通过犰狳解决逆矩阵错误
Solve Inverse Matrix error by armadillo
我得到了一个逆矩阵错误，同一个矩阵来自不同的方式。
来自矩阵乘法
从分配。
然后我从中抓取一个子矩阵，求解它的逆矩阵，得到不同的结果。
请检查我的简单代码，
#include <armadillo>
using namespace std;
using namespace arma;
int main()
{
#if 1
mat D;
D << 0.9601 << -0.8824 << 0.811 << -0.9798 << 0.9005 << 1.0 << endr
<< 0.9686 << -0.8837 << 0.8063 << -0.9842 << 0.8979 << 1.0 << endr
<< 0.9487 << -0.874 << 0.8052 << -0.974 << 0.8973 << 1.0 << endr
<< 0.9291 << -0.8498 << 0.7773 << -0.9639 << 0.8816 << 1.0 << endr
<< 0.9137 << -0.833 << 0.7595 << -0.9559 << 0.8715 << 1.0 << endr
<< 0.8649 << -0.7989 << 0.7379 << -0.93 << 0.859 << 1.0 << endr
<< 0.8481 << -0.7704 << 0.6998 << -0.9209 << 0.8365 << 1.0 << endr
<< 0.7856 << -0.7227 << 0.6648 << -0.8863 << 0.8154 << 1.0 << endr
<< 0.7413 << -0.6764 << 0.6173 << -0.861 << 0.7857 << 1.0 << endr
<< 0.6674 << -0.6207 << 0.5774 << -0.8169 << 0.7599 << 1.0 << endr
<< 0.6415 << -0.5792 << 0.523 << -0.8009 << 0.7232 << 1.0 << endr
<< 0.5641 << -0.518 << 0.4757 << -0.7511 << 0.6897 << 1.0 << endr
<< 0.4988 << -0.4582 << 0.4209 << -0.7062 << 0.6488 << 1.0 << endr
<< 0.4343 << -0.4006 << 0.3696 << -0.659 << 0.6079 << 1.0 << endr
<< 0.3867 << -0.3536 << 0.3234 << -0.6218 << 0.5687 << 1.0 << endr
<< 0.3201 << -0.2954 << 0.2725 << -0.5658 << 0.522 << 1.0 << endr
<< 0.2664 << -0.2436 << 0.2227 << -0.5162 << 0.4719 << 1.0 << endr
<< 0.2104 << -0.1937 << 0.1783 << -0.4587 << 0.4223 << 1.0 << endr
<< 0.1667 << -0.1519 << 0.1383 << -0.4083 << 0.3719 << 1.0 << endr
<< 0.1202 << -0.1111 << 0.1027 << -0.3467 << 0.3205 << 1.0 << endr
<< 0.0815 << -0.0747 << 0.0685 << -0.2854 << 0.2617 << 1.0 << endr
<< 0.0482 << -0.0446 << 0.0412 << -0.2194 << 0.2031 << 1.0 << endr
<< 0.0254 << -0.0237 << 0.0221 << -0.1594 << 0.1486 << 1.0 << endr
<< 0.0115 << -0.0103 << 0.0092 << -0.1073 << 0.0961 << 1.0 << endr
<< 0.0008 << -0.001 << 0.0013 << -0.0281 << 0.0355 << 1.0 << endr
<< 0.0007 << -0.0005 << 0.0004 << 0.027 << -0.0188 << 1.0 << endr
<< 0.0078 << -0.0071 << 0.0065 << 0.0883 << -0.0805 << 1.0 << endr
<< 0.0234 << -0.0219 << 0.0205 << 0.1531 << -0.1432 << 1.0 << endr
<< 0.0441 << -0.042 << 0.04 << 0.2099 << -0.1999 << 1.0 << endr
<< 0.0777 << -0.0707 << 0.0643 << 0.2787 << -0.2537 << 1.0 << endr
<< 0.1125 << -0.1055 << 0.0989 << 0.3354 << -0.3145 << 1.0 << endr
<< 0.1603 << -0.1439 << 0.1291 << 0.4004 << -0.3593 << 1.0 << endr
<< 0.2025 << -0.1833 << 0.1658 << 0.45 << -0.4072 << 1.0 << endr
<< 0.2606 << -0.2399 << 0.2208 << 0.5105 << -0.4699 << 1.0 << endr
<< 0.3075 << -0.2849 << 0.2639 << 0.5545 << -0.5138 << 1.0 << endr
<< 0.3693 << -0.3427 << 0.3181 << 0.6077 << -0.564 << 1.0 << endr
