I'm using VIT transformer in my code. How to convert the output of 1D layer of VIT into 2D with format SSCB?

I used the following code from Matlab answer to solve the errorrs that shown in the attached figure.

(Samuel Somuyiwa on 24 Jul 2023)

% Get Vision Transformer model

net = visionTransformer;

% Create dummy input

input = dlarray(rand(384,384,3),'SSCB');

% Obtain output embedding from last layerNormalizationLayer

out = forward(net, input, Outputs='encoder_norm');

% Reshape output patch embedding

out = reshapePatchEmbedding(out);

function out = reshapePatchEmbedding(in)

% Remove output embedding corresponding to class token from input

out = in(2:end,:,:);

% Reshape resulting embedding to input format

WH = sqrt(size(out, 1));

C = size(out, 2);

out = reshape(out, WH, WH, C, []); % Shape is W x H x C x N

out = permute(out, [2, 1, 3, 4]); % Shape is H x W x C x N

% Convert to formatted dlarray

out = dlarray(out, 'SSCB');

end

[Umar]

Hi @Abdulrahman,

Please see my response to your question.

I'm using VIT transformer in my code. How to convert the output of 1D layer of VIT into 2D with format SSCB?

Assuming your 1D output tensor is named vit_output_1d, you can reshape it using the following code snippet:

% Reshape 1D output to 2D SSCB format

vit_output_2d_sscb = reshape(vit_output_1d, [sequence_length,

sequence_length, num_channels, batch_size]);

In the code above, sequence_length represents the length of the sequence, num_channels is the number of channels, and batch_size is the size of the batch. Adjust these values based on your specific dimensions. This reshaping operation will convert the 1D output into a 2D SSCB format. Hope this answer your question.

[Abdulrahman]

Thank you Umarfor your response.

I applied your code but it gave me the same error 24(S) x 24(C) x 768(B) as shown in attached file (ma.png).

[Umar]

Hi Abdulrahman,

The error message indicating dimensions 24(S) x 24(C) x 768(B) suggests that there might be a mismatch in the reshaping process. When reshaping a 1D output tensor to a 2D SSCB format in Matlab, it is crucial to ensure that the dimensions match the intended structure.

[Umar]

Hi Abdulrahman,

I cannot execute the code because visionTransformer requires Computer Vision Toolbox. To illustrate resolving your error, I had to adapt your given code from mathworks for input dimensions of 24 x 24 x 768, by adjusting the reshaping and processing steps accordingly. Here is update the code step by step:

% Get Vision Transformer model

net = visionTransformer;

% Create dummy input

input = dlarray(rand(24,24,768),'SSCB');

% Obtain output embedding from the last LayerNormalizationLayer

out = forward(net, input, 'Outputs', 'encoder_norm');

% Reshape output patch embedding

out = reshapePatchEmbedding(out);

function out = reshapePatchEmbedding(in)

    % Remove output embedding corresponding to the class token from the input

    out = in(2:end,:,:);

    % Reshape the resulting embedding to the input format

    WH = sqrt(size(out, 1));

    C = size(out, 2);

    out = reshape(out, WH, WH, C, []); % Shape is W x H x C x N

    out = permute(out, [2, 1, 3, 4]); % Shape is H x W x C x N

    % Convert to formatted dlarray

out = dlarray(out, 'SSCB');

end

So, in my updated code snippet, I changed the dummy input dimensions to 24 x 24 x 768 to match the specified input size. The reshaping function reshapePatchEmbedding has been adjusted to handle the new dimensions correctly. Please let me know if this helps resolve your issue.

[Abdulrahman]

Dear Umar

This function I already used it, the problem in the input of previous layer where (input=dlarray(577,768),'SCB')) while the function is valid for the following dummy input

input = dlarray(rand(24,24,768),'SSCB');

[Umar]

Dear @Abdulrahman,

In the updated code snippet, the input dimensions were modified to 24 x 24 x 768 to align with the required input size for the Vision Transformer model. Additionally, the reshapePatchEmbedding function was adapted to handle the new dimensions correctly. These adjustments ensure compatibility between the input data and the reshaping process. If the input mismatch issue persists, it might be related to the format of the input data. Ensure that the input follows the format specified in the code snippet for proper functioning of the reshaping function. By aligning the input format with the model requirements, the reshaping function should work seamlessly. Please let me know if you have any further questions. Also, could you please share your code to find out what is going on exactly

[Abdulrahman]

Thank you Umar for your collaboration. function out = reshapePatchEmbedding(in) is correct, I already used it before. My problem has been solved by configration addLayer in my code.

[Umar]

Hi @ Abdulrahman,

Glad to know your problem has been solved. Please don’t forget to click “Accept Answer” and vote for @ Gayathri for her efforts. If you still have any further questions, please don’t hesitate to reach out, we will be more happy to help.

Answer 1

[Gayathri]

Hi @Abdulrahman,

I understand you are facing an issue with converting output from ViT(vision transformer) which is in “SCB” format to 2D “SSCB” format. I have implemented the code in MATLAB R2024a.

Please find the below code for your reference.

outputoftransformer = dlarray(rand(577,768),'SCB')

