Operations catalog

The catalog is organised thematically below, rather than by dotted path. Each operation adheres to a common contract: it accepts a typedargumentsobject, produces a single output bound to the caller's as placeholder, and incurs a fixed ECU cost proportional to arithmetic complexity and problem size. Argument validation occurs statically, before any dispatch to the compute backend.

Type labels used in the signatures below have their customary meanings: number and integer for numeric scalars; boolean, string; matrix denotes a two-dimensional numerical array (either an array of typed arrays or an array of arrays of numbers); enum denotes a value restricted to a fixed set of literals — the numeric parameter in parentheses indicates the size of the enumeration. Every operation also accepts an optional safe: boolean argument (defaulting to true) that toggles per-call input revalidation; setting it to false skips the redundant validation in performance-critical inner loops.

Constructors for standard matrices — zero, identity, random draws with optional uniqueness constraints, triangular random matrices — together with utilities for replication, reshaping, dimensional query, and copying. Predicate operations distinguish squares, symmetries, and matrix-typed values.

Operations that act point-wise on matrix entries. Arithmetic includes the standard field operations together with the Hadamard product and specialised multiplications between triangular factors. Elementary mathematical functions and their inverses and hyperbolic variants are provided in element-wise form. Comparison and logical operations return matrices of Boolean or 0/1 entries suitable for masking.

Reductions along rows, columns, or the entire matrix — sums, sums-of-squares, absolute sums, minima and maxima, together with diagonal-exclusion variants of the same. Induced and Frobenius norms are exposed as first-class operations.

Operations that read or modify structural regions of a matrix — rows, columns, arbitrary rectangular blocks, and diagonals — together with the family of vector-broadcast operations that add, subtract, multiply or divide a vector across a chosen matrix axis.

The customary matrix decompositions and related reductions. Each operation returns a structured value carrying the factor matrices and, where applicable, permutation data.

Building blocks for user-composed iterative procedures — a single step of the operation, exposed so that the caller can compose convergence tests, adaptive schedules, and stopping criteria within the DAG itself. Initial-approximation operations are supplied for the iterative inversion families.

Discrete convolution, pooling, and the activation functions used in contemporary architectures, expressed at matrix scale so that they compose naturally with the linear-algebra operations above.

Variance-stabilising and normality-inducing transformations applied element-wise to a matrix.

The scalar counterparts of the element-wise matrix operations, exposed under the math.operations namespace. These are the primitives of choice inside guard expressions on edges, where a single-value predicate is required.

A curated collection of numerical constants. Each is a nullary operation returning a scalar value; SI base units are assumed throughout for the physical quantities.

Market-data retrieval, return computation, index-constituent management, and mean–variance-style portfolio primitives. These operations are typically composed into multi-node graphs in which an initial retrieval node feeds a downstream optimisation node.

Operations for the introduction of external data into a computation. File-consuming operations reference an entry-node input under the filePath argument; the mechanisms for supplying such a file — multipart form-data and pre-uploaded references — are documented on the DAG schema page.