<< 0.4367 << -0.4006 << 0.3675 << 0.6608 << -0.6062 << 1.0 << endr
<< 0.4945 << -0.4529 << 0.4148 << 0.7032 << -0.6441 << 1.0 << endr
<< 0.5563 << -0.5136 << 0.4742 << 0.7459 << -0.6886 << 1.0 << endr
<< 0.6296 << -0.5739 << 0.5231 << 0.7935 << -0.7232 << 1.0 << endr
<< 0.692 << -0.6292 << 0.5722 << 0.8319 << -0.7564 << 1.0 << endr
<< 0.7417 << -0.6802 << 0.6239 << 0.8612 << -0.7898 << 1.0 << endr
<< 0.7973 << -0.7323 << 0.6725 << 0.8929 << -0.8201 << 1.0 << endr
<< 0.8413 << -0.775 << 0.714 << 0.9172 << -0.845 << 1.0 << endr
<< 0.8768 << -0.8051 << 0.7393 << 0.9364 << -0.8598 << 1.0 << endr
<< 0.9307 << -0.8537 << 0.783 << 0.9647 << -0.8849 << 1.0 << endr
<< 0.9536 << -0.8793 << 0.8108 << 0.9765 << -0.9005 << 1.0 << endr
<< 0.9941 << -0.9065 << 0.8265 << 0.9971 << -0.9091 << 1.0 << endr
<< 0.9998 << -0.9151 << 0.8375 << 0.9999 << -0.9151 << 1.0 << endr
<< 1.0247 << -0.9367 << 0.8563 << 1.0123 << -0.9254 << 1.0 << endr
<< 1.0068 << -0.9224 << 0.845 << 1.0034 << -0.9192 << 1.0 << endr
<< 0.9936 << -0.9189 << 0.8497 << 0.9968 << -0.9218 << 1.0 << endr
<< 0.9817 << -0.8981 << 0.8217 << 0.9908 << -0.9065 << 1.0 << endr
<< 0.9653 << -0.887 << 0.815 << 0.9825 << -0.9028 << 1.0 << endr
<< 0.931 << -0.856 << 0.787 << 0.9649 << -0.8871 << 1.0 << endr
<< 0.8921 << -0.8221 << 0.7576 << 0.9445 << -0.8704 << 1.0 << endr
<< 0.8399 << -0.7765 << 0.7179 << 0.9165 << -0.8473 << 1.0 << endr
<< 0.8055 << -0.7356 << 0.6718 << 0.8975 << -0.8196 << 1.0 << endr
<< 0.7539 << -0.6912 << 0.6337 << 0.8683 << -0.7961 << 1.0 << endr
<< 0.6765 << -0.624 << 0.5756 << 0.8225 << -0.7587 << 1.0 << endr
<< 0.6292 << -0.5763 << 0.5278 << 0.7932 << -0.7265 << 1.0 << endr
<< 0.5574 << -0.5134 << 0.473 << 0.7466 << -0.6877 << 1.0 << endr
<< 0.4988 << -0.4627 << 0.4291 << 0.7063 << -0.6551 << 1.0 << endr
<< 0.4422 << -0.4027 << 0.3668 << 0.665 << -0.6056 << 1.0 << endr
<< 0.3793 << -0.3454 << 0.3145 << 0.6159 << -0.5608 << 1.0 << endr
<< 0.3114 << -0.2883 << 0.267 << 0.5581 << -0.5167 << 1.0 << endr
<< 0.2556 << -0.2366 << 0.219 << 0.5056 << -0.468 << 1.0 << endr
<< 0.2048 << -0.184 << 0.1652 << 0.4526 << -0.4065 << 1.0 << endr
<< 0.1513 << -0.1399 << 0.1294 << 0.389 << -0.3597 << 1.0 << endr
<< 0.116 << -0.1049 << 0.0949 << 0.3405 << -0.308 << 1.0 << endr
<< 0.0766 << -0.0703 << 0.0645 << 0.2768 << -0.2539 << 1.0 << endr
<< 0.0456 << -0.0413 << 0.0373 << 0.2136 << -0.1932 << 1.0 << endr
<< 0.0233 << -0.0221 << 0.0209 << 0.1528 << -0.1447 << 1.0 << endr
<< 0.0085 << -0.0072 << 0.0061 << 0.0923 << -0.0781 << 1.0 << endr
<< 0.0006 << -0.0005 << 0.0005 << 0.0248 << -0.0218 << 1.0 << endr
<< 0.0012 << -0.0011 << 0.0011 << -0.0344 << 0.0324 << 1.0 << endr
