How to set a colorbar using specific RGB values and limit values?

The attached file contains a contour plot code which gets the following colorbar:

Please run the attached code to see the colorbar I'm currently obtaining (using a jet colorbar).

    % colorbar question

     clear;clc
 A=[1.941     1947.138      625.500       0.001599            14.014
   5.939     1947.077     1289.900       0.000775        19.300
   9.938     1947.015      581.960       0.001718        22.987
  13.936     1946.950      758.890       0.001318        28.259
  17.933     1946.882     1333.500       0.000750        31.257
  21.931     1946.812      217.800       0.004591        20.110
  25.929     1946.739      446.300       0.002241        23.991
  29.926     1946.662      261.310       0.003827        20.253
  33.260     1945.329      293.540       0.003407        21.296
  36.326     1943.093     4547.300       0.000220        18.993
  40.058     1942.137      638.980       0.001565        14.785
  44.057     1942.110      268.030       0.003731        18.367
  48.056     1942.084      248.240       0.004028        18.609
  52.055     1942.056      374.330       0.002671        28.995
  56.054     1942.028     1213.400       0.000824        23.916
  60.054     1941.998      126.760       0.007889        27.747
  64.053     1941.968      628.800       0.001590        16.702
  68.051     1941.937      316.540       0.003159        25.726
  72.050     1941.905      198.610       0.005035        26.283
  76.049     1941.871      246.990       0.004049        21.835
  80.048     1941.836      216.320       0.004623        16.395
  84.047     1941.800      150.220       0.006657        17.376
  88.045     1941.762      234.310       0.004268        13.832
  92.044     1941.722       28.310         0.0353         5.897
   1.824     1945.123      392.850       0.002546        14.733
   5.820     1945.023      159.100       0.006285        18.993
   9.816     1944.919      581.530       0.001720        21.716
  13.811     1944.812      512.470       0.001951        21.257
  17.807     1944.699      214.740       0.004657        32.690
  21.802     1944.582     7111.000       0.000141        19.865
  25.796     1944.459       40.650         0.0246        19.236
  29.791     1944.330      408.570       0.002448        21.704
  33.139     1943.253       20.157         0.0496        16.667
  36.228     1941.406       45.401         0.0220        19.619
  39.965     1940.547       36.044         0.0277        21.503
  43.963     1940.498      517.490       0.001932        22.070
  47.961     1940.447      503.470       0.001986        20.255
  51.959     1940.395      640.280       0.001562        29.378
  55.957     1940.341      148.020       0.006756        23.256
  59.954     1940.285      695.240       0.001438        25.728
  63.951     1940.227       52.922         0.0189        23.278
  67.949     1940.167       74.723         0.0134        16.712
  71.946     1940.104      202.610       0.004936        14.442
  75.943     1940.038      162.530       0.006153        22.836
  79.939     1939.970      313.060       0.003194        31.804
  83.936     1939.898      199.050       0.005024        17.033
  87.932     1939.824      152.240       0.006569        13.796
  91.929     1939.745      125.130       0.007992         7.540
   1.701     1943.011      384.880       0.002598        15.792
   5.696     1942.879      213.860       0.004676        18.482
   9.689     1942.743      443.110       0.002257        20.597
  13.683     1942.602      535.490       0.001867        20.139
  17.676     1942.455      169.240       0.005909        20.209
  21.669     1942.302      642.590       0.001556        16.612
  25.662     1942.142      422.030       0.002369        17.110
  29.654     1941.976     4123.000       0.000243        19.104
  33.014     1941.106       24.004         0.0417        17.199
  36.123     1939.584       15.608         0.0641        20.787
  39.865     1938.813     1870.500       0.000535        21.935
  43.861     1938.743      431.630       0.002317        22.631
  47.858     1938.670       25.172         0.0397        20.826
  51.854     1938.595      567.980       0.001761        26.448
  55.851     1938.517      173.370       0.005768        24.556
  59.847     1938.437      382.260       0.002616        25.764
  63.843     1938.353      356.150       0.002808        25.527
  67.838     1938.266      341.330       0.002930        17.118
  71.834     1938.176      258.650       0.003866        11.283
  75.829     1938.082       29.999         0.0333        11.573
  79.824     1937.984      311.460       0.003211        30.600
  83.819     1937.883      227.970       0.004387        17.021
  87.814     1937.776      151.200       0.006614        13.476
  91.808     1937.665      151.010       0.006622         8.100
   1.567     1940.692      384.870       0.002598        16.725
   5.559     1940.534      386.550       0.002587        18.166
   9.552     1940.372      498.560       0.002006        19.432
  13.544     1940.203      537.360       0.001861        19.138
  17.535     1940.030      168.210       0.005945        18.321
  21.527     1939.850      356.010       0.002809        16.273
  25.518     1939.664      406.370       0.002461        16.747
  29.508     1939.471     4157.500       0.000241        18.232
  32.879     1938.771       26.815         0.0373        18.019
  36.003     1937.528       15.534         0.0644        21.087
  39.750     1936.841     3401.900       0.000294        22.145
  43.746     1936.750      618.790       0.001616        22.334
  47.741     1936.655       35.707         0.0280        20.814
  51.736     1936.557      281.230       0.003556        23.143
  55.731     1936.457      175.170       0.005709        23.629
  59.726     1936.353      164.400       0.006083        24.666
  63.720     1936.245      201.820       0.004955        25.196
  67.714     1936.134      339.340       0.002947        17.284
  71.708     1936.018      322.740       0.003098        10.790
  75.702     1935.899       32.243         0.0310        10.311
  79.696     1935.775       97.517         0.0103        14.638
  83.689     1935.646      151.340       0.006608        14.587
  87.682     1935.512      150.830       0.006630        11.879
  91.675     1935.373      152.300       0.006566         8.259
   1.418     1938.141      384.210       0.002603        17.366
   5.410     1937.956      408.330       0.002449        18.067
   9.400     1937.766      636.350       0.001571        18.735
  13.391     1937.572      633.730       0.001578        18.507
  17.381     1937.373      534.120       0.001872        17.722
  21.371     1937.168      523.520       0.001910        16.456
  25.361     1936.959      664.740       0.001504        16.666
  29.350     1936.745     4573.900       0.000219        17.556
  32.731     1936.224       30.296         0.0330        17.962
  35.873     1935.295       31.815         0.0314        20.403
  39.627     1934.719     3264.300       0.000306        22.167
  43.621     1934.598     1165.700       0.000858        21.976
  47.614     1934.474      267.040       0.003745        20.134
  51.608     1934.347      282.380       0.003541        19.813
  55.601     1934.216      187.840       0.005324        19.716
  59.594     1934.081      125.860       0.007945        19.951
  63.586     1933.943      126.510       0.007905        20.009
  67.579     1933.801      209.800       0.004766        16.208
  71.571     1933.654      271.320       0.003686        10.129
  75.563     1933.503       87.792         0.0114         9.139
  79.555     1933.348       90.154         0.0111         9.242
  83.546     1933.187      136.170       0.007344         9.380
  87.537     1933.022      150.800       0.006631         9.006
  91.528     1932.852      154.120       0.006488         8.047
   1.256     1935.343      378.440       0.002642        17.755
   5.246     1935.143      445.620       0.002244        18.090
   9.236     1934.940     1464.600       0.000683        18.402
  13.226     1934.732     1486.600       0.000673        18.164
  17.215     1934.520     1464.900       0.000683        17.438
  21.205     1934.305     1455.700       0.000687        16.525
  25.194     1934.085     1474.000       0.000678        16.513
  29.182     1933.862     4996.600       0.000200        16.802
  32.569     1933.436       38.394         0.0260        16.726
  35.722     1932.685       46.085         0.0217        17.921
  39.479     1932.177     1215.300       0.000823        22.366
  43.472     1932.038     1160.500       0.000862        21.779
  47.464     1931.896      579.430       0.001726        18.674
  51.457     1931.749      492.920       0.002029        16.120
  55.449     1931.599      324.460       0.003082        13.764
  59.441     1931.446      118.570       0.008434        12.013
  63.432     1931.289      116.440       0.008588        11.813
  67.424     1931.127      166.740       0.005997        11.466
  71.415     1930.962      206.150       0.004851         8.868
  75.406     1930.792       88.028         0.0114         7.657
  79.396     1930.619       88.969         0.0112         7.558
  83.387     1930.440      129.280       0.007735         7.873
  87.377     1930.258      151.360       0.006607         7.960
  91.367     1930.070      161.070       0.006208         7.603];

