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
 1.0000000  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
 1.0000000  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
Bradford
 0.8951000  0.2664000 -0.1614000
-0.7502000 1.7135000 0.0367000
0.0389000 -0.0685000 1.0296000
 0.9869929 -0.1470543  0.1599627
0.4323053 0.5183603 0.0492912
-0.0085287 0.0400428 0.9684867
Von Kries
 0.4002400  0.7076000 -0.0808100
-0.2263000 1.1653200 0.0457000
0.0000000 0.0000000 0.9182200
 1.8599364 -1.1293816  0.2198974
0.3611914 0.6388125 -0.0000064
0.0000000 0.0000000 1.0890636

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
XYZ Scaling Bradford Von Kries
A B
 0.9018844  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 2.3949136
 0.8905163 -0.0829136  0.2680945
-0.0971524 1.0754262 0.0879463
0.0538970 -0.0908558 2.4838553
 0.9574884 -0.1643613  0.2902356
-0.0180539 1.0185379 0.0036373
0.0000000 0.0000000 2.3949136
C
 0.8927993  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 3.3225235
 0.8530161 -0.1130268  0.4404346
-0.1238786 1.0853435 0.1425803
0.0911907 -0.1553658 3.4776250
 0.9418277 -0.2249131  0.4806950
-0.0247051 1.0253682 0.0049749
0.0000000 0.0000000 3.3225235
D50
 0.8777606  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 2.3189827
 0.8779529 -0.0915288  0.2566181
-0.1117372 1.0924325 0.0851788
0.0502012 -0.0837636 2.3994031
 0.9531871 -0.1809896  0.2757725
-0.0198804 1.0204129 0.0040065
0.0000000 0.0000000 2.3189827
D55
 0.8710241  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 2.5895462
 0.8644459 -0.1021330  0.3073182
-0.1222890 1.0982532 0.1013945
0.0609732 -0.1022820 2.6887535
 0.9477017 -0.2021983  0.3315105
-0.0222101 1.0228052 0.0044754
0.0000000 0.0000000 2.5895462
D65
 0.8652435  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 3.0598005
 0.8446965 -0.1179225  0.3948108
-0.1366303 1.1041226 0.1291718
0.0798489 -0.1348999 3.1924009
 0.9394987 -0.2339150  0.4281177
-0.0256939 1.0263828 0.0051761
0.0000000 0.0000000 3.0598005
D75
 0.8645608  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 3.4463397
 0.8310208 -0.1290882  0.4662974
-0.1456744 1.1060318 0.1517254
0.0954696 -0.1620076 3.6068968
 0.9336695 -0.2564537  0.5073423
-0.0281696 1.0289253 0.0056737
0.0000000 0.0000000 3.4463397
E
 0.9103323  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 2.8101728
 0.8815963 -0.0908179  0.3439213
-0.1006757 1.0708986 0.1115462
0.0709158 -0.1206464 2.9302950
 0.9532875 -0.1806053  0.3749305
-0.0198382 1.0203706 0.0039951
0.0000000 0.0000000 2.8101728
F2
 0.9029222  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.8938598
 0.9083396 -0.0683719  0.1754134
-0.0853260 1.0728419 0.0587007
0.0336526 -0.0557284 1.9465816
 0.9650788 -0.1350128  0.1875333
-0.0148302 1.0152272 0.0029893
0.0000000 0.0000000 1.8938598
F7
 0.8651889  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 3.0559786
 0.8447932 -0.1178395  0.3941104
-0.1365823 1.1041477 0.1289531
0.0796929 -0.1346275 3.1882950
 0.9395426 -0.2337454  0.4273371
-0.0256753 1.0263637 0.0051723
0.0000000 0.0000000 3.0559786
F11
 0.9190897  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.8083462
 0.9214338 -0.0587653  0.1579041
-0.0725224 1.0609434 0.0526133
0.0306110 -0.0508982 1.8568836
 0.9699644 -0.1161244  0.1692805
-0.0127554 1.0130970 0.0025709
0.0000000 0.0000000 1.8083462
B A
 1.1087896  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.4175516
 1.1389718  0.0771960 -0.1256680
0.1046012 0.9341802 -0.0443668
-0.0208883 0.0324959 0.4037039
 1.0475866  0.1690489 -0.1272120
0.0185688 0.9847959 -0.0037460
0.0000000 0.0000000 0.4175516
C
 0.9899265  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3873250
 0.9505386 -0.0254257  0.0756230
-0.0305443 1.0089768 0.0249746
