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144 lines
3.4 KiB
Python
144 lines
3.4 KiB
Python
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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_Ch11_02.py
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import numpy as np
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import seaborn as sns
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from matplotlib import pyplot as plt
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# generate original data matrix, X
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np.random.default_rng()
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X = np.random.randn(9, 5)
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#%% QR decomposition， complete version
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Q_complete, R_complete = np.linalg.qr(X, mode = 'complete')
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fig, axs = plt.subplots(1, 5, figsize=(12, 3))
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plt.sca(axs[0])
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ax = sns.heatmap(X,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('X')
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plt.sca(axs[1])
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plt.title('=')
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plt.axis('off')
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plt.sca(axs[2])
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ax = sns.heatmap(Q_complete,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Qc')
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plt.sca(axs[3])
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plt.title('@')
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plt.axis('off')
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plt.sca(axs[4])
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ax = sns.heatmap(R_complete,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Rc')
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# properties of Q (reduced)
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fig, axs = plt.subplots(1, 5, figsize=(12, 3))
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plt.sca(axs[0])
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ax = sns.heatmap(Q_complete.T@Q_complete,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Qc.T@Qc')
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plt.sca(axs[1])
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plt.title('=')
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plt.axis('off')
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plt.sca(axs[2])
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ax = sns.heatmap(Q_complete.T,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Qc.T')
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plt.sca(axs[3])
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plt.title('@')
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plt.axis('off')
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plt.sca(axs[4])
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ax = sns.heatmap(Q_complete,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Qc')
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#%% QR decomposition， reduced version
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Q, R = np.linalg.qr(X)
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# default: reduced
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fig, axs = plt.subplots(1, 5, figsize=(12, 3))
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plt.sca(axs[0])
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ax = sns.heatmap(X,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('X')
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plt.sca(axs[1])
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plt.title('=')
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plt.axis('off')
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plt.sca(axs[2])
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ax = sns.heatmap(Q,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Q')
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plt.sca(axs[3])
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plt.title('@')
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plt.axis('off')
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plt.sca(axs[4])
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ax = sns.heatmap(R,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('R')
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# properties of Q (reduced)
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fig, axs = plt.subplots(1, 5, figsize=(12, 3))
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plt.sca(axs[0])
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ax = sns.heatmap(Q.T@Q,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Q.T@Q')
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plt.sca(axs[1])
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plt.title('=')
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plt.axis('off')
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plt.sca(axs[2])
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ax = sns.heatmap(Q.T,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Q.T')
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plt.sca(axs[3])
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plt.title('@')
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plt.axis('off')
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plt.sca(axs[4])
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ax = sns.heatmap(Q,cmap='RdBu_r',vmax = 2.5,vmin = -2.5,
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cbar_kws={"orientation": "horizontal"})
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ax.set_aspect("equal")
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plt.title('Q')
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