<< 0.0105 << -0.0101 << 0.0097 << -0.1024 << 0.0984 << 1.0 << endr
<< 0.0249 << -0.0234 << 0.022 << -0.1578 << 0.1484 << 1.0 << endr
<< 0.05 << -0.0459 << 0.0421 << -0.2237 << 0.2052 << 1.0 << endr
<< 0.0801 << -0.0723 << 0.0651 << -0.2831 << 0.2552 << 1.0 << endr
<< 0.1195 << -0.11 << 0.1012 << -0.3457 << 0.3182 << 1.0 << endr
<< 0.1681 << -0.1504 << 0.1346 << -0.41 << 0.3668 << 1.0 << endr
<< 0.2039 << -0.1905 << 0.178 << -0.4516 << 0.4219 << 1.0 << endr
<< 0.269 << -0.2439 << 0.2211 << -0.5187 << 0.4702 << 1.0 << endr
<< 0.3177 << -0.2917 << 0.2678 << -0.5637 << 0.5175 << 1.0 << endr
<< 0.389 << -0.3564 << 0.3266 << -0.6237 << 0.5715 << 1.0 << endr
<< 0.4364 << -0.4059 << 0.3774 << -0.6606 << 0.6143 << 1.0 << endr
<< 0.5083 << -0.4667 << 0.4286 << -0.713 << 0.6546 << 1.0 << endr
<< 0.5675 << -0.5182 << 0.4732 << -0.7533 << 0.6879 << 1.0 << endr
<< 0.6361 << -0.5757 << 0.5211 << -0.7976 << 0.7219 << 1.0 << endr
<< 0.6897 << -0.6334 << 0.5816 << -0.8305 << 0.7627 << 1.0 << endr
<< 0.7428 << -0.6835 << 0.6291 << -0.8618 << 0.7931 << 1.0 << endr
<< 0.7779 << -0.7218 << 0.6697 << -0.882 << 0.8184 << 1.0 << endr
<< 0.8511 << -0.7701 << 0.6968 << -0.9225 << 0.8348 << 1.0 << endr
<< 0.8745 << -0.8039 << 0.7389 << -0.9351 << 0.8596 << 1.0 << endr
<< 0.8945 << -0.8239 << 0.7589 << -0.9458 << 0.8712 << 1.0 << endr
<< 0.9216 << -0.8528 << 0.789 << -0.96 << 0.8883 << 1.0 << endr
<< 0.9621 << -0.8793 << 0.8036 << -0.9809 << 0.8965 << 1.0 << endr
<< 0.9542 << -0.8829 << 0.8169 << -0.9768 << 0.9038 << 1.0 << endr
<< 0.9756 << -0.8879 << 0.808 << -0.9877 << 0.8989 << 1.0 << endr;
mat S = D.t() * D;
#else
mat S;
S << 3.7243e+01 << -3.7361e+01 << 3.7482e+01 << 4.8177e-01 << -5.0223e-01 << 4.9913e+01 << endr
<<-3.7361e+01 << 3.7482e+01 << -3.7604e+01 << -5.0223e-01 << 5.2224e-01 << -5.0074e+01 << endr
<< 3.7482e+01 << -3.7604e+01 << 3.7728e+01 << 5.2224e-01 << -5.4180e-01 << 5.0238e+01 << endr
<< 4.8177e-01 << -5.0223e-01 << 5.2224e-01 << 4.9913e+01 << -5.0074e+01 << -3.2085e-14 << endr
<<-5.0223e-01 << 5.2224e-01 << -5.4180e-01 << -5.0074e+01 << 5.0238e+01 << 3.2196e-15 << endr
<< 4.9913e+01 << -5.0074e+01 << 5.0238e+01 << -3.2085e-14 << 3.2196e-15 << 1.0000e+02 << endr;
#endif
cout << "S = \n" << S << endl;
mat tmpC = S(span(3, 5), span(3, 5));
cout << "tmpC = \n" << tmpC << endl;
cout << "InvC = \n" << inv(tmpC) << endl;
return 0;
}
如果您将 if 1 改为 if 0，invC 会有所不同，
在我的机器上，它输出 InvC 为
InvC =
3.5358e+02 3.8534e+02 -1.0925e-03
3.8534e+02 4.1997e+02 -1.1906e-03
-1.0925e-03 -1.1906e-03 1.0000e-02
和
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
分别。注意矩阵 S 与代码相同，如果 0 和 1.