0.0149704 -0.0250917 1.3993642
 0.9824697 -0.0622785  0.0817457
-0.0068409 1.0056021 0.0013790
0.0000000 0.0000000 1.3873250
D50
 0.9732518  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9682949
 0.9850292 -0.0093910 -0.0026720
-0.0147751 1.0146711 -0.0000389
-0.0017035 0.0035957 0.9660561
 0.9951852 -0.0171026 -0.0054296
-0.0018786 1.0015377 0.0003795
0.0000000 0.0000000 0.9682949
D55
 0.9657825  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0812691
 0.9674769 -0.0186924  0.0199637
-0.0265230 1.0198211 0.0075752
0.0025844 -0.0034696 1.0823359
 0.9890450 -0.0389162  0.0186211
-0.0042747 1.0034998 0.0008627
0.0000000 0.0000000 1.0812691
D65
 0.9593730  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2776246
 0.9415037 -0.0321240  0.0584672
-0.0428238 1.0250998 0.0203309
0.0101511 -0.0161170 1.2847354
 0.9798627 -0.0715373  0.0601219
-0.0078579 1.0064341 0.0015850
0.0000000 0.0000000 1.2776246
D75
 0.9586160  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.4390247
 0.9232662 -0.0412875  0.0895406
-0.0533960 1.0269180 0.0304876
0.0164490 -0.0267652 1.4513087
 0.9733376 -0.0947188  0.0940283
-0.0104042 1.0085195 0.0020982
0.0000000 0.0000000 1.4390247
E
 1.0093669  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1733922
 0.9874297 -0.0056086  0.0320832
-0.0049796 0.9962653 0.0101710
0.0069424 -0.0120086 1.1794125
 0.9952976 -0.0167072  0.0359597
-0.0018352 1.0015032 0.0003695
0.0000000 0.0000000 1.1733922
F2
 1.0011507  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7907842
 1.0237573  0.0119487 -0.0403007
0.0138105 0.9975484 -0.0131781
-0.0081608 0.0137933 0.7840861
 1.0084966  0.0301855 -0.0439590
0.0033157 0.9972846 -0.0006683
0.0000000 0.0000000 0.7907842
F7
 0.9593124  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2760288
 0.9416371 -0.0320617  0.0581686
-0.0427619 1.0251198 0.0202354
0.0100877 -0.0160079 1.2830854
 0.9799118 -0.0713629  0.0597898
-0.0078387 1.0064184 0.0015812
0.0000000 0.0000000 1.2760288
F11
 1.0190770  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7550779
 1.0400419  0.0213649 -0.0494410
0.0272759 0.9872237 -0.0167167
-0.0092461 0.0151560 0.7480426
 1.0139654  0.0496126 -0.0522728
0.0054496 0.9955375 -0.0010989
0.0000000 0.0000000 0.7550779
C A
 1.1200726  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.3009760
 1.2040146  0.1029527 -0.1567072
0.1407450 0.9280261 -0.0558735
-0.0252839 0.0387607 0.2891656
 1.0679098  0.2342445 -0.1548534
0.0257301 0.9809032 -0.0051913
0.0000000 0.0000000 0.3009760
B
 1.0101760  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7208116
 1.0537465  0.0251266 -0.0573939
0.0321644 0.9914304 -0.0194323
-0.0106963 0.0175083 0.7148758
 1.0182822  0.0630638 -0.0600632
0.0069271 0.9948581 -0.0013971
0.0000000 0.0000000 0.7208116
D50
 0.9831556  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6979583
 1.0376976  0.0153932 -0.0582624
0.0170675 1.0056038 -0.0188973
-0.0120126 0.0204361 0.6906380
 1.0132609  0.0457455 -0.0636638
0.0050248 0.9962695 -0.0010128
0.0000000 0.0000000 0.6979583
D55
 0.9756103  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7793914
 1.0186606  0.0061268 -0.0408925
0.0047723 1.0105478 -0.0128799
-0.0089652 0.0155750 0.7736548
 1.0068573  0.0236569 -0.0459285
0.0025985 0.9980703 -0.0005234
0.0000000 0.0000000 0.7793914
D65
 0.9691356  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9209267
 0.9904476 -0.0071683 -0.0116156
-0.0123712 1.0155950 -0.0029282
-0.0035635 0.0067697 0.9181569
 0.9972812 -0.0093756 -0.0154171
-0.0010298 1.0007636 0.0002084
0.0000000 0.0000000 0.9209267
D75
 0.9683708  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0372657
 0.9706028 -0.0161674  0.0118229
-0.0235618 1.0173098 0.0049041
