(Error using vertcat) Dimensions of arrays being concatenated are not consistent

Hello all,

Here is my code. Some related .csv files are attached.

After running the code, I face this error:

Error using vertcat

Dimensions of arrays being concatenated are not consistent.

Error in Code_Yahya (line 105)

phia =[x;y;phix(:,a)';phiy(:,a)'];

>> both phix and phiy are of same sizes.

Can someone help me here ?

Thank you

%%% Tables are exported as vertices from STARCCM+
%%% ------------------------------------------------------------------%%%
clear; clc; close all;

f=dir('*.csv');                     % finding all csv files
n_snapshots=size(f,1);              % finding number of snapshots
for i=1:n_snapshots
    fn=f(i).name;                   % Listing filenames
    fid=fopen(fn, 'r');             % reading files
    data = fscanf(fid, '%f,%f,%f,%f,%f,%f,%f,%f,%f,%f,%f' , [11, inf]);
    
    % exporting columns
    x=data(9,:);
    y=data(10,:);
    %Ut(:,i) = data(:,1);
    u(:,i) = data(:,3);
    v(:,i) = data(:,2);  
    fclose(fid); 
end
%--------------------------------------------------------------

u = permute(u,[2 1]);
%Split u into two snapshot sets
X1 = u(:,1:end-1);
X2 = u(:,2:end);

%SVD on X1
[Ux, Sx, Vx] = svd(X1,'econ');

%Compute DMD (phix are Eigen vectors)
r = 3;    %truncate as 10 modes
%Reduce rank
Ux = Ux(:,1:r);
Sx = Sx(1:r,1:r);
Vx = Vx(:,1:r);
%Gets A_tilde
A_tildex = Ux'*X2*Vx/Sx;

%Compute A_tilde eigenvalues and eigenvectors
%[eVecs, Eigenvalues] = eig(A_tilde);
[Wx, eigsx] = eig(A_tildex);
%DMD modes
phix = X2*Vx/Sx*Wx;       %Eigenvectors

figure
theta = (0:1:100)*2*pi/100;
plot(cos(theta),sin(theta),'k--') % plot unit circle
hold on, grid on
scatter(real(max(eigsx)),imag(max(eigsx)),'ok')
axis([-1.1 1.1 -1.1 1.1]);

%--------------------------------------------------------------

v = permute(v,[2 1]);
%Split u into two snapshot sets
Y1 = v(:,1:end-1);
Y2 = v(:,2:end);

%SVD on X1
[Uy, Sy, Vy] = svd(Y1,'econ');

%Compute DMD (phix are Eigen vectors)
r = 3;    %truncate as 10 modes
%Reduce rank
Uy = Uy(:,1:r);
Sy = Sy(1:r,1:r);
Vy = Vy(:,1:r);
%Gets A_tilde
A_tildey = Uy'*Y2*Vy/Sy;

%Compute A_tilde eigenvalues and eigenvectors
%[eVecs, Eigenvalues] = eig(A_tilde);
[Wy, eigsy] = eig(A_tildey);
%DMD modes
phiy = Y2*Vy/Sy*Wy;       %Eigenvectors

figure
theta = (0:1:100)*2*pi/100;
plot(cos(theta),sin(theta),'k--') % plot unit circle
hold on, grid on
scatter(real(max(eigsy)),imag(max(eigsy)),'ok')
axis([-1.1 1.1 -1.1 1.1]);

%--------------------------------------------------------------

Gridnumber = size(x, 2);
for j=1:r       %n_snapshots
    phinor = 0;
    
    for i=1:r       %Gridnumber
        phinor = phinor + power(phix(i,j),2) + power(phiy(i,j),2);
        %phinor = phinor + power(phix(i,j),2);       
    end
    phinor = sqrt(phinor);
    
    phix(:, j) = phix(:, j) / phinor;
    phiy(:, j) = phiy(:, j) / phinor;
end

%Extracting modes
for a=1:r   %n_snapshots
    FilNamPhi=1000+a;  %FilNamPhi=1000+a;
    PhiOut = fopen([num2str(FilNamPhi), '.txt'], 'wt');
    fprintf(PhiOut,'');
    phia =[x;y;phix(:,a)';phiy(:,a)'];
    fprintf(PhiOut, '%20.9f %20.9f %20.9f %20.9f\n',phia);
    fclose(PhiOut);
end

