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 from the 2026-06 evidence audit (LAPACK dgesdd + G&VL 4e §8.6); see docs/reference/cost-model.md.

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

min(4*m*n*k, economy)

4*m*n*k is the verified leading-order cost of a rank-k randomized SVD (Halko-Martinsson-Tropp; two passes over A, Theta(m*n*k)). flopscope bills this standard truncated-algorithm cost even though the reference implementation computes the full economy SVD and slices — it bills the textbook cost of the operation (like matmul), not literal BLAS work. Values-only is NOT leading-order cheaper for the truncated case (unlike the full case). k >= min(m, n) bills the economy cost; the full_matrices full-U premium applies only to the 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.