Matlab+Find+the+largest+determinant+of+a+6+by+6+matrix+of+1'+s+and+-1'+s+.
时间: 2023-12-12 14:34:10 浏览: 39
以下是求解6x6矩阵最大行列式的Matlab代码:
```matlab
% 构造6x6矩阵
A = [1 1 1 1 1 1;
1 1 1 1 1 -1;
1 1 1 1 -1 1;
1 1 1 -1 1 1;
1 1 -1 1 1 1;
1 -1 1 1 1 1];
% 求解最大行列式
max_det = 0;
for i = 1:720
% 生成全排列
p = perms(1:6);
% 生成置换矩阵
P = zeros(6,6);
for j = 1:6
P(j,p(i,j)) = 1;
end
% 计算行列式
det_val = det(P*A);
% 更新最大值
if det_val > max_det
max_det = det_val;
end
end
% 输出结果
fprintf('The largest determinant of the 6x6 matrix is: %d\n', max_det);
```
相关问题
estimate_pose_for_tag_homographyC++ 使用
在使用 C++ 实现 "estimate_pose_for_tag_homography" 算法之前,需要确保已经安装了适当的开发环境和相关的计算机视觉库和工具包,如OpenCV和Eigen等。
以下是一个简单的示例代码,演示如何使用 OpenCV 库和 Eigen 库实现 "estimate_pose_for_tag_homography" 算法:
```
#include <iostream>
#include <opencv2/opencv.hpp>
#include <Eigen/Dense>
using namespace std;
using namespace cv;
using namespace Eigen;
int main()
{
// Load reference image and target image
Mat ref_img = imread("ref_image.jpg");
Mat target_img = imread("target_image.jpg");
// Detect and match features between reference image and target image
vector<KeyPoint> ref_kp, target_kp;
Mat ref_desc, target_desc;
Ptr<ORB> orb = ORB::create();
orb->detectAndCompute(ref_img, Mat(), ref_kp, ref_desc);
orb->detectAndCompute(target_img, Mat(), target_kp, target_desc);
BFMatcher matcher(NORM_HAMMING);
vector<DMatch> matches;
matcher.match(ref_desc, target_desc, matches);
// Extract matched feature points
vector<Point2f> ref_pts, target_pts;
for (int i = 0; i < matches.size(); i++)
{
ref_pts.push_back(ref_kp[matches[i].queryIdx].pt);
target_pts.push_back(target_kp[matches[i].trainIdx].pt);
}
// Compute homography matrix
Mat H = findHomography(ref_pts, target_pts, RANSAC);
// Compute pose from homography matrix
Matrix3d K, R;
Vector3d t;
K << 1000, 0, ref_img.cols/2,
0, 1000, ref_img.rows/2,
0, 0, 1;
Matrix3d H_eigen;
cv2eigen(H, H_eigen);
Matrix3d inv_K = K.inverse();
Matrix3d A = inv_K * H_eigen;
double scale = 1.0 / A.col(0).norm();
A *= scale;
double sign = (A.determinant() > 0) ? 1 : -1;
R.col(0) = A.col(0).normalized();
R.col(1) = A.col(1).normalized();
R.col(2) = R.col(0).cross(R.col(1));
t = sign * scale * A.col(2);
cout << "Rotation matrix:" << endl << R << endl;
cout << "Translation vector:" << endl << t << endl;
return 0;
}
```
该代码演示了如何使用 ORB 特征检测算法和 BFMatcher 特征匹配算法来检测和匹配参考图像和目标图像之间的特征点,然后使用 findHomography 函数计算单应性矩阵,并使用 Eigen 库和数学公式计算出姿态(旋转矩阵和平移向量)。在实际应用中,还需要对算法进行优化和调整,以提高估计精度和效率。
<a,b>R<c,d><=>a+d=b+c
This is the cross product rule. It states that the cross product of two vectors <a,b> and <c,d> is equal to the determinant of the matrix:
| a b |
| c d |
which is equal to ad - bc. Therefore, <a,b> x <c,d> = ad - bc.
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