0.0009486 -0.0007126 1.0370815
 0.9904762 -0.0328494  0.0094473
-0.0036083 1.0026776 0.0007284
0.0000000 0.0000000 1.0372657
E
 1.0196382  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8457947
 1.0399770  0.0198119 -0.0336279
0.0266883 0.9877806 -0.0118030
-0.0056861 0.0089182 0.8429683
 1.0133781  0.0461460 -0.0338372
0.0050688 0.9962378 -0.0010226
0.0000000 0.0000000 0.8457947
F2
 1.0113384  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5700064
 1.0795960  0.0368643 -0.0877996
0.0467792 0.9891161 -0.0295981
-0.0165425 0.0271981 0.5607245
 1.0271432  0.0936299 -0.0923019
0.0102846 0.9923658 -0.0020741
0.0000000 0.0000000 0.5700064
F7
 0.9690744  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9197764
 0.9905934 -0.0071084 -0.0118379
-0.0123043 1.0156147 -0.0030004
-0.0036092 0.0068474 0.9169788
 0.9973324 -0.0091990 -0.0156597
-0.0010104 1.0007492 0.0002045
0.0000000 0.0000000 0.9197764
F11
 1.0294472  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5442689
 1.0971565  0.0464489 -0.0954514
0.0606741 0.9791562 -0.0326999
-0.0172568 0.0278907 0.5349937
 1.0328466  0.1133021 -0.0986501
0.0124454 0.9907622 -0.0025103
0.0000000 0.0000000 0.5442689
D50 A
 1.1392628  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.4312236
 1.1573713  0.0872411 -0.1268788
0.1199410 0.9219445 -0.0455568
-0.0200278 0.0303599 0.4178345
 1.0530074  0.1867709 -0.1255459
0.0205155 0.9836342 -0.0041391
0.0000000 0.0000000 0.4312236
B
 1.0274834  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0327432
 1.0153440  0.0093873  0.0028087
0.0147849 0.9856776 0.0000806
0.0017354 -0.0036522 1.0351412
 1.0048705  0.0171595  0.0056280
0.0018849 0.9984968 -0.0003808
0.0000000 0.0000000 1.0327432
C
 1.0171330  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.4327505
 0.9648789 -0.0164148  0.0809482
-0.0160520 0.9941478 0.0258478
0.0172576 -0.0297025 1.4485796
 0.9871374 -0.0453262  0.0899753
-0.0049788 1.0039731 0.0010028
0.0000000 0.0000000 1.4327505
D55
 0.9923254  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1166733
 0.9820801 -0.0094156  0.0233811
-0.0118389 1.0049382 0.0078491
0.0044511 -0.0073485 1.1203775
 0.9937887 -0.0218861  0.0248120
-0.0024040 1.0019180 0.0004847
0.0000000 0.0000000 1.1166733
D65
 0.9857398  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3194581
 0.9555766 -0.0230393  0.0631636
-0.0282895 1.0099416 0.0210077
0.0122982 -0.0204830 1.3299098
 0.9845002 -0.0546158  0.0676324
-0.0059992 1.0047864 0.0012095
0.0000000 0.0000000 1.3194581
D75
 0.9849619  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.4861429
 0.9369777 -0.0323563  0.0952771
-0.0389795 1.0115975 0.0314918
0.0188243 -0.0315280 1.5023535
 0.9778997 -0.0778744  0.1026211
-0.0085539 1.0068249 0.0017244
0.0000000 0.0000000 1.4861429
E
 1.0371077  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2118128
 1.0025535  0.0036238  0.0359837
0.0096914 0.9819125 0.0105947
0.0089181 -0.0160789 1.2208770
 1.0001136  0.0003968  0.0427451
0.0000436 0.9999663 -0.0000100
0.0000000 0.0000000 1.2118128
F2
 1.0286657  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8166770
 1.0395725  0.0215350 -0.0388405
0.0287482 0.9834389 -0.0135220
-0.0067213 0.0106555 0.8116180
 1.0134653  0.0474454 -0.0397341
0.0052115 0.9958424 -0.0010512
0.0000000 0.0000000 0.8166770
F7
 0.9856775  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3178100
 0.9557124 -0.0229756  0.0628550
-0.0282266 1.0099623 0.0209090
0.0122325 -0.0203701 1.3282016
 0.9845499 -0.0544408  0.0672896
-0.0059799 1.0047711 0.0012056
0.0000000 0.0000000 1.3178100
F11
 1.0470847  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7798015
 1.0562303  0.0310026 -0.0482555
0.0422615 0.9734013 -0.0171480
-0.0078657 0.0121201 0.7743049
