Chromatic Adaptation

The chromatic adaptation algorithms on this web site may all be implemented as a linear transformation of a source color (XS, YS, ZS) into a destination color (XD, YD, ZD) by a linear transformation [M] which is dependent on the source reference white (XWS, YWS, ZWS) and the destination reference white (XWD, YWD, ZWD):

Equation 1

The idea behind all of these algorithms is to follow three steps:

  1. Transform from XYZ into a cone response domain, (ρ, γ, β).
  2. Scale the vector components by factors dependent upon both the source and destination reference whites.
  3. Transform from (ρ, γ, β) back to XYZ using the inverse transform of step 1.

These steps are represented by the three matrices shown here on the right:

Equation 2

Three methods are presented here: XYZ Scaling, Bradford and Von Kries. The differences among the three methods lie in the definition of the cone response domains, [MA].

Method [MA] [MA]-1
XYZ Scaling 
 1.0       0.0       0.0     
 0.0       1.0       0.0     
 0.0       0.0       1.0     
 1.0       0.0       0.0     
 0.0       1.0       0.0     
 0.0       0.0       1.0
Bradford 
 0.8951   -0.7502    0.0389  
 0.2664    1.7135   -0.0685  
-0.1614    0.0367    1.0296
 
 0.986993  0.432305 -0.008529
-0.147054  0.518360  0.040043
 0.159963  0.049291  0.968487
Von Kries 
 0.40024  -0.22630   0.00000 
 0.70760   1.16532   0.00000 
-0.08081   0.04570   0.91822
 
 1.859936  0.361191  0.000000
-1.129382  0.638812  0.000000
 0.219897 -0.000006  1.089064

XYZ Scaling is generally considered to be an inferior chromatic adaptation algorithm. Incidentally, this is the method that would result from transforming the source XYZ color to Lab using (XWS, YWS, ZWS) followed by conversion back to XYZ using (XWD, YWD, ZWD).

The Bradford method is the newest of the three methods, and is considered by most experts to be the best of them. This is the method used in Adobe Photoshop. A related article comparing the chromatic adaptation algorithms may be found here.

If you are interested in an implementation of chromatic adaptation, see the Chromatic Adaptation Calculator.

Some Common Chromatic Adaptation Matrices

I have done the math for you for many of the common chromatic adaptation mappings. Below are some precomputed matrices for [M]. In these calculations, the following reference illuminant tristimulus values were used (all come from ASTM E308-01 except B which comes from Wyszecki & Stiles, p. 769):

Illuminant X Y Z
A 1.09850 1.00000 0.35585
B 0.99072 1.00000 0.85223
C 0.98074 1.00000 1.18232
D50 0.96422 1.00000 0.82521
D55 0.95682 1.00000 0.92149
D65 0.95047 1.00000 1.08883
D75 0.94972 1.00000 1.22638
E 1.00000 1.00000 1.00000
F2 0.99186 1.00000 0.67393
F7 0.95041 1.00000 1.08747
F11 1.00962 1.00000 0.64350

Here are the adaptation matrices:

From To Adaptation Method
Bradford Von Kries XYZ Scaling
A B 
  0.890516 -0.097152  0.053897
 -0.082913  1.075426 -0.090856
  0.268095  0.087946  2.483856
 
  0.957488 -0.018054  0.000000
 -0.164362  1.018537  0.000000
  0.290235  0.003638  2.394914
 
  0.901884  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  2.394914
C 
  0.853016 -0.123879  0.091190
 -0.113026  1.085343 -0.155366
  0.440436  0.142579  3.477626
 
  0.941828 -0.024705  0.000000
 -0.224914  1.025367  0.000000
  0.480694  0.004976  3.322525
 
  0.892799  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  3.322524
D50 
  0.877953 -0.111737  0.050201
 -0.091528  1.092432 -0.083763
  0.256619  0.085178  2.399404
 
  0.953187 -0.019880  0.000000
 -0.180990  1.020412  0.000000
  0.275772  0.004007  2.318984
 
  0.877761  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  2.318983
D55 
  0.864446 -0.122289  0.060973
 -0.102133  1.098253 -0.102282
  0.307319  0.101394  2.688754
 
  0.947702 -0.022210  0.000000
 -0.202199  1.022804  0.000000
  0.331510  0.004476  2.589547
 
  0.871024  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  2.589546
D65 
  0.844696 -0.136630  0.079849
 -0.117922  1.104122 -0.134900
  0.394812  0.129171  3.192402
 
  0.939499 -0.025694  0.000000
 -0.233916  1.026382  0.000000
  0.428117  0.005177  3.059802
 
