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 Wikipedia's article on Singular Value Decomposition.

Note

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