C++矩阵计算库Eigen3之：矩阵的基本操作和运算

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我写了一个示例程序来展示Eigen3的一些接口使用，一些来自官网示例，后续我还会写这种程序展示更复杂的矩阵运算功能。你必须在使用时，注释掉其他主函数，使用编译链接语句、运行 :

root@master:# g++ mat.cpp -o mat -I/download/eigenroot@master:# ./matm =94.0188  89.844 43.522349.4383 101.165  86.82388.3099 29.7551 37.7775v =123m * v =404.274512.237261.153   0.10794   0.257742  0.0268018-0.0452059  -0.270431   0.904459

下面是这个程序：

#include <iostream>#include <Eigen/Dense>//g++ mat.cpp -o mat -I/download/eigenusing namespace Eigen;using namespace std;//矩阵的按元素赋值int main(){  //------------------------  MatrixXd m(2,2);  m(0,0) = 3;  m(1,0) = 2.5;  m(0,1) = -1;  m(1,1) = m(1,0) + m(0,1);  cout << "Here is the matrix m:\n" << m << endl;  VectorXd v(2);  v(0) = 4;  v(1) = v(0) - 1;  cout << "Here is the vector v:\n" << v << endl;  //------------------------  Matrix3f m;  m << 1, 2, 3,     4, 5, 6,     7, 8, 9;  cout << m << endl;}//矩阵的加减运算int main(){  Matrix2d a;  a << 1, 2,       3, 4;  MatrixXd b(2,2);  b << 2, 3,       1, 4;  std::cout << "a + b =\n" << a + b << std::endl;  std::cout << "a - b =\n" << a - b << std::endl;  std::cout << "Doing a += b;" << std::endl;  a += b;  std::cout << "Now a =\n" << a << std::endl;  Vector3d v(1,2,3);  Vector3d w(1,0,0);  std::cout << "-v + w - v =\n" << -v + w - v << std::endl;}//矩阵与实数相乘int main(){  Matrix2d a;  a << 1, 2,       3, 4;  Vector3d v(1,2,3);  std::cout << "a * 2.5 =\n" << a * 2.5 << std::endl;  std::cout << "0.1 * v =\n" << 0.1 * v << std::endl;  std::cout << "Doing v *= 2;" << std::endl;  v *= 2;  std::cout << "Now v =\n" << v << std::endl;}//转置int main(){  Matrix2d mat;  mat << 1, 2,         3, 4;  Vector2d u(-1,1), v(2,0);  std::cout << "Here is mat*mat:\n" << mat*mat << std::endl;  std::cout << "Here is mat*u:\n" << mat*u << std::endl;  std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;  std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;  std::cout << "Here is u*v^T:\n" << u*v.transpose() << std::endl;  std::cout << "Let's multiply mat by itself" << std::endl;  mat = mat*mat;  std::cout << "Now mat is mat:\n" << mat << std::endl;}//向量内积、求共轭向量int main(){  Vector3d v(1,2,3);  Vector3d w(0,1,2);  cout << "Dot product: " << v.dot(w) << endl;  double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar  cout << "Dot product via a matrix product: " << dp << endl;  cout << "Cross product:\n" << v.cross(w) << endl;}//矩阵内一些性质：平均值、和、迹int main(){  Eigen::Matrix2d mat;  mat << 1, 2,         3, 4;  cout << "Here is mat.sum():       " << mat.sum()       << endl;  cout << "Here is mat.prod():      " << mat.prod()      << endl;  cout << "Here is mat.mean():      " << mat.mean()      << endl;  cout << "Here is mat.minCoeff():  " << mat.minCoeff()  << endl;  cout << "Here is mat.maxCoeff():  " << mat.maxCoeff()  << endl;  cout << "Here is mat.trace():     " << mat.trace()     << endl;}//矩阵极大小值元素及其位置int main(int argc, char const *argv[]){  Matrix3f m = Matrix3f::Random();  std::ptrdiff_t i, j;  float minOfM = m.minCoeff(&i,&j);  cout << "Here is the matrix m:\n" << m << endl;  cout << "Its minimum coefficient (" << minOfM        << ") is at position (" << i << "," << j << ")\n\n";  RowVector4i v = RowVector4i::Random();  int maxOfV = v.maxCoeff(&i);  cout << "Here is the vector v: " << v << endl;  cout << "Its maximum coefficient (" << maxOfV        << ") is at position " << i << endl;  return 0;}//矩阵子块（子矩阵）int main(){  Eigen::MatrixXf m(4,4);  m <<  1, 2, 3, 4,        5, 6, 7, 8,        9,10,11,12,       13,14,15,16;  cout << "Block in the middle" << endl;  cout << m.block<2,2>(1,1) << endl << endl;  for (int i = 1; i <= 3; ++i)  {    cout << "Block of size " << i << "x" << i << endl;    cout << m.block(0,0,i,i) << endl << endl;  }}//矩阵子块操作int main(){  Array22f m;  m << 1,2,       3,4;  Array44f a = Array44f::Constant(0.6);  cout << "Here is the array a:" << endl << a << endl << endl;  a.block<2,2>(1,1) = m;  cout << "Here