outputoftransformer = 
  577(S) x 768(C) x 1(B) dlarray

  Columns 1 through 18

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    0.1912    0.2385    0.8691    0.7075    0.9930    0.0401    0.5963    0.6376    0.3120    0.5427    0.3614    0.1583    0.2975    0.5101    0.5771    0.0083    0.9349    0.3970
    0.2029    0.3611    0.0704    0.2886    0.4901    0.7798    0.1092    0.4199    0.9558    0.5569    0.2840    0.3603    0.7096    0.7679    0.7961    0.4545    0.8874    0.9366
    0.2741    0.1724    0.1294    0.0913    0.0714    0.1504    0.9717    0.4346    0.4943    0.3917    0.7574    0.5603    0.7504    0.1937    0.4377    0.7868    0.8310    0.0742
    0.7316    0.3052    0.6569    0.5220    0.5243    0.2351    0.0619    0.3639    0.9509    0.8347    0.2678    0.5231    0.6468    0.9959    0.9375    0.5554    0.5742    0.9534
    0.6930    0.9637    0.4851    0.2657    0.5932    0.8780    0.6511    0.3704    0.1581    0.0813    0.7822    0.4421    0.4222    0.0883    0.8188    0.9705    0.9847    0.8118
    0.6002    0.0232    0.9742    0.4664    0.0386    0.0801    0.0266    0.3288    0.5615    0.6931    0.6598    0.6863    0.4803    0.9157    0.5670    0.8981    0.3734    0.6171
    0.1083    0.5555    0.0158    0.3732    0.5491    0.7647    0.6669    0.8761    0.2608    0.0589    0.9620    0.5603    0.1100    0.5890    0.9349    0.4561    0.4806    0.4554
    0.8738    0.2253    0.4410    0.1600    0.1048    0.0679    0.0774    0.2437    0.1898    0.5529    0.5513    0.0566    0.3248    0.8635    0.0344    0.1904    0.7043    0.2643
    0.9824    0.7913    0.8944    0.0758    0.5749    0.6953    0.0100    0.9045    0.0142    0.5124    0.7537    0.7291    0.6949    0.8333    0.8602    0.5954    0.5237    0.0832
    0.8854    0.6848    0.1827    0.7746    0.0572    0.5426    0.2190    0.7946    0.3294    0.2850    0.2042    0.1831    0.7899    0.4124    0.7730    0.7542    0.6006    0.3345
    0.6640    0.1866    0.3433    0.1174    0.6581    0.9361    0.2784    0.0386    0.4259    0.7737    0.2665    0.1070    0.7585    0.0046    0.8659    0.1104    0.3040    0.4076
    0.2982    0.8769    0.7803    0.3669    0.9838    0.0516    0.4840    0.7096    0.1636    0.0825    0.7239    0.3626    0.8519    0.7659    0.4406    0.7641    0.1879    0.7339
    0.2811    0.9257    0.7142    0.5042    0.6910    0.8653    0.0144    0.8745    0.7731    0.1890    0.1840    0.9771    0.4554    0.0149    0.9441    0.2385    0.7362    0.7755
    0.3693    0.0601    0.5361    0.9070    0.2760    0.1970    0.2926    0.6307    0.8374    0.9794    0.6581    0.5917    0.2429    0.0680    0.4359    0.4826    0.8289    0.1300
    0.4177    0.7273    0.2215    0.4202    0.5962    0.2539    0.1639    0.9843    0.2253    0.7009    0.0428    0.7011    0.2182    0.5015    0.3441    0.1134    0.9738    0.0273
    0.5003    0.5612    0.0019    0.7569    0.3462    0.7173    0.7054    0.8240    0.3035    0.4237    0.8001    0.8564    0.4749    0.5908    0.7158    0.9570    0.7258    0.8287
    0.5880    0.8317    0.5715    0.4548    0.5838    0.1945    0.8200    0.4717    0.4488    0.8874    0.4934    0.3345    0.3438    0.0056    0.9614    0.4633    0.7716    0.1464
    0.8511    0.4989    0.4518    0.0325    0.8981    0.1583    0.5110    0.0634    0.0601    0.1029    0.4002    0.4040    0.2646    0.9025    0.9286    0.5934    0.0724    0.5763
    0.8647    0.9068    0.4366    0.6371    0.1897    0.7424    0.1625    0.8939    0.4654    0.3451    0.9446    0.0779    0.1096    0.2993    0.3420    0.3386    0.4099    0.5030
    0.8183    0.2980    0.4585    0.9054    0.8926    0.8174    0.1534    0.9027    0.3546    0.8529    0.3774    0.6733    0.6349    0.5789    0.8147    0.4251    0.5867    0.2526
    0.6085    0.6170    0.3883    0.3542    0.1861    0.4303    0.4307    0.8546    0.1642    0.9592    0.9393    0.3755    0.0820    0.1023    0.6155    0.1174    0.4529    0.2476
    0.0515    0.7865    0.6664    0.7637    0.3359    0.2977    0.6190    0.5617    0.9279    0.5462    0.3187    0.2780    0.9994    0.2460    0.7060    0.1091    0.5616    0.2390
    0.4950    0.4772    0.7247    0.8420    0.2116    0.2532    0.3318    0.9871    0.2539    0.1721    0.6665    0.6368    0.7562    0.3135    0.2607    0.8353    0.1683    0.8161
    0.2137    0.4953    0.5652    0.3088    0.4526    0.0656    0.7641    0.9842    0.4620    0.4826    0.6234    0.9881    0.9337    0.3637    0.8939    0.1982    0.2923    0.4122
    0.7633    0.7371    0.6421    0.8239    0.6535    0.0075    0.3611    0.2582    0.2871    0.7483    0.4143    0.0767    0.3108    0.2685    0.9183    0.5237    0.9401    0.5407
    0.3650    0.3526    0.1734    0.6490    0.4653    0.2179    0.9206    0.8664    0.2860    0.5574    0.0118    0.8000    0.0034    0.7449    0.5504    0.4987    0.7911    0.1748
    0.3171    0.8520    0.4292    0.4488    0.1870    0.0639    0.3368    0.3629    0.2602    0.5694    0.0770    0.2854    0.4083    0.1702    0.2251    0.3749    0.1746    0.2364
    0.5684    0.3382    0.1332    0.4391    0.4651    0.7568    0.6183    0.2411    0.6352    0.4275    0.2092    0.7195    0.3195    0.6587    0.8536    0.3933    0.2314    0.9301
    0.2182    0.0823    0.2343    0.9983    0.7101    0.4101    0.9757    0.7759    0.3312    0.8582    0.4892    0.7449    0.1750    0.0677    0.1159    0.8969    0.3400    0.3427
    0.8779    0.8867    0.8867    0.5561    0.8864    0.0364    0.1434    0.1643    0.7374    0.5236    0.7206    0.3068    0.4272    0.5492    0.5507    0.2754    0.5836    0.1023
    0.3610    0.8388    0.1793    0.1741    0.8738    0.2008    0.2619    0.5379    0.8816    0.1799    0.8340    0.8992    0.7723    0.8073    0.9642    0.0151    0.0309    0.7914
    0.6248    0.6934    0.7654    0.1704    0.3073    0.9373    0.7125    0.4667    0.2636    0.5344    0.8665    0.9959    0.9482    0.5689    0.6584    0.2902    0.0490    0.9838
    0.3653    0.0575    0.0061    0.7140    0.5716    0.3692    0.7862    0.7730    0.6886    0.5452    0.0918    0.9137    0.4379    0.4496    0.0552    0.8485    0.7724    0.6339
    0.9353    0.4708    0.6917    0.7219    0.7952    0.1366    0.8045    0.8818    0.9948    0.5469    0.3948    0.8633    0.5912    0.6294    0.6216    0.2192    0.5733    0.4088
    0.2559    0.6060    0.2051    0.1616    0.2537    0.3236    0.1469    0.4267    0.8528    0.8860    0.3397    0.3838    0.6259    0.3596    0.4941    0.8198    0.7328    0.1493
    0.4182    0.6815    0.4050    0.7491    0.6316    0.2705    0.6994    0.1060    0.2061    0.6641    0.9960    0.0213    0.0829    0.3016    0.4490    0.0475    0.3109    0.4622
    0.6340    0.0053    0.3303    0.9050    0.3814    0.4274    0.3703    0.5256    0.9832    0.7897    0.1479    0.5083    0.1285    0.6553    0.2124    0.8001    0.2190    0.3924
    0.2930    0.4366    0.5457    0.3980    0.1464    0.5525    0.3034    0.0047    0.0863    0.3162    0.2079    0.0063    0.1872    0.5560    0.8493    0.9380    0.0698    0.1410
    0.7698    0.7612    0.3071    0.9188    0.1250    0.5781    0.4056    0.7918    0.0386    0.4302    0.8071    0.1878    0.9902    0.3786    0.0526    0.6916    0.9040    0.1845
    0.8731    0.1068    0.5436    0.5498    0.5966    0.4154    0.2230    0.4034    0.7233    0.5585    0.5853    0.2732    0.5031    0.7376    0.6215    0.8905    0.4173    0.3902
    0.2335    0.3718    0.0923    0.4097    0.4751    0.6256    0.3351    0.2210    0.3746    0.9314    0.9630    0.5466    0.9750    0.4633    0.7592    0.7743    0.8858    0.2649
    0.2614    0.4358    0.3611    0.5623    0.3454    0.8430    0.0501    0.0989    0.2028    0.8538    0.8229    0.5347    0.8353    0.3026    0.5590    0.0553    0.2530    0.7742
    0.4963    0.3619    0.4614    0.7723    0.0294    0.5469    0.7800    0.0494    0.7513    0.3868    0.0358    0.2507    0.7737    0.2960    0.0382    0.6355    0.0656    0.0118
    0.1537    0.8786    0.4513    0.4503    0.7017    0.1429    0.0705    0.2614    0.8975    0.6848    0.8621    0.7144    0.0860    0.8033    0.7977    0.4540    0.1781    0.4792
    0.0689    0.2714    0.6291    0.2515    0.6391    0.1331    0.7661    0.7873    0.9668    0.0340    0.7924    0.5857    0.8042    0.1402    0.0990    0.8023    0.6062    0.6865
    0.0722    0.4011    0.8904    0.7035    0.1320    0.8677    0.6603    0.6923    0.6922    0.4133    0.7807    0.8848    0.6841    0.2143    0.6209    0.6357    0.2608    0.3185
    0.8640    0.3325    0.3689    0.6136    0.9808    0.0552    0.2624    0.7953    0.5973    0.8543    0.7678    0.0539    0.6326    0.9433    0.8105    0.9976    0.1050    0.2406
    0.5365    0.3917    0.6573    0.0493    0.1689    0.0146    0.9027    0.0925    0.4119    0.3539    0.2883    0.8398    0.1749    0.6558    0.3346    0.7448    0.6137    0.7137
    0.3748    0.9180    0.3670    0.2076    0.5780    0.0948    0.3472    0.1226    0.8355    0.9213    0.9647    0.2382    0.4631    0.4433    0.6060    0.4820    0.8547    0.0941
    0.0721    0.5239    0.5300    0.2634    0.1457    0.1443    0.5401    0.1978    0.6228    0.7576    0.1879    0.7622    0.9239    0.0974    0.6576    0.0217    0.5678    0.3106
    0.4055    0.6031    0.8841    0.4832    0.6741    0.6157    0.1015    0.4915    0.9525    0.4541    0.5474    0.5444    0.3618    0.1643    0.5184    0.2211    0.2790    0.5836
    0.1543    0.7703    0.3843    0.7019    0.7826    0.7159    0.1684    0.6162    0.2874    0.3189    0.4655    0.9369    0.1776    0.0007    0.4023    0.6632    0.5305    0.0690
    0.2320    0.5486    0.0352    0.9854    0.3991    0.0900    0.4029    0.8503    0.4979    0.0069    0.9003    0.9280    0.0631    0.6765    0.4298    0.5549    0.0073    0.9690
    0.1760    0.2317    0.7504    0.8544    0.5058    0.2033    0.2336    0.5398    0.6273    0.6571    0.9875    0.0489    0.3191    0.0172    0.7446    0.1825    0.0875    0.9488
    0.2392    0.0829    0.5248    0.0226    0.5628    0.5858    0.6951    0.7374    0.0775    0.3737    0.1735    0.9873    0.4577    0.0545    0.1470    0.4037    0.7122    0.3966
    0.0666    0.7504    0.8107    0.2417    0.7101    0.0618    0.5816    0.3168    0.2878    0.8774    0.2047    0.6036    0.1719    0.7046    0.8814    0.7571    0.0372    0.0232
    0.9307    0.5812    0.0933    0.9456    0.0283    0.7399    0.2953    0.8869    0.8717    0.6373    0.0175    0.9120    0.2703    0.7735    0.1333    0.8897    0.6863    0.5533
    0.7832    0.5017    0.8057    0.8075    0.2440    0.0011    0.6283    0.6104    0.8165    0.3947    0.4782    0.7785    0.0399    0.4195    0.6563    0.5180    0.0697    0.7001
    0.1220    0.7851    0.7113    0.6061    0.6146    0.7403    0.5473    0.8663    0.7472    0.3808    0.0245    0.2890    0.0828    0.5756    0.1285    0.1639    0.8283    0.6675
    0.5300    0.4556    0.1164    0.9015    0.6053    0.5419    0.4233    0.6794    0.5305    0.1297    0.6347    0.1245    0.9568    0.3852    0.1463    0.5308    0.8748    0.6537
    0.1368    0.8587    0.1284    0.2963    0.4298    0.7105    0.9791    0.0385    0.4912    0.2508    0.1416    0.3805    0.6889    0.6409    0.3938    0.9946    0.6509    0.0656
    0.4683    0.6124    0.5189    0.6452    0.5485    0.4428    0.9139    0.3023    0.2503    0.2735    0.1658    0.0581    0.1728    0.3879    0.7221    0.3807    0.8549    0.9857
    0.8011    0.2653    0.5542    0.3957    0.2492    0.5913    0.1002    0.4819    0.9801    0.3316    0.6354    0.6513    0.4973    0.4041    0.8707    0.9495    0.3380    0.2370
    0.7079    0.0937    0.7479    0.4592    0.2263    0.7168    0.7650    0.2761    0.2583    0.8669    0.9387    0.7991    0.2000    0.3667    0.6467    0.8836    0.6198    0.4745
    0.5964    0.6453    0.9351    0.5673    0.2009    0.4414    0.8197    0.5300    0.2180    0.8848    0.4926    0.3196    0.6003    0.6601    0.0284    0.4260    0.0213    0.0793
    0.1298    0.8951    0.5782    0.6556    0.4123    0.2150    0.7986    0.4947    0.0855    0.3900    0.9756    0.2986    0.1402    0.1414    0.7983    0.9633    0.6975    0.6088
    0.9264    0.8318    0.4278    0.9725    0.3760    0.0963    0.5302    0.5921    0.0701    0.9648    0.8048    0.2546    0.2728    0.4936    0.2617    0.7990    0.2931    0.3484
    0.9510    0.2043    0.9723    0.6599    0.8337    0.6767    0.4352    0.4122    0.4489    0.5579    0.2399    0.8778    0.0833    0.4448    0.1994    0.5615    0.8779    0.4196
    0.2484    0.2062    0.7035    0.7401    0.2616    0.8670    0.7281    0.1326    0.7553    0.3617    0.8339    0.7287    0.6027    0.9875    0.8261    0.8610    0.2763    0.6030
    0.3708    0.4909    0.0151    0.0823    0.8788    0.1777    0.5657    0.1854    0.8487    0.6618    0.1648    0.6977    0.5547    0.7995    0.2400    0.8311    0.0846    0.5044
    0.8695    0.9438    0.6903    0.2485    0.1864    0.7796    0.1445    0.4595    0.3523    0.2889    0.1175    0.4478    0.6340    0.4083    0.3568    0.8240    0.9419    0.0107
    0.9247    0.8258    0.8413    0.0058    0.0305    0.2868    0.8022    0.3384    0.5710    0.7373    0.8136    0.3976    0.2199    0.0539    0.6321    0.8262    0.9853    0.4481
    0.1483    0.7535    0.8862    0.8520    0.3123    0.4837    0.6030    0.2596    0.0582    0.2355    0.4968    0.2538    0.4254    0.5596    0.3679    0.2810    0.0875    0.9777
    0.0265    0.0984    0.1872    0.1506    0.4661    0.5971    0.0616    0.9415    0.2850    0.4891    0.3432    0.0066    0.3420    0.9844    0.1551    0.6387    0.5791    0.9575
    0.6777    0.1638    0.0345    0.0387    0.6618    0.4597    0.0790    0.9305    0.4872    0.7458    0.6673    0.2914    0.8892    0.3820    0.4079    0.2072    0.0993    0.2680
    0.2807    0.9237    0.0401    0.9312    0.4297    0.1912    0.1125    0.1523    0.5176    0.5688    0.0770    0.0472    0.5011    0.3121    0.1671    0.0867    0.6320    0.5751
    0.6756    0.1026    0.4948    0.2111    0.0033    0.8374    0.5465    0.5253    0.8912    0.3039    0.9384    0.1713    0.0644    0.1655    0.9540    0.1741    0.4654    0.5606
    0.9798    0.0198    0.6442    0.4832    0.8768    0.3670    0.0805    0.5752    0.3205    0.4539    0.9170    0.6134    0.4711    0.4610    0.3909    0.8442    0.4437    0.6505
    0.3160    0.4638    0.5606    0.5534    0.0992    0.2663    0.4088    0.8979    0.8166    0.6907    0.2043    0.5558    0.6952    0.6121    0.1609    0.8986    0.9060    0.8106
    0.1721    0.7661    0.5707    0.7846    0.2495    0.9134    0.2743    0.5376    0.3666    0.4845    0.2189    0.1294    0.8853    0.7466    0.3050    0.5653    0.2814    0.9510
    0.8449    0.7298    0.3268    0.4458    0.3086    0.3685    0.3571    0.9668    0.2543    0.9577    0.7592    0.7452    0.5450    0.1535    0.1018    0.7062    0.8198    0.1786
    0.7999    0.5152    0.4572    0.2701    0.3045    0.7793    0.3742    0.9356    0.9950    0.8226    0.4070    0.2843    0.6740    0.0060    0.2080    0.4839    0.2226    0.5565
    0.6321    0.1734    0.6099    0.6146    0.6023    0.1391    0.7688    0.2489    0.6825    0.0598    0.3034    0.0951    0.8411    0.8132    0.3938    0.6000    0.9691    0.7561
    0.7672    0.9558    0.8370    0.9006    0.8785    0.8538    0.4401    0.7658    0.5600    0.9995    0.5250    0.7112    0.8828    0.0805    0.5156    0.4268    0.8032    0.2131
    0.5224    0.3369    0.8848    0.8806    0.8175    0.6953    0.6940    0.7119    0.5677    0.3748    0.7739    0.7990    0.7363    0.4517    0.0356    0.9021    0.0715    0.0048
    0.8337    0.4953    0.6881    0.0386    0.7167    0.1860    0.3917    0.6213    0.8568    0.0397    0.6990    0.9763    0.2037    0.0790    0.8947    0.2213    0.1551    0.3457
    0.2282    0.3542    0.7925    0.8270    0.4185    0.6299    0.5200    0.9534    0.8141    0.8349    0.4060    0.1189    0.9434    0.4205    0.8344    0.2044    0.8853    0.7985