 1.0189974  0.0669372 -0.0482967
0.0073526 0.9941346 -0.0014833
0.0000000 0.0000000 0.7798015
D55 A
 1.1480738  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.3861681
 1.1802853  0.0968577 -0.1385564
0.1334256 0.9182995 -0.0498798
-0.0216899 0.0327363 0.3731642
 1.0600958  0.2095703 -0.1360743
0.0230198 0.9822541 -0.0046445
0.0000000 0.0000000 0.3861681
B
 1.0354299  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9248391
 1.0341856  0.0188903 -0.0192078
0.0269143 0.9810324 -0.0073626
-0.0023832 0.0030997 0.9239498
 1.0112458  0.0392165 -0.0174465
0.0043077 0.9966794 -0.0008694
0.0000000 0.0000000 0.9248391
C
 1.0249995  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2830524
 0.9821687 -0.0067531  0.0518013
-0.0044921 0.9893393 0.0162333
0.0114719 -0.0199953 1.2928395
 0.9932501 -0.0235426  0.0585151
-0.0025860 1.0019947 0.0005205
0.0000000 0.0000000 1.2830524
D50
 1.0077340  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8955170
 1.0184567  0.0093864 -0.0213199
0.0120291 0.9951460 -0.0072228
-0.0039673 0.0064899 0.8925936
 1.0063032  0.0219819 -0.0223692
0.0024146 0.9981384 -0.0004869
0.0000000 0.0000000 0.8955170
D65
 0.9933634  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1815972
 0.9726856 -0.0135482  0.0361731
-0.0167463 1.0049102 0.0120598
0.0070026 -0.0116372 1.1869548
 0.9905739 -0.0328729  0.0385701
-0.0036109 1.0027841 0.0007280
0.0000000 0.0000000 1.1815972
D75
 0.9925796  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3308663
 0.9535040 -0.0227860  0.0653011
-0.0276552 1.0065257 0.0216339
0.0128323 -0.0214482 1.3408176
 0.9838756 -0.0562333  0.0700620
-0.0061768 1.0047626 0.0012453
0.0000000 0.0000000 1.3308663
E
 1.0451287  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0851990
 1.0209581  0.0132500  0.0107183
0.0216398 0.9773060 0.0021580
0.0040457 -0.0079939 1.0896730
 1.0064186  0.0223804  0.0159070
0.0024583 0.9981057 -0.0004969
0.0000000 0.0000000 1.0851990
F2
 1.0366213  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7313481
 1.0591726  0.0309362 -0.0569879
0.0411624 0.9788474 -0.0197857
-0.0099371 0.0158080 0.7245114
 1.0199680  0.0696350 -0.0582760
0.0076489 0.9941031 -0.0015429
0.0000000 0.0000000 0.7313481
F7
 0.9933007  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1801213
 0.9728260 -0.0134855  0.0358942
-0.0166815 1.0049307 0.0119703
0.0069439 -0.0115365 1.1854306
 0.9906243 -0.0326972  0.0382619
-0.0035916 1.0027692 0.0007241
0.0000000 0.0000000 1.1801213
F11
 1.0551828  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6983255
 1.0762891  0.0404531 -0.0658152
0.0548187 0.9689618 -0.0232379
-0.0109370 0.0170126 0.6912198
 1.0255820  0.0892121 -0.0660772
0.0097993 0.9924455 -0.0019769
0.0000000 0.0000000 0.6983255
D65 A
 1.1557440  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.3268187
 1.2164557  0.1109905 -0.1549325
0.1533326 0.9152313 -0.0559953
-0.0239469 0.0358984 0.3147529
 1.0710732  0.2441000 -0.1502741
0.0268127 0.9804060 -0.0054100
0.0000000 0.0000000 0.3268187
B
 1.0423475  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7827025
 1.0641402  0.0325780 -0.0489436
0.0446103 0.9766379 -0.0174854
-0.0078485 0.0119945 0.7785377
 1.0211332  0.0725821 -0.0481421
0.0079726 0.9941737 -0.0016085
0.0000000 0.0000000 0.7827025
C
 1.0318474  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0858628
 1.0097785  0.0070419  0.0127971
0.0123113 0.9847094 0.0032962
0.0038284 -0.0072331 1.0891639
 1.0027359  0.0093941  0.0167846
0.0010319 0.9992466 -0.0002089
0.0000000 0.0000000 1.0858628
D50
 1.0144665  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7578869
 1.0478112  0.0228866 -0.0501270
0.0295424 0.9904844 -0.0170491
-0.0092345 0.0150436 0.7521316
 1.0160803  0.0552297 -0.0521326