is now a with m copied into its central 2x2 block:" << endl << a << endl << endl;  a.block(0,0,2,3) = a.block(2,1,2,3);  cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x2 block:" << endl << a << endl << endl;}//列操作int main(){  Eigen::MatrixXf m(3,3);  m << 1,2,3,       4,5,6,       7,8,9;  cout << "Here is the matrix m:" << endl << m << endl;  cout << "2nd Row: " << m.row(1) << endl;  m.col(2) += 3 * m.col(0);  cout << "After adding 3 times the first column into the third column, the matrix m is:\n";  cout << m << endl;}//子列、子行int main(){  Eigen::Matrix4f m;  m << 1, 2, 3, 4,       5, 6, 7, 8,       9, 10,11,12,       13,14,15,16;  cout << "m.leftCols(2) =" << endl << m.leftCols(2) << endl << endl;  cout << "m.bottomRows<2>() =" << endl << m.bottomRows<2>() << endl << endl;  m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose();  cout << "After assignment, m = " << endl << m << endl;}//向量的分拆int main(){  Eigen::ArrayXf v(6);  v << 1, 2, 3, 4, 5, 6;  cout << "v.head(3) =" << endl << v.head(3) << endl << endl;  cout << "v.tail<3>() = " << endl << v.tail<3>() << endl << endl;  v.segment(1,4) *= 2;  cout << "after 'v.segment(1,4) *= 2', v =" << endl << v << endl;}//向量拼接int main(){  RowVectorXd vec1(3);  vec1 << 1, 2, 3;  std::cout << "vec1 = " << vec1 << std::endl;  RowVectorXd vec2(4);  vec2 << 1, 4, 9, 16;  std::cout << "vec2 = " << vec2 << std::endl;  RowVectorXd joined(7);  joined << vec1, vec2;  std::cout << "joined = " << joined << std::endl;  return 0;}//向量子块的操作与赋值int main(int argc, char const *argv[]){  MatrixXf matA(2, 2);  matA << 1, 2, 3, 4;  MatrixXf matB(4, 4);  matB << matA, matA/10, matA/10, matA;  std::cout << matB << std::endl;  Matrix3f m;  m.row(0) << 1, 2, 3;  m.block(1,0,2,2) << 4, 5, 7, 8;  m.col(2).tail(2) << 6, 9;                     std::cout << m <<std::endl;  return 0;}//多维数组赋值int main(int argc, char const *argv[]){  std::cout << "A fixed-size array:\n";  Array33f a1 = Array33f::Zero();  std::cout << a1 << "\n\n";  std::cout << "A one-dimensional dynamic-size array:\n";  ArrayXf a2 = ArrayXf::Zero(3);  std::cout << a2 << "\n\n";  std::cout << "A two-dimensional dynamic-size array:\n";  ArrayXXf a3 = ArrayXXf::Zero(3, 4);  std::cout << a3 << "\n";  return 0;}//多维数组的数学函数运算int main(int argc, char const *argv[]){  ArrayXXf table(10, 4);  table.col(0) = ArrayXf::LinSpaced(10, 0, 90);  table.col(1) = M_PI / 180 * table.col(0);  table.col(2) = table.col(1).sin();  table.col(3) = table.col(1).cos();  std::cout << "  Degrees        Radians          Sine        Cosine\n";  std::cout << table << std::endl;  return 0;}//矩阵子块赋值等等int main(int argc, char const *argv[]){  const int size = 6;  MatrixXd mat1(size, size);  mat1.topLeftCorner(size/2, size/2)     = MatrixXd::Zero(size/2, size/2);  mat1.topRightCorner(size/2, size/2)    = MatrixXd::Identity(size/2, size/2);  mat1.bottomLeftCorner(size/2, size/2)  = MatrixXd::Identity(size/2, size/2);  mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);  std::cout << mat1 << std::endl << std::endl;  MatrixXd mat2(size, size);  mat2.topLeftCorner(size/2, size/2).setZero();  mat2.topRightCorner(size/2, size/2).setIdentity();  mat2.bottomLeftCorner(size/2, size/2).setIdentity();  mat2.bottomRightCorner(size/2, size/2).setZero();  std::cout << mat2 << std::endl << std::endl;  MatrixXd mat3(size, size);  mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2),          MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2);  std::cout << mat3 << std::endl;  return 0;}//矩阵间运算int main(){  MatrixXd m = MatrixXd::Random(3,3);  m = (m + MatrixXd::Constant(3,3,1.2)) * 50;  cout << "m =" << endl << m << endl;  VectorXd v(3);  v << 1, 2, 3;  cout << "v =" << endl << v << endl;  cout << "m * v =" << endl << m * v << endl << endl;  MatrixXf mat = MatrixXf::Random(2, 3);  std::cout << mat << std::endl << std::endl;  mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat;  std::cout << mat << std::endl;}