% Remove output embedding corresponding to class token from input
out = outputoftransformer(2:end,:,:);
WH = sqrt(size(out, 1));
C = size(out, 2);
out = reshape(out, WH, WH, C, []);
out=dlarray(out,'SSCB')

out = 
  24(S) x 24(S) x 768(C) x 1(B) dlarray


(:,:,1) =

  Columns 1 through 18

    0.9143    0.2926    0.1351    0.8059    0.9718    0.9962    0.9877    0.2279    0.6642    0.5073    0.2448    0.0515    0.0722    0.3708    0.4003    0.8988    0.3371    0.6168
    0.6877    0.8485    0.4077    0.6029    0.1243    0.4368    0.5479    0.8402    0.8824    0.3584    0.6902    0.4950    0.8640    0.8695    0.1306    0.8948    0.4641    0.1741
    0.7212    0.9903    0.6051    0.9650    0.6823    0.5631    0.8128    0.1202    0.3952    0.0610    0.8260    0.2137    0.5365    0.9247    0.8422    0.2599    0.4635    0.4776
    0.8288    0.0139    0.8718    0.2901    0.7130    0.5770    0.9560    0.6210    0.9834    0.2400    0.1912    0.7633    0.3748    0.1483    0.6609    0.2045    0.8042    0.9425
    0.4867    0.3525    0.5314    0.6859    0.1096    0.8389    0.9963    0.0947    0.1419    0.6462    0.2029    0.3650    0.0721    0.0265    0.6644    0.7364    0.1724    0.8389
    0.4433    0.1655    0.7015    0.2651    0.1968    0.3695    0.6278    0.6414    0.2888    0.8770    0.2741    0.3171    0.4055    0.6777    0.5104    0.4697    0.5893    0.2498
    0.6331    0.1528    0.8933    0.2203    0.8601    0.0913    0.9983    0.7025    0.8896    0.0024    0.7316    0.5684    0.1543    0.2807    0.3270    0.1379    0.7763    0.8344
    0.2802    0.4240    0.0721    0.6994    0.5807    0.2058    0.9373    0.7810    0.8667    0.9303    0.6930    0.2182    0.2320    0.6756    0.5727    0.2337    0.6065    0.8790
    0.7322    0.8313    0.1648    0.2803    0.2800    0.6114    0.9417    0.4777    0.4716    0.2652    0.6002    0.8779    0.1760    0.9798    0.2537    0.4364    0.2288    0.2970
    0.7993    0.6927    0.5336    0.1315    0.7234    0.6609    0.9253    0.5832    0.4358    0.2189    0.1083    0.3610    0.2392    0.3160    0.8207    0.0148    0.4494    0.2760
    0.1978    0.3212    0.3803    0.7032    0.3686    0.6826    0.0219    0.9289    0.3347    0.3020    0.8738    0.6248    0.0666    0.1721    0.2518    0.6223    0.5302    0.3679
    0.4858    0.2582    0.1357    0.0390    0.1232    0.9948    0.2624    0.2618    0.3627    0.4696    0.9824    0.3653    0.9307    0.8449    0.1041    0.3519    0.1013    0.5456
    0.0777    0.2032    0.1217    0.1765    0.5382    0.9010    0.3021    0.3782    0.4894    0.2601    0.8854    0.9353    0.7832    0.7999    0.8523    0.5265    0.7607    0.1219
    0.9689    0.6214    0.2874    0.6755    0.6649    0.1268    0.1615    0.5746    0.8315    0.8719    0.6640    0.2559    0.1220    0.6321    0.6578    0.7979    0.2026    0.9101
    0.9854    0.1659    0.6999    0.9556    0.0614    0.8576    0.2732    0.0405    0.2763    0.0745    0.2982    0.4182    0.5300    0.7672    0.7790    0.7275    0.9912    0.6791
    0.0218    0.8157    0.6692    0.5266    0.7544    0.8949    0.9704    0.4954    0.4092    0.1072    0.2811    0.6340    0.1368    0.5224    0.7850    0.4167    0.5297    0.0832
    0.6245    0.9492    0.7152    0.6857    0.0124    0.8346    0.4096    0.7354    0.3983    0.0502    0.3693    0.2930    0.4683    0.8337    0.8658    0.8070    0.1771    0.9775
    0.6870    0.6068    0.0948    0.1037    0.2172    0.7207    0.7607    0.4923    0.4281    0.8444    0.4177    0.7698    0.8011    0.2282    0.9263    0.2867    0.6608    0.0106
    0.3416    0.7350    0.1311    0.5630    0.4326    0.9521    0.3382    0.8601    0.1831    0.9803    0.5003    0.8731    0.7079    0.7518    0.7566    0.3792    0.3389    0.0066
    0.2675    0.1755    0.3883    0.5547    0.6371    0.5354    0.2249    0.2185    0.9214    0.2970    0.5880    0.2335    0.5964    0.8210    0.7455    0.4742    0.8233    0.3696
    0.9226    0.4389    0.2317    0.0394    0.9769    0.5066    0.9891    0.9546    0.3161    0.5429    0.8511    0.2614    0.1298    0.3348    0.0529    0.6891    0.7804    0.5700
    0.1555    0.1156    0.3545    0.6355    0.2026    0.7657    0.8106    0.6579    0.5160    0.9835    0.8647    0.4963    0.9264    0.3115    0.0675    0.4077    0.9339    0.9659
    0.6028    0.4042    0.6713    0.7824    0.6801    0.2555    0.1761    0.7524    0.5642    0.6044    0.8183    0.1537    0.9510    0.7757    0.8191    0.9808    0.0996    0.5567
    0.2172    0.7580    0.4633    0.5550    0.9238    0.4427    0.4571    0.8057    0.6456    0.5347    0.6085    0.0689    0.2484    0.7027    0.7900    0.4691    0.0006    0.2475

  Columns 19 through 24

    0.8961    0.0185    0.4097    0.9820    0.4861    0.1358
    0.6896    0.3560    0.0611    0.2565    0.6567    0.5527
    0.9853    0.4790    0.4022    0.4059    0.2297    0.2899
    0.6199    0.9724    0.0968    0.2518    0.7909    0.3703
    0.7431    0.4402    0.1016    0.7441    0.1046    0.5387
    0.5874    0.4211    0.8784    0.4174    0.9354    0.4600
    0.2468    0.0025    0.3265    0.5686    0.3060    0.7895
    0.1318    0.7410    0.4084    0.2953    0.7816    0.8401
    0.7108    0.7672    0.4406    0.8921    0.8060    0.9904
    0.1390    0.6684    0.9163    0.6846    0.3518    0.6135
    0.6851    0.2261    0.9798    0.2165    0.6147    0.7627
    0.7724    0.1517    0.3109    0.9782    0.7471    0.2690
    0.5132    0.3901    0.4891    0.7970    0.9795    0.0272
    0.8987    0.4079    0.6082    0.0012    0.5494    0.6086
    0.7871    0.8517    0.0269    0.4020    0.6207    0.5877
    0.6179    0.5386    0.0519    0.3862    0.8829    0.9346
    0.7416    0.3274    0.6704    0.9744    0.9963    0.8781
    0.9112    0.1536    0.2371    0.3388    0.3357    0.9540
    0.1748    0.1987    0.5937    0.8423    0.8329    0.6167
    0.0712    0.0584    0.9423    0.6098    0.6731    0.9422
    0.5297    0.7098    0.5149    0.1008    0.9636    0.6208
    0.8082    0.7363    0.3139    0.2025    0.4811    0.6240
    0.8196    0.2994    0.8661    0.2874    0.2558    0.5696
    0.9389    0.1150    0.7261    0.0519    0.8548    0.0834


(:,:,2) =

  Columns 1 through 18

    0.4161    0.8839    0.9901    0.1626    0.5487    0.4478    0.9689    0.4949    0.3178    0.0750    0.9463    0.7865    0.4011    0.4909    0.5797    0.3040    0.7563    0.3784
    0.7904    0.2249    0.5681    0.1411    0.1626    0.5047    0.5832    0.9303    0.7208    0.1541    0.1857    0.4772    0.3325    0.9438    0.2230    0.8887    0.3851    0.9683
    0.3335    0.8849    0.1631    0.9949    0.1668    0.8721    0.4724    0.7629    0.7847    0.6068    0.4128    0.4953    0.3917    0.8258    0.5887    0.5397    0.8976    0.6097
    0.5495    0.0128    0.1610    0.9086    0.8884    0.5779    0.3105    0.6749    0.2623    0.1983    0.2385    0.7371    0.9180    0.7535    0.7741    0.3495    0.1483    0.1554
    0.6389    0.8440    0.0943    0.8073    0.8530    0.0336    0.8789    0.6836    0.5290    0.8265    0.3611    0.3526    0.5239    0.0984    0.3264    0.9481    0.8620    0.1277
    0.4159    0.7037    0.9194    0.0122    0.8043    0.0688    0.5169    0.6376    0.1980    0.6789    0.1724    0.8520    0.6031    0.1638    0.0044    0.2127    0.7811    0.8241
    0.5387    0.1871    0.6193    0.8296    0.5497    0.8706    0.4651    0.1027    0.8921    0.1102    0.3052    0.3382    0.7703    0.9237    0.5569    0.5889    0.5370    0.1549
    0.8833    0.2132    0.6204    0.7227    0.7203    0.6385    0.4217    0.5866    0.2012    0.7564    0.9637    0.0823    0.5486    0.1026    0.8838    0.1993    0.1709    0.9858
    0.3892    0.8247    0.7854    0.5722    0.5661    0.9401    0.5614    0.1489    0.5353    0.4966    0.0232    0.8867    0.2317    0.0198    0.7216    0.4681    0.2236    0.1682
    0.0108    0.8239    0.2776    0.0778    0.5409    0.5065    0.6267    0.3933    0.6916    0.8861    0.5555    0.8388    0.0829    0.4638    0.6946    0.4200    0.2629    0.4120
    0.0807    0.1955    0.1096    0.0771    0.2812    0.2401    0.3633    0.5385    0.0545    0.3184    0.2253    0.6934    0.7504    0.7661    0.7223    0.1901    0.6583    0.8088
    0.0779    0.3900    0.9041    0.6470    0.1562    0.6900    0.0189    0.2805    0.7573    0.6440    0.7913    0.0575    0.5812    0.7298    0.4705    0.3588    0.7010    0.1391
    0.3502    0.1195    0.0664    0.5948    0.4015    0.4921    0.2560    0.7541    0.4582    0.1296    0.6848    0.4708    0.5017    0.5152    0.5597    0.6039    0.2892    0.1629
    0.8923    0.4202    0.5960    0.8055    0.9837    0.6006    0.1783    0.0829    0.4075    0.5915    0.1866    0.6060    0.7851    0.1734    0.3470    0.0264    0.2273    0.0307
    0.2149    0.4920    0.4459    0.0938    0.9644    0.0517    0.2212    0.0804    0.9585    0.9300    0.8769    0.6815    0.4556    0.9558    0.6407    0.2735    0.4671    0.3248
    0.6069    0.3535    0.9728    0.3485    0.0396    0.5302    0.3624    0.9807    0.5787    0.5984    0.9257    0.0053    0.8587    0.3369    0.9665    0.4010    0.8554    0.8674
    0.9124    0.0078    0.3438    0.0680    0.6062    0.4214    0.1819    0.3256    0.4040    0.4939    0.0601    0.4366    0.6124    0.4953    0.7785    0.1912    0.7543    0.6663
    0.5459    0.4128    0.6975    0.0049    0.3612    0.6614    0.0454    0.2826    0.7058    0.5522    0.7273    0.7612    0.2653    0.3542    0.5319    0.1051    0.1433    0.1224
    0.9476    0.4458    0.3365    0.4988    0.7646    0.4999    0.4141    0.3371    0.8990    0.7792    0.5612    0.1068    0.0937    0.0489    0.0660    0.5289    0.2987    0.0633
    0.0694    0.6018    0.8901    0.2814    0.9158    0.6084    0.5434    0.9569    0.9746    0.7050    0.8317    0.3718    0.6453    0.5815    0.2616    0.6141    0.1424    0.1543
    0.2529    0.5856    0.7839    0.6696    0.8159    0.9853    0.4181    0.9001    0.7254    0.2250    0.4989    0.4358    0.8951    0.5010    0.7408    0.3580    0.3027    0.1902
    0.9148    0.6096    0.9300    0.2355    0.9626    0.1885    0.5149    0.7309    0.3588    0.5299    0.9068    0.3619    0.8318    0.6977    0.2999    0.0266    0.6713    0.9094
    0.0361    0.8749    0.8145    0.2374    0.6148    0.9767    0.8278    0.2559    0.6791    0.2415    0.2980    0.8786    0.2043    0.4299    0.5005    0.4241    0.7754    0.9003
    0.1944    0.4058    0.2908    0.9131    0.3227    0.3582    0.6439    0.4238    0.7533    0.5685    0.6170    0.2714    0.2062    0.1020    0.1088    0.2966    0.2005    0.6493