%xlswrite('eigenvaluesX.xlsx',[real(max(eigsx))',imag(max(eigsx))'];
%xlswrite('eigenvaluesY.xlsx',[real(max(eigsy))',imag(max(eigsy))'];

Answer 1

[Torsten]

x and y are of size 1x500, phix(:,a)' and phiy(:,a)' are of size 1x8. So either x and y had to be of size 1x8 or phix(:,a)' and phiy(:,a)' had to be of size 1x500 for that phia =[x;y;phix(:,a)';phiy(:,a)']; would make sense.

[Kumaresh Kumaresh]

Hello Mr. Torsten,

Thank you for your response. you are right. If sizes of x, y, phix, and phiy are same, it works.

But in my case, x and y are of fixed size and can't be modified (as inputs). phix and phiy are outputs.

In this scenario, how can I modify the specific line in the code to get my required output ? Kindly share your opinion.

Thank you

[Walter Roberson]

If you need to have a 1 x 500 followed by a 1 x 500 followed by a 1 x 8 and then another 1 x 8, then you will need to use a cell array.

Perhaps you want

[x.'; y.'; phix(:,a); phiy(:,a)]

which would be [500 x 1; 500 x 1; 8 x 1; 8 x 1] giving 1016 x 1 overall.

[Kumaresh Kumaresh]

@Walter Roberson

Thank you so much. It worked. ^^

[Kumaresh Kumaresh]

Hello Mr. Walter,

I have some more queries.

1) In the above code, when I fix the "r" value greater than 10 (for many csv files), it says:

Index in position 2 exceeds array bounds (must not exceed 10).

Error in DMD_Code_Yahya (line 33)

Ux = Ux(:,1:r);

I am kind of not sure, why it is ? r = number of energy modes extracted from the solution.

2) Added to that, when my "r" value is lesser or equal to 10, I get these warnings (for many csv files), can it be optimized ?

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.748731e-22.

> In DMD_Code_Yahya (line 37)

Line 37: A_tildex = Ux'*X2*Vx/Sx;

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.748731e-22.

> In DMD_Code_Yahya (line 43)

Line 43: phix = X2*Vx/Sx*Wx;

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 9.387731e-23.

> In DMD_Code_Yahya (line 73)

Line 73: A_tildey = Uy'*Y2*Vy/Sy;

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 9.387731e-23.

> In DMD_Code_Yahya (line 79)

Line 79: phiy = Y2*Vy/Sy*Wy;

Thank you once again ^^

[Torsten]

The Ux you get from the command

%SVD on X1
[Ux, Sx, Vx] = svd(X1,'econ');

is a 8x8 matrix for your first .csv-file. Thus for r > 8, the command

Ux = Ux(:,1:r);

references columns in Ux that do not exist.

The other warnings tell you that you try to find inverses of matrices that are numerically singular (i.e. for which numerically a senseful inverse cannot be computed).

Example:

A = [1 0;0 1e-65];
B = [1 2;3 4];
B/A

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.000000e-65.

ans = 2×2

1.0e+65 * 0.0000 2.0000 0.0000 4.0000

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[Kumaresh Kumaresh]

Dear Mr. Torsten,

Thank you for your valuable time. I have attached 20 .csv files. Previously it was 8 files. Now, if I give "r = 15", I am still facing the same error:

Index in position 2 exceeds array bounds (must not exceed 10).

Error in DMD_Code_Yahya (line 33)

Ux = Ux(:,1:r);

[Torsten]

The number of rows of Ux is 20, but the number of columns of Ux is 10. Thus still r <= 10 is required.