svd

Builtin index · Core maths

result = svd(A)

Input: A · Output: result

What it is

Thin SVD of A (r×c Mat or CMat), A = U·diag(s)·Vᵀ.

Overloads

A can be Mat or CMat.

2 forms. Each carries its own inputs, outputs and worked example — pick the tab for the one you are calling.

real complex

Code	Input	Output	Description
`result = svd(A)`	`A` Matnot documented yet	`u` Mat`r×k` `Mat` `s` Veclength-`k` `Vec` of singular values `vt` Mat`k×c` `Mat`	Returns a `Model` with fields `u` (`r×k` `Mat`), `s` (length-`k` `Vec` of singular values), and `vt` (`k×c` `Mat`), where `k = min(r,c)` — the full factorization, ready to reassemble `A`.

Examples

Written for this form and run by the build -- the output below is what the engine actually produced.

A = [4, 1; 1, 3]
r = svd(A)
print(r.s)   # [4.618034, 2.381966]

output

[4.618034, 2.381966]

Code	Input	Output	Description
`result = svd(A)`	`A` CMatnot documented yet	`values` —the singular values	Returns a differently-shaped `Model` — only `values` (the singular values), `condition`, and `rank`; there is no `u`/`vt` factor pair to reassemble `A` from in this branch.

Examples

Written for this form and run by the build -- the output below is what the engine actually produced.

C = [1 + 1j, 2; 3, 4 - 1j]
rc = svd(C)
print("values={rc.values}  condition={round(rc.condition, 3)}  rank={rc.rank}")

output

values=[5.628889, 0.561794]  condition=10.019  rank=2

How it works

svd(A) — the thin SVD A = U * diag(s) * V^T. Model kind "svd", fields u/s/vt — the same named-field multi-return convention as kalman_init/ols_model, since the three factors are one related result.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.