singular value decomposition
npm install svd-finderThis procedure computes the singular values and complete orthogonal decomposition of a real rectangular matrix A:
``ts`
A = U diag(q) V(t), U(t) U = V(t) V = I
where the arrays a, u, v, q represent A, U, V, q respectively. The actual parameters corresponding to a, u, v maywithu = withv = true
all be identical unless . In this case, the actual parameters corresponding to u and v must
differ.
m >= n is assumed (with m = a.length and n = a[0].length)
`ts
let a = [
[22, 10, 2, 3, 7],
[14, 7, 10, 0, 8],
[-1, 13, -1, -11, 3],
[-3, -2, 13, -2, 4],
[9, 8, 1, -2, 4],
[9, 1, -7, 5, -1],
[2, -6, 6, 5, 1],
[4, 5, 0, -2, 2]
];
let { u, v, q } = SVD(a);
`
`ts`
// Represents the matrix A to be decomposed
a: number[][]
#### Options
`tsfalse
{
// if U is desired otherwise
u: boolean = true,
// if V is desired false otherwise
v: boolean = true,
// A constant used in the test for convergence; should not be smaller than the machine precision
eps: number = Math.pow(2, -52)
}
`
`tsif withu is true
{
// Represents the matrix U with orthonormalized columns ( otherwise u is used as a working storage)
u: number[][],
//Represents the orthogonal matrix V (if u === true, otherwise v is not used)
v: number[][],
// A vector holding the singular values of A; they are non-negative but not necessarily ordered in decreasing sequence``
q: number[]
}