Matrix 如何从eigen中的稀疏矩阵解算器获得精确结果
最近我试着用Eigen做我的研究工作。我使用解算器试图找出方程A*X=B中的X值，其中A和B是已知矩阵。使用了以下两种方法，但两种方法得出的结果似乎不同：Matrix 如何从eigen中的稀疏矩阵解算器获得精确结果,matrix,reverse,eigen,Matrix,Reverse,Eigen,最近我试着用Eigen做我的研究工作。我使用解算器试图找出方程A*X=B中的X值，其中A和B是已知矩阵。使用了以下两种方法，但两种方法得出的结果似乎不同： MatrixXcd A，MatrixXcd B，X=A.逆（）*B SparseMatrix A、SparseMatrix B、SparseQR solverA；解算（A）；X=解算A.解算（L） 下面是方法1和2的输入和输出，结果不一样。稀疏解算器似乎不精确。有人知道如何使用稀疏解算器获得正确的结果吗 矩阵A： (1e+20
MatrixXcd A，MatrixXcd B，X=A.逆（）*BSparseMatrix A、SparseMatrix B、SparseQR solverA；解算（A）；X=解算A.解算（L） (1e+20,1e+20) (0,0) (0,0) (0,0) (0.00178347,-5.5e-07) (-0.00135281,-9.732e-05) (0.090243,0.00043181) (2.94443,2.79482) (0.00099333,1.91e-06) (-0.00043913,-0.00020801) (-0.0267104,-0.00025275) (5.59117,6.73686) (0,0) (0.00095055,-7.527e-05) (0,0) (2.94443,2.79482) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0)
(0,0) (1e+20,1e+20) (0,0) (0,0) (-0.00025576,1.1e-07) (0.00178347,-5.5e-07) (0.00010056,4.315e-05) (-0.090243,-0.00043181) (0.00018179,-8e-08) (0.00099333,1.91e-06) (0.00021957,0.00010401) (0.0267104,0.00025275) (-0.00044497,3.8e-07) (0,0) (0.0090243,4.318e-05) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (-0.217866,-0.00104248) (7.10848,6.74728) (0.5,0) (0,0) (0,0) (0,0) (5.73e-06,8.1e-07) (0.00229483,-0.00018173) (0.127623,0.00061067) (7.10848,6.74728) (-0.0006716,-7.8e-07) (-0.00018189,-8.616e-05) (0.0644847,0.0006102) (2.31594,2.7905) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0.00024278,0.00010417) (0.217866,0.00104248) (0,0) (0,0) (0,0) (0,0) (-0.0008087,2.6e-07) (5.73e-06,8.1e-07) (0.00393912,0.00010418) (-0.127623,-0.00061067) (0.00011683,-1.9e-07) (-0.0006716,-7.8e-07) (9.095e-05,4.308e-05) (-0.0644847,-0.0006102) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (2.31594,2.7905) (-0.00130676,-1.39e-06) (-0.00102149,-0.00021714) (0.0413077,0.00019766) (7.23664,6.86893) (0.500641,5.6e-07) (-0.00018189,-8.616e-05) (-0.0781991,-0.00073998) (2.31594,2.7905) (0,0) (0,0) (0,0) (0,0) (0,0) (-0.00042231,-0.00012091) (0,0) (1.73321,3.53729) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0.00455975,4.315e-05) (0,0) (-0.00089467,7.6e-07) (-0.00130676,-1.39e-06) (0.00024716,0.00010605) (-0.0413077,-0.00019766) (0.0001107,-1.7e-07) (0.00064098,5.6e-07) (-0.00201202,4.305e-05) (0.0781991,0.00073998) (0,0) (0,0) (0,0) (0,0) (0,0) (0.00014839,4.4e-07) (0,0) (-0.0193833,-0.00049809) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0.090243,0.00043181) (2.94443,2.79482) (0.499494,-1.12e-06) (-0.00018189,-8.616e-05) (0,0) (2.31594,2.7905) (-0.0008912,9.1e-07) (-0.00096261,-0.0002129) (-0.211439,-0.00101173) (7.10848,6.74728) (0,0) (0,0) (0,0) (0,0) (0,0) (-0.00056253,-0.0001165) (0,0) (2.88173,3.55652) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0.00010056,4.315e-05) (-0.090243,-0.00043181) (6.703e-05,0) (-0.00050568,-1.12e-06) (0.00455975,4.315e-05) (0,0) (-0.00113032,5.3e-07) (-0.0008912,9.1e-07) (-0.0045034,0.00010415) (0.211439,0.00101173) (0,0) (0,0) (0,0) (0,0) (0,0) (0.00038673,9.4e-07) (0,0) (-0.0534256,-0.00053643) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (-0.0251163,-0.0006454) (4.63487,6.72124) (0.00063547,1.45e-06) (-0.00108457,-0.00022461) (-0.117256,-0.00117733) (5.55601,6.85699) (0.499971,-3.07e-06) (-0.00228556,-0.00034268) (0.230853,0.00178218) (8.99968,10.298) (0.00062601,-1.23e-06) (-0.00040226,-0.00017259) (0.0568305,0.00027193) (5.88886,5.58963) (0,0) (0,0) (0,0) (0,0) (0,0) (3.691e-05,-0.00011153) (0,0) (1.982,4.04505)