  0.865244  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  3.059800
D75 
  0.831021 -0.145674  0.095469
 -0.129088  1.106031 -0.162007
  0.466299  0.151725  3.606898
 
  0.933669 -0.028170  0.000000
 -0.256454  1.028924  0.000000
  0.507341  0.005675  3.446341
 
  0.864561  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  3.446340
E 
  0.881596 -0.100676  0.070915
 -0.090818  1.070898 -0.120646
  0.343922  0.111545  2.930296
 
  0.953287 -0.019838  0.000000
 -0.180606  1.020370  0.000000
  0.374929  0.003996  2.810174
 
  0.910332  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  2.810173
F2 
  0.908339 -0.085326  0.033652
 -0.068371  1.072841 -0.055728
  0.175414  0.058700  1.946582
 
  0.965079 -0.014830  0.000000
 -0.135013  1.015226  0.000000
  0.187533  0.002990  1.893860
 
  0.902922  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.893860
F7 
  0.844793 -0.136582  0.079693
 -0.117839  1.104147 -0.134627
  0.394112  0.128952  3.188296
 
  0.939543 -0.025675  0.000000
 -0.233746  1.026363  0.000000
  0.427336  0.005173  3.055980
 
  0.865189  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  3.055979
F11 
  0.921434 -0.072522  0.030611
 -0.058765  1.060943 -0.050898
  0.157905  0.052613  1.856884
 
  0.969964 -0.012755  0.000000
 -0.116125  1.013096  0.000000
  0.169280  0.002571  1.808347
 
  0.919090  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.808346
B A 
  1.138972  0.104601 -0.020889
  0.077196  0.934180  0.032496
 -0.125668 -0.044367  0.403704
 
  1.047586  0.018569  0.000000
  0.169048  0.984795  0.000000
 -0.127212 -0.003746  0.417552
 
  1.108790  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.417552
C 
  0.950538 -0.030544  0.014970
 -0.025425  1.008976 -0.025091
  0.075623  0.024974  1.399365
 
  0.982470 -0.006841  0.000000
 -0.062279  1.005601  0.000000
  0.081745  0.001380  1.387325
 
  0.989927  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.387325
D50 
  0.985029 -0.014775 -0.001704
 -0.009391  1.014671  0.003596
 -0.002672 -0.000039  0.966056
 
  0.995185 -0.001879  0.000000
 -0.017103  1.001537  0.000000
 -0.005430  0.000380  0.968295
 
  0.973252  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.968295
D55 
  0.967477 -0.026523  0.002584
 -0.018692  1.019821 -0.003469
  0.019964  0.007575  1.082336
 
  0.989045 -0.004275  0.000000
 -0.038917  1.003499  0.000000
  0.018621  0.000863  1.081270
 
  0.965782  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.081269
D65 
  0.941504 -0.042824  0.010151
 -0.032124  1.025099 -0.016117
  0.058468  0.020331  1.284736
 
  0.979863 -0.007858  0.000000
 -0.071538  1.006433  0.000000
  0.060121  0.001585  1.277625
 
  0.959373  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.277625
D75 
  0.923266 -0.053396  0.016449
 -0.041287  1.026918 -0.026765
  0.089541  0.030487  1.451309
 
  0.973338 -0.010404  0.000000
 -0.094719  1.008519  0.000000
  0.094028  0.002099  1.439025
 
  0.958616  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.439025
E 
  0.987430 -0.004980  0.006942
 -0.005608  0.996265 -0.012008
  0.032084  0.010171  1.179413
 
  0.995298 -0.001835  0.000000
 -0.016708  1.001502  0.000000
  0.035959  0.000370  1.173393
 
  1.009367  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.173392
F2 
  1.023757  0.013810 -0.008161
  0.011949  0.997548  0.013794
 -0.040300 -0.013178  0.784086
 
  1.008496  0.003316  0.000000
  0.030185  0.997284  0.000000
 -0.043959 -0.000668  0.790784
 
  1.001151  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.790784
F7 
  0.941637 -0.042762  0.010087
 -0.032061  1.025119 -0.016008
  0.058169  0.020235  1.283086
 
  0.979912 -0.007839  0.000000
 -0.071364  1.006418  0.000000
  0.059789  0.001582  1.276029
 
  0.959312  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.276029
F11 
  1.040042  0.027276 -0.009247
  0.021365  0.987223  0.015156
 -0.049441 -0.016717  0.748043
 
  1.013965  0.005450  0.000000
  0.049612  0.995537  0.000000
 -0.052273 -0.001099  0.755078
 
