kp = <\/span><\/div>
81\u00d7225 KronProd array with properties:\r\n\r\n opset: {[3\u00d73 double] [3\u00d75 double] [9\u00d715 double]}\r\n opinds: [1 2 3]\r\n numops: 3\r\n eyemask: [0 0 0]\r\n domainset: [3 5 15]\r\n maxdim: 3\r\n scalarcoeff: 1\r\n scalarcumprods: [1 1 1]\r\n scalarmask: [0 0 0]\r\n domainsizes: [3 5 15]\r\n rangesizes: [3 3 9]<\/div><\/div><\/div><\/div><\/div><\/div>
Now we can work with this as if the full expansion you'd get from the <\/span>kron<\/span> function.<\/span><\/div>nzeros = nnz(kp)<\/span><\/span><\/div>nzeros = 14580<\/div><\/div><\/div><\/div>Or a matrix operation where I get back KronProds.<\/span><\/div>[u, s, v] = svd(kp)<\/span><\/span><\/div>u = <\/span><\/div>  81\u00d781 KronProd array with properties:\r\n\r\n             opset: {3\u00d71 cell}\r\n            opinds: [1 2 3]\r\n            numops: 3\r\n           eyemask: [0 0 0]\r\n         domainset: [3\u00d71 double]\r\n            maxdim: 3\r\n       scalarcoeff: 1\r\n    scalarcumprods: [1 1 1]\r\n        scalarmask: [0 0 0]\r\n       domainsizes: [3 3 9]\r\n        rangesizes: [3 3 9]<\/div><\/div><\/div>s = <\/span><\/div>  81\u00d7225 KronProd array with properties:\r\n\r\n             opset: {3\u00d71 cell}\r\n            opinds: [1 2 3]\r\n            numops: 3\r\n           eyemask: [0 0 0]\r\n         domainset: [3\u00d71 double]\r\n            maxdim: 3\r\n       scalarcoeff: 1\r\n    scalarcumprods: [1 1 1]\r\n        scalarmask: [0 0 0]\r\n       domainsizes: [3 5 15]\r\n        rangesizes: [3 3 9]<\/div><\/div><\/div>v = <\/span><\/div>  225\u00d7225 KronProd array with properties:\r\n\r\n             opset: {3\u00d71 cell}\r\n            opinds: [1 2 3]\r\n            numops: 3\r\n           eyemask: [0 0 0]\r\n         domainset: [3\u00d71 double]\r\n            maxdim: 3\r\n       scalarcoeff: 1\r\n    scalarcumprods: [1 1 1]\r\n        scalarmask: [0 0 0]\r\n       domainsizes: [3 5 15]\r\n        rangesizes: [3 5 15]<\/div><\/div><\/div><\/div><\/div><\/div>Matt has overloaded <\/span>subsref<\/span> so when you index into the KronProd, you get back a KronProd or just matrix.<\/span><\/div>kkp = kp(1)<\/span><\/span><\/div>kkp = <\/span><\/div>  3\u00d73 KronProd array with properties:\r\n\r\n             opset: {[3\u00d73 double]}\r\n            opinds: 1\r\n            numops: 1\r\n           eyemask: 0\r\n         domainset: 3\r\n            maxdim: 1\r\n       scalarcoeff: 1\r\n    scalarcumprods: 1\r\n        scalarmask: 0\r\n       domainsizes: 3\r\n        rangesizes: 3<\/div><\/div><\/div><\/div><\/div>km = kp{1}<\/span><\/span><\/div>km = <\/span>3\u00d73<\/span><\/div><\/div>     8     1     6\r\n     3     5     7\r\n     4     9     2\r\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>He did not overload <\/span>subsasgn<\/span> though, so we can't do the opposite.<\/span><\/div>try<\/span><\/span><\/div><\/div>    kp{1} = rand(3)<\/span><\/span><\/div><\/div>catch <\/span>ME<\/span><\/span><\/div><\/div>    fprintf(2, ME.message)<\/span><\/span><\/div><\/div>end<\/span><\/span><\/div>Unable to perform assignment because brace indexing is not supported for variables of this type.<\/div><\/div><\/div><\/div><\/div>He's also overloaded <\/span>size<\/span> so the appearance of size is that of the full Kronecker product.  Under the hood, however, the <\/span>KronProd<\/span> is actually a scalar, it just <\/span>appears<\/span> to be the expanded size.  <\/span><\/div>sz = size(s)<\/span><\/span><\/div>sz = <\/span>1\u00d72<\/span><\/div><\/div>    81   225\r\n<\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>Starting in MATLAB R2021b, we now have an easier and more formal means for controlling indexing and creating scalar objects using <\/span>modular indexing<\/span><\/a>.  <\/span><\/div>Right now <\/span>subsref<\/span> overloads (), {}, and dot(.).  It overloads dot, just because it has to with the old approach, so we don't need to do that with the newer indexing.  So the class definition line would need to be:<\/span><\/div>classdef <\/span>KronProd < matlab.mixin.indexing.RedefinesParen & matlab.mixin.indexing.RedefinesBrace<\/span><\/span><\/div><\/div>Now, we'd need to implement the abstract methods for <\/span>parenAssign, parenReference, braceAssign, braceReference<\/span>.  These methods would then use similar logic to what's used today, in a protected methods block, something along these lines:<\/span><\/div>function <\/span>B = braceReference(obj, indexOp)<\/span><\/span><\/div><\/div>    inds = M.opinds(indexOp(1).Indices{1});<\/span><\/span><\/div><\/div>    B=M.opset(inds);<\/span><\/span><\/div><\/div>    <\/span>if <\/span>isnum(inds)<\/span><\/span><\/div><\/div>        B=B{:};<\/span><\/span><\/div><\/div>    <\/span>end<\/span><\/span><\/div><\/div>end<\/span><\/span><\/div><\/div><\/div>Comments<\/span><\/h2>Matt, if we ever meet in real life, I owe you a beer!<\/span><\/div>Give it a try and let us know what you think <\/span>here<\/span><\/a> or leave a<\/span> <\/span>comment<\/span><\/a> for Matt.<\/span><\/div>\r\n<\/div><\/body><\/html>