(0,0) (0,0) (0.00748371,0.00010397) (0.0251163,0.0006454) (6.774e-05,3.6e-07) (0.00063547,1.45e-06) (0.0019205,0.00010589) (0.117256,0.00117733) (-0.00024843,-2.4e-07) (-2.913e-05,-3.07e-06) (-0.00461883,0.00015896) (-0.230853,-0.00178218) (-0.00083939,2.2e-07) (0.00062601,-1.23e-06) (-0.0052904,8.627e-05) (-0.0568305,-0.00027193) (0,0) (0.5,0) (0,0) (0,0) (0,0) (-3.719e-05,6.6e-07) (0,0) (-0.0763484,-0.0019619)
(0,0) (0,0) (0.152739,0.00125608) (5.52369,6.72735) (-9.162e-05,-6e-08) (0.00019941,-0.00018336) (0.0300956,0.00070779) (3.55668,6.82522) (0.00322718,2.7e-07) (0.00100646,-0.00037669) (-0.138197,-0.00072924) (12.7453,13.0983) (0.499417,-1.09e-06) (-0.00018189,-8.616e-05) (0.0178848,0.00016924) (2.31594,2.7905) (0,0) (-0.00020301,-0.00010941) (0,0) (1.99984,3.54347) (0,0) (0.00011828,-0.00010875) (0,0) (2.10955,4.04819)
(0,0) (0,0) (0.00117747,0.00010397) (-0.152739,-0.00125608) (-2.717e-05,8e-08) (-9.162e-05,-6e-08) (1.513e-05,0.00010535) (-0.0300956,-0.00070779) (-0.000866,1.48e-06) (0.00322718,2.7e-07) (0.0220268,0.00020238) (0.138197,0.00072924) (8.619e-05,-7e-08) (-0.00058296,-1.09e-06) (0.004216,4.314e-05) (-0.0178848,-0.00016924) (0,0) (-6e-06,-6.9e-07) (0,0) (0.058675,0.0012186) (0,0) (2.581e-05,6e-07) (0,0) (-0.0852486,-0.00200487)
(0,0) (0,0) (-0.0355198,-0.00091274) (1.92282,3.92427) (0,0) (0,0) (0,0) (0,0) (-0.0002382,6.2e-07) (-0.00193505,-0.0002194) (-0.0871354,-0.00067268) (5.69809,6.35139) (0.00017221,-7.4e-07) (-0.00078467,-0.00019377) (0.103106,0.00242483) (2.89427,5.55407) (0,0) (0,0) (0,0) (0,0) (0,0) (-0.00023215,-0.00012512) (0,0) (2.2869,4.05211)
(0,0) (0,0) (0.00146406,6.074e-05) (0.0355198,0.00091274) (0,0) (0,0) (0,0) (0,0) (-0.00022689,5.1e-07) (-0.0002382,6.2e-07) (0.00259242,9.808e-05) (0.0871354,0.00067268) (-2.649e-05,1e-08) (0.00017221,-7.4e-07) (-0.00185659,8.555e-05) (-0.103106,-0.00242483) (0,0) (0,0) (0,0) (0,0) (0,0) (6.86e-06,7.9e-07) (0,0) (-0.0670974,-0.00139353)
(0,0) (0,0) (0.0355198,0.00091274) (1.92282,3.92427) (0,0) (0,0) (0,0) (0,0) (-0.00050754,-3.8e-07) (0.00108126,-0.00017282) (0.00807103,6.231e-05) (5.69809,6.35139) (-0.00135942,-8.3e-07) (0.00016175,-0.0001618) (0.12563,0.00126141) (4.52124,5.57992) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0.00146406,6.074e-05) (-0.0355198,-0.00091274) (0,0) (0,0) (0,0) (0,0) (-0.00015569,2.3e-07) (-0.00050754,-3.8e-07) (-0.00755564,9.798e-05) (-0.00807103,-6.231e-05) (0.00012808,-3.1e-07) (-0.00135942,-8.3e-07) (-0.00050506,8.613e-05) (-0.12563,-0.00126141) (0,0) (0,0) (0,0) (0,0) (0,0) (0.5,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (0,0) (5.9e-06,8.3e-07) (0.00138565,-0.00010973) (0.131551,0.00062947) (4.29221,4.07411) (0.5,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (1e+20,1e+20) (-0.00108439,-0.00012295) (0,0) (3.19317,3.55927) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (0,0) (-0.00050333,3.1e-07) (5.9e-06,8.3e-07) (0.0001