0.0060666 0.9955661 -0.0012235
0.0000000 0.0000000 0.7578869
D55
 1.0066809  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8463121
 1.0285405  0.0135022 -0.0314825
0.0172109 0.9952227 -0.0106363
-0.0058993 0.0096778 0.8425735
 1.0096364  0.0330975 -0.0329773
0.0036355 0.9973428 -0.0007332
0.0000000 0.0000000 0.8463121
D75
 0.9992109  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1263283
 0.9799401 -0.0091708  0.0252447
-0.0112490 1.0015532 0.0083931
0.0049195 -0.0081963 1.1295615
 0.9931522 -0.0235200  0.0268900
-0.0025835 1.0018884 0.0005209
0.0000000 0.0000000 1.1263283
E
 1.0521111  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9184170
 1.0502616  0.0270757 -0.0232523
0.0390650 0.9729502 -0.0092579
-0.0024047 0.0026446 0.9180873
 1.0161982  0.0556310 -0.0197431
0.0061107 0.9955349 -0.0012334
0.0000000 0.0000000 0.9184170
F2
 1.0435469  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6189488
 1.0902706  0.0445381 -0.0816910
0.0593007 0.9745354 -0.0283781
-0.0142228 0.0226100 0.6105988
 1.0300500  0.1032084 -0.0830066
0.0113367 0.9917148 -0.0022869
0.0000000 0.0000000 0.6189488
F7
 0.9999369  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9987510
 1.0001471  0.0000616 -0.0002400
0.0000675 1.0000204 -0.0000777
-0.0000497 0.0000847 0.9987166
 1.0000515  0.0001770 -0.0002626
0.0000194 0.9999858 -0.0000039
0.0000000 0.0000000 0.9987510
F11
 1.0622324  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5910014
 1.1080915  0.0541551 -0.0897687
0.0731970 0.9648481 -0.0316116
-0.0150340 0.0234731 0.5825669
 1.0357893  0.1229193 -0.0898083
0.0135018 0.9901328 -0.0027239
0.0000000 0.0000000 0.5910014
D75 A
 1.1566567  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.2901629
 1.2435770  0.1208481 -0.1658524
0.1672750 0.9148518 -0.0601088
-0.0254024 0.0378929 0.2789367
 1.0791580  0.2689739 -0.1593077
0.0295449 0.9792517 -0.0059615
0.0000000 0.0000000 0.2901629
B
 1.0431706  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6949151
 1.0867460  0.0419224 -0.0679290
0.0568414 0.9754474 -0.0239981
-0.0112688 0.0175142 0.6893606
 1.0284252  0.0965883 -0.0673399
0.0106095 0.9925489 -0.0021405
0.0000000 0.0000000 0.6949151
C
 1.0326623  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9640731
 1.0306965  0.0163719 -0.0118275
0.0238763 0.9833607 -0.0049222
-0.0009264 0.0006607 0.9642518
 1.0097359  0.0330806 -0.0092198
0.0036337 0.9974486 -0.0007335
0.0000000 0.0000000 0.9640731
D50
 1.0152677  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6728828
 1.0699729  0.0320876 -0.0685287
0.0416191 0.9891382 -0.0233734
-0.0125333 0.0203557 0.6659904
 1.0232921  0.0791480 -0.0707522
0.0086939 0.9938938 -0.0017535
0.0000000 0.0000000 0.6728828
D55
 1.0074759  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7513903
 1.0501142  0.0226752 -0.0515090
0.0290589 0.9938026 -0.0174501
-0.0095853 0.0156802 0.7460274
 1.0167459  0.0569040 -0.0535787
0.0062505 0.9956098 -0.0012606
0.0000000 0.0000000 0.7513903
D65
 1.0007897  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8878406
 1.0206905  0.0091588 -0.0228796
0.0115005 0.9984917 -0.0076762
-0.0043619 0.0072053 0.8853432
 1.0069565  0.0236390 -0.0240510
0.0025966 0.9981762 -0.0005236
0.0000000 0.0000000 0.8878406
E
 1.0529419  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8154079
 1.0724049  0.0364864 -0.0448236
0.0511030 0.9717738 -0.0165588
-0.0064286 0.0092337 0.8128571
 1.0234118  0.0795514 -0.0419985
0.0087382 0.9938637 -0.0017633
0.0000000 0.0000000 0.8154079
F2
 1.0443710  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5495279
 1.1136974  0.0538679 -0.0976113
0.0718591 0.9734042 -0.0339619
-0.0169204 0.0268452 0.5407414
 1.0374835  0.1273695 -0.0985244
0.0139906 0.9901741 -0.0028223