我也用Octave测试了一下，结果出来了
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
谁能帮我找出原因？为什么我得到错误的逆矩阵？
有了#if 0，我得到
tmpC =
4.9913e+01 -5.0074e+01 -3.2085e-14
-5.0074e+01 5.0238e+01 3.2196e-15
-3.2085e-14 3.2196e-15 1.0000e+02
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
同时 #if 1:
tmpC =
4.9913e+01 -4.5797e+01 2.0000e-04
-4.5797e+01 4.2023e+01 1.0000e-04
2.0000e-04 1.0000e-04 1.0000e+02
InvC =
3.5358e+02 3.8534e+02 -1.0925e-03
3.8534e+02 4.1997e+02 -1.1906e-03
-1.0925e-03 -1.1906e-03 1.0000e-02
由于矩阵 tmpC 在两种情况下都不同，因此逆矩阵也不同...
根据armadillo作者的评论，说矩阵tmpC有pool conditioning number，导致计算精度较低
我得到了一个逆矩阵错误，同一个矩阵来自不同的方式。
来自矩阵乘法 从分配。 然后我从中抓取一个子矩阵，求解它的逆矩阵，得到不同的结果。
请检查我的简单代码，
#include <armadillo>
using namespace std;
using namespace arma;
int main()
{
#if 1
mat D;
D << 0.9601 << -0.8824 << 0.811 << -0.9798 << 0.9005 << 1.0 << endr
<< 0.9686 << -0.8837 << 0.8063 << -0.9842 << 0.8979 << 1.0 << endr
<< 0.9487 << -0.874 << 0.8052 << -0.974 << 0.8973 << 1.0 << endr
<< 0.9291 << -0.8498 << 0.7773 << -0.9639 << 0.8816 << 1.0 << endr
<< 0.9137 << -0.833 << 0.7595 << -0.9559 << 0.8715 << 1.0 << endr
<< 0.8649 << -0.7989 << 0.7379 << -0.93 << 0.859 << 1.0 << endr
<< 0.8481 << -0.7704 << 0.6998 << -0.9209 << 0.8365 << 1.0 << endr
<< 0.7856 << -0.7227 << 0.6648 << -0.8863 << 0.8154 << 1.0 << endr
<< 0.7413 << -0.6764 << 0.6173 << -0.861 << 0.7857 << 1.0 << endr
<< 0.6674 << -0.6207 << 0.5774 << -0.8169 << 0.7599 << 1.0 << endr
<< 0.6415 << -0.5792 << 0.523 << -0.8009 << 0.7232 << 1.0 << endr
<< 0.5641 << -0.518 << 0.4757 << -0.7511 << 0.6897 << 1.0 << endr
<< 0.4988 << -0.4582 << 0.4209 << -0.7062 << 0.6488 << 1.0 << endr
<< 0.4343 << -0.4006 << 0.3696 << -0.659 << 0.6079 << 1.0 << endr
<< 0.3867 << -0.3536 << 0.3234 << -0.6218 << 0.5687 << 1.0 << endr
<< 0.3201 << -0.2954 << 0.2725 << -0.5658 << 0.522 << 1.0 << endr
<< 0.2664 << -0.2436 << 0.2227 << -0.5162 << 0.4719 << 1.0 << endr
<< 0.2104 << -0.1937 << 0.1783 << -0.4587 << 0.4223 << 1.0 << endr
<< 0.1667 << -0.1519 << 0.1383 << -0.4083 << 0.3719 << 1.0 << endr
<< 0.1202 << -0.1111 << 0.1027 << -0.3467 << 0.3205 << 1.0 << endr
<< 0.0815 << -0.0747 << 0.0685 << -0.2854 << 0.2617 << 1.0 << endr
<< 0.0482 << -0.0446 << 0.0412 << -0.2194 << 0.2031 << 1.0 << endr
<< 0.0254 << -0.0237 << 0.0221 << -0.1594 << 0.1486 << 1.0 << endr
