float)
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#get only the coordinates from -3 to 3
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# X = np.array(xv[6:-6])
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# Y = np.array(yv[6:-6])
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X = np.array(xv)
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Y = np.array(yv)
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# transform by T the vector of coordinates [x, y]^T where the vector runs over the columns of np.stack((X, Y))
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Txvyv = A@np.stack((X, Y)) #transform by T the vertical lines
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# X = np.array(xh[6:-6])
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# Y = np.array(yh[6:-6])
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X = np.array(xh)
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Y = np.array(yh)
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Txhyh = A@np.stack((X, Y))# #transform by T the horizontal lines
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st.latex(r'A = ' + bmatrix(A))
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a1 = A[:,0].reshape((-1, 1))
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a2 = A[:,1].reshape((-1, 1))
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st.latex(r'''
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a_1 = Ae_1 = ''' + bmatrix(A) +
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'e_1 = ' + bmatrix(a1)
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)
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st.latex(r'''
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a_2 = Ae_2 = ''' + bmatrix(A) +
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'e_2 = ' + bmatrix(a2)
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)
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st.latex(r'\begin{vmatrix} A \end{vmatrix} = ' + str(np.linalg.det(A)))
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square_x = np.array([0, 1, 1, 0])
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square_y = np.array([0, 0, 1, 1])
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square_array = np.stack((square_x, square_y))
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fig.add_trace(go.Scatter(x=square_x, y=square_y,
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fill="toself", line_color='orange'), 1, 1)
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A_times_square_array = A@square_array
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fig.add_trace(go.Scatter(x=A_times_square_array[0,:],
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y=A_times_square_array[1,:],
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fill="toself", line_color='orange'), 1, 2)
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fig.add_trace(go.Scatter(x=Txvyv[0], y=Txvyv[1],
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mode="lines", line_width=lw,
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line_color = 'red'), 1, 2)
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fig.add_trace(go.Scatter(x=Txhyh[0], y=Txhyh[1],
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mode="lines", line_width=lw,
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line_color = 'blue'), 1, 2)
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fig.update_xaxes(range=[-4, 4])
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fig.update_yaxes(range=[-4, 4])
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fig.update_layout(width=800, height=500, showlegend=False, template="none",
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plot_bgcolor="white", yaxis2_showgrid=False, xaxis2_showgrid=False)
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st.plotly_chart(fig)
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