0.0000000 0.0000000 0.5495279
F7
 1.0007265  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8867317
 1.0208424  0.0092199 -0.0230959
0.0115700 0.9985122 -0.0077467
-0.0044060 0.0072802 0.8842074
 1.0070088  0.0238168 -0.0242855
0.0026161 0.9981624 -0.0005276
0.0000000 0.0000000 0.8867317
F11
 1.0630712  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5247150
 1.1320328  0.0635755 -0.1052445
0.0859456 0.9638355 -0.0370682
-0.0176162 0.0274976 0.5159354
 1.0433139  0.1471802 -0.1047116
0.0161667 0.9886461 -0.0032616
0.0000000 0.0000000 0.5247150
E A
 1.0985000  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.3558500
 1.1548614  0.0823153 -0.1386766
0.1110042 0.9377198 -0.0487240
-0.0233784 0.0366158 0.3426126
 1.0528797  0.1863594 -0.1407391
0.0204703 0.9836593 -0.0041296
0.0000000 0.0000000 0.3558500
B
 0.9907200  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8522300
 1.0129515  0.0053699 -0.0276014
0.0051233 1.0036715 -0.0087948
-0.0059104 0.0101876 0.8479527
 1.0047555  0.0167614 -0.0307970
0.0018411 0.9985298 -0.0003709
0.0000000 0.0000000 0.8522300
C
 0.9807400  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1823200
 0.9622722 -0.0196444  0.0381122
-0.0259182 1.0127717 0.0131466
0.0067650 -0.0108472 1.1864022
 0.9870272 -0.0457193  0.0394321
-0.0050219 1.0040090 0.0010130
0.0000000 0.0000000 1.1823200
D50
 0.9642200  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8252100
 0.9977545 -0.0041632 -0.0293713
-0.0097677 1.0183168 -0.0085490
-0.0074169 0.0134416 0.8191853
 0.9998864 -0.0003967 -0.0352696
-0.0000436 1.0000338 0.0000098
0.0000000 0.0000000 0.8252100
D55
 0.9568200  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9214900
 0.9797934 -0.0133624 -0.0096110
-0.0216865 1.0235002 -0.0018137
-0.0037969 0.0075580 0.9177289
 0.9936768 -0.0222811 -0.0145757
-0.0024474 1.0019528 0.0004946
0.0000000 0.0000000 0.9214900
D65
 0.9504700  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0888300
 0.9531874 -0.0265906  0.0238731
-0.0382467 1.0288406 0.0094060
0.0026068 -0.0030332 1.0892565
 0.9843908 -0.0550082  0.0210874
-0.0060423 1.0048227 0.0012195
0.0000000 0.0000000 1.0888300
D75
 0.9497200  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2263800
 0.9344831 -0.0355691  0.0508059
-0.0490066 1.0307122 0.0182943
0.0079472 -0.0119897 1.2304226
 0.9777920 -0.0782650  0.0501930
-0.0085969 1.0068623 0.0017345
0.0000000 0.0000000 1.2263800
F2
 0.9918600  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6739300
 1.0373158  0.0170794 -0.0625353
0.0191780 1.0011509 -0.0203289
-0.0128300 0.0217881 0.6649719
 1.0133481  0.0470450 -0.0685331
0.0051676 0.9958740 -0.0010415
0.0000000 0.0000000 0.6739300
F7
 0.9504100  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0874700
 0.9533246 -0.0265304  0.0236158
-0.0381833 1.0288601 0.0093232
0.0025528 -0.0029409 1.0878581
 0.9844404 -0.0548332  0.0208028
-0.0060230 1.0048074 0.0012157
0.0000000 0.0000000 1.0874700
F11
 1.0096200  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6435000
 1.0539136  0.0265245 -0.0708181
0.0327858 0.9908245 -0.0236103
-0.0137094 0.0227828 0.6344266
 1.0188787  0.0665352 -0.0757939
0.0073084 0.9941652 -0.0014736
0.0000000 0.0000000 0.6435000
F2 A
 1.1075152  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5280222
 1.1108436  0.0654914 -0.1020770
0.0892593 0.9359084 -0.0362665
-0.0166489 0.0256618 0.5144475
 1.0383067  0.1380821 -0.1030329
0.0151673 0.9870182 -0.0030598
0.0000000 0.0000000 0.5280222
B
 0.9988506  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2645675
 0.9773601 -0.0123986  0.0500263
-0.0133935 1.0023946 0.0161588
0.0104080 -0.0177628 1.2756066
 0.9916737 -0.0300157  0.0551010
-0.0032970 1.0028226 0.0006642
