logarithmic binning of "x" values

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Sim on 2 May 2025

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Edited: Sim on 2 May 2025

The following code performs a logarithmic binning of the "x" values:

clear all;clc;
% Input
x = [74.5, 149, 223.5, 298, 372.5, 447, 521.5, 596, 670.5, 745, 819.5, 894, 968.5, 1043, 1117.5, 1192, 1266.5, 1341, 1415.5, 1490, 1564.5, 1639, 1713.5, 1788, 1862.5, 1937, 2011.5, 2086, 2160.5, 2235, 2309.5, 2384, 2458.5, 2533, 2607.5, 2682, 2756.5, 2831, 2905.5, 2980, 3054.5, 3129, 3203.5, 3278, 3352.5, 3427, 3501.5, 3576, 3650.5, 3725, 3799.5, 3948.5, 4023, 4097.5, 4172, 4470, 4544.5, 4619, 4693.5, 4768, 5364, 6034.5, 6556];
y = [2.0245, 0.50611, 0.22388, 0.12812, 0.080214, 0.055174, 0.040926, 0.031831, 0.026172, 0.021645, 0.017941, 0.01565, 0.012732, 0.011823, 0.010186, 0.0077588, 0.0074896, 0.006543, 0.0060311, 0.0042972, 0.0045473, 0.0037618, 0.0034599, 0.0031831, 0.0026738, 0.0022037, 0.0024757, 0.0020463, 0.0017562, 0.002016, 0.0016429, 0.0013926, 0.0012539, 0.0011234, 0.00090946, 0.00097261, 0.00060221, 0.00075389, 0.0008978, 0.00063662, 0.00054346, 0.0006063, 0.00051818, 0.00036172, 0.00021221, 0.00034599, 0.00020318, 0.00019894, 6.4961e-05, 0.00019099, 0.00018724, 0.00018018, 5.8946e-05, 0.00011575, 0.00017052, 0.00015915, 5.2182e-05, 5.134e-05, 5.0525e-05, 4.9736e-05, 4.421e-05, 3.9298e-05, 3.6172e-05];
% logarithmic binning
factor = 2.2;
binsF = 1;
i = 2;
while( binsF(i-1) < max( x ) )
    binsF(i) = binsF(i-1)*factor;
    i = i + 1;
end
mean_v = [];
kc = zeros( length(binsF) - 1,1 );
for( i = 1:length( binsF ) - 1 )
    in = find( x >= binsF(i) & x < binsF(i+1) );
    if ~isempty(in)
        mean_v = [mean_v;mean(y(in))];
        kc(i) = 0.5*(binsF(i + 1)+binsF(i));
    else
        mean_v = [mean_v; NaN]; % Handle empty bins
        kc(i) = NaN;
    end
end
mean_v, kc,
mean_v = 12×1
       NaN
       NaN
       NaN
       NaN
       NaN
    2.0245
    0.3650
    0.0761
    0.0173
    0.0031
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kc = 12×1
1.0e+03 *

       NaN
       NaN
       NaN
       NaN
       NaN
    0.0825
    0.1814
    0.3991
    0.8780
    1.9316
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<mw-icon class=""></mw-icon>
●

Is there a function in Matlab which performs the same logarithmic binning?

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Answer 1

Cris LaPierre on 2 May 2025

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I'm not sure the end result is much simpler, but the function that comes to mind is discretize. You'd still need to define your bin edges.

