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svdJs is broken, qrJs too, probably from identSize #2

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@xionluhnis

Description

See NaturalNode/node-lapack#2

Using the following on matlab / octave:

A = [ 1, 2; 3, 4; 5, 6];
[u, s, v] = svd(A)

I obtain:

u =
 -0.22985 0.88346 0.40825
 -0.52474 0.24078 -0.81650
 -0.81964 -0.40190 0.40825
 s =
 9.52552 0.00000
 0.00000 0.51430
 0.00000 0.00000
 v =
 -0.61963 -0.78489
 -0.78489 0.61963

Now with the js implementation:

require('sylvester');
var A = $M([
 [1, 2],
 [3, 4],
 [5, 6]
]);
var svd = A.svd();
console.log(JSON.stringify(svd));

I obtain nothing because it crashes:

 /[...]/node_modules/sylvester/lib/node-sylvester
 /matrix.js:60
 var e = S.triu(1).unroll().norm();
 ^
 TypeError: Cannot call method 'triu' of null
 at Object.svdJs (/[...]/node_modules/sylvester
 /lib/node-sylvester/matrix.js:60:15)

Error summary: it breaks because of a null value being returned by qrJs, which in turn starts with the R matrix being null at some point. That comes from identSize.

However, it's mostly just an issue notification. I personally needed to have reliable and fast svd, so I used SVDLIBC and bound it as a C++ module (see node-svd). You may look at SVDLIBC if you think it can help you with svd / qr processing.

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