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在实际项目中，需要存储大于等于三维的矩阵，而平常中我们使用Eigen::MatrixXd二维数据，这里我们使用Eigen::Tensor来定义
1.Using the Tensor module
#include <unsupported/Eigen/CXX11/Tensor>
2.定义矩阵
2.一般矩阵
官方文档
// 定义一个2x3x4大小的矩阵Eigen::Tensor<float, 3> a(2, 3, 4);// 初始化为0a.setZero();// 访问元素a(0, 1, 0) = 12.0f;for (int i = 0; i < 2; i++) {for (int j = 0; j < 3; j++) {for (int k = 0; k < 4; k++) {std::cout << a(i, j, k) << " ";}std::cout << std::endl;}std::cout << std::endl << std::endl;}// 输出维度std::cout<<a.dimension(0)<<" "<<a.dimension(1)<<" "<<a.dimension(2)<<std::endl;
上面输出结果
0 0 0 0
12 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 02 3 4
2.固定大小矩阵TensorFixedSize
参考官方解释
The fixed sized equivalent of Eigen::Tensor<float, 3> t(3, 5, 7); is Eigen::TensorFixedSize<float, Size<3,5,7>> t;
这里我们定义
// 固定 大小的Size 2x3x4Eigen::TensorFixedSize<float, Eigen::Sizes<2, 3, 4>> b;// 每个元素都设置固定值b.setConstant(3.f);for (int i = 0; i < 2; i++) {for (int j = 0; j < 3; j++) {for (int k = 0; k < 4; k++) {std::cout << b(i, j, k) << " ";}std::cout << std::endl;}std::cout << std::endl << std::endl;}
结果如下
3 3 3 3
3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3
3 3 3 3
3.常用函数API
参考从零开始编写深度学习库（四）Eigen::Tensor学习使用及代码重构
1.维度
Eigen::Tensor<float, 2> a(3, 4);std::cout << "Dims " << a.NumDimensions;//=> Dims 2
Eigen::Tensor<float, 2> a(3, 4);int dim1 = a.dimension(1);std::cout << "Dim 1: " << dim1;//=> Dim 1: 4
2.形状
Eigen::Tensor<float, 2> a(3, 4);const Eigen::Tensor<float, 2>::Dimensions& d = a.dimensions();std::cout << "Dim size: " << d.size << ", dim 0: " << d[0]<< ", dim 1: " << d[1];//=> Dim size: 2, dim 0: 3, dim 1: 4
3.矩阵元素个数
Eigen::Tensor<float, 2> a(3, 4);std::cout << "Size: " << a.size();//=> Size: 12
4.初始化
/// 1.// setConstant(const Scalar& val)，用于把一个矩阵的所有元素设置成一个指定的常数。Eigen::Tensor<string, 2> a(2, 3);a.setConstant("yolo");std::cout << "String tensor: " << endl << a << endl << endl;//=>// String tensor:// yolo yolo yolo// yolo yolo yolo/// 2.// setZero() 全部置零a.setZero();/// 3.// setRandom() 随机初始化a.setRandom();std::cout << "Random: " << endl << a << endl << endl;//=>//Random:// 0.680375 0.59688 -0.329554 0.10794// -0.211234 0.823295 0.536459 -0.0452059// 0.566198 -0.604897 -0.444451 0.257742/// 4.// setValues({..initializer_list}) 从列表、数据初始化Eigen::Tensor<float, 2> a(2, 3);a.setValues({{0.0f, 1.0f, 2.0f}, {3.0f, 4.0f, 5.0f}});std::cout << "a" << endl << a << endl << endl;//=>// a// 0 1 2// 3 4 5//如果给定的数组数据，少于矩阵元素的个数，那么后面不足的元素其值不变：Eigen::Tensor<int, 2> a(2, 3);a.setConstant(1000);a.setValues({{10, 20, 30}});std::cout << "a" << endl << a << endl << endl;//=>// a// 10 20 30// 1000 1000 1000
4.运算
参考Eigen Tensor详解【二】
4.1 一元运算
<Operation> operator-() 求相反数
<Operation> sqrt() 平方根
<Operation> rsqrt() 逆平方根
<Operation> square() 平方
<Operation> inverse()求逆
<Operation> exp()指数
<Operation> log() log运算
<Operation> abs() 绝对值
<Operation> pow(Scalar exponent)
<Operation> operator * (Scalar scale) 乘以某个值
void testUnary()