  1.019077  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.755078
C A 
  1.204015  0.140745 -0.025284
  0.102953  0.928026  0.038761
 -0.156707 -0.055874  0.289166
 
  1.067910  0.025730  0.000000
  0.234244  0.980902  0.000000
 -0.154854 -0.005191  0.300976
 
  1.120073  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.300976
B 
  1.053746  0.032164 -0.010697
  0.025127  0.991430  0.017508
 -0.057394 -0.019432  0.714876
 
  1.018282  0.006927  0.000000
  0.063063  0.994857  0.000000
 -0.060063 -0.001397  0.720812
 
  1.010176  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.720812
D50 
  1.037698  0.017067 -0.012013
  0.015394  1.005603  0.020436
 -0.058262 -0.018897  0.690638
 
  1.013261  0.005025  0.000000
  0.045745  0.996269  0.000000
 -0.063664 -0.001013  0.697958
 
  0.983156  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.697958
D55 
  1.018661  0.004772 -0.008966
  0.006127  1.010547  0.015575
 -0.040892 -0.012880  0.773655
 
  1.006857  0.002598  0.000000
  0.023656  0.998069  0.000000
 -0.045929 -0.000523  0.779392
 
  0.975610  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.779391
D65 
  0.990448 -0.012371 -0.003564
 -0.007168  1.015594  0.006770
 -0.011615 -0.002928  0.918157
 
  0.997281 -0.001030  0.000000
 -0.009376  1.000763  0.000000
 -0.015417  0.000209  0.920927
 
  0.969136  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.920927
D75 
  0.970603 -0.023562  0.000948
 -0.016167  1.017309 -0.000712
  0.011823  0.004904  1.037082
 
  0.990476 -0.003608  0.000000
 -0.032850  1.002677  0.000000
  0.009447  0.000729  1.037266
 
  0.968371  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.037266
E 
  1.039977  0.026688 -0.005686
  0.019812  0.987780  0.008918
 -0.033628 -0.011803  0.842969
 
  1.013378  0.005069  0.000000
  0.046145  0.996237  0.000000
 -0.033837 -0.001022  0.845795
 
  1.019638  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.845795
F2 
  1.079596  0.046779 -0.016543
  0.036865  0.989116  0.027198
 -0.087799 -0.029598  0.560725
 
  1.027143  0.010285  0.000000
  0.093629  0.992365  0.000000
 -0.092302 -0.002074  0.570007
 
  1.011338  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.570006
F7 
  0.990593 -0.012304 -0.003610
 -0.007108  1.015614  0.006848
 -0.011838 -0.003001  0.916979
 
  0.997332 -0.001011  0.000000
 -0.009200  1.000748  0.000000
 -0.015660  0.000205  0.919777
 
  0.969074  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.919776
F11 
  1.097156  0.060674 -0.017257
  0.046449  0.979156  0.027891
 -0.095451 -0.032700  0.534994
 
  1.032846  0.012445  0.000000
  0.113301  0.990761  0.000000
 -0.098650 -0.002510  0.544269
 
  1.029447  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.544269
D50 A 
  1.157371  0.119941 -0.020028
  0.087242  0.921944  0.030360
 -0.126879 -0.045557  0.417835
 
  1.053007  0.020515  0.000000
  0.186770  0.983633  0.000000
 -0.125546 -0.004139  0.431224
 
  1.139263  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.431224
B 
  1.015344  0.014785  0.001735
  0.009388  0.985677 -0.003652
  0.002809  0.000080  1.035142
 
  1.004870  0.001885  0.000000
  0.017159  0.998496  0.000000
  0.005628 -0.000380  1.032744
 
  1.027483  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.032743
C 
  0.964879 -0.016052  0.017257
 -0.016414  0.994147 -0.029702
  0.080949  0.025847  1.448580
 
  0.987137 -0.004979  0.000000
 -0.045327  1.003972  0.000000
  0.089975  0.001003  1.432751
 
  1.017133  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.432750
D55 
  0.982080 -0.011839  0.004451
 -0.009415  1.004938 -0.007348
  0.023382  0.007849  1.120378
 
  0.993789 -0.002404  0.000000
 -0.021887  1.001917  0.000000
  0.024812  0.000485  1.116674
 
  0.992325  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.116673
D65 
  0.955577 -0.028290  0.012298
 -0.023039  1.009941 -0.020483
  0.063164  0.021007  1.329910
 
  0.984500 -0.005999  0.000000
 -0.054616  1.004786  0.000000
  0.067632  0.001210  1.319459
 
