matlab如何判断矩阵中元素都大于0,在MATLAB中找到矩阵中零元素的数量

￡神魔★判官ぃ 2022-08-30 06:39 316阅读 0赞

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I have a NxM matrix for example named A. After some processes I want to count the zero elements.

How can I do this in one line code? I tried A==0 which returns a 2D matrix.

解决方案

There is a function to find the number of nonzero matrix elements nnz. You can use this function on a logical matrix, which will return the number of true.

In this case, we apply nnz on the matrix A==0, hence the elements of the logical matrix are true, if the original element was 0, false for any other element than 0.

A = \[1, 3, 1;

0, 0, 2;

0, 2, 1\];

nnz(A==0) %// returns 3, i.e. the number of zeros of A (the amount of true in A==0)

The credits for the benchmarking belong to Divarkar.

Benchmarking

Using the following paramters and inputs, one can benchmark the solutions presented here with timeit.

Input sizes

Small sized datasize - 1:10:100

Medium sized datasize - 50:50:1000

Large sized datasize - 500:500:4000

Varying % of zeros

~10% of zeros case - A = round(rand(N)\*5);

~50% of zeros case - A = rand(N);A(A<=0.5)=0;

~90% of zeros case - A = rand(N);A(A<=0.9)=0;

The results are shown next -

1) Small Datasizes

![2bf5f8a2880d4f82763f39477b04414f.png][]

![15b69f85b078c7055807cb9f18ad35dc.png][]

![254a19c03e1b11c200bbaac687257bf0.png][]

2. Medium Datasizes

![293ac3e29084f07df880bae11c5aa30b.png][]

![a28e7031dee29ee678df534f337466f1.png][]

![e1e41fa6957ac0af875bbeef247b474c.png][]

3. Large Datasizes

![bbebe8fd8890e3b137790e0cc4af20b2.png][]

![0849dfc32b0e31660c5a4cfc92c35dc8.png][]

![76b7fd16198fb9d6cfad258ecb969511.png][]

Observations

If you look closely into the NNZ and SUM performance plots for medium and large datasizes, you would notice that their performances get closer to each other for 10% and 90% zeros cases. For 50% zeros case, the performance gap between SUM and NNZ methods is comparatively wider.

As a general observation across all datasizes and all three fraction cases of zeros,

SUM method seems to be the undisputed winner. Again, an interesting thing was observed here that the general case solution sum(A(:)==0) seems to be better in performance than sum(~A(:)).

[Image 1]: 
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[254a19c03e1b11c200bbaac687257bf0.png]: /images/20220829/0322eda40d984a488b59922783f6fe89.png
[293ac3e29084f07df880bae11c5aa30b.png]: /images/20220829/afa40f7838d845fd8e61ee564683eafa.png
[a28e7031dee29ee678df534f337466f1.png]: /images/20220829/225a5d3f059d4cde9cf703c68f6dc891.png
[e1e41fa6957ac0af875bbeef247b474c.png]: /images/20220829/d60cee21f45b493b892744956b64d9d5.png
[bbebe8fd8890e3b137790e0cc4af20b2.png]: /images/20220829/42faf48f501845d3b02f0d696c7b02ef.png
[0849dfc32b0e31660c5a4cfc92c35dc8.png]: /images/20220829/47fd0e304fb94f7d9e1f01cd60989b4a.png
[76b7fd16198fb9d6cfad258ecb969511.png]: /images/20220829/4b4a0d66ca6e472cba05629ad3617d12.png