  Columns 19 through 24

    0.2503    0.0712    0.3321    0.8080    0.7354    0.9571
    0.0923    0.6577    0.1056    0.4116    0.3650    0.4557
    0.6037    0.9274    0.0697    0.3006    0.5531    0.7836
    0.2627    0.2036    0.9331    0.1008    0.9645    0.9759
    0.6825    0.4509    0.5659    0.1715    0.0454    0.9487
    0.9350    0.3323    0.8636    0.9348    0.5196    0.8343
    0.5856    0.8101    0.1453    0.5455    0.2648    0.8814
    0.2282    0.9630    0.1748    0.4286    0.3005    0.2836
    0.4034    0.3854    0.8549    0.6907    0.1196    0.4534
    0.0389    0.8953    0.5794    0.1445    0.1093    0.7760
    0.9053    0.0409    0.3175    0.0360    0.8201    0.6723
    0.3003    0.3680    0.9631    0.1052    0.5779    0.7454
    0.1910    0.2215    0.0577    0.0583    0.5479    0.1493
    0.5764    0.5711    0.3261    0.7362    0.8544    0.6865
    0.2083    0.0314    0.4148    0.9497    0.5558    0.8024
    0.7600    0.4743    0.9833    0.4169    0.7781    0.7961
    0.4637    0.3168    0.6889    0.8119    0.2137    0.9546
    0.0626    0.6823    0.3516    0.6268    0.3096    0.7219
    0.1084    0.3532    0.4783    0.6901    0.2567    0.5016
    0.3957    0.1401    0.6221    0.9627    0.9776    0.4102
    0.4505    0.6083    0.4875    0.1254    0.3526    0.1698
    0.2706    0.5080    0.9880    0.2636    0.4430    0.7665
    0.1419    0.3048    0.6101    0.1425    0.8649    0.6328
    0.1488    0.5828    0.4112    0.9833    0.9509    0.3904


(:,:,3) =

  Columns 1 through 18

    0.9096    0.3632    0.8107    0.3129    0.4775    0.8760    0.7465    0.4627    0.8095    0.4694    0.4409    0.6664    0.8904    0.0151    0.7266    0.1980    0.5191    0.8011
    0.7220    0.2391    0.3598    0.3943    0.8658    0.6611    0.0499    0.9507    0.8177    0.2780    0.5347    0.7247    0.3689    0.6903    0.3469    0.4156    0.3235    0.3565
    0.2552    0.2471    0.8766    0.0439    0.4671    0.1414    0.2955    0.1295    0.1054    0.7743    0.1817    0.5652    0.6573    0.8413    0.1299    0.6697    0.4699    0.6645
    0.1395    0.5898    0.0712    0.5984    0.0921    0.0028    0.9971    0.0243    0.6226    0.0580    0.8691    0.6421    0.3670    0.8862    0.7513    0.6879    0.4962    0.3757
    0.6973    0.7880    0.2280    0.4488    0.1969    0.0232    0.8439    0.4120    0.8127    0.0738    0.0704    0.1734    0.5300    0.1872    0.7607    0.6043    0.8856    0.3630
    0.8842    0.4656    0.0161    0.5691    0.3770    0.6098    0.3903    0.7416    0.9411    0.0843    0.1294    0.4292    0.8841    0.0345    0.5542    0.2204    0.0161    0.3342
    0.2306    0.0996    0.2542    0.2886    0.9689    0.5777    0.5286    0.9984    0.9075    0.7563    0.6569    0.1332    0.3843    0.0401    0.0966    0.6220    0.6638    0.4109
    0.9055    0.7155    0.9450    0.8547    0.1205    0.6189    0.0286    0.3130    0.6592    0.1225    0.4851    0.2343    0.0352    0.4948    0.8859    0.7056    0.7209    0.3797
    0.4791    0.4542    0.4066    0.6667    0.8468    0.4530    0.8790    0.0971    0.3792    0.7539    0.9742    0.8867    0.7504    0.6442    0.4498    0.1905    0.2184    0.6800
    0.9840    0.4064    0.6066    0.1340    0.0869    0.8441    0.3375    0.9221    0.1844    0.5530    0.0158    0.1793    0.5248    0.5606    0.7729    0.8824    0.5450    0.8912
    0.5511    0.9057    0.4506    0.2271    0.1907    0.6072    0.9413    0.5153    0.5837    0.3482    0.4410    0.7654    0.8107    0.5707    0.9818    0.2624    0.0458    0.9381
    0.8067    0.2843    0.0038    0.9158    0.3024    0.2627    0.6316    0.7178    0.5973    0.2603    0.8944    0.0061    0.0933    0.3268    0.2761    0.4859    0.0874    0.5990
    0.1531    0.8378    0.4524    0.3258    0.9601    0.9294    0.9032    0.6785    0.7272    0.0744    0.1827    0.6917    0.8057    0.4572    0.8381    0.9615    0.4883    0.3467
    0.0268    0.7928    0.1964    0.9763    0.3889    0.7217    0.6655    0.6413    0.6625    0.4561    0.3433    0.2051    0.7113    0.6099    0.5328    0.6778    0.4609    0.9088
    0.2940    0.5734    0.9834    0.5861    0.6340    0.9407    0.1521    0.1856    0.5413    0.2675    0.7803    0.4050    0.1164    0.8370    0.8726    0.6550    0.8619    0.3447
    0.0649    0.0283    0.9864    0.6222    0.2651    0.6185    0.4190    0.7742    0.6409    0.4803    0.7142    0.3303    0.1284    0.8848    0.0745    0.6691    0.5376    0.4558
    0.9802    0.5199    0.2292    0.7138    0.7867    0.3927    0.7014    0.1241    0.7581    0.8482    0.5361    0.5457    0.5189    0.6881    0.8936    0.0797    0.9169    0.9242
    0.2512    0.2853    0.9964    0.8142    0.6361    0.9579    0.5180    0.8315    0.3730    0.3882    0.2215    0.3071    0.5542    0.7925    0.5925    0.7271    0.6980    0.2703
    0.7405    0.0935    0.8825    0.4746    0.7850    0.3369    0.4765    0.5722    0.6502    0.1300    0.0019    0.5436    0.7479    0.2930    0.7597    0.2704    0.7803    0.9603
    0.8348    0.6606    0.4480    0.8105    0.7768    0.4130    0.9387    0.1887    0.1900    0.2846    0.5715    0.0923    0.9351    0.2660    0.6589    0.7598    0.5394    0.8449
    0.7373    0.5760    0.5874    0.0441    0.5981    0.3639    0.7334    0.4823    0.5651    0.7932    0.4518    0.3611    0.5782    0.4342    0.1080    0.0968    0.0382    0.2413
    0.0436    0.4888    0.1186    0.4915    0.1855    0.9751    0.4172    0.4530    0.5845    0.4417    0.4366    0.4614    0.4278    0.6352    0.9192    0.8633    0.2150    0.5850
    0.4842    0.7598    0.9972    0.2251    0.0449    0.5175    0.7410    0.4615    0.8325    0.3779    0.4585    0.4513    0.9723    0.3228    0.7479    0.8848    0.7749    0.3216
    0.6424    0.3180    0.3952    0.4905    0.3845    0.7604    0.1176    0.9363    0.2984    0.5879    0.3883    0.6291    0.7035    0.5308    0.0865    0.7527    0.6821    0.2741

  Columns 19 through 24

    0.1198    0.9906    0.5852    0.5529    0.8885    0.9849
    0.5252    0.7294    0.8147    0.5417    0.7884    0.0777
    0.1807    0.4948    0.9925    0.0843    0.7378    0.9452
    0.3255    0.2063    0.0022    0.5146    0.4873    0.4632
    0.0718    0.6109    0.3904    0.3419    0.2541    0.5134
    0.6510    0.0828    0.6122    0.8316    0.8275    0.2416
    0.0401    0.7252    0.2685    0.2045    0.8550    0.9120
    0.7909    0.6029    0.6674    0.3387    0.0433    0.2029
    0.8384    0.1395    0.4025    0.8678    0.4599    0.9137
    0.4419    0.5085    0.9907    0.4721    0.9553    0.5840
    0.7399    0.8951    0.5190    0.3015    0.2350    0.2997
    0.0433    0.3391    0.4639    0.6861    0.7665    0.1689
    0.8827    0.7271    0.6184    0.7209    0.4297    0.6433
    0.8428    0.0208    0.9854    0.3917    0.5065    0.9744
    0.1038    0.7772    0.1787    0.1654    0.0670    0.8314
    0.9409    0.8278    0.7209    0.4858    0.3856    0.0675
    0.5323    0.6430    0.4650    0.9236    0.1306    0.3027
    0.2948    0.8435    0.3218    0.2686    0.4927    0.3531
    0.1762    0.6059    0.5228    0.5061    0.5236    0.1677
    0.7554    0.4129    0.2102    0.2705    0.5215    0.8361
    0.7002    0.1177    0.0256    0.6401    0.0456    0.3008
    0.5429    0.3483    0.4267    0.9438    0.9621    0.8940
    0.7704    0.2141    0.8112    0.6379    0.0851    0.3999
    0.9298    0.2669    0.0976    0.0829    0.0731    0.6715


(:,:,4) =

  Columns 1 through 18

    0.5744    0.0597    0.3644    0.9607    0.9667    0.6341    0.5389    0.5190    0.4218    0.0544    0.2446    0.7637    0.7035    0.0823    0.4017    0.3111    0.6274    0.5403
    0.3862    0.6102    0.0683    0.4315    0.0992    0.7520    0.6483    0.4515    0.3001    0.5050    0.3239    0.8420    0.6136    0.2485    0.0429    0.7736    0.7978    0.4760
    0.2239    0.9563    0.6434    0.6329    0.7197    0.0472    0.1433    0.9269    0.3735    0.7928    0.2729    0.3088    0.0493    0.0058    0.2441    0.4190    0.8822    0.1373
    0.5954    0.1348    0.3112    0.9615    0.1001    0.8380    0.1780    0.6270    0.8155    0.7245    0.7075    0.8239    0.2076    0.8520    0.9835    0.6235    0.4481    0.7904
    0.5620    0.1366    0.4693    0.6656    0.0865    0.7361    0.5467    0.5311    0.2254    0.5113    0.2886    0.6490    0.2634    0.1506    0.5226    0.2826    0.1913    0.7964
    0.8619    0.1590    0.3997    0.0767    0.0022    0.9975    0.7864    0.4516    0.1922    0.0081    0.0913    0.4488    0.4832    0.0387    0.8950    0.2098    0.8545    0.1968
    0.0977    0.0057    0.2449    0.0497    0.5574    0.3985    0.0409    0.2511    0.2780    0.9502    0.5220    0.4391    0.7019    0.9312    0.5350    0.1598    0.5123    0.3002
    0.8300    0.0376    0.8876    0.6902    0.5468    0.9818    0.2933    0.8014    0.8060    0.6166    0.2657    0.9983    0.9854    0.2111    0.6472    0.4483    0.9977    0.5974
    0.0089    0.3993    0.8686    0.0266    0.5729    0.9126    0.7179    0.1973    0.2732    0.0292    0.4664    0.5561    0.8544    0.4832    0.6408    0.2515    0.2198    0.6458
    0.8404    0.0848    0.4457    0.3859    0.0003    0.7614    0.3755    0.4714    0.6591    0.0946    0.3732    0.1741    0.0226    0.5534    0.0858    0.3653    0.1616    0.6939
    0.7896    0.8630    0.5430    0.4766    0.8038    0.2614    0.5143    0.0851    0.3001    0.1761    0.1600    0.1704    0.2417    0.7846    0.1767    0.2027    0.8020    0.4293
    0.2562    0.8058    0.9191    0.6740    0.8484    0.4821    0.5225    0.4378    0.7452    0.4037    0.0758    0.7140    0.9456    0.4458    0.3991    0.4238    0.5229    0.3723
    0.4871    0.1079    0.5909    0.9938    0.1206    0.9262    0.1785    0.1683    0.8922    0.9275    0.7746    0.7219    0.8075    0.2701    0.0336    0.8108    0.5648    0.7859
    0.6471    0.4243    0.1698    0.5520    0.4355    0.6046    0.7234    0.2581    0.7309    0.7205    0.1174    0.1616    0.6061    0.6146    0.1207    0.3155    0.1555    0.8025
    0.8770    0.3445    0.4101    0.3505    0.2323    0.2243    0.1949    0.0179    0.6963    0.7133    0.3669    0.7491    0.9015    0.9006    0.9095    0.8209    0.9172    0.5900
    0.0169    0.8591    0.0679    0.7794    0.0084    0.2666    0.1370    0.2329    0.3110    0.5431    0.5042    0.9050    0.2963    0.8806    0.0089    0.5276    0.1716    0.7625
    0.6115    0.3283    0.9729    0.0243    0.3105    0.9751    0.8372    0.3112    0.6812    0.1861    0.9070    0.3980    0.6452    0.0386    0.3018    0.6557    0.8638    0.7143
    0.5478    0.5694    0.9830    0.6124    0.9529    0.0271    0.4924    0.9118    0.5902    0.2028    0.4202    0.9188    0.3957    0.8270    0.2985    0.3853    0.5735    0.8213
    0.6444    0.6511    0.9084    0.6291    0.1903    0.0093    0.3566    0.1317    0.1244    0.2749    0.7569    0.5498    0.4592    0.8140    0.0681    0.8674    0.9880    0.3174
    0.7707    0.2358    0.4725    0.4595    0.7799    0.5010    0.0564    0.7418    0.9501    0.6084    0.4548    0.4097    0.5673    0.2320    0.9628    0.3768    0.4491    0.4783
    0.4352    0.7941    0.4097    0.8482    0.6518    0.1219    0.2563    0.3143    0.6425    0.0852    0.0325    0.5623    0.6556    0.3918    0.2084    0.0729    0.3848    0.4346
    0.1941    0.6108    0.1919    0.2480    0.0095    0.7669    0.8160    0.6503    0.9410    0.5511    0.6371    0.7723    0.9725    0.0763    0.0862    0.4552    0.1300    0.9998
    0.2044    0.1009    0.2921    0.4127    0.4225    0.6841    0.5627    0.9361    0.4108    0.5126    0.9054    0.4503    0.6599    0.6068    0.1429    0.6928    0.3775    0.6047
    0.7287    0.8931    0.8555    0.2026    0.4405    0.4718    0.7118    0.5512    0.8773    0.9065    0.3542    0.2515    0.7401    0.1013    0.9535    0.1540    0.0533    0.6596