  0.985740  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.319458
D75 
  0.936978 -0.038980  0.018824
 -0.032356  1.011597 -0.031528
  0.095278  0.031491  1.502354
 
  0.977900 -0.008554  0.000000
 -0.077875  1.006824  0.000000
  0.102621  0.001725  1.486143
 
  0.984962  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.486143
E 
  1.002553  0.009691  0.008918
  0.003624  0.981912 -0.016079
  0.035984  0.010594  1.220877
 
  1.000114  0.000044  0.000000
  0.000396  0.999965  0.000000
  0.042745 -0.000010  1.211813
 
  1.037108  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.211813
F2 
  1.039572  0.028748 -0.006722
  0.021535  0.983438  0.010656
 -0.038840 -0.013522  0.811618
 
  1.013465  0.005211  0.000000
  0.047445  0.995842  0.000000
 -0.039734 -0.001051  0.816677
 
  1.028666  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.816677
F7 
  0.955712 -0.028227  0.012232
 -0.022975  1.009962 -0.020370
  0.062855  0.020909  1.328202
 
  0.984550 -0.005980  0.000000
 -0.054441  1.004770  0.000000
  0.067289  0.001206  1.317810
 
  0.985678  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.317810
F11 
  1.056230  0.042261 -0.007866
  0.031003  0.973401  0.012120
 -0.048255 -0.017148  0.774305
 
  1.018997  0.007353  0.000000
  0.066937  0.994134  0.000000
 -0.048297 -0.001483  0.779802
 
  1.047085  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.779802
D55 A 
  1.180285  0.133425 -0.021690
  0.096858  0.918299  0.032736
 -0.138556 -0.049880  0.373164
 
  1.060096  0.023020  0.000000
  0.209570  0.982253  0.000000
 -0.136074 -0.004644  0.386168
 
  1.148074  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.386168
B 
  1.034185  0.026914 -0.002384
  0.018891  0.981032  0.003100
 -0.019207 -0.007363  0.923950
 
  1.011246  0.004308  0.000000
  0.039216  0.996679  0.000000
 -0.017447 -0.000869  0.924839
 
  1.035430  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.924839
C 
  0.982169 -0.004492  0.011472
 -0.006753  0.989339 -0.019995
  0.051802  0.016233  1.292840
 
  0.993250 -0.002586  0.000000
 -0.023543  1.001994  0.000000
  0.058515  0.000521  1.283053
 
  1.024999  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.283052
D50 
  1.018457  0.012029 -0.003968
  0.009387  0.995145  0.006490
 -0.021320 -0.007223  0.892594
 
  1.006303  0.002414  0.000000
  0.021981  0.998138  0.000000
 -0.022370 -0.000487  0.895517
 
  1.007734  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.895517
D65 
  0.972686 -0.016746  0.007002
 -0.013548  1.004910 -0.011637
  0.036173  0.012060  1.186955
 
  0.990574 -0.003611  0.000000
 -0.032874  1.002783  0.000000
  0.038570  0.000728  1.181598
 
  0.993363  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.181597
D75 
  0.953504 -0.027655  0.012832
 -0.022786  1.006525 -0.021448
  0.065302  0.021634  1.340818
 
  0.983876 -0.006177  0.000000
 -0.056234  1.004762  0.000000
  0.070062  0.001246  1.330867
 
  0.992580  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.330866
E 
  1.020958  0.021640  0.004045
  0.013250  0.977305 -0.007994
  0.010719  0.002158  1.089673
 
  1.006418  0.002458  0.000000
  0.022380  0.998105  0.000000
  0.015907 -0.000496  1.085199
 
  1.045129  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.085199
F2 
  1.059173  0.041162 -0.009938
  0.030937  0.978847  0.015808
 -0.056988 -0.019786  0.724512
 
  1.019968  0.007649  0.000000
  0.069634  0.994102  0.000000
 -0.058276 -0.001543  0.731348
 
  1.036621  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.731348
F7 
  0.972826 -0.016682  0.006943
 -0.013485  1.004930 -0.011536
  0.035895  0.011970  1.185431
 
  0.990624 -0.003592  0.000000
 -0.032698  1.002768  0.000000
  0.038262  0.000725  1.180122
 
  0.993301  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.180121
F11 
  1.076289  0.054819 -0.010937
  0.040454  0.968961  0.017013
 -0.065815 -0.023238  0.691220
 
  1.025582  0.009799  0.000000
  0.089211  0.992445  0.000000
 -0.066077 -0.001977  0.698326
 