{Eigen::Tensor<int, 2> a(2, 3);a.setValues({ {0, 1, 8}, {27, 64, 125} });Eigen::Tensor<double, 2> b = a.cast<double>().pow(1.0 / 3.0);Eigen::Tensor<double, 2> sqrt = a.cast<double>().sqrt();Eigen::Tensor<double, 2> rsqrt = a.cast<double>().rsqrt();Eigen::Tensor<double, 2> square = a.cast<double>().square();Eigen::Tensor<double, 2> inverse = a.cast<double>().inverse();Eigen::Tensor<double, 2> exp = a.cast<double>().exp();Eigen::Tensor<double, 2> log = a.cast<double>().log();Eigen::Tensor<double, 2> abs = a.cast<double>().abs();Eigen::Tensor<int, 2> multiply = a * 2;std::cout << "a" << std::endl << a << std::endl <<std:: endl;
}
4.2 二元运算
<Operation> operator+(const OtherDerived& other)
<Operation> operator-(const OtherDerived& other)
<Operation> operator*(const OtherDerived& other)
<Operation> operator/(const OtherDerived& other)
<Operation> cwiseMax(const OtherDerived& other) //返回与原tensor同类型，同尺寸的tensor,且以两个原tensor的最大值填充
<Operation> cwiseMin(const OtherDerived& other)
//返回与原tensor同类型，同尺寸的tensor,且以两个原tensor的最小值填充
operator&&(const OtherDerived& other)
operator||(const OtherDerived& other)
operator<(const OtherDerived& other)
operator<=(const OtherDerived& other)
operator>(const OtherDerived& other)
operator>=(const OtherDerived& other)
operator==(const OtherDerived& other)
operator!=(const OtherDerived& other)
void testBinary()
{Eigen::Tensor<int, 2> a(2, 3);a.setValues({ {0, 1, 8}, {27, 64, 125} });Eigen::Tensor<int, 2> b = a * 3;std::cout << "a" << std::endl << a << std::endl << std::endl;std::cout << "b" << std::endl << b << std::endl << std::endl;std::cout << "a+b" << std::endl << a + b << std::endl << std::endl;std::cout << "a-b" << std::endl << a - b << std::endl << std::endl;std::cout << "a*b" << std::endl << a * b << std::endl << std::endl;std::cout << "a.cwiseMax(b)" << std::endl <<a.cwiseMax(b) << std::endl << std::endl;std::cout << "b.cwiseMax(a)" << std::endl << b.cwiseMax(a) << std::endl << std::endl;std::cout << "a.cwiseMin(b)" << std::endl << a.cwiseMin(b) << std::endl << std::endl;std::cout << "b.cwiseMin(a)" << std::endl << b.cwiseMin(a) << std::endl << std::endl;
}
4.3 三元运算和降维运算
看参考链接Eigen Tensor详解【二】
4.其他方式
参考Eigen构造使用三维矩阵
如果定义多维数据也可以使用Matrix模板来自定义，
Matrix<typename Scalar, int RowsAtCompileTime, int ColsAtCompileTime>
Eigen::Matrix<Eigen::MatrixXd,1,1> a;
Eigen::Matrix<Eigen::Matrix<double,1,5>,1,1> a;Eigen::Matrix<Eigen::MatrixXd, 1, 1> a;//声明a，一个1*1矩阵
Eigen::MatrixXd b; //声明b
b.setZero(1, 5); //对b初始化
b << 1, 2, 3, 4, 5;//对b赋值
a(0, 0) = b;//对a（0，0）赋值
std::cout << "a(0,0): " << a(0, 0) << std::endl;//输出a（0，0）
std::cout << "b: " << b << std::endl;//输出b
int row = a(0, 0).rows();//row为a(0,0)处矩阵的行维数
int col = a(0, 0).cols();//col为a(0,0)处矩阵的列维数
std::cout << "row: " << row << " col: " << col << std::endl;//输出row和col值
参考
https://blog.csdn.net/hjimce/article/details/71710893
https://blog.csdn.net/fengshengwei3/article/details/103591178
http://eigen.tuxfamily.org/index.php?title=Tensor_support#Using_the_Tensor_module
https://eigen.tuxfamily.org/dox/unsupported/classEigen_1_1TensorFixedSize.html
https://zhuanlan.zhihu.com/p/148019818
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