matrixtest.ref

GPSTK:做gpS的人都应当知道这个东西

      0.488      1.345      3.000      0.831     -0.320
     -0.009      6.205     -0.948      4.000      1.920
 ATA Matrix(5,5) :
      6.026      6.322      6.101     22.711     -2.183
      6.322     46.120      3.602     48.170      9.461
      6.101      3.602     18.569     17.404     -4.586
     22.711     48.170     17.404    103.080     -0.379
     -2.183      9.461     -4.586     -0.379      4.495
Condition number is 137.365/8.060e-16 = 170417882939630016.000
Inverse matrix (5,5) :
 569690437243218.375 -153491934607408.938 63711765288702.539 -62123530101840.875 659602886497507.750
 -153491934607410.125 41355396631781.578 -17165887773611.408 16737968897838.145 -177717083704378.906
 63711765288703.070 -17165887773611.418 7125253946416.606 -6947632450892.240 73767192743556.812
 -62123530101840.398 16737968897837.887 -6947632450892.129 6774438782911.870 -71928291394319.719
 659602886497510.875 -177717083704378.375 73767192743556.547 -71928291394320.609 763705934719958.250
Unity matrix (5,5) ? :
  1.337524414  1.358398438  0.705810547  1.383651733  0.194580078
 -0.167602539  0.597290039 -0.252258301 -0.103622437  0.016662598
  0.041564941  0.117553711  1.005187988 -0.043363571  0.007507324
  0.024551392 -0.108520508  0.027740479  1.060203552 -0.056213379
  0.194580078  1.710449219  0.536376953  0.343444824  1.187255859

File ./data/ut.dat (0) Matrix(4,4) :
      1.834      2.837      3.223      4.808
      0.000      5.837      6.774      7.083
      0.000      0.000      8.237      9.118
      0.000      0.000      0.000     10.838
Condition number is 19.305/4.345e+00 = 4.443
Inverse matrix (4,4) :
      0.545     -0.265      0.005     -0.073
      0.000      0.171     -0.141      0.007
      0.000      0.000      0.121     -0.102
      0.000      0.000      0.000      0.092
Unity matrix (4,4) ? :
  1.000000000 -0.000000000 -0.000000000 -0.000000000
  0.000000000  1.000000000  0.000000000 -0.000000000
  0.000000000  0.000000000  1.000000000  0.000000000
  0.000000000  0.000000000  0.000000000  1.000000000


 -------------- Matrix Test 4 ---------------------------------
Matrix A(7,7) :
   8.317   0.212   5.740   4.317  -1.109   0.174   1.960
   6.212   3.292   1.574   1.028   7.438   5.408   6.592
   2.574   1.574   1.911   1.039   7.236  -9.503   9.440
   5.317   1.028   1.390   7.126   6.783  -6.527   4.428
   2.080   3.370   8.544   4.512   0.356  -6.589  -4.531
  -9.133  -2.077   8.930   8.538  -9.509  -6.375   5.084
  -2.755  -2.739   9.216   5.226  -0.109  -7.239   4.296
Vector b(7) :
  14.289   9.284  -1.128   8.389  -6.929   4.664   7.590

Now solve using SVD
Singular Values (7) :
  26.619  21.861  12.423  10.365   5.533   4.560   3.420
Matrix U(7,7) :
   0.203   0.207  -0.573   0.370  -0.368   0.556   0.073
  -0.006   0.525  -0.066   0.603   0.476  -0.355   0.063
   0.369   0.447   0.525  -0.221   0.127   0.419   0.384
   0.335   0.434   0.016  -0.184  -0.601  -0.518  -0.191
   0.342   0.002  -0.603  -0.511   0.401  -0.176   0.260
   0.578  -0.536   0.153   0.393  -0.100  -0.230   0.371
   0.509  -0.079   0.068   0.037   0.301   0.190  -0.776
Matrix V(7,7) :
  -0.060   0.620  -0.530   0.050  -0.371   0.430   0.078
  -0.019   0.195  -0.163  -0.107   0.326  -0.342   0.837
   0.567  -0.092  -0.445   0.181   0.605   0.198  -0.184
   0.480   0.001  -0.236   0.186  -0.492  -0.655  -0.088
  -0.029   0.684   0.191  -0.260   0.335  -0.357  -0.432
  -0.575  -0.011  -0.245   0.697   0.188  -0.258  -0.148
   0.334   0.318   0.585   0.605  -0.015   0.188   0.208
Difference (7,7) :
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
Determinant of A = 6.466e+06 -- Compare to 6.466e+06
Solution via backsubstitution (7) :
   0.898  -2.119   0.214   1.096   0.064   0.849   0.631
Solution residuals (7) :
 5.329e-15 -7.105e-15 7.994e-15 5.329e-15 -1.776e-15 8.882e-16 0.000e+00

