Mult

Published configurations

Public scalar-weighted basis production benchmark entry point.

Measured operation

Measures leaf and weighted basis production through public expression nodes.

Mathematical foundation

For each mapped sample \(x_q\) and local basis index \(a\), stores \(\phi_a(x_q)\), \(\rho(x_q)\phi_a(x_q)\) or \(\phi_a(x_q)\rho(x_q)\), respectively. The scalar coefficient is \(\rho=s(2+x_0)\) over the reals and \(\rho=s(2+x_0+i/2)\) over the complex numbers. Point uses \(x_0=0\). Component values are stored in quadrature/basis/component order, with row-major logical components for matrices. This is an output layout, not an assumption about global DOF numbering or nodal interpolation.

Measurement boundary

One sweep includes integration-point rebinding, coefficient-cache binding, public getBasis calls and active-value stores. Mesh/space/node construction, mapped quadrature and public-binding priming are outside timing. Binding priming alone does not guarantee reference-table readiness for matrix leaves. Prepared-reference scopes explicitly construct the scalar table before priming and require its presence immediately before and after the measured loop. Preparation is not included in their reported consumption time. No basis pairs, Frobenius contractions, weighted integration, scatter or solving are included. The leaf control is a separate operation, not a timing to subtract to obtain coefficient or allocation cost. All node borrows refer to one owned integration-point context that outlives the nodes.

Numerical qualification

Returned logical vector and matrix dimensions are checked outside timing. Every output is compared exactly with the public unweighted basis and the corresponding scalar multiplication in its original operand order. This isolates materialisation, not independent basis accuracy. Changed output must be rejected. Coefficient scales \(1\to2\to1\) exercise rebinding without changing logical sample identities. Only one flattened active-value output is retained; a second full basis-value table is not constructed.

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

RodinBasisScalingBenchmarks · auto · slow · ranks: 1