<< 0.0115 << -0.0103 << 0.0092 << -0.1073 << 0.0961 << 1.0 << endr
<< 0.0008 << -0.001 << 0.0013 << -0.0281 << 0.0355 << 1.0 << endr
<< 0.0007 << -0.0005 << 0.0004 << 0.027 << -0.0188 << 1.0 << endr
<< 0.0078 << -0.0071 << 0.0065 << 0.0883 << -0.0805 << 1.0 << endr
<< 0.0234 << -0.0219 << 0.0205 << 0.1531 << -0.1432 << 1.0 << endr
<< 0.0441 << -0.042 << 0.04 << 0.2099 << -0.1999 << 1.0 << endr
<< 0.0777 << -0.0707 << 0.0643 << 0.2787 << -0.2537 << 1.0 << endr
<< 0.1125 << -0.1055 << 0.0989 << 0.3354 << -0.3145 << 1.0 << endr
<< 0.1603 << -0.1439 << 0.1291 << 0.4004 << -0.3593 << 1.0 << endr
<< 0.2025 << -0.1833 << 0.1658 << 0.45 << -0.4072 << 1.0 << endr
<< 0.2606 << -0.2399 << 0.2208 << 0.5105 << -0.4699 << 1.0 << endr
<< 0.3075 << -0.2849 << 0.2639 << 0.5545 << -0.5138 << 1.0 << endr
<< 0.3693 << -0.3427 << 0.3181 << 0.6077 << -0.564 << 1.0 << endr
<< 0.4367 << -0.4006 << 0.3675 << 0.6608 << -0.6062 << 1.0 << endr
<< 0.4945 << -0.4529 << 0.4148 << 0.7032 << -0.6441 << 1.0 << endr
<< 0.5563 << -0.5136 << 0.4742 << 0.7459 << -0.6886 << 1.0 << endr
<< 0.6296 << -0.5739 << 0.5231 << 0.7935 << -0.7232 << 1.0 << endr
<< 0.692 << -0.6292 << 0.5722 << 0.8319 << -0.7564 << 1.0 << endr
<< 0.7417 << -0.6802 << 0.6239 << 0.8612 << -0.7898 << 1.0 << endr
<< 0.7973 << -0.7323 << 0.6725 << 0.8929 << -0.8201 << 1.0 << endr
<< 0.8413 << -0.775 << 0.714 << 0.9172 << -0.845 << 1.0 << endr
<< 0.8768 << -0.8051 << 0.7393 << 0.9364 << -0.8598 << 1.0 << endr
<< 0.9307 << -0.8537 << 0.783 << 0.9647 << -0.8849 << 1.0 << endr
<< 0.9536 << -0.8793 << 0.8108 << 0.9765 << -0.9005 << 1.0 << endr
<< 0.9941 << -0.9065 << 0.8265 << 0.9971 << -0.9091 << 1.0 << endr
<< 0.9998 << -0.9151 << 0.8375 << 0.9999 << -0.9151 << 1.0 << endr
<< 1.0247 << -0.9367 << 0.8563 << 1.0123 << -0.9254 << 1.0 << endr
<< 1.0068 << -0.9224 << 0.845 << 1.0034 << -0.9192 << 1.0 << endr
<< 0.9936 << -0.9189 << 0.8497 << 0.9968 << -0.9218 << 1.0 << endr
<< 0.9817 << -0.8981 << 0.8217 << 0.9908 << -0.9065 << 1.0 << endr
<< 0.9653 << -0.887 << 0.815 << 0.9825 << -0.9028 << 1.0 << endr
<< 0.931 << -0.856 << 0.787 << 0.9649 << -0.8871 << 1.0 << endr
<< 0.8921 << -0.8221 << 0.7576 << 0.9445 << -0.8704 << 1.0 << endr
<< 0.8399 << -0.7765 << 0.7179 << 0.9165 << -0.8473 << 1.0 << endr
