网站的建设运营收费是哪些,智能建站,网络营销的五个特点,wordpress 输出标签文章目录 一、代码仓库二、旋转矩阵的推导及图形学中的矩阵变换2.1 让横坐标扩大a倍#xff0c;纵坐标扩大b倍2.2 关于x轴翻转2.3 关于y轴翻转2.4 关于原点翻转#xff08;x轴#xff0c;y轴均翻转#xff09;2.5 沿x方向错切2.6 沿y方向错切2.7 旋转2.8 单位矩阵2.9 矩阵的… 文章目录 一、代码仓库二、旋转矩阵的推导及图形学中的矩阵变换2.1 让横坐标扩大a倍纵坐标扩大b倍2.2 关于x轴翻转2.3 关于y轴翻转2.4 关于原点翻转x轴y轴均翻转2.5 沿x方向错切2.6 沿y方向错切2.7 旋转2.8 单位矩阵2.9 矩阵的逆 三、看待矩阵的关键视角用矩阵表示空间3.1 行视角3.2 列视角3.3 标准单位向量和列视角3.4 矩阵表示空间 四、代码matrix.pymatrix_transformationnumpy_matrix.py 一、代码仓库 https://github.com/Chufeng-Jiang/Python-Linear-Algebra-for-Beginner/tree/main 二、旋转矩阵的推导及图形学中的矩阵变换
2.1 让横坐标扩大a倍纵坐标扩大b倍 2.2 关于x轴翻转 2.3 关于y轴翻转 2.4 关于原点翻转x轴y轴均翻转 2.5 沿x方向错切 2.6 沿y方向错切 2.7 旋转
theta math.pi / 3
T Matrix([[math.cos(theta), math.sin(theta)], [-math.sin(theta), math.cos(theta)]])2.8 单位矩阵 2.9 矩阵的逆 三、看待矩阵的关键视角用矩阵表示空间
3.1 行视角 3.2 列视角 3.3 标准单位向量和列视角 3.4 矩阵表示空间 四、代码
matrix.py
from .Vector import Vectorclass Matrix:def __init__(self, list2d):self._values [row[:] for row in list2d]classmethoddef zero(cls, r, c):返回一个r行c列的零矩阵return cls([[0] * c for _ in range(r)])classmethoddef identity(cls, n):返回一个n行n列的单位矩阵m [[0]*n for _ in range(n)]for i in range(n):m[i][i] 1;return cls(m)def T(self):返回矩阵的转置矩阵return Matrix([[e for e in self.col_vector(i)]for i in range(self.col_num())])def __add__(self, another):返回两个矩阵的加法结果assert self.shape() another.shape(), \Error in adding. Shape of matrix must be same.return Matrix([[a b for a, b in zip(self.row_vector(i), another.row_vector(i))]for i in range(self.row_num())])def __sub__(self, another):返回两个矩阵的减法结果assert self.shape() another.shape(), \Error in subtracting. Shape of matrix must be same.return Matrix([[a - b for a, b in zip(self.row_vector(i), another.row_vector(i))]for i in range(self.row_num())])def dot(self, another):返回矩阵乘法的结果if isinstance(another, Vector):# 矩阵和向量的乘法assert self.col_num() len(another), \Error in Matrix-Vector Multiplication.return Vector([self.row_vector(i).dot(another) for i in range(self.row_num())])if isinstance(another, Matrix):# 矩阵和矩阵的乘法assert self.col_num() another.row_num(), \Error in Matrix-Matrix Multiplication.return Matrix([[self.row_vector(i).dot(another.col_vector(j)) for j in range(another.col_num())]for i in range(self.row_num())])def __mul__(self, k):返回矩阵的数量乘结果: self * kreturn Matrix([[e * k for e in self.row_vector(i)]for i in range(self.row_num())])def __rmul__(self, k):返回矩阵的数量乘结果: k * selfreturn self * kdef __truediv__(self, k):返回数量除法的结果矩阵self / kreturn (1 / k) * selfdef __pos__(self):返回矩阵取正的结果return 1 * selfdef __neg__(self):返回矩阵取负的结果return -1 * selfdef row_vector(self, index):返回矩阵的第index个行向量return Vector(self._values[index])def col_vector(self, index):返回矩阵的第index个列向量return Vector([row[index] for row in self._values])def __getitem__(self, pos):返回矩阵pos位置的元素r, c posreturn self._values[r][c]def size(self):返回矩阵的元素个数r, c self.shape()return r * cdef row_num(self):返回矩阵的行数return self.shape()[0]__len__ row_numdef col_num(self):返回矩阵的列数return self.shape()[1]def shape(self):返回矩阵的形状: (行数 列数)return len(self._values), len(self._values[0])def __repr__(self):return Matrix({}).format(self._values)__str__ __repr__
matrix_transformation
import matplotlib.pyplot as plt
from playLA.Matrix import Matrix
from playLA.Vector import Vector
import mathif __name__ __main__:points [[0, 0], [0, 5], [3, 5], [3, 4], [1, 4], [1, 3], [2, 3], [2, 2], [1, 2], [1, 0]]x [point[0] for point in points]y [point[1] for point in points]plt.figure(figsize(5, 5))plt.xlim(-10, 10)plt.ylim(-10, 10)plt.plot(x, y)# plt.show()P Matrix(points)# T Matrix([[2, 0], [0, 1.5]])# T Matrix([[1, 0], [0, -1]])# T Matrix([[-1, 0], [0, 1]])# T Matrix([[-1, 0], [0, -1]])# T Matrix([[1, 0.5], [0, 1]])# T Matrix([[1, 0], [0.5, 1]])theta math.pi / 3T Matrix([[math.cos(theta), math.sin(theta)], [-math.sin(theta), math.cos(theta)]])# 逆时针旋转90度# theta math.pi / -2# T Matrix([[math.cos(theta), math.sin(theta)], [-math.sin(theta), math.cos(theta)]])# 根据矩阵表示空间的法则直接写出的逆时针旋转90度的变换矩阵#T Matrix([[0, -1], [1, 0]])P2 T.dot(P.T())plt.plot([P2.col_vector(i)[0] for i in range(P2.col_num())],[P2.col_vector(i)[1] for i in range(P2.col_num())])plt.show()numpy_matrix.py
import numpy as npif __name__ __main__:# 矩阵的创建A np.array([[1, 2], [3, 4]])print(A)# 矩阵的属性print(A.shape)print(A.T)# 获取矩阵的元素print(A[1, 1])print(A[0])print(A[:, 0])print(A[1, :])# 矩阵的基本运算B np.array([[5, 6], [7, 8]])print(A B)print(A - B)print(10 * A)print(A * 10)print(A * B)print(A.dot(B))p np.array([10, 100])print(A p)print(A 1)print(A.dot(p))# 单位矩阵I np.identity(2)print(I)print(A.dot(I))print(I.dot(A))# 逆矩阵invA np.linalg.inv(A)print(invA)print(invA.dot(A))print(A.dot(invA))# C np.array([[1, 2, 3], [4, 5, 6]])# np.linalg.inv(C)