  Columns 19 through 24

    0.9861    0.9888    0.5054    0.8058    0.2826    0.9902
    0.7995    0.5021    0.4339    0.2141    0.9741    0.9868
    0.7989    0.8645    0.8837    0.0632    0.2944    0.4547
    0.8295    0.6990    0.9077    0.1180    0.5152    0.6857
    0.2683    0.4186    0.8451    0.5149    0.7711    0.0865
    0.0902    0.1124    0.9376    0.2906    0.4967    0.6534
    0.1819    0.0453    0.6726    0.0114    0.5757    0.2910
    0.9884    0.7406    0.0866    0.6364    0.7216    0.9845
    0.4936    0.2492    0.5300    0.3110    0.0910    0.3037
    0.0549    0.9437    0.4833    0.1015    0.4176    0.0271
    0.2570    0.2014    0.3186    0.8915    0.5841    0.9486
    0.1823    0.5233    0.4164    0.3992    0.3524    0.4707
    0.3031    0.5103    0.3381    0.9473    0.0594    0.0731
    0.8151    0.0422    0.8662    0.0410    0.0309    0.9982
    0.0948    0.2719    0.0225    0.5189    0.0823    0.2480
    0.3979    0.6899    0.9562    0.8021    0.6276    0.4429
    0.8409    0.1937    0.9709    0.4663    0.8408    0.8353
    0.7803    0.4046    0.1673    0.7211    0.9678    0.1201
    0.6621    0.1189    0.1156    0.8426    0.3322    0.4016
    0.5923    0.2347    0.6635    0.4817    0.2025    0.8551
    0.5295    0.9671    0.3456    0.7753    0.9157    0.3238
    0.6396    0.1693    0.4366    0.0663    0.7183    0.2405
    0.7700    0.8481    0.9884    0.8039    0.9964    0.1257
    0.1854    0.4819    0.2607    0.5123    0.2392    0.2363


(:,:,5) =

  Columns 1 through 18

    0.6192    0.8152    0.7712    0.5391    0.7826    0.7986    0.3673    0.3895    0.8254    0.4806    0.7384    0.3359    0.1320    0.8788    0.6391    0.8380    0.0131    0.9871
    0.1422    0.4842    0.2868    0.0763    0.1997    0.4351    0.6427    0.3131    0.8300    0.5520    0.7946    0.2116    0.9808    0.1864    0.6410    0.3233    0.0768    0.8914
    0.3453    0.2298    0.1391    0.1300    0.9933    0.7638    0.7112    0.2606    0.2282    0.7786    0.0347    0.4526    0.1689    0.0305    0.6790    0.0712    0.9307    0.1007
    0.3073    0.0902    0.3875    0.2950    0.4544    0.1607    0.7627    0.9123    0.7100    0.1563    0.9930    0.6535    0.5780    0.3123    0.0851    0.4970    0.1441    0.5234
    0.9170    0.8923    0.0243    0.1319    0.7439    0.2842    0.1398    0.6758    0.9590    0.7465    0.4901    0.4653    0.1457    0.4661    0.4282    0.3914    0.0244    0.6609
    0.0418    0.6886    0.7956    0.5427    0.2563    0.4637    0.4523    0.5096    0.7813    0.2468    0.0714    0.1870    0.6741    0.6618    0.4762    0.3280    0.9310    0.3073
    0.9566    0.4000    0.3519    0.6490    0.9711    0.0164    0.0284    0.3465    0.8234    0.6003    0.5243    0.4651    0.7826    0.4297    0.1171    0.6466    0.2951    0.2956
    0.1605    0.0271    0.3064    0.7754    0.4970    0.6814    0.8281    0.6951    0.4022    0.2424    0.5932    0.7101    0.3991    0.0033    0.7155    0.2232    0.3602    0.5844
    0.6399    0.8267    0.4890    0.1504    0.4670    0.2350    0.1878    0.3338    0.0832    0.3721    0.0386    0.8864    0.5058    0.8768    0.0108    0.9346    0.9287    0.3025
    0.4780    0.0698    0.9560    0.0069    0.7720    0.1637    0.5181    0.5324    0.1860    0.9195    0.5491    0.8738    0.5628    0.0992    0.5555    0.7991    0.7062    0.6179
    0.9997    0.8587    0.7709    0.3532    0.0869    0.2917    0.2443    0.8968    0.4299    0.5607    0.1048    0.3073    0.7101    0.2495    0.9367    0.0022    0.4499    0.4651
    0.5040    0.8511    0.8076    0.4355    0.4289    0.3805    0.9098    0.0108    0.2504    0.1602    0.5749    0.5716    0.0283    0.3086    0.5540    0.5387    0.1313    0.3577
    0.9306    0.6643    0.8891    0.8270    0.6868    0.6342    0.8457    0.2981    0.1454    0.9020    0.0572    0.7952    0.2440    0.3045    0.1764    0.7674    0.8983    0.0809
    0.6282    0.2227    0.1864    0.1106    0.8982    0.3756    0.6262    0.9720    0.2810    0.5002    0.6581    0.2537    0.6146    0.6023    0.7460    0.9886    0.7984    0.0616
    0.0939    0.4412    0.5348    0.2333    0.2915    0.0394    0.2651    0.1687    0.1653    0.4264    0.9838    0.6316    0.6053    0.8785    0.9944    0.7515    0.5557    0.0334
    0.2544    0.3427    0.2111    0.0298    0.0842    0.5913    0.9591    0.8618    0.0165    0.8826    0.6910    0.3814    0.4298    0.8175    0.5903    0.7212    0.9572    0.7010
    0.6740    0.1984    0.9758    0.8571    0.5873    0.8921    0.0224    0.1630    0.6414    0.3712    0.2760    0.1464    0.5485    0.7167    0.4866    0.5138    0.1710    0.7311
    0.4983    0.1884    0.4872    0.1388    0.4278    0.1971    0.7111    0.9620    0.0833    0.0794    0.5962    0.1250    0.2492    0.4185    0.0387    0.2324    0.6273    0.8493
    0.0123    0.2234    0.8289    0.7506    0.4695    0.1524    0.0784    0.9611    0.7290    0.9576    0.3462    0.5966    0.2263    0.2880    0.0589    0.2549    0.3951    0.6823
    0.1041    0.1661    0.8555    0.4885    0.7692    0.2717    0.4233    0.2733    0.5606    0.3662    0.5838    0.4751    0.2009    0.6046    0.5000    0.6294    0.8777    0.7537
    0.4421    0.8519    0.0565    0.7126    0.8175    0.9884    0.0920    0.4063    0.9865    0.7398    0.8981    0.3454    0.4123    0.7269    0.5684    0.5609    0.3071    0.9530
    0.4579    0.9704    0.8695    0.3790    0.0057    0.5131    0.6609    0.3448    0.2187    0.6666    0.1897    0.0294    0.3760    0.4534    0.4624    0.4078    0.0260    0.3893
    0.9996    0.5771    0.4205    0.4326    0.0746    0.0348    0.4283    0.1399    0.2689    0.8625    0.8926    0.7017    0.8337    0.6382    0.8347    0.4441    0.0627    0.5349
    0.3158    0.5192    0.6941    0.8744    0.4127    0.0632    0.4178    0.0770    0.9556    0.3976    0.1861    0.6391    0.2616    0.8150    0.4390    0.2152    0.0351    0.5076

  Columns 19 through 24

    0.2902    0.6711    0.8909    0.3890    0.1183    0.5289
    0.3974    0.9958    0.8293    0.8746    0.1739    0.4905
    0.1205    0.0953    0.7629    0.5988    0.6061    0.1467
    0.8669    0.3632    0.7884    0.2336    0.4425    0.4707
    0.0761    0.9884    0.3554    0.3660    0.4406    0.1011
    0.2283    0.3248    0.9197    0.7331    0.7545    0.8440
    0.5729    0.1958    0.4761    0.5111    0.1432    0.2432
    0.3130    0.1591    0.2653    0.0537    0.6645    0.0651
    0.0382    0.4827    0.1856    0.1963    0.5450    0.1018
    0.0184    0.8792    0.6616    0.7111    0.1808    0.1174
    0.7730    0.1084    0.3635    0.8619    0.3069    0.9767
    0.0055    0.0839    0.9656    0.8430    0.4220    0.3183
    0.9419    0.3997    0.6915    0.0960    0.0288    0.0271
    0.1282    0.0418    0.4091    0.9017    0.9052    0.0951
    0.6424    0.7607    0.8239    0.0817    0.8655    0.1104
    0.5545    0.8713    0.8666    0.5962    0.0550    0.5824
    0.8699    0.6295    0.4589    0.5215    0.3328    0.6430
    0.7081    0.4396    0.8458    0.1564    0.7672    0.6274
    0.9764    0.9380    0.2260    0.6797    0.5456    0.9355
    0.5806    0.4329    0.8973    0.3814    0.8199    0.5725
    0.4925    0.0424    0.9892    0.6347    0.7967    0.5947
    0.7591    0.3318    0.4734    0.2078    0.5573    0.7674
    0.3521    0.4166    0.8434    0.3832    0.1115    0.7701
    0.0534    0.3183    0.1704    0.5722    0.3787    0.4528