Sort in ascending order
Singular Values (7) :
   3.420   4.560   5.533  10.365  12.423  21.861  26.619
Matrix U(7,7) :
   0.073   0.556  -0.368   0.370  -0.573   0.207   0.203
   0.063  -0.355   0.476   0.603  -0.066   0.525  -0.006
   0.384   0.419   0.127  -0.221   0.525   0.447   0.369
  -0.191  -0.518  -0.601  -0.184   0.016   0.434   0.335
   0.260  -0.176   0.401  -0.511  -0.603   0.002   0.342
   0.371  -0.230  -0.100   0.393   0.153  -0.536   0.578
  -0.776   0.190   0.301   0.037   0.068  -0.079   0.509
Matrix V(7,7) :
   0.078   0.430  -0.371   0.050  -0.530   0.620  -0.060
   0.837  -0.342   0.326  -0.107  -0.163   0.195  -0.019
  -0.184   0.198   0.605   0.181  -0.445  -0.092   0.567
  -0.088  -0.655  -0.492   0.186  -0.236   0.001   0.480
  -0.432  -0.357   0.335  -0.260   0.191   0.684  -0.029
  -0.148  -0.258   0.188   0.697  -0.245  -0.011  -0.575
   0.208   0.188  -0.015   0.605   0.585   0.318   0.334


Now reduce A by one column and repeat
Matrix A(7,6) :
   8.317   0.212   5.740   4.317  -1.109   0.174
   6.212   3.292   1.574   1.028   7.438   5.408
   2.574   1.574   1.911   1.039   7.236  -9.503
   5.317   1.028   1.390   7.126   6.783  -6.527
   2.080   3.370   8.544   4.512   0.356  -6.589
  -9.133  -2.077   8.930   8.538  -9.509  -6.375
  -2.755  -2.739   9.216   5.226  -0.109  -7.239
Singular Values (6) :
  25.574  20.763  11.481   5.543   5.272   3.877
Matrix U(7,7) :
  -0.167   0.282  -0.672   0.423   0.354  -0.255  -0.267
   0.161   0.441  -0.395  -0.571  -0.474   0.086  -0.258
  -0.216   0.433   0.570  -0.092   0.286  -0.014  -0.593
  -0.238   0.512   0.172   0.530  -0.521   0.124   0.289
  -0.416   0.238  -0.140  -0.311   0.430   0.530   0.434
  -0.643  -0.468  -0.131   0.041  -0.323   0.287  -0.402
  -0.506   0.020   0.053  -0.328  -0.088  -0.741   0.277
Matrix V(6,6) :
   0.164   0.657  -0.427   0.440   0.391  -0.114
   0.048   0.214  -0.062  -0.293   0.150   0.916
  -0.603   0.091  -0.437  -0.581   0.207  -0.239
  -0.488   0.142  -0.257   0.388  -0.692   0.212
   0.165   0.679   0.373  -0.406  -0.406  -0.205
   0.585  -0.181  -0.646  -0.259  -0.371  -0.054
Difference (7,6) :
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00
  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00  0.000e+00

 -------------- Matrix Test 5 ---------------------------------
Matrix A(7,7) :
   8.317   0.212   5.740   4.317  -1.109   0.174   1.960
   6.212   3.292   1.574   1.028   7.438   5.408