  1.055183  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.698326
D65 A 
  1.216456  0.153332 -0.023947
  0.110991  0.915231  0.035899
 -0.154932 -0.055995  0.314753
 
  1.071073  0.026813  0.000000
  0.244099  0.980405  0.000000
 -0.150274 -0.005410  0.326819
 
  1.155744  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.326819
B 
  1.064140  0.044610 -0.007849
  0.032578  0.976637  0.011995
 -0.048943 -0.017486  0.778538
 
  1.021133  0.007973  0.000000
  0.072581  0.994173  0.000000
 -0.048142 -0.001608  0.782703
 
  1.042347  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.782703
C 
  1.009778  0.012311  0.003828
  0.007042  0.984709 -0.007233
  0.012798  0.003296  1.089164
 
  1.002736  0.001032  0.000000
  0.009393  0.999246  0.000000
  0.016784 -0.000208  1.085863
 
  1.031847  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.085863
D50 
  1.047811  0.029542 -0.009235
  0.022887  0.990484  0.015044
 -0.050127 -0.017049  0.752132
 
  1.016080  0.006067  0.000000
  0.055229  0.995565  0.000000
 -0.052133 -0.001223  0.757887
 
  1.014467  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.757887
D55 
  1.028540  0.017211 -0.005900
  0.013503  0.995222  0.009678
 -0.031482 -0.010636  0.842574
 
  1.009636  0.003635  0.000000
  0.033097  0.997342  0.000000
 -0.032978 -0.000733  0.846312
 
  1.006681  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.846312
D75 
  0.979940 -0.011249  0.004919
 -0.009170  1.001553 -0.008196
  0.025245  0.008393  1.129562
 
  0.993152 -0.002584  0.000000
 -0.023521  1.001888  0.000000
  0.026890  0.000521  1.126329
 
  0.999211  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.126328
E 
  1.050262  0.039065 -0.002405
  0.027076  0.972950  0.002645
 -0.023252 -0.009258  0.918088
 
  1.016198  0.006111  0.000000
  0.055630  0.995534  0.000000
 -0.019743 -0.001233  0.918417
 
  1.052111  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.918417
F2 
  1.090271  0.059301 -0.014223
  0.044538  0.974535  0.022610
 -0.081691 -0.028378  0.610599
 
  1.030050  0.011337  0.000000
  0.103208  0.991714  0.000000
 -0.083007 -0.002287  0.618949
 
  1.043547  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.618949
F7 
  1.000147  0.000067 -0.000050
  0.000062  1.000020  0.000085
 -0.000240 -0.000078  0.998717
 
  1.000051  0.000019  0.000000
  0.000176  0.999985  0.000000
 -0.000263 -0.000004  0.998751
 
  0.999937  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.998751
F11 
  1.108091  0.073197 -0.015034
  0.054156  0.964848  0.023473
 -0.089768 -0.031612  0.582567
 
  1.035789  0.013502  0.000000
  0.122919  0.990132  0.000000
 -0.089808 -0.002724  0.591002
 
  1.062232  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.591001
D75 A 
  1.243577  0.167275 -0.025403
  0.120848  0.914851  0.037893
 -0.165852 -0.060109  0.278937
 
  1.079158  0.029545  0.000000
  0.268973  0.979251  0.000000
 -0.159308 -0.005961  0.290163
 
  1.156657  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.290163
B 
  1.086746  0.056841 -0.011269
  0.041923  0.975447  0.017514
 -0.067929 -0.023998  0.689361
 
  1.028425  0.010609  0.000000
  0.096588  0.992548  0.000000
 -0.067340 -0.002140  0.694915
 
  1.043171  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.694915
C 
  1.030696  0.023876 -0.000927
  0.016372  0.983360  0.000661
 -0.011827 -0.004922  0.964252
 
  1.009736  0.003634  0.000000
  0.033080  0.997448  0.000000
 -0.009220 -0.000733  0.964073
 
  1.032662  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.964073
D50 
  1.069973  0.041619 -0.012534
  0.032088  0.989138  0.020356
 -0.068528 -0.023374  0.665991
 
  1.023292  0.008694  0.000000
  0.079147  0.993893  0.000000
 -0.070752 -0.001753  0.672883
 
  1.015268  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.672883
D55 
  1.050114  0.029059 -0.009586
  0.022676  0.993802  0.015680
 -0.051509 -0.017450  0.746028
 
  1.016746  0.006250  0.000000
  0.056903  0.995609  0.000000
 -0.053579 -0.001260  0.751391
 