% Input
x = [74.5, 149, 223.5, 298, 372.5, 447, 521.5, 596, 670.5, 745, 819.5, 894, 968.5, 1043, 1117.5, 1192, 1266.5, 1341, 1415.5, 1490, 1564.5, 1639, 1713.5, 1788, 1862.5, 1937, 2011.5, 2086, 2160.5, 2235, 2309.5, 2384, 2458.5, 2533, 2607.5, 2682, 2756.5, 2831, 2905.5, 2980, 3054.5, 3129, 3203.5, 3278, 3352.5, 3427, 3501.5, 3576, 3650.5, 3725, 3799.5, 3948.5, 4023, 4097.5, 4172, 4470, 4544.5, 4619, 4693.5, 4768, 5364, 6034.5, 6556];
y = [2.0245, 0.50611, 0.22388, 0.12812, 0.080214, 0.055174, 0.040926, 0.031831, 0.026172, 0.021645, 0.017941, 0.01565, 0.012732, 0.011823, 0.010186, 0.0077588, 0.0074896, 0.006543, 0.0060311, 0.0042972, 0.0045473, 0.0037618, 0.0034599, 0.0031831, 0.0026738, 0.0022037, 0.0024757, 0.0020463, 0.0017562, 0.002016, 0.0016429, 0.0013926, 0.0012539, 0.0011234, 0.00090946, 0.00097261, 0.00060221, 0.00075389, 0.0008978, 0.00063662, 0.00054346, 0.0006063, 0.00051818, 0.00036172, 0.00021221, 0.00034599, 0.00020318, 0.00019894, 6.4961e-05, 0.00019099, 0.00018724, 0.00018018, 5.8946e-05, 0.00011575, 0.00017052, 0.00015915, 5.2182e-05, 5.134e-05, 5.0525e-05, 4.9736e-05, 4.421e-05, 3.9298e-05, 3.6172e-05];
% logarithmic binning
factor = 2.2;
nbins = ceil(log2(max(x))/log2(2.2));
E = factor.^(0:nbins)
E = 1×13
1.0e+04 *

    0.0001    0.0002    0.0005    0.0011    0.0023    0.0052    0.0113    0.0249    0.0549    0.1207    0.2656    0.5843    1.2855
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 %Bin data
 bIdx = discretize(x,E)
bIdx = 1×63
     6     7     7     8     8     8     8     9     9     9     9     9     9     9     9     9    10    10    10    10    10    10    10    10    10    10    10    10    10    10
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[B,BG,BC] = groupsummary(y',bIdx','mean','IncludeEmptyGroups',true)
B = 7×1
    2.0245
    0.3650
    0.0761
    0.0173
    0.0031
    0.0003
    0.0000
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●
BG = 7×1
     6
     7
     8
     9
    10
    11
    12
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BC = 7×1
     1
     2
     4
     9
    19
    26
     2
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mean_v = nan(nbins,1);
mean_v(BG) = B
mean_v = 12×1
       NaN
       NaN
       NaN
       NaN
       NaN
    2.0245
    0.3650
    0.0761
    0.0173
    0.0031
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
kc = nan(nbins,1);
kc(BG) = 0.5*(E(BG(1:end)+1)+E(BG(1:end)))
kc = 12×1
1.0e+03 *

       NaN
       NaN
       NaN
       NaN
       NaN
    0.0825
    0.1814
    0.3991
    0.8780
    1.9316
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

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Cris LaPierre on 2 May 2025

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If the data is in a table, then groupsummary might do what you want as well. Again, you still need to define your bin edges.

% Input
x = [74.5, 149, 223.5, 298, 372.5, 447, 521.5, 596, 670.5, 745, 819.5, 894, 968.5, 1043, 1117.5, 1192, 1266.5, 1341, 1415.5, 1490, 1564.5, 1639, 1713.5, 1788, 1862.5, 1937, 2011.5, 2086, 2160.5, 2235, 2309.5, 2384, 2458.5, 2533, 2607.5, 2682, 2756.5, 2831, 2905.5, 2980, 3054.5, 3129, 3203.5, 3278, 3352.5, 3427, 3501.5, 3576, 3650.5, 3725, 3799.5, 3948.5, 4023, 4097.5, 4172, 4470, 4544.5, 4619, 4693.5, 4768, 5364, 6034.5, 6556];
y = [2.0245, 0.50611, 0.22388, 0.12812, 0.080214, 0.055174, 0.040926, 0.031831, 0.026172, 0.021645, 0.017941, 0.01565, 0.012732, 0.011823, 0.010186, 0.0077588, 0.0074896, 0.006543, 0.0060311, 0.0042972, 0.0045473, 0.0037618, 0.0034599, 0.0031831, 0.0026738, 0.0022037, 0.0024757, 0.0020463, 0.0017562, 0.002016, 0.0016429, 0.0013926, 0.0012539, 0.0011234, 0.00090946, 0.00097261, 0.00060221, 0.00075389, 0.0008978, 0.00063662, 0.00054346, 0.0006063, 0.00051818, 0.00036172, 0.00021221, 0.00034599, 0.00020318, 0.00019894, 6.4961e-05, 0.00019099, 0.00018724, 0.00018018, 5.8946e-05, 0.00011575, 0.00017052, 0.00015915, 5.2182e-05, 5.134e-05, 5.0525e-05, 4.9736e-05, 4.421e-05, 3.9298e-05, 3.6172e-05];
% add to table
T = table(x',y','VariableNames',["x","y"])
T = 63x2 table
      x           y    
    ______    _________

