After using griddata, standard deviation is changed.

I rewritten it with the code and data. Thank you.

Hello. Respected seniors.

I'm not familiar with English, so I'm using a translator, so please forgive me if the sentences are weird.

New data was created using grid data for use in other programs.

The maximum and minimum values of the data were made within the expected or acceptable margin of error, but the standard deviation was greatly reduced to create unacceptable figures.

This is the code used.

clear,close all;
Fin=fopen('data1.csv','rt');

if(Fin==-1)
    errordlg('File Open Error ! Program stoped!','Error');
    error('File Open Error ! Program stoped!');
end

State=0;
radius = 300;

while(~State)
    npoints = 2839 ;
        
        A=fscanf(Fin,'%e ',[8,npoints]);
        Nx=A(2,:);
        Ny=A(3,:);
        Nz=A(7,:);
        Nx7=Nx ;
        Ny7=Ny ;
        Nz7=Nz ;
  
    State=feof(Fin);
end
%% make_int
deltaZ = max(Nz) - min(Nz);

X_int = -255:0.9961:255 ;
Y_int = -255:0.9961:255 ;
Y2_int = flip(Y_int);

[xq_int,yq_int] = meshgrid(X_int,Y2_int);

gd_int = griddata(Nx7,Ny7,Nz7,xq_int,yq_int);

gd_int1 = gd_int*(10^5);

gd_int2 = gd_int1;

gd_int3 = round(gd_int2);

gridsize = 512;

for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int3(i,j))
        gd_int4(i,j) = -32767;
    else
        gd_int4(i,j) = gd_int3(i,j);
    end
    end
end


M = gd_int4;

dlmwrite('L1_front_gx_codierite_grid512_ssz0.1.int', M , 'delimiter' , ' ' , 'precision' , '%d');  

%%
for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int3(i,j))
        gd5(i,j) = 0;
    else
        gd5(i,j) = gd_int3(i,j);
    end
    end
end

AB2 = nonzeros(gd5);
%%
for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int(i,j))
        gd6(i,j) = 0;
    else
        gd6(i,j) = gd_int(i,j);
    end
    end
end

AB = nonzeros(gd6);

%%
%%figure

%%mesh(xq_int,yq_int,gd_int);
%%hold on
%%plot3(Nx,Ny,Nz,'o');
%%h = gca;
%%h.XLim = [-255 255];
%%h.YLim = [-255 255];
%%colormap('jet')

figure

mesh(xq_int,yq_int,gd_int);
h = gca;
h.XLim = [-255 255];
h.YLim = [-255 255];
colormap('jet')

%%figure 

%%surface(xq_int,yq_int,gd_int);
%%h = gca;
%%h.XLim = [-255 255];
%%h.YLim = [-255 255];
%%colormap('jet')

%%
fclose(Fin);

This is a result from code. red box is calculated standard deviation value.

It is the rms value calculated by another code. change the unit, it's 486.7774.

The difference between the two values is fifty.

Can I know if the standard deviation value decreases using the grid data?

[KSSV]

Show us your data and code.

[Walter Roberson]

Do you mean like this, where std(V) is different from std(Vq) ?

rng(12345)
No = 30;
Nn = 50;
x = randn(1,No);
y = randn(1,No);
V = sin(x) + cos(y);

xvec = linspace(-3, 3, Nn);
yvec = linspace(-3, 3, Nn);
[xq, yq] = ndgrid(xvec, yvec);
Vq = griddata(x, y, V, xq, yq);

scatter3(x, y, V, 'r*');
hold on
scatter3(xq(:), yq(:), Vq(:), 'k.');
hold off
legend({'original', 'interpolated'})

std(V)

ans = 0.9184

std(Vq(:), 'omitnan')

ans = 0.8312

[Bruno Luong]

Your question is strange mathematically.

V and Vq are not noise so how do you interpret std ?

There is a function underlined the interpolation, The

std(Vq) / sqrt(numel(Vq)) 

approximates perhaps the RMS of the function, but

std(V) / sqrt(numel(V)) 

would not approximate it, but they should have the same order if V and Vq are more or less sampling the domain X, Y. That is the hint that

std(V) ~ RMS(f)*sqrt(numel(V))

The more youi increases the density, the more you get big value of std, it increases line sqrt of the number of points.

[Han]

@Bruno Luong @Walter Roberson @KSSV Code and data updated. can you watch it again?

[Bjorn Gustavsson]

@Han: You need to look at @Jan's example and have a think about what that example shows.

[Jan]

@Han: Just a note, you can simplify:

gd_int = griddata(Nx7,Ny7,Nz7,xq_int,yq_int);
gd_int1 = gd_int*(10^5);
gd_int2 = gd_int1;
gd_int3 = round(gd_int2);
gridsize = 512;
for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int3(i,j))
        gd_int4(i,j) = -32767;
    else
        gd_int4(i,j) = gd_int3(i,j);
    end
    end
end
M = gd_int4;

for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int3(i,j))
        gd5(i,j) = 0;
    else
        gd5(i,j) = gd_int3(i,j);
    end
    end
end
AB2 = nonzeros(gd5);

for i = 1:gridsize
    for j = 1:gridsize
    if isnan(gd_int(i,j))
        gd6(i,j) = 0;
    else
        gd6(i,j) = gd_int(i,j);
    end
    end
end
AB = nonzeros(gd6);

to:

A = griddata(Nx7, Ny7, Nz7, xq_int, yq_int);
B = round(A * 1e5);
M = fillmissing(B, 'constant', -32767);

AB2 = nonzeros(fillmissing(B, 'constant', 0));
AB  = nonzeros(fillmissing(A, 'constant', 0));

Answer 1

[Jan]

Of course increasing the number of points by an interpolation reduces the standard deviation:

std([1,100])

ans = 70.0036

std(interp1([1, 2], [1, 100], linspace(1, 2, 100)))

ans = 29.0115

std(1:100)  % Which is the same except for rounding effects

ans = 29.0115

[Han]

Code and data updated. can you watch it again?