(:,:,6) =

  Columns 1 through 18

    0.2022    0.5692    0.2408    0.0137    0.2520    0.0162    0.9362    0.9059    0.7996    0.7717    0.0348    0.2977    0.8677    0.1777    0.6964    0.9165    0.9135    0.8336
    0.9794    0.4546    0.7063    0.9111    0.3624    0.8810    0.3023    0.6265    0.6166    0.3651    0.9731    0.2532    0.0552    0.7796    0.9114    0.2146    0.7755    0.1964
    0.6124    0.5209    0.4406    0.2584    0.6610    0.6274    0.3756    0.7092    0.2416    0.3691    0.2692    0.0656    0.0146    0.2868    0.9547    0.8952    0.7519    0.7859
    0.9952    0.4583    0.7724    0.2923    0.1717    0.2168    0.8517    0.2883    0.7224    0.5101    0.0401    0.0075    0.0948    0.4837    0.4227    0.7649    0.6871    0.3702
    0.6042    0.0435    0.1198    0.8912    0.5793    0.4560    0.7563    0.8721    0.7956    0.8540    0.7798    0.2179    0.1443    0.5971    0.0225    0.5679    0.6796    0.6592
    0.9189    0.3048    0.2426    0.9138    0.9334    0.4640    0.9266    0.8789    0.5041    0.2558    0.1504    0.0639    0.6157    0.4597    0.2307    0.4656    0.7061    0.6376
    0.9714    0.6210    0.2045    0.6090    0.6971    0.6927    0.8648    0.2061    0.5963    0.2634    0.2351    0.7568    0.7159    0.1912    0.9308    0.8299    0.6944    0.0230
    0.6243    0.3748    0.7896    0.0413    0.4326    0.6449    0.7971    0.5123    0.2049    0.9283    0.8780    0.4101    0.0900    0.8374    0.1130    0.2739    0.0989    0.3427
    0.1859    0.1696    0.5091    0.5275    0.7694    0.8754    0.1849    0.9461    0.5070    0.7340    0.0801    0.0364    0.2033    0.3670    0.7676    0.0636    0.2411    0.8797
    0.9005    0.6626    0.9364    0.3421    0.7114    0.7121    0.6647    0.0880    0.0108    0.4616    0.7647    0.2008    0.5858    0.2663    0.0261    0.7476    0.9907    0.6004
    0.5099    0.6540    0.3704    0.0624    0.0783    0.7765    0.7890    0.4824    0.7004    0.2804    0.0679    0.9373    0.0618    0.9134    0.2936    0.6556    0.6459    0.7307
    0.1634    0.0520    0.8513    0.4048    0.2841    0.0088    0.6757    0.1280    0.4319    0.2768    0.6953    0.3692    0.7399    0.3685    0.0191    0.7334    0.5849    0.1420
    0.9483    0.2242    0.9893    0.2290    0.4477    0.1365    0.0318    0.8086    0.3253    0.4313    0.5426    0.1366    0.0011    0.7793    0.8164    0.2820    0.0825    0.6890
    0.7993    0.6295    0.6552    0.2355    0.8468    0.4534    0.6468    0.5584    0.8330    0.8546    0.9361    0.3236    0.7403    0.1391    0.6016    0.8296    0.6723    0.4418
    0.0307    0.4326    0.2968    0.2273    0.3926    0.0468    0.6602    0.0258    0.5042    0.3131    0.0516    0.2705    0.5419    0.8538    0.1161    0.0565    0.1218    0.8025
    0.1114    0.7026    0.5080    0.9784    0.7675    0.6871    0.7022    0.4648    0.2963    0.0340    0.8653    0.4274    0.7105    0.6953    0.1934    0.9974    0.0039    0.8499
    0.9422    0.6192    0.3865    0.0652    0.7920    0.0419    0.6368    0.6908    0.4732    0.8457    0.1970    0.5525    0.4428    0.1860    0.6861    0.3552    0.2843    0.5264
    0.8739    0.9512    0.8436    0.1602    0.1674    0.6532    0.6853    0.4134    0.8436    0.6120    0.2539    0.5781    0.5913    0.6299    0.8499    0.9957    0.0396    0.4862
    0.5608    0.4847    0.2699    0.9875    0.6843    0.5511    0.3247    0.9494    0.0157    0.7446    0.7173    0.4154    0.7168    0.1524    0.9586    0.9924    0.3384    0.4412
    0.4204    0.7661    0.9045    0.6200    0.6986    0.5999    0.1008    0.7912    0.7599    0.8475    0.1945    0.6256    0.4414    0.4148    0.4969    0.7429    0.0084    0.3197
    0.0591    0.6292    0.9025    0.5270    0.0213    0.9272    0.7330    0.2965    0.1209    0.8159    0.1583    0.8430    0.2150    0.3661    0.6069    0.1048    0.3704    0.2419
    0.8729    0.1238    0.2673    0.9827    0.7135    0.0765    0.0140    0.4417    0.4736    0.0491    0.7424    0.5469    0.0963    0.1943    0.9794    0.8147    0.2988    0.0533
    0.0985    0.9801    0.1655    0.6200    0.7065    0.1441    0.4745    0.9817    0.9257    0.5862    0.8174    0.1429    0.6767    0.1236    0.0800    0.9050    0.2154    0.5024
    0.5291    0.6747    0.6980    0.4990    0.4035    0.0557    0.7117    0.6234    0.2983    0.8248    0.4303    0.1331    0.8670    0.5462    0.4164    0.3479    0.0425    0.7879

  Columns 19 through 24

    0.5983    0.8906    0.9851    0.6878    0.7229    0.7414
    0.4321    0.3745    0.5429    0.2218    0.3966    0.7972
    0.6220    0.2917    0.3432    0.3743    0.0404    0.6031
    0.0394    0.0711    0.4516    0.1541    0.7017    0.8764
    0.6188    0.9337    0.8879    0.3730    0.7913    0.9720
    0.2571    0.4299    0.9550    0.1715    0.9739    0.9582
    0.0978    0.5845    0.6494    0.7271    0.2531    0.1180
    0.5996    0.2562    0.6178    0.2518    0.7035    0.0062
    0.0828    0.8763    0.6587    0.1042    0.7637    0.5367
    0.4074    0.5389    0.3385    0.5757    0.1311    0.9663
    0.3478    0.9208    0.6379    0.5696    0.8489    0.5928
    0.4017    0.8571    0.1704    0.0518    0.8221    0.8162
    0.4735    0.6354    0.1658    0.9254    0.9991    0.2004
    0.6666    0.8138    0.9553    0.1699    0.9579    0.7898
    0.6145    0.4582    0.5816    0.0935    0.0766    0.6876
    0.8978    0.0709    0.6985    0.4659    0.7129    0.6206
    0.3079    0.1724    0.9443    0.3539    0.2699    0.1614
    0.8176    0.3048    0.3507    0.0047    0.1950    0.0039
    0.4681    0.8808    0.6961    0.5128    0.9107    0.6388
    0.9012    0.4133    0.6582    0.0099    0.5317    0.5900
    0.1782    0.4804    0.9096    0.3805    0.7459    0.9793
    0.2942    0.1596    0.3769    0.0704    0.7049    0.8463
    0.4901    0.5461    0.8209    0.5807    0.8984    0.4646
    0.2174    0.6901    0.6630    0.6433    0.5961    0.1847


(:,:,7) =

  Columns 1 through 18

    0.4007    0.4268    0.5693    0.4505    0.0617    0.6495    0.7079    0.8900    0.3902    0.6946    0.9655    0.6190    0.6603    0.5657    0.0640    0.5890    0.6471    0.1558
    0.5824    0.7686    0.2058    0.4685    0.5563    0.3060    0.5093    0.3759    0.7530    0.4762    0.2146    0.3318    0.2624    0.1445    0.6891    0.2272    0.5963    0.8544
    0.0292    0.7116    0.7823    0.8553    0.6191    0.0667    0.2003    0.9647    0.3436    0.7023    0.2851    0.7641    0.9027    0.8022    0.1665    0.1296    0.6408    0.7898
    0.6893    0.6073    0.3835    0.4808    0.6761    0.7155    0.2135    0.2111    0.3938    0.1366    0.5963    0.3611    0.3472    0.6030    0.1909    0.8332    0.5098    0.7257
    0.5081    0.9628    0.6164    0.0519    0.2850    0.5988    0.4395    0.1636    0.2645    0.5013    0.1092    0.9206    0.5401    0.0616    0.5253    0.6525    0.1656    0.0775
    0.2445    0.7089    0.1742    0.6237    0.5178    0.8952    0.0272    0.1028    0.1245    0.4843    0.9717    0.3368    0.1015    0.0790    0.0207    0.4785    0.3876    0.1616
    0.5247    0.1334    0.9854    0.3022    0.2175    0.0605    0.4310    0.0538    0.2336    0.1651    0.0619    0.6183    0.1684    0.1125    0.7344    0.7699    0.9203    0.7862
    0.2963    0.6848    0.1417    0.3750    0.7336    0.5530    0.4605    0.7562    0.2284    0.4102    0.6511    0.9757    0.4029    0.5465    0.6662    0.7761    0.1729    0.6932
    0.7668    0.6493    0.5492    0.7501    0.4091    0.3871    0.0700    0.0894    0.7675    0.8426    0.0266    0.1434    0.2336    0.0805    0.6515    0.0848    0.4373    0.9493
    0.0070    0.3931    0.4364    0.4039    0.3785    0.1518    0.5264    0.4765    0.3182    0.6780    0.6669    0.2619    0.6951    0.4088    0.5391    0.6920    0.5301    0.6735
    0.8009    0.9053    0.0697    0.4945    0.0515    0.6994    0.6191    0.7080    0.9018    0.7401    0.0774    0.7125    0.5816    0.2743    0.1426    0.7260    0.1664    0.9302
    0.1571    0.5861    0.4174    0.3900    0.3706    0.0884    0.8760    0.4800    0.0038    0.5718    0.0100    0.7862    0.2953    0.3571    0.7537    0.3157    0.9564    0.2957
    0.5365    0.6143    0.9066    0.0490    0.7993    0.9935    0.3518    0.5420    0.3386    0.7447    0.2190    0.8045    0.6283    0.3742    0.4198    0.3607    0.1489    0.3272
    0.4531    0.2220    0.8935    0.7189    0.2083    0.3160    0.5993    0.1513    0.8501    0.1949    0.2784    0.1469    0.5473    0.7688    0.0196    0.8606    0.2249    0.8151
    0.5952    0.4278    0.1514    0.2288    0.6281    0.0718    0.2745    0.3114    0.3866    0.2480    0.4840    0.6994    0.4233    0.4401    0.5150    0.9652    0.6155    0.2036
    0.8486    0.4820    0.6913    0.0368    0.2276    0.9045    0.2474    0.2526    0.3246    0.5626    0.0144    0.3703    0.9791    0.6940    0.5164    0.9672    0.5218    0.3396
    0.4874    0.1790    0.1495    0.9944    0.7056    0.8852    0.8277    0.5113    0.7154    0.7883    0.2926    0.3034    0.9139    0.3917    0.3625    0.5909    0.6117    0.1902
    0.8670    0.8965    0.0216    0.5037    0.3125    0.9766    0.0110    0.0573    0.7786    0.4743    0.1639    0.4056    0.1002    0.5200    0.6919    0.9036    0.9978    0.5350
    0.6604    0.1634    0.5513    0.3686    0.8912    0.1203    0.2428    0.4291    0.0777    0.5254    0.7054    0.2230    0.7650    0.1536    0.3545    0.9725    0.6099    0.4683
    0.7643    0.0365    0.8577    0.0858    0.2391    0.9554    0.1295    0.3264    0.7030    0.5125    0.8200    0.3351    0.8197    0.3425    0.7026    0.2175    0.7738    0.3069
    0.7328    0.2673    0.2244    0.9120    0.2607    0.2498    0.8112    0.3500    0.2238    0.8884    0.5110    0.0501    0.7986    0.8664    0.6515    0.2676    0.5506    0.4189
    0.4043    0.5068    0.5161    0.2691    0.1082    0.2707    0.9872    0.6110    0.6261    0.3614    0.1625    0.7800    0.5302    0.3334    0.7048    0.3040    0.4869    0.3979
    0.9890    0.0496    0.9862    0.1125    0.9626    0.6107    0.6783    0.6875    0.8619    0.3725    0.1534    0.0705    0.4352    0.7113    0.1122    0.0380    0.4217    0.5162
    0.5838    0.3134    0.3766    0.7594    0.1184    0.4499    0.1881    0.2031    0.7393    0.6835    0.4307    0.7661    0.7281    0.7733    0.9277    0.6605    0.4274    0.9576

  Columns 19 through 24

    0.4139    0.6674    0.4803    0.0992    0.2870    0.2148
    0.1876    0.2609    0.0515    0.5531    0.3509    0.4404
    0.0613    0.1016    0.0926    0.8273    0.6731    0.0222
    0.9471    0.3396    0.8048    0.6285    0.8357    0.4332
    0.7367    0.6128    0.8297    0.0262    0.1235    0.0981
    0.1896    0.5777    0.3848    0.9139    0.9860    0.4859
    0.2322    0.5906    0.5045    0.2979    0.8785    0.7720
    0.2411    0.1685    0.1940    0.9121    0.9567    0.6463
    0.1430    0.3749    0.7220    0.2875    0.4049    0.6758
    0.6981    0.0475    0.0499    0.2121    0.8056    0.2917
    0.0151    0.0784    0.0609    0.2536    0.9159    0.7126
    0.2604    0.7083    0.3211    0.4569    0.1580    0.3569
    0.1206    0.5913    0.9151    0.8595    0.6612    0.1619
    0.8480    0.4035    0.0724    0.3968    0.1270    0.5552
    0.4052    0.9182    0.8140    0.4262    0.5997    0.4059
    0.7009    0.0258    0.7703    0.1836    0.0371    0.2188
    0.7332    0.4320    0.5511    0.1729    0.1460    0.5555
    0.5281    0.9754    0.1328    0.1617    0.9039    0.5858
    0.5480    0.5076    0.1126    0.8638    0.2164    0.5631
    0.6235    0.7260    0.4289    0.6850    0.8676    0.9980
    0.2335    0.5374    0.5940    0.2926    0.9093    0.2339
    0.6319    0.5736    0.1991    0.1701    0.7647    0.6903
    0.7852    0.3402    0.0117    0.0115    0.5891    0.3160
    0.8898    0.0217    0.6102    0.0938    0.5142    0.1041


