flopscope.accounting.svd_cost

Full decomposition (k is None), with a = max(m, n), b = min(m, n):

values only (with_vectors=False): 2*a*b^2 + 2*b^3 thin U, V (full_matrices=False): 6*a*b^2 + 20*b^3 full U (full_matrices=True and m != n): 4*a^2*b + 22*b^3

Constants follow the LAPACK dgesdd path; see docs/reference/cost-model.md.

Top-k truncated SVD (1 <= k < min(m, n)):

with vectors: min(4mnk + 6(m+n)k^2 + 20k^3, thin economy) values only: min(4mnk + 2(m+n)k^2 + 2k^3, values-only economy)

The rank-dependent model includes two matrix passes plus quadratic basis/factor work and a cubic small-decomposition term. This is an analytical pricing convention, not a literal count of the backend, which computes an exact economy SVD and slices its outputs. k >= min(m, n) bills the corresponding economy cost. The full-U premium applies only to a full decomposition (k is None). See docs/reference/cost-model.md.

m:int

Number of rows in the input matrix.

n:int

Number of columns in the input matrix.

k:int | None, optional

Target rank or number of singular components to estimate. Defaults to None.

with_vectors:bool, optional

Argument forwarded to the analytical linalg.svd cost formula. Defaults to False.

full_matrices:bool, optional

Argument forwarded to the analytical linalg.svd cost formula. Defaults to False.

:int

Weighted public cost estimate, floored to match runtime accounting.

This helper multiplies the analytical FLOP count by the active weight from flopscope._weights and then applies int(...) so public estimates match budget deductions.