      74.5       2.0245
       149      0.50611
     223.5      0.22388
       298      0.12812
     372.5     0.080214
       447     0.055174
     521.5     0.040926
       596     0.031831
     670.5     0.026172
       745     0.021645
     819.5     0.017941
       894      0.01565
     968.5     0.012732
      1043     0.011823
    1117.5     0.010186
      1192    0.0077588
% logarithmic binning
factor = 2.2;
nbins = ceil(log2(max(x))/log2(2.2));
E = factor.^(0:nbins);
% Bin data and compute mean
Tbinned = groupsummary(T,"x",E,"mean","y",'IncludeMissingGroups',true,"IncludeEmptyGroups",true)
Tbinned = 12x3 table
         disc_x         GroupCount      mean_y  
    ________________    __________    __________

    [1, 2.2)                 0               NaN
    [2.2, 4.84)              0               NaN
    [4.84, 10.648)           0               NaN
    [10.648, 23.426)         0               NaN
    [23.426, 51.536)         0               NaN
    [51.536, 113.38)         1            2.0245
    [113.38, 249.44)         2           0.36499
    [249.44, 548.76)         4          0.076109
    [548.76, 1207.3)         9          0.017304
    [1207.3, 2656)          19         0.0030951
    [2656, 5843.2)          26        0.00031649
    [5843.2, 12855]          2        3.7735e-05
Tbinned.kc = movmean(E,[0 1],'Endpoints','discard')';
Tbinned.kc(isnan(Tbinned.mean_y)) = nan
Tbinned = 12x4 table
         disc_x         GroupCount      mean_y        kc  
    ________________    __________    __________    ______

    [1, 2.2)                 0               NaN       NaN
    [2.2, 4.84)              0               NaN       NaN
    [4.84, 10.648)           0               NaN       NaN
    [10.648, 23.426)         0               NaN       NaN
    [23.426, 51.536)         0               NaN       NaN
    [51.536, 113.38)         1            2.0245    82.458
    [113.38, 249.44)         2           0.36499    181.41
    [249.44, 548.76)         4          0.076109     399.1
    [548.76, 1207.3)         9          0.017304    878.01
    [1207.3, 2656)          19         0.0030951    1931.6
    [2656, 5843.2)          26        0.00031649    4249.6
    [5843.2, 12855]          2        3.7735e-05    9349.1

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Answer 2

Steven Lord on 2 May 2025

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Use histogram, histcounts, discretize, and/or groupsummary. Since your application is that you want to perform an operation summarizing the data in each bin, using discretize or findgroups to generate a vector of group numbers then using those group vectors with groupsummary to compute the mean of the data in each bin is probably the right approach.

sampleData = randi(100, 5, 5)
sampleData = 5×5
     1    47    53    35    95
     7    27    92    56     7
    24    55    97    43    60
    12    92    66    51    96
    80    38    92    78    73
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nonlinearBinEdges = (1:10).^2
nonlinearBinEdges = 1×10
     1     4     9    16    25    36    49    64    81   100
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groupNumber = discretize(sampleData, nonlinearBinEdges)
groupNumber = 5×5
     1     6     7     5     9
     2     5     9     7     2
     4     7     9     6     7
     3     9     8     7     9
     8     6     9     8     8
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Sim on 2 May 2025

Edited: Sim on 2 May 2025

thanks a lot both @Steven Lord and @Cris LaPierre!!

I accept the @Cris LaPierre’s answer because it’s a bit clearer to me, but that doesn’t take away from the fact that @Steven Lord’s response is also excellent!!!

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logarithmic binning of "x" values

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