[R] Some difficulties to use the apply command on an array

[Laurent Rhelp]

It is good trick and we have to know that R arrays use the 'column major 
mode' to store the value.
Thank you
Laurent


Le 05/07/2021 à 19:03, David Winsemius a écrit :
>
>> On Jul 5, 2021, at 7:56 AM, Laurent Rhelp <LaurentRHelp using free.fr> wrote:
>>
>> Dear R-Help,
>>
>> I have an array x made up of three matrices of 5 rows and 3 columns of complex numbers (the complex numbers are not the problem)
>>
>> ## my array
>> x <- structure(c(5.6196790161893828+0i, 5.7565523942393364+0i, 8.5242834298729342+0i,
>>                10.304766710160479+0i, 11.412967010108229+0i, -2.6952197604866495-5.7324226520260237e-18i,
>>                -3.8053698833683476-1.5535793240880411i, -4.440850591952894-0.21277190153473785i,
>>                -4.9049897326853316+0.22487294128201613i, -4.6982778900868931-0.35986943359186585i,
>>                -6.7722948827866034-1.8252881225149525e-16i, -5.6864255243941733-0.82149125972147463i,
>>                -2.5321753317962115-3.4309121438578525i, 0.85377696343414344-4.3720244641138883i,
>>                6.3363344379954638-2.23654533694011i, -2.6952197604866495+5.7324226520260237e-18i,
>>                -3.8053698833683476+1.5535793240880411i, -4.440850591952894+0.21277190153473785i,
>>                -4.9049897326853316-0.22487294128201613i, -4.6982778900868931+0.35986943359186585i,
>>                3.1683154084671417+0i, 5.397392162921844+0i, 8.3085887222115922+0i,
>>                11.150391891976289+0i, 13.173434845070231+0i, 3.7978840709983359+5.0735539531499429e-17i,
>>                3.0599215005995717-2.3669737981128267i, 0.5951827523696811-3.2116907301709845i,
>>                -1.7735244105472532-3.8366652813316566i, -5.0558348297797169-2.6645747173403049i,
>>                -6.7722948827866034+1.8252881225149525e-16i, -5.6864255243941733+0.82149125972147463i,
>>                -2.5321753317962115+3.4309121438578525i, 0.85377696343414344+4.3720244641138883i,
>>                6.3363344379954638+2.23654533694011i, 3.7978840709983359-5.0735539531499429e-17i,
>>                3.0599215005995717+2.3669737981128267i, 0.5951827523696811+3.2116907301709845i,
>>                -1.7735244105472532+3.8366652813316566i, -5.0558348297797169+2.6645747173403049i,
>>                8.5581082281979697+0i, 8.6908832216086331+0i, 12.394094469562258+0i,
>>                16.106350896659897+0i, 19.569513600539693+0i), .Dim = c(5L, 3L,
>> 3L))
>>
>> str(x)
>> #  cplx [1:5, 1:3, 1:3] 5.62+0i 5.76+0i 8.52+0i ...
>>
>> The dimensions (i,j,k) of my array are 5, 3, 3. For every value of i, I am interested in the squared matrices made up of the j columns for all the k indice. For a given value i I have to keep the row i for every k. For example if i=1, I am interested by the matrix x[1,,]
>> ##
>> x[1,,]
>>
>> ##              [,1]         [,2]         [,3]
>> ## [1,]  5.619679+0i -2.695220+0i -6.772295+0i
>> ## [2,] -2.695220-0i  3.168315+0i  3.797884-0i
>> ## [3,] -6.772295-0i  3.797884+0i  8.558108+0i
>>
>> Now, for every value of i, I want to calculate the SVD decomposition and get the diagonal matrix created by the singular values. When I set the i value it works:
>> diag( svd(x[1,,])$d )
>>
>> # [,1]     [,2]      [,3]
>> # [1,] 15.73833 0.000000 0.0000000
>> # [2,]  0.00000 1.502771 0.0000000
>> # [3,]  0.00000 0.000000 0.1049992
>>
>>
>> But when I try to do a loop on the i value it doesn't work:
>>
>> apply(x, c(2,3), FUN = function(x) diag( svd(x)$d ))
>>
> Use a different indexing strategy:
>
> res <- apply(x, 1, FUN = function(x) diag( svd(x)$d ))
>
> The result is flattened but each of the columns in that `res`-object are the entries in a 3x3 matrix. Reform it by:
>
>> dim(res) <- c(3,3,5)
>> res
> , , 1
>
>           [,1]     [,2]      [,3]
> [1,] 15.73833 0.000000 0.0000000
> [2,]  0.00000 1.502771 0.0000000
> [3,]  0.00000 0.000000 0.1049992
>
> , , 2
>
>          [,1]     [,2]     [,3]
> [1,] 16.0011 0.000000 0.000000
> [2,]  0.0000 3.357086 0.000000
> [3,]  0.0000 0.000000 0.486643
>
> , , 3
>
>           [,1]     [,2]    [,3]
> [1,] 16.05269  0.00000 0.00000
> [2,]  0.00000 11.49007 0.00000
> [3,]  0.00000  0.00000 1.68421
>
> , , 4
>
>           [,1]     [,2]     [,3]
> [1,] 19.58508  0.00000 0.000000
> [2,]  0.00000 14.83712 0.000000
> [3,]  0.00000  0.00000 3.139307
>
> , , 5
>
>           [,1]     [,2]     [,3]
> [1,] 26.75931  0.00000 0.000000
> [2,]  0.00000 11.81372 0.000000
> [3,]  0.00000  0.00000 5.582891
>
>


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