  1.007476  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.751390
D65 
  1.020690  0.011500 -0.004362
  0.009159  0.998491  0.007206
 -0.022879 -0.007676  0.885344
 
  1.006956  0.002597  0.000000
  0.023638  0.998175  0.000000
 -0.024051 -0.000523  0.887841
 
  1.000790  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.887841
E 
  1.072405  0.051103 -0.006429
  0.036487  0.971773  0.009234
 -0.044823 -0.016559  0.812857
 
  1.023412  0.008738  0.000000
  0.079551  0.993863  0.000000
 -0.041999 -0.001763  0.815408
 
  1.052942  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.815408
F2 
  1.113697  0.071859 -0.016921
  0.053868  0.973404  0.026845
 -0.097611 -0.033962  0.540742
 
  1.037483  0.013991  0.000000
  0.127369  0.990173  0.000000
 -0.098525 -0.002822  0.549528
 
  1.044371  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.549528
F7 
  1.020842  0.011570 -0.004406
  0.009220  0.998512  0.007280
 -0.023096 -0.007747  0.884208
 
  1.007009  0.002616  0.000000
  0.023816  0.998162  0.000000
 -0.024286 -0.000527  0.886732
 
  1.000727  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.886732
F11 
  1.132033  0.085945 -0.017617
  0.063576  0.963835  0.027498
 -0.105244 -0.037068  0.515936
 
  1.043314  0.016167  0.000000
  0.147179  0.988645  0.000000
 -0.104712 -0.003261  0.524715
 
  1.063071  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.524715
E A 
  1.154861  0.111004 -0.023379
  0.082316  0.937719  0.036616
 -0.138677 -0.048724  0.342613
 
  1.052880  0.020470  0.000000
  0.186359  0.983658  0.000000
 -0.140739 -0.004129  0.355850
 
  1.098500  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.355850
B 
  1.012951  0.005123 -0.005911
  0.005370  1.003671  0.010188
 -0.027601 -0.008795  0.847953
 
  1.004755  0.001841  0.000000
  0.016761  0.998529  0.000000
 -0.030797 -0.000371  0.852230
 
  0.990720  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.852230
C 
  0.962272 -0.025918  0.006765
 -0.019644  1.012771 -0.010847
  0.038113  0.013146  1.186403
 
  0.987027 -0.005022  0.000000
 -0.045720  1.004008  0.000000
  0.039432  0.001013  1.182320
 
  0.980740  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.182320
D50 
  0.997754 -0.009768 -0.007417
 -0.004163  1.018316  0.013442
 -0.029371 -0.008549  0.819186
 
  0.999886 -0.000044  0.000000
 -0.000397  1.000033  0.000000
 -0.035270  0.000010  0.825210
 
  0.964220  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.825210
D55 
  0.979793 -0.021687 -0.003797
 -0.013362  1.023500  0.007558
 -0.009611 -0.001814  0.917729
 
  0.993677 -0.002447  0.000000
 -0.022282  1.001952  0.000000
 -0.014576  0.000495  0.921490
 
  0.956820  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.921490
D65 
  0.953187 -0.038247  0.002606
 -0.026590  1.028840 -0.003033
  0.023874  0.009406  1.089257
 
  0.984391 -0.006042  0.000000
 -0.055009  1.004822  0.000000
  0.021087  0.001220  1.088830
 
  0.950470  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.088830
D75 
  0.934483 -0.049007  0.007947
 -0.035569  1.030712 -0.011990
  0.050806  0.018294  1.230423
 
  0.977792 -0.008597  0.000000
 -0.078266  1.006861  0.000000
  0.050193  0.001735  1.226380
 
  0.949720  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.226380
F2 
  1.037316  0.019178 -0.012830
  0.017080  1.001150  0.021788
 -0.062535 -0.020329  0.664972
 
  1.013348  0.005167  0.000000
  0.047044  0.995873  0.000000
 -0.068533 -0.001041  0.673930
 
  0.991860  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.673930
F7 
  0.953325 -0.038183  0.002552
 -0.026530  1.028860 -0.002941
  0.023616  0.009323  1.087858
 
  0.984440 -0.006023  0.000000
 -0.054834  1.004807  0.000000
  0.020802  0.001216  1.087470
 
  0.950410  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.087470
F11 
  1.053914  0.032786 -0.013710
  0.026525  0.990824  0.022783
 -0.070818 -0.023610  0.634427
 
  1.018879  0.007308  0.000000
  0.066534  0.994164  0.000000
 -0.075794 -0.001473  0.643500
 
