pinv operation in matlab

I have a matrix X of size [32X32X10]. I want to do pinv(X). But it suggested to use pagesvd(X). Now the dimension becomes [32X1X10]. However I want the matrix dimension to remain same that is [32X32X10].

Answer 1

[Voss]

X = rand(32,32,10);

XI = pageinv(X);

size(XI)

ans = 1x3

32 32 10

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[Bruno Luong]

This solution only valid if ll matrices aresquare and invertible/*.

.I'm surprise TMW has not release pagepinv.

[Steven Lord]

From the pagepinv documentation page: "Introduced in R2024a"

[Bruno Luong]

Thanks somehow I missed pagepinv when I looked up earlier.

Answer 2

[Bruno Luong]

NOTE: This code is useful fonly or users who run version greater than R2021a and before R2024a, where pagesvd is supported by pagepinv is not..

A = pagemtimes(rand(4,2,5), rand(2,3,5)); % This should be your 32 x 32 x 10 matrix

piA = pagepinv(A)

piA = 
piA(:,:,1) =

   -0.7143   -0.1994    0.8830    0.5803
    3.6830    0.8982   -3.7827   -2.1157
   -3.5004   -0.9739    4.3082    2.8220


piA(:,:,2) =

    1.7339   -1.6101    0.2768    0.1140
   -0.5683    0.8934    0.0456    0.2565
   -1.1307    1.3152   -0.0816    0.1389


piA(:,:,3) =

   -0.7173    0.8751    0.5408   -0.0777
    3.3456   -2.3089   -1.7138    0.8681
   -1.6643    1.5736    1.0465   -0.3106


piA(:,:,4) =

   11.6667    8.3580  -12.7967   -5.3279
   -3.8216   -2.6054    4.4286    1.9206
  -10.5258   -7.3566   11.8744    5.0506


piA(:,:,5) =

   -0.1933    0.0253   -0.3618    0.9475
   -0.6336   -0.0070   -0.9652    2.2255
    1.4941    0.2434    1.7190   -3.0276

% Check correctness
for k = 1:size(A,3)
    norm(pinv(A(:,:,k))-piA(:,:,k),'fro')
end

ans = 0

ans = 0

ans = 0

ans = 0

ans = 0

function piA = pagepinv(A, tol)
sizeA = size(A);
m = sizeA(1);
n = sizeA(2);
if min(m,n) == 0
    piA = zeros([n,m,sizeA(3:end)], 'like', A));
    return
end
A = reshape(A,m,n,[]);
p = size(A,3);
[U,s,V]=pagesvd(A,'econ','vector');
if nargin >= 2
    % user providestol, scalae or vector of length p
    tol = reshape(tol, 1, 1, []);
else
    smax = s(1,:,:); % ,porms of matrices
    tol = max(m,n)*eps(smax); 
end
s(s <= tol) = Inf;
S = reshape(s,1,size(V,2),p);
piA = pagemtimes(V./S,'none',U,'ctranspose');
piA = reshape(piA,[n,m,sizeA(3:end)]);
end

[Paul]

Is this better than looping over the pages and calling pinv on each?

[Bruno Luong]

It's vectorized and potentially multithreaded via pagesvd, better I don't know. But it could be a stock function.