Incorrect results of inverse tall array

Hi,

I am using tall array and testing the inverse of A? (pseudo inverse). The system is linear Ax=b. A:245*9, x: 9*1, b:245*1.

However, with the same matrices, the results of gather(A/b) is incorrect, 1st to 7th elements are NaN, 8th is -inf. The last one is the same with non-tall array results.

C = load("C.mat")

C = struct with fields:
    dataSitesAugm: [6615x9 double]

C = C.dataSitesAugm;
d = load("d.mat")

d = struct with fields:
    functionValues: [6615x1 double]

d = d.functionValues;
A_ds = arrayDatastore([C d], "OutputType","same");
At = tall(A_ds);
A = At(:,1:9);
B1 = At(:,10);
X=A\B1; % solve X in equation A*X=B1
X_1=gather(X)

Evaluating tall expression using the Local MATLAB Session:
- Pass 1 of 1: 0% complete
- Pass 1 of 1: 9% complete
- Pass 1 of 1: 22% complete
- Pass 1 of 1: 36% complete
- Pass 1 of 1: 50% complete
- Pass 1 of 1: 63% complete
- Pass 1 of 1: 77% complete
- Pass 1 of 1: 91% complete
- Pass 1 of 1: Completed in 7.7 sec
Evaluation completed in 8.1 sec

X_1 = 9x1

NaN NaN NaN NaN Inf 0.8010 0.6198 0.4161 0.0042

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Y=C\d; % solve X in non-tall array, benchmark

Warning: Rank deficient, rank = 7, tol = 1.194634e-10.

Any one can help this case?

Thanks in advance.

Answer 1

[Ayush Modi]

Hi Chen,

Your code looks good to me. The issue might be with the data.

I tested the code with randomly generated matrix as well as the attached data. I am able to reproduce the issue with the attached data but is working fine with random data:

% Generate sample data
rng(0); 
C = rand(245, 9); 
d = rand(245, 1);

data = [C d];
A_ds = arrayDatastore(data, "OutputType", "same");

At = tall(A_ds);

A = At(:, 1:9);
B1 = At(:, 10);

X = A \ B1;

X_1 = gather(X);

Evaluating tall expression using the Local MATLAB Session:
- Pass 1 of 1: 0% complete
- Pass 1 of 1: Completed in 0.72 sec
Evaluation completed in 1.1 sec

Y = C \ d;

disp('Results using tall arrays:');

Results using tall arrays:

disp(X_1);

    0.0471
    0.1917
    0.1769
    0.0630
    0.0034
    0.0588
    0.1110
    0.0537
    0.2454

disp('Results using non-tall arrays:');

Results using non-tall arrays:

disp(Y);

    0.0471
    0.1917
    0.1769
    0.0630
    0.0034
    0.0588
    0.1110
    0.0537
    0.2454

[chen zhe]

Yeah, could be the data issue.

But do you know why the non-tall array works well while the tall array with gather() cannot have the reasonable results?

Not sure if this is a bug.