(:,:,8) =

  Columns 1 through 18

    0.8776    0.9793    0.0218    0.1383    0.1303    0.0488    0.4842    0.0976    0.4616    0.4540    0.8273    0.5617    0.6923    0.1854    0.2358    0.6741    0.3535    0.1504
    0.8261    0.7076    0.8670    0.6873    0.0956    0.7530    0.4120    0.0066    0.3169    0.5355    0.3592    0.9871    0.7953    0.4595    0.6572    0.8488    0.0086    0.7529
    0.6285    0.9433    0.4916    0.3702    0.6261    0.9358    0.8748    0.1386    0.1283    0.9599    0.4605    0.9842    0.0925    0.3384    0.0308    0.5712    0.0625    0.5523
    0.5701    0.6871    0.4962    0.5533    0.8008    0.3501    0.7898    0.4153    0.8386    0.4504    0.6376    0.2582    0.1226    0.2596    0.5632    0.2751    0.3016    0.4177
    0.9402    0.2241    0.6021    0.6425    0.2565    0.0159    0.3260    0.2738    0.4753    0.3879    0.4199    0.8664    0.1978    0.9415    0.6058    0.3740    0.9793    0.8063
    0.8417    0.6563    0.7315    0.7525    0.1239    0.9300    0.7415    0.0167    0.0952    0.1072    0.4346    0.3629    0.4915    0.9305    0.6692    0.9023    0.3518    0.0678
    0.8929    0.5534    0.9419    0.9201    0.4917    0.0001    0.4649    0.4178    0.5022    0.5742    0.3639    0.2411    0.6162    0.1523    0.4919    0.1124    0.8178    0.8608
    0.7278    0.4734    0.6453    0.7913    0.0185    0.2997    0.9926    0.2450    0.3519    0.0429    0.3704    0.7759    0.8503    0.5253    0.7069    0.7523    0.8517    0.2248
    0.2579    0.2479    0.0970    0.5347    0.8758    0.4441    0.6099    0.3145    0.2526    0.7157    0.3288    0.1643    0.5398    0.5752    0.7692    0.4056    0.2944    0.7982
    0.9346    0.2461    0.6171    0.5802    0.6283    0.1363    0.0660    0.3633    0.8551    0.5202    0.8761    0.5379    0.7374    0.8979    0.2755    0.1328    0.6577    0.1240
    0.7223    0.8975    0.4891    0.3744    0.2128    0.0104    0.4068    0.9831    0.6468    0.6863    0.2437    0.4667    0.3168    0.5376    0.7130    0.9675    0.2741    0.3043
    0.7558    0.4578    0.6588    0.8134    0.2177    0.6382    0.6755    0.6141    0.3369    0.1001    0.9045    0.7730    0.8869    0.9668    0.9379    0.3656    0.0934    0.6349
    0.8133    0.1127    0.8430    0.1837    0.3041    0.5308    0.9703    0.6506    0.1006    0.5698    0.7946    0.8818    0.6104    0.9356    0.2064    0.2282    0.0265    0.8594
    0.6782    0.0294    0.6990    0.1189    0.5183    0.8882    0.0883    0.3272    0.2898    0.3961    0.0386    0.4267    0.8663    0.2489    0.0629    0.9357    0.8247    0.5222
    0.4742    0.0833    0.2755    0.6449    0.5482    0.2733    0.3854    0.8550    0.0835    0.6862    0.7096    0.1060    0.6794    0.7658    0.5218    0.3421    0.4768    0.2648
    0.9252    0.5055    0.6625    0.7867    0.7851    0.6498    0.4838    0.5365    0.8787    0.4572    0.8745    0.5256    0.0385    0.7119    0.1041    0.5323    0.1230    0.1369
    0.2064    0.2712    0.9862    0.8562    0.9090    0.5787    0.4189    0.9966    0.6923    0.7361    0.6307    0.0047    0.3023    0.6213    0.2735    0.8737    0.3076    0.1087
    0.3019    0.7722    0.2528    0.0560    0.3998    0.0168    0.9924    0.3487    0.3809    0.7974    0.9843    0.7918    0.4819    0.9534    0.7446    0.0541    0.0087    0.9340
    0.2485    0.3740    0.7080    0.3111    0.5028    0.0586    0.5614    0.4550    0.0874    0.6422    0.8240    0.4034    0.2761    0.1720    0.9883    0.1329    0.5780    0.3971
    0.8093    0.3569    0.2962    0.2519    0.0392    0.9973    0.9241    0.5400    0.0642    0.2584    0.4717    0.2210    0.5300    0.1129    0.8052    0.9536    0.1670    0.3500
    0.3921    0.8422    0.8065    0.9486    0.6855    0.4390    0.0401    0.7460    0.1022    0.0035    0.0634    0.0989    0.4947    0.2147    0.0156    0.4651    0.7762    0.9747
    0.0756    0.7022    0.9971    0.9081    0.8519    0.7562    0.0078    0.1012    0.4118    0.3584    0.8939    0.0494    0.5921    0.9737    0.0716    0.3118    0.2775    0.6756
    0.2865    0.7353    0.0248    0.6956    0.6504    0.4422    0.6761    0.7845    0.7946    0.6644    0.9027    0.2614    0.4122    0.4920    0.8337    0.7553    0.1864    0.8723
    0.7932    0.2367    0.2406    0.9531    0.7901    0.1225    0.2542    0.9170    0.5266    0.8358    0.8546    0.7873    0.1326    0.3500    0.3827    0.3490    0.4897    0.3987

  Columns 19 through 24

    0.7344    0.2308    0.6538    0.0709    0.8753    0.1864
    0.2628    0.5960    0.3169    0.2999    0.5953    0.9433
    0.3166    0.4100    0.2867    0.8331    0.5060    0.1928
    0.5466    0.5313    0.7845    0.2238    0.2111    0.5749
    0.5352    0.4638    0.5088    0.0584    0.1002    0.0528
    0.2294    0.5141    0.2436    0.5692    0.3658    0.6107
    0.6061    0.3701    0.2430    0.5970    0.6338    0.7758
    0.3900    0.7883    0.3385    0.4503    0.4402    0.4165
    0.2607    0.2025    0.8939    0.7690    0.9584    0.9307
    0.1300    0.0255    0.0268    0.9117    0.0288    0.1174
    0.6619    0.6750    0.6399    0.4811    0.9654    0.8593
    0.6122    0.5836    0.9191    0.2658    0.6849    0.7828
    0.7095    0.8999    0.1564    0.7670    0.2882    0.5653
    0.5425    0.3244    0.1561    0.1143    0.8451    0.2753
    0.8727    0.8641    0.0418    0.5294    0.1445    0.5469
    0.1651    0.3051    0.4714    0.1570    0.1787    0.8231
    0.7410    0.6591    0.4628    0.1392    0.4182    0.2294
    0.9686    0.0938    0.5656    0.0003    0.4332    0.9976
    0.4950    0.4063    0.7152    0.3342    0.7597    0.8886
    0.5336    0.7873    0.7536    0.8626    0.1465    0.9327
    0.5756    0.9581    0.6451    0.9717    0.6996    0.5119
    0.3072    0.4024    0.1142    0.9648    0.0907    0.9144
    0.2861    0.5004    0.7380    0.1240    0.7274    0.2708
    0.7044    0.8307    0.0444    0.4475    0.4826    0.3153


(:,:,9) =

  Columns 1 through 18

    0.6991    0.0695    0.2322    0.6056    0.5874    0.4615    0.5887    0.1538    0.5248    0.8994    0.1694    0.9279    0.6922    0.8487    0.4518    0.8864    0.3304    0.1041
    0.7400    0.6953    0.7502    0.8792    0.8474    0.4444    0.7959    0.9917    0.5916    0.1500    0.2878    0.2539    0.5973    0.3523    0.9045    0.9331    0.1376    0.8557
    0.2922    0.1280    0.7092    0.1395    0.4048    0.3167    0.2471    0.0059    0.6905    0.0132    0.6173    0.4620    0.4119    0.5710    0.3528    0.4927    0.2909    0.6715
    0.3682    0.7136    0.6238    0.5544    0.6738    0.8630    0.9316    0.1160    0.1155    0.4122    0.3120    0.2871    0.8355    0.0582    0.6293    0.6557    0.6212    0.4650
    0.8043    0.1871    0.7754    0.0856    0.3862    0.3529    0.4189    0.2365    0.2517    0.7308    0.9558    0.2860    0.6228    0.2850    0.3444    0.6449    0.1206    0.6654
    0.9792    0.1478    0.9664    0.9693    0.7984    0.8148    0.1844    0.9639    0.2612    0.4048    0.4943    0.2602    0.9525    0.4872    0.2458    0.7047    0.4861    0.4160
    0.1690    0.0588    0.2532    0.4375    0.6487    0.5193    0.8269    0.5428    0.4667    0.0088    0.9509    0.6352    0.2874    0.5176    0.6724    0.1575    0.7897    0.3258
    0.3957    0.9349    0.1148    0.6616    0.5258    0.0064    0.3659    0.1058    0.0488    0.0166    0.1581    0.3312    0.4979    0.8912    0.2007    0.4107    0.7018    0.6195
    0.5229    0.6258    0.7128    0.5234    0.8098    0.7807    0.3132    0.4358    0.9889    0.5198    0.5615    0.7374    0.6273    0.3205    0.9407    0.2671    0.2137    0.3669
    0.5427    0.3664    0.9831    0.9303    0.2160    0.9024    0.3529    0.4416    0.8696    0.6470    0.2608    0.8816    0.0775    0.8166    0.9627    0.7417    0.3544    0.8132
    0.4922    0.0744    0.8303    0.8286    0.2494    0.6572    0.4849    0.5722    0.9795    0.5110    0.1898    0.2636    0.2878    0.3666    0.0562    0.0807    0.3802    0.7789
    0.7478    0.6929    0.5743    0.9049    0.1681    0.6347    0.9714    0.8907    0.6182    0.7414    0.0142    0.6886    0.8717    0.2543    0.4080    0.8341    0.7509    0.1281
    0.1110    0.3789    0.8085    0.2265    0.4095    0.2250    0.5875    0.4218    0.0026    0.1846    0.3294    0.9948    0.8165    0.9950    0.2849    0.1603    0.3301    0.6563
    0.9432    0.9085    0.1495    0.3347    0.4430    0.4097    0.6217    0.2718    0.0572    0.2940    0.4259    0.8528    0.7472    0.6825    0.3890    0.5645    0.0590    0.1084
    0.4013    0.3130    0.7441    0.5868    0.4857    0.2728    0.9937    0.5751    0.4518    0.3288    0.1636    0.2061    0.5305    0.5600    0.4337    0.6925    0.3171    0.2525
    0.6437    0.1269    0.6686    0.2139    0.2625    0.5035    0.0828    0.9175    0.3290    0.6333    0.7731    0.9832    0.4912    0.5677    0.3736    0.2684    0.8991    0.7196
    0.3625    0.6485    0.2955    0.0243    0.9848    0.5801    0.3220    0.6125    0.4718    0.1024    0.8374    0.0863    0.2503    0.8568    0.1342    0.1731    0.8382    0.4493
    0.9795    0.9868    0.3983    0.2915    0.4879    0.4803    0.7869    0.9222    0.8698    0.7813    0.2253    0.0386    0.9801    0.8141    0.3656    0.8703    0.1645    0.1795
    0.4233    0.0755    0.3693    0.1111    0.8487    0.4310    0.8337    0.7505    0.5678    0.4733    0.3035    0.7233    0.2583    0.0867    0.0195    0.0192    0.2215    0.1761
    0.1237    0.4891    0.5379    0.1646    0.8247    0.9390    0.6168    0.9627    0.6483    0.8270    0.4488    0.3746    0.2180    0.0883    0.1794    0.6031    0.1642    0.2467
    0.3597    0.3573    0.9717    0.4979    0.7266    0.9005    0.4188    0.8899    0.8411    0.7937    0.0601    0.2028    0.0855    0.4199    0.8923    0.7064    0.7254    0.9059
    0.3103    0.2037    0.4808    0.5393    0.1445    0.0350    0.7835    0.2312    0.0858    0.7656    0.4654    0.7513    0.0701    0.8799    0.4939    0.8918    0.9440    0.6284
    0.7668    0.9575    0.5571    0.1121    0.9596    0.8908    0.5014    0.7900    0.9190    0.7067    0.3546    0.8975    0.4489    0.0521    0.8277    0.2785    0.3639    0.5441
    0.4800    0.4922    0.9510    0.3595    0.3488    0.8502    0.0011    0.6288    0.9761    0.3919    0.1642    0.9668    0.7553    0.1549    0.7188    0.2729    0.5541    0.8409