0.0000000 0.0000000 1.2645675
C
 0.9887887  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.7543662
 0.9301461 -0.0386152  0.1436063
-0.0431066 1.0113279 0.0466336
0.0295321 -0.0501939 1.7853816
 0.9744947 -0.0919438  0.1574666
-0.0100994 1.0086458 0.0020348
0.0000000 0.0000000 1.7543662
D50
 0.9721332  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2244744
 0.9628262 -0.0215790  0.0457172
-0.0280310 1.0172847 0.0156071
0.0083415 -0.0135344 1.2322804
 0.9869554 -0.0470220  0.0479582
-0.0051650 1.0044210 0.0010416
0.0000000 0.0000000 1.2244744
D55
 0.9646724  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3673379
 0.9460314 -0.0310871  0.0735630
-0.0395027 1.0224574 0.0248152
0.0138373 -0.0227352 1.3807080
 0.9809382 -0.0687128  0.0780192
-0.0075476 1.0064606 0.0015219
0.0000000 0.0000000 1.3673379
D65
 0.9582703  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.6156426
 0.9212269 -0.0449128  0.1211620
-0.0553723 1.0277243 0.0403563
0.0235086 -0.0391019 1.6390644
 0.9719399 -0.1011504  0.1299721
-0.0111107 1.0095107 0.0022399
0.0000000 0.0000000 1.6156426
D75
 0.9575142  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.8197439
 0.9038485 -0.0544241  0.1597390
-0.0656239 1.0294976 0.0528128
0.0315403 -0.0528125 1.8516893
 0.9655456 -0.1242015  0.1724740
-0.0136427 1.0116783 0.0027499
0.0000000 0.0000000 1.8197439
E
 1.0082068  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.4838336
 0.9654834 -0.0184347  0.0902324
-0.0181044 0.9985320 0.0288236
0.0192213 -0.0330731 1.5046195
 0.9870655 -0.0466289  0.1003043
-0.0051218 1.0043851 0.0010314
0.0000000 0.0000000 1.4838336
F7
 0.9582098  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.6136246
 0.9213533 -0.0448467  0.1207888
-0.0553131 1.0277453 0.0402379
0.0234280 -0.0389625 1.6369581
 0.9719880 -0.1009770  0.1295549
-0.0110916 1.0094944 0.0022360
0.0000000 0.0000000 1.6136246
F11
 1.0179058  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9548469
 1.0156947  0.0093992 -0.0106926
0.0132620 0.9895464 -0.0040071
-0.0014541 0.0020196 0.9539904
 1.0053592  0.0193178 -0.0101990
0.0021219 0.9981839 -0.0004282
0.0000000 0.0000000 0.9548469
F7 A
 1.1558170  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.3272274
 1.2162616  0.1109265 -0.1548306
0.1532455 0.9152079 -0.0559592
-0.0239302 0.0358725 0.3151544
 1.0710133  0.2439140 -0.1501795
0.0267922 0.9804152 -0.0054059
0.0000000 0.0000000 0.3272274
B
 1.0424133  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7836814
 1.0639791  0.0325159 -0.0487483
0.0445370 0.9766166 -0.0174212
-0.0078094 0.0119287 0.7795373
 1.0210792  0.0724024 -0.0479336
0.0079529 0.9941864 -0.0016046
0.0000000 0.0000000 0.7836814
C
 1.0319125  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0872208
 1.0096302  0.0069785  0.0130568
0.0122432 0.9846882 0.0033800
0.0038825 -0.0073255 1.0905639
 1.0026841  0.0092168  0.0170692
0.0010124 0.9992607 -0.0002049
0.0000000 0.0000000 1.0872208
D50
 1.0145306  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.7588347
 1.0476532  0.0228258 -0.0499378
0.0294704 0.9904638 -0.0169869
-0.0091967 0.0149801 0.7530971
 1.0160269  0.0550506 -0.0519304
0.0060469 0.9955792 -0.0012196
0.0000000 0.0000000 0.7588347
D55
 1.0067445  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.8473705
 1.0283868  0.0134412 -0.0312747
0.0171406 0.9952022 -0.0105684
-0.0058572 0.0096065 0.8436556
 1.0095838  0.0329194 -0.0327530
0.0036160 0.9973564 -0.0007292
0.0000000 0.0000000 0.8473705
D65
 1.0000631  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0012506
 0.9998530 -0.0000616  0.0002403
-0.0000675 0.9999796 0.0000778
0.0000498 -0.0000848 1.0012851
 0.9999485 -0.0001770  0.0002629
-0.0000194 1.0000142 0.0000039
0.0000000 0.0000000 1.0012506