<< 0.8055 << -0.7356 << 0.6718 << 0.8975 << -0.8196 << 1.0 << endr
<< 0.7539 << -0.6912 << 0.6337 << 0.8683 << -0.7961 << 1.0 << endr
<< 0.6765 << -0.624 << 0.5756 << 0.8225 << -0.7587 << 1.0 << endr
<< 0.6292 << -0.5763 << 0.5278 << 0.7932 << -0.7265 << 1.0 << endr
<< 0.5574 << -0.5134 << 0.473 << 0.7466 << -0.6877 << 1.0 << endr
<< 0.4988 << -0.4627 << 0.4291 << 0.7063 << -0.6551 << 1.0 << endr
<< 0.4422 << -0.4027 << 0.3668 << 0.665 << -0.6056 << 1.0 << endr
<< 0.3793 << -0.3454 << 0.3145 << 0.6159 << -0.5608 << 1.0 << endr
<< 0.3114 << -0.2883 << 0.267 << 0.5581 << -0.5167 << 1.0 << endr
<< 0.2556 << -0.2366 << 0.219 << 0.5056 << -0.468 << 1.0 << endr
<< 0.2048 << -0.184 << 0.1652 << 0.4526 << -0.4065 << 1.0 << endr
<< 0.1513 << -0.1399 << 0.1294 << 0.389 << -0.3597 << 1.0 << endr
<< 0.116 << -0.1049 << 0.0949 << 0.3405 << -0.308 << 1.0 << endr
<< 0.0766 << -0.0703 << 0.0645 << 0.2768 << -0.2539 << 1.0 << endr
<< 0.0456 << -0.0413 << 0.0373 << 0.2136 << -0.1932 << 1.0 << endr
<< 0.0233 << -0.0221 << 0.0209 << 0.1528 << -0.1447 << 1.0 << endr
<< 0.0085 << -0.0072 << 0.0061 << 0.0923 << -0.0781 << 1.0 << endr
<< 0.0006 << -0.0005 << 0.0005 << 0.0248 << -0.0218 << 1.0 << endr
<< 0.0012 << -0.0011 << 0.0011 << -0.0344 << 0.0324 << 1.0 << endr
<< 0.0105 << -0.0101 << 0.0097 << -0.1024 << 0.0984 << 1.0 << endr
<< 0.0249 << -0.0234 << 0.022 << -0.1578 << 0.1484 << 1.0 << endr
<< 0.05 << -0.0459 << 0.0421 << -0.2237 << 0.2052 << 1.0 << endr
<< 0.0801 << -0.0723 << 0.0651 << -0.2831 << 0.2552 << 1.0 << endr
<< 0.1195 << -0.11 << 0.1012 << -0.3457 << 0.3182 << 1.0 << endr
<< 0.1681 << -0.1504 << 0.1346 << -0.41 << 0.3668 << 1.0 << endr
<< 0.2039 << -0.1905 << 0.178 << -0.4516 << 0.4219 << 1.0 << endr
<< 0.269 << -0.2439 << 0.2211 << -0.5187 << 0.4702 << 1.0 << endr
<< 0.3177 << -0.2917 << 0.2678 << -0.5637 << 0.5175 << 1.0 << endr
<< 0.389 << -0.3564 << 0.3266 << -0.6237 << 0.5715 << 1.0 << endr
<< 0.4364 << -0.4059 << 0.3774 << -0.6606 << 0.6143 << 1.0 << endr
<< 0.5083 << -0.4667 << 0.4286 << -0.713 << 0.6546 << 1.0 << endr
<< 0.5675 << -0.5182 << 0.4732 << -0.7533 << 0.6879 << 1.0 << endr
<< 0.6361 << -0.5757 << 0.5211 << -0.7976 << 0.7219 << 1.0 << endr
<< 0.6897 << -0.6334 << 0.5816 << -0.8305 << 0.7627 << 1.0 << endr
