gather() in tall array inverse is incorrect

Question

chen zhe 2024-6-27，9:10

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2132496-gather-in-tall-array-inverse-is-incorrect

编辑： Stephen23 2024-6-27，14:13

Hi,

I am testing simple code with tall array inverse and gather(). The following results are different, anyone knows how to fix gather? As I am using tall array for AA and bb.

AA = ones(13,9);
bb = ones(13,1);
AA_t = tall(ones(13,9));
bb_t = tall(ones(13,1));
gather(AA_t\bb_t);
Unrecognized function or variable 'AA_t'.
AA \ bb;

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Stephen23 2024-6-27，11:21

编辑：Stephen23 2024-6-27，11:29

在 MATLAB Online 中打开

AAbb.mat

Defining AA and bb consist of only 1's is ... not going to work, as the warning tells us:

AA = ones(13,9);
bb = ones(13,1);
gather(tall(AA)\tall(bb))
Evaluating tall expression using the Local MATLAB Session:
- Pass 1 of 1: 0% complete
- Pass 1 of 1: Completed in 0.13 sec
Evaluation completed in 0.22 sec
ans = 9x1
1.0e+109 *

   -0.0000
    0.0000
   -0.0000
    0.0000
   -0.0000
    0.0000
   -0.0000
   -2.7433
    2.7433
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
AA \ bb
Warning: Rank deficient, rank = 1, tol =  1.040771e-14.
ans = 9x1
    1.0000
         0
         0
         0
         0
         0
         0
         0
         0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

Using values that are not rank deficient produces much more sensible results:

AA = rand(13,9);
bb = rand(13,1);
gather(tall(AA)\tall(bb))
Evaluating tall expression using the Local MATLAB Session:
- Pass 1 of 1: 0% complete
- Pass 1 of 1: Completed in 0.022 sec
Evaluation completed in 0.053 sec
ans = 9x1
    0.4724
    0.3454
   -0.3305
   -0.1144
    0.0596
    0.2326
   -0.0436
    0.4004
   -0.0722
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
AA \ bb
ans = 9x1
    0.4724
    0.3454
   -0.3305
   -0.1144
    0.0596
    0.2326
   -0.0436
    0.4004
   -0.0722
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

Lets try with the uploaded data:

S = load('AAbb.mat')
Warning: You must use MATLAB release 2023a to load this file. Alternatively, use WRITE(LOCATION,TT) to write a tall array to disk with version independent files.
Warning: You must use MATLAB release 2023a to load this file. Alternatively, use WRITE(LOCATION,TT) to write a tall array to disk with version independent files.
S = struct with fields:
      AA: [13x9 double]
    AA_t: [13x9 tall]
      bb: [13x1 double]
    bb_t: [13x1 tall]
S.AA \ S.bb
Warning: Rank deficient, rank = 7, tol =  1.040771e-14.
ans = 9x1
    0.0195
    0.0461
    0.9691
    0.8912
    0.9073
    0.9145
         0
         0
    0.0034
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>

Note how the warning even tells us the rank of your matrix AA.

Apart from the values that you are using, it is unclear what the problem is.

chen zhe 2024-6-27，11:39

So the problem still here: why gather（）cannot evaluate the same results as non-tall array case？ Is there a solution to make consistent results： A/b and gather（A_t/b_t）？ They all have the rank deficient issue

Stephen23 2024-6-27，14:10

编辑：Stephen23 2024-6-27，14:13

"why gather（）cannot evaluate the same results as non-tall array case?"

For efficient handling of the different data types they use different algorithms. No surprises there.

"Is there a solution to make consistent results： A/b and gather（A_t/b_t）？ They all have the rank deficient issue"

There are infinitely many solutions. Why should we expect any one solution to be preferred?

https://www.mathworks.com/matlabcentral/answers/562967-solution-to-ax-b

https://www.mathworks.com/matlabcentral/answers/260330-given-a-rank-deficient-design-matrix-fitlm-does-not-use-pinv-or-lsqr-to-find-the-minimum-norm-solut

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Answer 1

Aditya 2024-6-27，10:23

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2132496-gather-in-tall-array-inverse-is-incorrect#answer_1477921

在 MATLAB Online 中打开

Hi Chen,

please modify this line and see whether the issue persists or not!

gather(AA_t)\gather(bb_t);

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chen zhe 2024-6-27，10:45

It works. But this is not what we want, as it uses two gather(). When we process tall arrays, we try to use gather() as less as possible due to time consuming.

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