How read Matrix Market data into MATLAB?

Hello. I'd like to read matrix data from the following link: https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Linear_1D_Beam

The link tells me that it is in Matrix Market format, but I am unsure how to extract the M, E, K, B, and C matrices from the attached .m file. Could someone help me extract the data? I'd like to have access to the M, E, K, B, and C matrices the correspond to the following equation:

Here is what the .m file, LF10.m, looks like. There are 18 rows. There is also a .b, .c, .e, and .k file:

• Thank you

Answer 1

[jonas-schulze]

If you would like to obtain a sparse matrix, you can try load and spconvert

load LF10.m
M = spconvert(LF10(2:end,:))

or sparse if the matrix has some leading or trailing zero columns or rows

load LF10.m
m = LF10(1, 1)
n = LF10(1, 2)
i = LF10(2:end, 1)
j = LF10(2:end, 2)
v = LF10(2:end, 3)
M = sparse(i, j, v, m, n)

If the underlying matrix is symmetric, the market file will only contain half the matrix. In this case it's the lower triangular part, but I don't know whether it always is.

D = diag(diag(M))
L = tril(M, -1)
M = L + D + L'

Answer 2

[Alan Stevens]

Do you mean like this:

%%MatrixMarket matrix coordinate real symmetric
% System: M x_dotdot + E x_dot + K x = B u
%         y = C x
%
% Steel beam, 5 nodes
% Properties: Length: 0.1 m, Density: 8000 kg/m^3, Diameter: 1 mm,
% Modulus of elasticity: 2.0e11 Pa, Poisson ratio: 0.29,
% Contr.of M to damping: 1e2, Contr. of K to damping: 1e-2.
% The output node is the node in the middle.
%
Mx = [18 18 50
1 1    8.2666855418381347E-11
2 1    2.3970604543209878E-08
2 2    5.1946160853333332E-05
3 1   -6.1709237860082308E-11
3 3    1.6533371083676269E-10
4 2    8.9335862399999995E-06
4 3    2.3970604543209878E-08
4 4    5.1946160853333332E-05
5 2   -2.3970604543209878E-08
5 3   -6.1709237860082308E-11
5 5    1.6533371083676269E-10
6 4    8.9335862399999995E-06
6 5    2.3970604543209878E-08
6 6    5.1946160853333332E-05
7 4   -2.3970604543209878E-08
7 5   -6.1709237860082308E-11
7 7    1.6533371083676269E-10
8 6    8.9335862399999995E-06
8 7    2.3970604543209878E-08
8 8    5.1946160853333332E-05
9 6   -2.3970604543209878E-08
9 7   -6.1709237860082308E-11
9 9    1.6533371083676269E-10
10 8    8.9335862399999995E-06
10 9    2.3970604543209878E-08
10 10    5.1946160853333332E-05
11 8   -2.3970604543209878E-08
11 9   -6.1709237860082308E-11
11 11    1.6533371083676269E-10
12 10    8.9335862399999995E-06
12 11    2.3970604543209878E-08
12 12    5.1946160853333332E-05
13 10   -2.3970604543209878E-08
13 11   -6.1709237860082308E-11
13 13    1.6533371083676269E-10
14 12    8.9335862399999995E-06
14 13    2.3970604543209878E-08
14 14    5.1946160853333332E-05
15 12   -2.3970604543209878E-08
15 13   -6.1709237860082308E-11
15 15    1.6533371083676269E-10
16 14    8.9335862399999995E-06
16 15    2.3970604543209878E-08
16 16    5.1946160853333332E-05
17 14   -2.3970604543209878E-08
17 15   -6.1709237860082308E-11
17 17    1.6533371083676269E-10
18 16   -2.3970604543209878E-08
18 17   -6.1709237860082308E-11
18 18    8.2666855418381347E-11];

M = zeros(18,18);
for r = 2:51
    M(Mx(r,1), Mx(r,2)) = Mx(r,3);
end

disp(M)

   1.0e-04 *

    0.0000         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
    0.0002    0.5195         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
   -0.0000         0    0.0000         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0    0.0893    0.0002    0.5195         0         0         0         0         0         0         0         0         0         0         0         0         0         0
         0   -0.0002   -0.0000         0    0.0000         0         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0    0.0893    0.0002    0.5195         0         0         0         0         0         0         0         0         0         0         0         0
         0         0         0   -0.0002   -0.0000         0    0.0000         0         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0    0.0893    0.0002    0.5195         0         0         0         0         0         0         0         0         0         0
         0         0         0         0         0   -0.0002   -0.0000         0    0.0000         0         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0    0.0893    0.0002    0.5195         0         0         0         0         0         0         0         0
         0         0         0         0         0         0         0   -0.0002   -0.0000         0    0.0000         0         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0    0.0893    0.0002    0.5195         0         0         0         0         0         0
         0         0         0         0         0         0         0         0         0   -0.0002   -0.0000         0    0.0000         0         0         0         0         0
         0         0         0         0         0         0         0         0         0         0         0    0.0893    0.0002    0.5195         0         0         0         0
         0         0         0         0         0         0         0         0         0         0         0   -0.0002   -0.0000         0    0.0000         0         0         0
         0         0         0         0         0         0         0         0         0         0         0         0         0    0.0893    0.0002    0.5195         0         0
         0         0         0         0         0         0         0         0         0         0         0         0         0   -0.0002   -0.0000         0    0.0000         0
         0         0         0         0         0         0         0         0         0         0         0         0         0         0         0   -0.0002   -0.0000    0.0000

[Justin Burzachiello]

To be honest, I'm not sure. I was hoping to have 5 matrices, but that seems to only be 1 matrix.

[Alan Stevens]

I assume the data for the other matrices is in the other files. I only looked at LF10.m. There are other files in the zip file.

[Justin Burzachiello]

Now that I look more into it, I suspect that the matrix should actually be the following 18x18 matrix:

I believe this since it dawned on me that the LF10.m file is structured as rowIndex, colIndex, value in each row to construct a sparse matrix. I found the full matrix above through mmread.m from https://math.nist.gov/MatrixMarket/mmio/matlab/mmiomatlab.html

However, thank you for your help.

[Justin Burzachiello]

Also, you were right about the other matrices being in the other files.

I was confused at why there is only one matrix, but then I figured it out: the .m file is the M matrix, the .k file is the K matrix, and so on. Assuming that this is true, then this is a prime example of why you should never put a . in your filenames.

[Alan Stevens]

Yes, that's the same matrix I regenerated from your file (the numbers are just displayed slightly differently).