  Columns 19 through 24

    0.3378    0.6548    0.0150    0.2001    0.6720    0.5376
    0.3980    0.1453    0.7340    0.2617    0.1515    0.5048
    0.9695    0.8448    0.6054    0.3723    0.1947    0.5573
    0.1440    0.5884    0.6974    0.1268    0.1877    0.4444
    0.9033    0.6661    0.6574    0.8276    0.0142    0.1069
    0.0998    0.4573    0.2806    0.6843    0.8329    0.3105
    0.9426    0.6322    0.5704    0.5361    0.4791    0.6612
    0.9345    0.2697    0.7879    0.6030    0.7230    0.3557
    0.5742    0.4289    0.8833    0.5743    0.4916    0.0598
    0.4214    0.6725    0.4225    0.6025    0.3102    0.1433
    0.5406    0.5582    0.6791    0.0106    0.7653    0.9819
    0.3632    0.1392    0.0464    0.6609    0.2072    0.0609
    0.0672    0.9357    0.6099    0.0271    0.2437    0.7397
    0.8045    0.1355    0.0190    0.6685    0.8439    0.3333
    0.3793    0.4783    0.6419    0.5093    0.7227    0.2885
    0.8405    0.2118    0.2151    0.6269    0.5661    0.8369
    0.2576    0.0304    0.8941    0.2526    0.6289    0.2567
    0.3014    0.9545    0.2204    0.1948    0.5473    0.8503
    0.0860    0.3403    0.9135    0.3625    0.5257    0.9389
    0.7498    0.5529    0.3014    0.3965    0.2696    0.5448
    0.4503    0.2648    0.4633    0.1114    0.6046    0.1318
    0.9522    0.7488    0.5123    0.4647    0.1868    0.1408
    0.0182    0.9269    0.8856    0.2778    0.7508    0.5254
    0.4917    0.4593    0.2965    0.6244    0.8160    0.5873


(:,:,10) =

  Columns 1 through 18

    0.0584    0.9429    0.1751    0.1992    0.4964    0.0729    0.5581    0.5682    0.7955    0.5093    0.3643    0.5462    0.4133    0.6618    0.3757    0.5869    0.0815    0.2162
    0.0052    0.5062    0.3626    0.6745    0.2275    0.0726    0.3606    0.1643    0.0912    0.2422    0.8408    0.1721    0.8543    0.2889    0.6145    0.1222    0.1976    0.9433
    0.5436    0.2320    0.5136    0.4362    0.0619    0.4654    0.9554    0.0488    0.9311    0.0172    0.4915    0.4826    0.3539    0.7373    0.6750    0.2922    0.4873    0.8284
    0.8344    0.1237    0.4939    0.5882    0.0531    0.5924    0.9782    0.5321    0.7747    0.0366    0.5427    0.7483    0.9213    0.2355    0.9100    0.4834    0.0314    0.8422
    0.4989    0.2491    0.0019    0.3355    0.0564    0.8056    0.9879    0.4177    0.3649    0.9771    0.5569    0.5574    0.7576    0.4891    0.5325    0.0926    0.4181    0.2488
    0.7672    0.6816    0.9683    0.7925    0.6088    0.6470    0.2478    0.1074    0.0744    0.0575    0.3917    0.5694    0.4541    0.7458    0.9046    0.3310    0.1601    0.6955
    0.1532    0.7016    0.5434    0.3605    0.2906    0.2288    0.2481    0.0272    0.0530    0.8085    0.8347    0.4275    0.3189    0.5688    0.6842    0.3431    0.8446    0.6889
    0.5763    0.8380    0.6941    0.9284    0.9491    0.3128    0.0640    0.2270    0.0530    0.4418    0.0813    0.8582    0.0069    0.3039    0.5322    0.0965    0.1809    0.6398
    0.9946    0.0818    0.5972    0.0282    0.5404    0.5296    0.8710    0.9068    0.5624    0.4327    0.6931    0.5236    0.6571    0.4539    0.0410    0.9652    0.9638    0.5625
    0.5313    0.0268    0.5673    0.7911    0.3940    0.7393    0.3608    0.0833    0.1080    0.9031    0.0589    0.1799    0.3737    0.6907    0.0087    0.3619    0.4904    0.4371
    0.9163    0.1919    0.7355    0.2160    0.5642    0.6993    0.8975    0.8819    0.6025    0.3460    0.5529    0.5344    0.8774    0.4845    0.7811    0.6910    0.4889    0.1880
    0.0010    0.5466    0.3734    0.3871    0.0503    0.7664    0.4667    0.4578    0.2999    0.6955    0.5124    0.5452    0.6373    0.9577    0.2084    0.6057    0.8504    0.0469
    0.2081    0.0636    0.9926    0.9634    0.5632    0.6345    0.0890    0.5869    0.5832    0.3250    0.2850    0.5469    0.3947    0.8226    0.8812    0.3490    0.0681    0.0241
    0.7095    0.2309    0.7839    0.3665    0.8807    0.8585    0.2142    0.6393    0.2421    0.8853    0.7737    0.8860    0.3808    0.0598    0.2915    0.7863    0.0753    0.0604
    0.1930    0.3258    0.0202    0.5753    0.1237    0.3604    0.7830    0.9910    0.9716    0.9108    0.0825    0.6641    0.1297    0.9995    0.1296    0.5465    0.0537    0.0614
    0.9145    0.8884    0.1511    0.6567    0.0137    0.8928    0.6727    0.0600    0.6229    0.5562    0.1890    0.7897    0.2508    0.3748    0.1387    0.4378    0.6435    0.3266
    0.1613    0.3733    0.3880    0.5209    0.2118    0.9868    0.3926    0.1741    0.3891    0.0679    0.9794    0.3162    0.2735    0.0397    0.0860    0.5353    0.5231    0.8253
    0.1743    0.4109    0.4445    0.7394    0.8637    0.8227    0.6698    0.9932    0.6119    0.3833    0.7009    0.4302    0.3316    0.8349    0.2380    0.7181    0.4128    0.9060
    0.6998    0.3709    0.5228    0.2591    0.2091    0.0384    0.5784    0.3144    0.9105    0.6575    0.4237    0.5585    0.8669    0.3643    0.8213    0.4044    0.8895    0.7519
    0.6570    0.3504    0.5114    0.4369    0.1088    0.1880    0.5095    0.2359    0.9480    0.8283    0.8874    0.9314    0.8848    0.7766    0.5727    0.7674    0.4483    0.0328
    0.9991    0.6284    0.2135    0.1999    0.8159    0.5322    0.2672    0.0643    0.0589    0.3339    0.1029    0.8538    0.3900    0.3725    0.0412    0.6471    0.0297    0.8769
    0.3488    0.0464    0.3497    0.5928    0.4885    0.3133    0.3542    0.2549    0.8651    0.7433    0.3451    0.3868    0.9648    0.8061    0.8913    0.4918    0.8062    0.1514
    0.4072    0.7936    0.1172    0.5589    0.8469    0.6211    0.4847    0.9689    0.7189    0.0216    0.8529    0.6848    0.5579    0.9126    0.6546    0.0458    0.9409    0.5936
    0.5102    0.4028    0.6913    0.7241    0.6081    0.6012    0.4762    0.2801    0.1890    0.9946    0.9592    0.0340    0.3617    0.6433    0.7086    0.1356    0.4773    0.7324

  Columns 19 through 24

    0.7047    0.4943    0.0098    0.2356    0.1182    0.9708
    0.1834    0.2210    0.0518    0.2423    0.7932    0.9026
    0.2111    0.9581    0.6989    0.9188    0.0447    0.9488
    0.1472    0.4446    0.4746    0.8046    0.9449    0.3293
    0.0568    0.1073    0.4142    0.6347    0.0511    0.7700
    0.3202    0.4525    0.3252    0.1457    0.4061    0.6256
    0.6406    0.2662    0.9086    0.3967    0.7733    0.9000
    0.1402    0.8552    0.1484    0.8900    0.4697    0.3994
    0.8624    0.3261    0.8160    0.8573    0.7544    0.1772
    0.9385    0.4825    0.8214    0.2668    0.5970    0.0781
    0.5708    0.6174    0.0732    0.9816    0.8650    0.1179
    0.5356    0.4946    0.5866    0.1166    0.1908    0.2007
    0.3028    0.4035    0.4208    0.2847    0.9652    0.1386
    0.4452    0.2182    0.5004    0.2793    0.7040    0.1950
    0.2106    0.5960    0.0311    0.4822    0.7076    0.3931
    0.8050    0.7850    0.5793    0.2008    0.8437    0.1274
    0.5481    0.9944    0.8352    0.5645    0.3887    0.9151
    0.1484    0.3331    0.3123    0.4065    0.2315    0.4450
    0.4794    0.2827    0.9283    0.1437    0.5945    0.5562
    0.8249    0.7325    0.0403    0.7099    0.4137    0.9439
    0.7573    0.2475    0.0940    0.5177    0.1668    0.8149
    0.0695    0.4141    0.4023    0.6732    0.8178    0.9253
    0.3171    0.3612    0.5277    0.7900    0.0730    0.1462
    0.4481    0.8067    0.2355    0.2019    0.7373    0.4291


(:,:,11) =

  Columns 1 through 18

    0.7074    0.8864    0.5949    0.7214    0.2830    0.5170    0.9441    0.8589    0.6749    0.2671    0.1589    0.3187    0.7807    0.1648    0.3418    0.2809    0.6423    0.6758
    0.8880    0.1022    0.2864    0.2781    0.2911    0.7165    0.9877    0.7721    0.4716    0.0107    0.9628    0.6665    0.7678    0.1175    0.2947    0.0195    0.5184    0.6025
    0.5124    0.3319    0.6499    0.6100    0.6851    0.2829    0.5496    0.1271    0.3363    0.0246    0.8058    0.6234    0.2883    0.8136    0.7759    0.1887    0.2900    0.5692
    0.9343    0.7111    0.3734    0.0448    0.1261    0.4660    0.5912    0.0722    0.8287    0.6299    0.3614    0.4143    0.9647    0.4968    0.2635    0.6111    0.2162    0.4913
    0.7754    0.2459    0.4664    0.9917    0.6869    0.4920    0.5461    0.4805    0.8148    0.3620    0.2840    0.0118    0.1879    0.3432    0.7055    0.9625    0.1980    0.4849
    0.9045    0.5134    0.9532    0.1527    0.5730    0.8680    0.1077    0.4624    0.6709    0.7857    0.7574    0.0770    0.5474    0.6673    0.0374    0.9918    0.7550    0.7091

Hope you find this information helpful.

[Abdulrahman]

Thank you so much Gayathri for your information. My problem has been solved.

Answer 2

[Umar]

Hi Abdulrahman,

I cannot execute the code because visionTransformer requires Computer Vision Toolbox. To illustrate resolving your error, I had to adapt your given code from mathworks for input dimensions of 24 x 24 x 768, by adjusting the reshaping and processing steps accordingly. Here is update the code step by step:

% Get Vision Transformer model

net = visionTransformer;

% Create dummy input

input = dlarray(rand(24,24,768),'SSCB');

% Obtain output embedding from the last LayerNormalizationLayer

out = forward(net, input, 'Outputs', 'encoder_norm');

% Reshape output patch embedding

out = reshapePatchEmbedding(out);

function out = reshapePatchEmbedding(in)

% Remove output embedding corresponding to the class token from the input

out = in(2:end,:,:);

% Reshape the resulting embedding to the input format

   WH = sqrt(size(out, 1));

   C = size(out, 2);

   out = reshape(out, WH, WH, C, []); % Shape is W x H x C x N

   out = permute(out, [2, 1, 3, 4]); % Shape is H x W x C x N

   % Convert to formatted dlarray

   out = dlarray(out, 'SSCB');

   end

So, in my updated code snippet, I changed the dummy input dimensions to 24 x 24 x 768 to match the specified input size. The reshaping function reshapePatchEmbedding has been adjusted to handle the new dimensions correctly. Please let me know if this helps resolve your issue.