MatrixProduct

Published configurations

Spatial matrix products underlying vector-basis gradient transforms.

Measured operation

Measures the canonical matrix product over retained basis-sized arrays.

Mathematical operation

For \(A_a\in\mathbb F^{r\times k}\) and \(B\in\mathbb G^{k\times c}\), the operation is \(C_a=A_aB\). There is no conjugation in this product. Reference Jacobians have \(r=m\), \(k=d\) and the geometric inverse has \(c=s\), where \(m\) is the field component count and \(d,s\) are reference and ambient dimensions. The real/real and complex/real selections therefore isolate the product used by vector-basis pullbacks in assembly. The other scalar pairs cover the same public arithmetic contract.

Measurement boundary

Each iteration multiplies every retained left matrix by the same right matrix, including result construction and assignment to retained output. Counts 6, 12, 30 and 81 model local vector-basis sizes; they do not identify particular geometries. No finite-element evaluation, geometric inverse, symmetric-gradient construction, coefficient weighting, pair contraction or sparse insertion is included. This is a primitive measurement, not a decomposition into additive fractions of a complete cell-kernel time.

All dimensions zero through three and all real/complex scalar pairs are qualified. Bounded dyadic inputs admit an exact independent scalar-loop reference. Inactive input storage is poisoned, while inactive output must remain zero. Wrong values or dimensions must be rejected outside timing.

Recorded results

Each case retains its original inputs, iteration policy and correctness checks. Raw reports preserve counters, repetitions and the Google Benchmark context. CPU, wall and manually supplied times are labeled separately; unlike operations and configurations are not averaged together.

Timing history

RodinSpatialMatrixProductBenchmarks · auto · regular · ranks: 1