      X = A(:,1);
      Y = A(:,2);
      Z = A(:,3);
      [xq,yq]=meshgrid(linspace(min(X),max(X),100),linspace(min(Y),max(Y),100));
      zq=griddata(X,Y,Z,xq(:),yq(:),'cubic');
      figure()
      [c,h]=contourf(xq,yq,reshape(zq,100,100));
     hold on 
     colormap(jet)
     h = colorbar;
     set( h, 'YDir', 'reverse' );

I would like to obtain the same contour plot but with these colors and values for the ploting colorbar, i defined also RGB values for eacth limit value.

https://drive.google.com/file/d/1L6TBG_Uh-OgUXUpA0doWkMJjW1cGwy1_/view?usp=sharing

the values are:

    colorbarlimits=[6.5696e+000
9.4236e+000
1.3517e+001
1.9390e+001
2.7813e+001
3.9896e+001
5.7228e+001
8.2089e+001
1.1775e+002
1.6890e+002
2.4228e+002
3.4753e+002
4.9851e+002
7.1508e+002
1.0257e+003
1.4713e+003]; 

The colorbar RGB values may be the following (instead of using colorbar):

     RGB=[153 0 0
     204 0 0
     153 76 0
     204 102 0
     153 153 0
     204 204 0
     76 153 0
     102 204 0
     0 153 0
     0 204 0
     0 153 76
     0 204 102
     0 76 153
     0 102 204
     0 0 153
     0 0 204];

Answer 1

[Cris LaPierre]

If you want specific colors at specific values, specify the contour lines. Then you can set the colormap and Caxis limits to force a particular coloring. Perhaps some of the discussion in this post might help.

This might get you started. Note that the colorbar is still linearly spacing the colors. The only way I've found to do nonlinear spacing is to create a color entry for each data point (see this post).

[c,h]=contourf(xq,yq,reshape(zq,100,100),[-1000; colorbarlimits]);
colormap(RGB./255)
h = colorbar;
caxis(colorbarlimits([1 end]))

[Philippe Corner]

Thanks for your comment, I checked it already. Do you think there is any way to keep the thicknesses of each color equal, even if the ranges are different? As you can see, doing this plots a colorbar that doesn't show all the color values. Cheers!

[Cris LaPierre]

In this case, you may just need to set your Caxis limits to the desired range.