the tranpose of transpose doed not equals the original matrix

I find that on my data(see the attachment) ,the tranpose of transpose doed not equals the original matrix. This is my code. I donot understand why (a')' does not equals a. My matlab version is R2022a.

load("a.mat")
norm((a')' - a, 'fro')

ans = 140.4280

Answer 1

[Walter Roberson]

You have a broken sparse matrix, probably build by a third-party product, but possibly built by a broken mex file.

See a similar discussion at https://www.mathworks.com/matlabcentral/answers/1954909-sparse-matrix-entries-are-not-displayed-correctly#answer_1225544

load("a.mat")
whos a

  Name          Size             Bytes  Class     Attributes

  a         30084x1             157808  double    sparse    

at = a';
att = at';
whos a at att

  Name          Size                Bytes  Class     Attributes

  a         30084x1                157808  double    sparse    
  at            1x30084            398472  double    sparse    
  att       30084x1                157808  double    sparse    

mask = att ~= a;
locs = find(mask, 1)

locs = 499

a(locs)

ans = 
   All zero sparse: 1×1

at(locs)

ans = 
   (1,1)      -0.1000

att(locs)

ans = 
   (1,1)      -0.1000

d = att - a;

max(d(:))

ans = 
   (1,1)        1

min(d(:))

ans = 
   (1,1)       -1

nnz(imag(d))

ans = 0

[James Tursa]

I see that Tim Davis's SPOK has been removed from the FEX. I will write a replacement and upload it when I get some free time, maybe this weekend. Should I call it SPOK for consistency in searches or give it a new name?

[Walter Roberson]

In view of tomorrow's date, perhaps it should be SPOOK ;-)

Answer 2

[James Tursa]

I finally finished my sparse matrix integrity checker. You can find it in the FEX under the name SAREK (I think you will be able to figure out the inside joke):

https://www.mathworks.com/matlabcentral/fileexchange/158161-sarek-sparse-analyzer-real-et-komplex?s_tid=srchtitle

Here is what it reports for the posted matrix:

>> sarek(a)

SAREK -- Sparse Analyzer Real Et Komplex , by James Tursa

Compiled in version R2023a (with -R2018a option)
Running  in version R2023a

Matrix is double ...
Matrix is real ...
M = 30084 >= 0 OK ...
N = 1 >= 0 OK ...
Nzmax = 9862 >= 1 OK ...
Jc[0] == 0 OK ...
Jc[N] = 9862 <= Nzmax = 9862 OK ...
Jc array OK ...
ERROR: There are 9861 Ir entries out of order or out of range
TO FIX: [M,N] = size(A); [I,J,V] = find(A); B = sparse(I,J,V,max(max(I),M),N);
All stored elements nonzero OK ...
    
There were ERRORS found in matrix!

ans =
9861

And if you plot the row indexes, you can see that the matrix was built in reverse order since they are all decreasing!

>> [I,J,V] = find(a);
>> plot(I)

After applying the recommended fix and re-plotting you can see that the row indexing order has been corrected:

>> [M,N] = size(a); [I,J,V] = find(a); B = sparse(I,J,V,max(max(I),M),N);
>> sarek(B)

SAREK -- Sparse Analyzer Real Et Komplex , by James Tursa

Compiled in version R2020a (with -R2018a option)
Running  in version R2020a

Matrix is double ...
Matrix is real ...
M = 30084 >= 0 OK ...
N = 1 >= 0 OK ...
Nzmax = 9862 >= 1 OK ...
Jc[0] == 0 OK ...
Jc[N] = 9862 <= Nzmax = 9862 OK ...
Jc array OK ...
Ir array OK ...
All stored elements nonzero OK ...
    
All sparse integrity checks OK

ans =
0
>> [I,J,K] = find(B);
>> plot(I)