<< 0.7428 << -0.6835 << 0.6291 << -0.8618 << 0.7931 << 1.0 << endr
<< 0.7779 << -0.7218 << 0.6697 << -0.882 << 0.8184 << 1.0 << endr
<< 0.8511 << -0.7701 << 0.6968 << -0.9225 << 0.8348 << 1.0 << endr
<< 0.8745 << -0.8039 << 0.7389 << -0.9351 << 0.8596 << 1.0 << endr
<< 0.8945 << -0.8239 << 0.7589 << -0.9458 << 0.8712 << 1.0 << endr
<< 0.9216 << -0.8528 << 0.789 << -0.96 << 0.8883 << 1.0 << endr
<< 0.9621 << -0.8793 << 0.8036 << -0.9809 << 0.8965 << 1.0 << endr
<< 0.9542 << -0.8829 << 0.8169 << -0.9768 << 0.9038 << 1.0 << endr
<< 0.9756 << -0.8879 << 0.808 << -0.9877 << 0.8989 << 1.0 << endr;
mat S = D.t() * D;
#else
mat S;
S << 3.7243e+01 << -3.7361e+01 << 3.7482e+01 << 4.8177e-01 << -5.0223e-01 << 4.9913e+01 << endr
<<-3.7361e+01 << 3.7482e+01 << -3.7604e+01 << -5.0223e-01 << 5.2224e-01 << -5.0074e+01 << endr
<< 3.7482e+01 << -3.7604e+01 << 3.7728e+01 << 5.2224e-01 << -5.4180e-01 << 5.0238e+01 << endr
<< 4.8177e-01 << -5.0223e-01 << 5.2224e-01 << 4.9913e+01 << -5.0074e+01 << -3.2085e-14 << endr
<<-5.0223e-01 << 5.2224e-01 << -5.4180e-01 << -5.0074e+01 << 5.0238e+01 << 3.2196e-15 << endr
<< 4.9913e+01 << -5.0074e+01 << 5.0238e+01 << -3.2085e-14 << 3.2196e-15 << 1.0000e+02 << endr;
#endif
cout << "S = \n" << S << endl;
mat tmpC = S(span(3, 5), span(3, 5));
cout << "tmpC = \n" << tmpC << endl;
cout << "InvC = \n" << inv(tmpC) << endl;
return 0;
}
如果您将 if 1 改为 if 0，invC 会有所不同， 在我的机器上，它输出 InvC 为
InvC =
3.5358e+02 3.8534e+02 -1.0925e-03
3.8534e+02 4.1997e+02 -1.1906e-03
-1.0925e-03 -1.1906e-03 1.0000e-02
和
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
分别。注意矩阵 S 与代码相同，如果 0 和 1.
我也用Octave测试了一下，结果出来了
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
谁能帮我找出原因？为什么我得到错误的逆矩阵？
有了#if 0，我得到
tmpC =
4.9913e+01 -5.0074e+01 -3.2085e-14
-5.0074e+01 5.0238e+01 3.2196e-15
-3.2085e-14 3.2196e-15 1.0000e+02
InvC =
4.0574e+02 4.0442e+02 1.1716e-13
4.0442e+02 4.0312e+02 1.1678e-13
1.1716e-13 1.1678e-13 1.0000e-02
同时 #if 1:
tmpC =
4.9913e+01 -4.5797e+01 2.0000e-04
-4.5797e+01 4.2023e+01 1.0000e-04
2.0000e-04 1.0000e-04 1.0000e+02
InvC =
3.5358e+02 3.8534e+02 -1.0925e-03
3.8534e+02 4.1997e+02 -1.1906e-03
-1.0925e-03 -1.1906e-03 1.0000e-02
由于矩阵 tmpC 在两种情况下都不同，因此逆矩阵也不同...
根据armadillo作者的评论，说矩阵tmpC有pool conditioning number，导致计算精度较低