  1.009620  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.643500
F2 A 
  1.110844  0.089259 -0.016649
  0.065492  0.935908  0.025662
 -0.102077 -0.036267  0.514448
 
  1.038307  0.015167  0.000000
  0.138081  0.987017  0.000000
 -0.103033 -0.003060  0.528022
 
  1.107515  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.528022
B 
  0.977360 -0.013394  0.010408
 -0.012398  1.002394 -0.017763
  0.050027  0.016159  1.275607
 
  0.991674 -0.003297  0.000000
 -0.030016  1.002822  0.000000
  0.055101  0.000665  1.264568
 
  0.998851  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.264568
C 
  0.930146 -0.043107  0.029532
 -0.038615  1.011327 -0.050194
  0.143607  0.046633  1.785382
 
  0.974495 -0.010099  0.000000
 -0.091944  1.008645  0.000000
  0.157466  0.002035  1.754367
 
  0.988789  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.754366
D50 
  0.962826 -0.028031  0.008341
 -0.021579  1.017284 -0.013534
  0.045718  0.015607  1.232281
 
  0.986955 -0.005165  0.000000
 -0.047023  1.004420  0.000000
  0.047958  0.001042  1.224475
 
  0.972133  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.224474
D55 
  0.946031 -0.039503  0.013837
 -0.031087  1.022457 -0.022735
  0.073564  0.024815  1.380709
 
  0.980938 -0.007548  0.000000
 -0.068714  1.006460  0.000000
  0.078019  0.001522  1.367338
 
  0.964672  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.367338
D65 
  0.921227 -0.055372  0.023508
 -0.044912  1.027724 -0.039102
  0.121163  0.040356  1.639065
 
  0.971940 -0.011111  0.000000
 -0.101151  1.009510  0.000000
  0.129972  0.002240  1.615643
 
  0.958270  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.615643
D75 
  0.903848 -0.065624  0.031540
 -0.054424  1.029497 -0.052812
  0.159740  0.052812  1.851690
 
  0.965546 -0.013643  0.000000
 -0.124202  1.011677  0.000000
  0.172473  0.002751  1.819745
 
  0.957514  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.819744
E 
  0.965483 -0.018104  0.019221
 -0.018434  0.998532 -0.033073
  0.090233  0.028823  1.504620
 
  0.987065 -0.005122  0.000000
 -0.046630  1.004384  0.000000
  0.100304  0.001032  1.483834
 
  1.008207  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.483834
F7 
  0.921353 -0.055313  0.023428
 -0.044846  1.027745 -0.038962
  0.120789  0.040238  1.636959
 
  0.971988 -0.011092  0.000000
 -0.100978  1.009494  0.000000
  0.129554  0.002237  1.613625
 
  0.958210  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.613625
F11 
  1.015695  0.013262 -0.001455
  0.009400  0.989546  0.002020
 -0.010692 -0.004007  0.953991
 
  1.005359  0.002122  0.000000
  0.019317  0.998183  0.000000
 -0.010199 -0.000428  0.954847
 
  1.017906  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.954847
F7 A 
  1.216262  0.153245 -0.023931
  0.110927  0.915207  0.035873
 -0.154831 -0.055959  0.315155
 
  1.071013  0.026792  0.000000
  0.243913  0.980414  0.000000
 -0.150180 -0.005406  0.327228
 
  1.155817  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.327227
B 
  1.063979  0.044537 -0.007810
  0.032516  0.976616  0.011929
 -0.048748 -0.017421  0.779538
 
  1.021079  0.007953  0.000000
  0.072402  0.994186  0.000000
 -0.047934 -0.001604  0.783682
 
  1.042413  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.783681
C 
  1.009630  0.012243  0.003882
  0.006979  0.984688 -0.007325
  0.013057  0.003380  1.090564
 
  1.002684  0.001012  0.000000
  0.009216  0.999260  0.000000
  0.017069 -0.000205  1.087221
 
  1.031913  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.087221
D50 
  1.047653  0.029470 -0.009197
  0.022826  0.990463  0.014980
 -0.049938 -0.016987  0.753097
 
  1.016027  0.006047  0.000000
  0.055050  0.995578  0.000000
 -0.051931 -0.001219  0.758835
 
  1.014531  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.758835
D55 
  1.028387  0.017141 -0.005858
  0.013442  0.995202  0.009607
 -0.031274 -0.010569  0.843656
 
  1.009584  0.003616  0.000000
  0.032919  0.997356  0.000000
 -0.032753 -0.000729  0.847371
 
  1.006744  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.847371
D65 
  0.999853 -0.000068  0.000049
 -0.000061  0.999979 -0.000085
  0.000241  0.000078  1.001285
 