466,6.29e-05) (-0.131551,-0.00062947) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0.00100481,-4e-07) (0,0) (0.0311609,0.00024056) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (0,0) (-0.00064738,3e-08) (-0.00026515,-0.0001256) (0.132939,0.00125796) (3.37603,4.06782) (-0.00106953,7.6e-07) (-0.00135281,-9.732e-05) (-0.123812,-0.00059244) (2.94443,2.79482) (0,0) (0,0) (0,0) (0,0) (0,0) (-0.00050013,-0.00012351) (1e+20,1e+20) (1.84474,3.54004) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (0,0) (9.772e-05,0) (-0.00064738,3e-08) (-0.00638177,6.27e-05) (-0.132939,-0.00125796) (-0.00044777,9e-08) (-0.00106953,7.6e-07) (-0.00777332,4.312e-05) (0.123812,0.00059244) (0,0) (0,0) (0,0) (0,0) (0,0) (0.00019554,-1.1e-07) (0,0) (0.0117707,0.00027682) (0,0) (0,0) (0,0) (0,0)
(0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0,0) (0.5,0) (0,0) (0,0) (0,0) (0.00157357,-6.5e-07) (-0.00135281,-9.732e-05) (0.106189,0.00050811) (2.94443,2.79482) (0,0) (0,0) (0,0) (0,0) (1e+20,1e+20) (0.00069291,-0.00011075) (0,0) (3.65152,4.07018)
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(559.117,673.686)
(2.67104,0.0252753)
(-12.7623,-0.0610671)
(-12.7623,-0.0610671)
(231.594,279.05)
(7.81991,0.0739976)
(21.1439,0.101173)
(21.1439,0.101173)
(899.968,1029.8)
(-23.0853,-0.178218)
(13.8197,0.0729243)
(13.8197,0.0729243)
(569.809,635.139)
(8.71354,0.0672685)
(-0.807101,-0.00623082)
(-0.807101,-0.00623082)
(0,0)
(0,0)
(12.3812,0.0592438)
(12.3812,0.0592438)
(0,0)
(0,0)
(-11.5038,-0.0550452)
(-11.5038,-0.0550452)
(1.56546e-16,-8.48356e-18)
(-1.55778e-17,-1.02004e-18)
(54620.7,54007)
(-522.627,940.18)
(47233.7,22653.3)
(174133,198381)
(-10668.3,9850)
(-1248.97,-43.9305)
(49122.2,47145.1)
(-80005.4,-52797.6)
(6906.72,-12481.2)
(-569.706,403.242)
(52814.2,32728.2)
(227838,248521)
(128718,149736)
(-2714.91,-889.217)
(-3.91875e-17,-3.83846e-18)
(185.826,131.33)
(1.81417e-16,3.26206e-18)
(-4471.34,118.032)
(-3.59122e-16,1.92743e-17)
(-85.6079,245.052)
(-2.40525e-16,4.58839e-17)
(1334.04,-128.885)
(6.16402e-18,5.72847e-19)
(1.34816e-20,-1.32288e-20)
(0,0)
(0,0)
(0,0)
(0,0)
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(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(0,0)
(6.22024e-20,-6.161e-20)
(0,0)
(0,0)
(0,0)
(-5.77941e-20,5.72436e-20)
(0,0)
(1.56546e-16,-8.48356e-18)
(-1.55778e-17,-1.02004e-18)
(54620.7,54007)
(-522.627,940.18)
(47233.7,22653.3)
(174133,198381)
(-10668.3,9850)
(-1248.97,-43.9305)
(49122.2,47145.1)
(-80005.4,-52797.6)
(6906.72,-12481.2)
(-569.706,403.242)
(52814.2,32728.2)
(227838,248521)
(128718,149736)
(-2714.91,-889.217)
(-3.91875e-17,-3.83846e-18)
(185.826,131.33)
(1.81417e-16,3.26206e-18)
(-4471.34,118.032)
(-3.59122e-16,1.92743e-17)
(-85.6079,245.052)
(-2.40525e-16,4.58839e-17)
(1334.04,-128.885)
你的矩阵显然是不可逆的，除非你能保证
BSparseQRstd::cout << (A.transpose()*(A*x-b)).norm() / (A.transpose()*b) << "\n";
std:：cout在矩阵求解过程中，我在第一篇文章中将A矩阵更改为更新后的矩阵（通过在某些对角线位置添加大量数字，很抱歉之前没有提到这一点）。但SparseQR解算器似乎与稠密解算器给出了不同的结果。SparseLU解算器似乎运行良好，并与稠密解算器获得一致的结果。@Kevin您使用的是哪种Eigen版本？今年SparseQR中有一个针对复杂矩阵的错误修复程序：@chtz我几天前刚从网站上下载，所以它应该是最新版本。您的大数字太大，wrt数值精度为双精度（1e-16）。因此，您的初始条目被视为零。。。如果要修正某些条目，请将固定的X移动到方程的右侧，并以最小二乘法求解剩余的未知数（这是QR在默认情况下所做的）。