Singular Value Decomposition R←(8415⌶)Y

Y is a simple numeric matrix. ⎕FR must be 645.

The result R is a 4 element vector whose elements are as follows.

[1] U a unitary matrix
[2] S a diagonal matrix
[3] V a unitary matrix
[4] f a Boolean flag indicating whether the algorithm converged (1)or not (0)

This function computes a factorisation of the matrix Y such that:

      Y ≡ U +.× S +.× ⍉+V

This can be useful for analysing matrices for which cannot compute an inverse, because they are singular or nearly singular.

For further information, see https://en.wikipedia.org/wiki/Singular_value_decomposition.

Note:

This function signals DOMAIN ERROR if ⎕FR is 1287. See Floating-Point Representation .