  0.999948 -0.000020  0.000000
 -0.000178  1.000013  0.000000
  0.000263  0.000004  1.001251
 
  1.000063  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.001251
D75 
  0.979798 -0.011315  0.004975
 -0.009233  1.001532 -0.008292
  0.025512  0.008479  1.131014
 
  0.993101 -0.002603  0.000000
 -0.023697  1.001902  0.000000
  0.027184  0.000525  1.127737
 
  0.999274  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.127737
E 
  1.050104  0.038993 -0.002359
  0.027013  0.972928  0.002567
 -0.023027 -0.009185  0.919267
 
  1.016145  0.006091  0.000000
  0.055451  0.995547  0.000000
 -0.019501 -0.001229  0.919566
 
  1.052177  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.919566
F2 
  1.090103  0.059225 -0.014192
  0.044477  0.974514  0.022559
 -0.081530 -0.028325  0.611382
 
  1.029995  0.011317  0.000000
  0.103027  0.991726  0.000000
 -0.082839 -0.002283  0.619723
 
  1.043613  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.619723
F11 
  1.107920  0.073119 -0.015005
  0.054094  0.964826  0.023424
 -0.089613 -0.031560  0.583314
 
  1.035733  0.013482  0.000000
  0.122737  0.990144  0.000000
 -0.089648 -0.002720  0.591741
 
  1.062299  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.591740
F11 A 
  1.092812  0.075492 -0.015946
  0.055997  0.945146  0.024984
 -0.094516 -0.033200  0.539185
 
  1.032522  0.013000  0.000000
  0.118350  0.988562  0.000000
 -0.096824 -0.002622  0.552992
 
  1.088033  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  0.552991
B 
  0.962633 -0.026386  0.012433
 -0.021802  1.013191 -0.020797
  0.063137  0.020898  1.337180
 
  0.986491 -0.005400  0.000000
 -0.049163  1.004751  0.000000
  0.068221  0.001089  1.324367
 
  0.981280  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.324367
C 
  0.916631 -0.055715  0.032471
 -0.048057  1.022433 -0.054852
  0.160605  0.052552  1.871622
 
  0.969534 -0.012179  0.000000
 -0.110875  1.010716  0.000000
  0.175218  0.002455  1.837328
 
  0.971395  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.837327
D50 
  0.948436 -0.040997  0.010276
 -0.030934  1.028379 -0.016411
  0.058423  0.020220  1.291758
 
  0.981834 -0.007262  0.000000
 -0.066110  1.006388  0.000000
  0.060683  0.001465  1.282378
 
  0.955033  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.282378
D55 
  0.932066 -0.052347  0.016036
 -0.040447  1.033695 -0.026081
  0.087388  0.029767  1.447368
 
  0.975894 -0.009636  0.000000
 -0.087725  1.008477  0.000000
  0.092093  0.001944  1.431997
 
  0.947703  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.431997
D65 
  0.907897 -0.068019  0.026170
 -0.054290  1.039133 -0.043270
  0.136954  0.045905  1.718226
 
  0.967012 -0.013187  0.000000
 -0.120050  1.011602  0.000000
  0.146393  0.002659  1.692044
 
  0.941414  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.692044
D75 
  0.890969 -0.078118  0.034584
 -0.063823  1.040995 -0.057660
  0.177162  0.058856  1.941140
 
  0.960700 -0.015710  0.000000
 -0.143021  1.013822  0.000000
  0.190827  0.003167  1.905797
 
  0.940671  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.905796
E 
  0.951079 -0.030955  0.021663
 -0.027877  1.009304 -0.036847
  0.105128  0.034106  1.577274
 
  0.981942 -0.007219  0.000000
 -0.065718  1.006351  0.000000
  0.115506  0.001455  1.554002
 
  0.990472  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.554002
F2 
  0.984686 -0.013191  0.001528
 -0.009375  1.010680 -0.002154
  0.010998  0.004097  1.048237
 
  0.994710 -0.002115  0.000000
 -0.019251  1.001859  0.000000
  0.010616  0.000427  1.047289
 
  0.982409  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.047288
F7 
  0.908020 -0.067961  0.026085
 -0.054224  1.039154 -0.043124
  0.136565  0.045781  1.716018
 
  0.967060 -0.013168  0.000000
 -0.119877  1.011585  0.000000
  0.145956  0.002655  1.689931
 
  0.941354  0.000000  0.000000
  0.000000  1.000000  0.000000
  0.000000  0.000000  1.689930