D75
 0.9992740  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.1277369
 0.9797979 -0.0092332  0.0255119
-0.0113145 1.0015327 0.0084791
0.0049755 -0.0082922 1.1310137
 0.9931015 -0.0236961  0.0271847
-0.0026028 1.0019031 0.0005248
0.0000000 0.0000000 1.1277369
E
 1.0521775  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.9195656
 1.0501042  0.0270124 -0.0230277
0.0389931 0.9729287 -0.0091847
-0.0023588 0.0025668 0.9192667
 1.0161448  0.0554519 -0.0195004
0.0060910 0.9955480 -0.0012294
0.0000000 0.0000000 0.9195656
F2
 1.0436128  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.6197228
 1.0901032  0.0444769 -0.0815305
0.0592248 0.9745143 -0.0283245
-0.0141918 0.0225586 0.6113819
 1.0299949  0.1030276 -0.0828392
0.0113169 0.9917269 -0.0022829
0.0000000 0.0000000 0.6197228
F11
 1.0622994  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5917405
 1.1079204  0.0540934 -0.0896135
0.0731195 0.9648265 -0.0315596
-0.0150044 0.0234241 0.5833138
 1.0357335  0.1227378 -0.0896478
0.0134819 0.9901444 -0.0027199
0.0000000 0.0000000 0.5917405
F11 A
 1.0880331  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 0.5529915
 1.0928123  0.0559961 -0.0945162
0.0754916 0.9451460 -0.0331995
-0.0159459 0.0249839 0.5391848
 1.0325220  0.1183509 -0.0968233
0.0130000 0.9885624 -0.0026223
0.0000000 0.0000000 0.5529915
B
 0.9812801  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.3243667
 0.9626328 -0.0218020  0.0631369
-0.0263860 1.0131919 0.0208981
0.0124331 -0.0207976 1.3371793
 0.9864912 -0.0491618  0.0682216
-0.0054001 1.0047516 0.0010885
0.0000000 0.0000000 1.3243667
C
 0.9713952  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.8373271
 0.9166307 -0.0480575  0.1606042
-0.0557153 1.0224336 0.0525528
0.0324715 -0.0548525 1.8716217
 0.9695340 -0.1108744  0.1752191
-0.0121788 1.0107166 0.0024542
0.0000000 0.0000000 1.8373271
D50
 0.9550326  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.2823776
 0.9484361 -0.0309349  0.0584225
-0.0409965 1.0283794 0.0202198
0.0102763 -0.0164113 1.2917578
 0.9818338 -0.0661090  0.0606837
-0.0072616 1.0063890 0.0014646
0.0000000 0.0000000 1.2823776
D55
 0.9477031  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.4319969
 0.9320665 -0.0404470  0.0873879
-0.0523468 1.0336952 0.0297671
0.0160362 -0.0260817 1.4473678
 0.9758943 -0.0877243  0.0920931
-0.0096359 1.0084782 0.0019431
0.0000000 0.0000000 1.4319969
D65
 0.9414136  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.6920435
 0.9078969 -0.0542904  0.1369534
-0.0680190 1.0391336 0.0459049
0.0261703 -0.0432704 1.7182258
 0.9670122 -0.1200490  0.1463934
-0.0131865 1.0116026 0.0026586
0.0000000 0.0000000 1.6920435
D75
 0.9406707  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.9057964
 0.8909691 -0.0638234  0.1771612
-0.0781180 1.0409951 0.0588569
0.0345849 -0.0576607 1.9411392
 0.9607005 -0.1430199  0.1908275
-0.0157097 1.0138230 0.0031668
0.0000000 0.0000000 1.9057964
E
 0.9904717  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.5540016
 0.9510791 -0.0278778  0.1051271
-0.0309545 1.0093049 0.0341061
0.0216636 -0.0368473 1.5772733
 0.9819425 -0.0657172  0.1155065
-0.0072186 1.0063522 0.0014543
0.0000000 0.0000000 1.5540016
F2
 0.9824092  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0472883
 0.9846860 -0.0093755  0.0109973
-0.0131907 1.0106809 0.0040974
0.0015289 -0.0021539 1.0482367
 0.9947100 -0.0192506  0.0106162
-0.0021145 1.0018603 0.0004267
0.0000000 0.0000000 1.0472883
F7
 0.9413542  0.0000000  0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.6899301
 0.9080200 -0.0542240  0.1365639
-0.0679612 1.0391545 0.0457816
0.0260859 -0.0431241 1.7160176
 0.9670597 -0.1198762  0.1459571
-0.0131676 1.0115859 0.0026547
0.0000000 0.0000000 1.6899301