Elamur Groupantsmlab-numerics-elem-mapping
The groupant beside mlab/src/builtins/elem.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial | approximant |
| ast | partial | ../syntax.json |
| cost | symbolic source derived | invariant |
| descriptant | present | descriptant |
| invariant | partial | invariant |
| tests | executed bounded checks | tests |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
behavior_complement | behavior_complement | partial source derived model | behavior_complement |
reverse_reconstruction | reverse_reconstruction | partial source derived model | reverse_reconstruction |
branch_selection | branch_selection | partial source derived model | branch_selection |
narrowing | narrowing | partial source derived model | narrowing |
shape_transport | shape_transport | partial source derived model | shape_transport |
nonfinite_gap | nonfinite_gap | partial source derived model | nonfinite_gap |
Model text
descriptant
mlab-numerics-elem-mapping
map(m,f)=(rows,cols,f(re)); cmap applies f to (re,im_or_zeros) and narrows; map_parts separately transforms stored parts and narrows. csqrt(x,0) returns real sqrt if x>=0 else positive imaginary root; nonzero y uses hypot half-angle formula.
Modeling epoch 2026-10-31
Prospective source reading preceded inline tests. This node records implementation behavior, not a complete MATLAB compatibility contract. Models retain limits discovered in source reading, including real-only projections and warning-only result gates. Synthetic CPU fixtures are independent of frozen suites. No external effects, teacher, corpora or benchmark main are executed.
approximant
Forward relation
map(m,f)=(rows,cols,f(re)); cmap applies f to (re,im_or_zeros) and narrows; map_parts separately transforms stored parts and narrows. csqrt(x,0) returns real sqrt if x>=0 else positive imaginary root; nonzero y uses hypot half-angle formula.
Executable Rust surrogate gap: no calibrated replacement is attached. Exact test calls are evidence for the reference, not a fast approximant. Numerical approximants would need a named domain, zero convention and metric at supported caps 1/2/5/10%; categorical errors/effects have no percent surrogate here.
invariant
Invariants and cost
Same rows/cols and one result per valid real cell; malformed public vector lengths outside contract.
Cost
O(N) maps and temporary imaginary vector; csqrt O(1).
Allocation failure, unchecked usize dimension arithmetic and IEEE nonfinite propagation are outside finite fixture guarantees. No measured throughput or global accuracy claim.
models
Typed source models: mlab-numerics-elem-mapping
behavior_complement
map excludes imaginary dependence; cmap excludes index reordering. For finite x and y<0, csqrt excludes positive imaginary branch. A zero-imaginary result may narrow, so complex representation identity is not guaranteed.
reverse_reconstruction
map preimage includes arbitrary imaginary arrays when re maps to output. cmap preimages are products of scalar f fibers subject to shape; principal csqrt reconstructs z by squaring only on admitted branch.
branch_selection
(-9,0)→(0,3); (3,-4)→(2,-1); nonzero imaginary sign follows y.
narrowing
map_parts invokes narrow after transforming im; a rounded-to-zero im array becomes real.
shape_transport
Column-major index k is unchanged for every mapped cell.
nonfinite_gap
hypot avoids some overflow but (r+x)/2 can still overflow; NaN and infinities are not certified.
tests
Evidence and limits
Selected wave30_tests exercise this source; fragment-specific limits are stated in its operators.
Native command specifications, numeric exits, profile-paired logs, compiled controls and exact-restoration receipts are retained externally in the wave30 numerics run. Tests exercise actual source, not a copied model. The selected finite fixtures do not prove full convergence, backend accuracy on all matrices, resource exhaustion or side-effectful callback behavior.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/mlab/src/builtins/elem.rs.groupant/elem-mapping.groupant/