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Reading a loaded model#

This page is for whoever writes an engine that builds models, a renderer, or a checker. A tool reads the model through two objects, Spec and Program.

Spec and Program#

A Spec holds the file as written: its macros:, its descriptions, and a piecewise: block as one block. A Program holds the model the file builds: every macro expanded, every name typed, every operator resolved to a node, and every dimension and degree rule already checked. A curve stays one curve there until spec.expand() writes it out. The file and the program says why the two are split, and which tool reads which.

The curve below expands into a weight per breakpoint, a convexity row and one row per link:

curve.yaml
dimensions:
  generator: { dtype: str }
  bp: { dtype: int }
parameters:
  bp_x: { dims: [generator, bp] }
  bp_y: { dims: [generator, bp] }
variables:
  p:
    dims: [generator]
    bounds: { lower: 0 }
  cost:
    dims: [generator]
    bounds: { lower: 0 }
piecewise:
  curve:
    over: bp
    links:
      - [p, bp_x]
      - [cost, bp_y, ">="]
    method: convex
assumptions:
  cost_is_never_negative:
    holds: "bp_y >= 0"
    description: a negative cost is a gain the objective would chase
constraints:
  target:
    dims: []
    expression: sum(p, over=generator) >= 100
objective:
  sense: minimize
  expression: sum(cost)

from math_spec import to_spec

spec = to_spec('curve.yaml')
program = spec.program
sorted(program.constraints)  # ['target']
sorted(program.piecewise)  # ['curve']

rows = spec.expand('piecewise').program
sorted(rows.constraints)  # ['curve_convexity', 'curve_link0', 'curve_link1', 'target']
sorted(rows.variables)  # ['cost', 'curve_lam', 'p']

to_spec takes a path, the YAML, a mapping or a Spec. spec.program is the program built when the model loaded, so every ask on one model returns one object. A piecewise: block is a curve under program.piecewise, typed, and a sos: block is a set under program.sos. Every parameter the program declares is one the file declared.

Formulations written out#

spec.expand(*kinds) returns a new Spec with each piecewise: and sos: block replaced by the variables and constraints it states. Writing a formulation out says what those are.

expanded = spec.expand()
expanded == spec  # False
expanded.expand() is expanded  # True
spec.expand('sos') is spec  # True
  • The kinds are 'piecewise' and 'sos', and no argument means both. Any other string raises ValueError, naming the two. Curves go first whatever the order of the arguments, so the set a method: sos2 curve states is written out too.
  • The expansion is a different model. It declares more variables and constraints, so it does not compare equal to the model it came from. It declares the same dimensions and parameters, so the same data binds both.
  • A model with nothing to write out comes back as itself. So does an expansion asked for the same kinds again.
  • The spec keeps no expansion. A second call builds it again.
  • Nothing expands a model unasked. A program holds its curves until expand() writes them out. The expansion is a model like any other: to_yaml() writes it, and its program holds the rows and no curve.
sorted(rows.piecewise)  # []

What the data has to satisfy#

program.assumptions maps a name to an Assumption: each entry the file declared, and each one a curve's method derives (what a curve assumes). An Assumption carries a predicate and the where it is checked under, both masks, and the description a refusal ends with. assumption_message returns the message for an assumption the data does not meet:

from math_spec.program import Assumption, assumption_message

sorted(program.assumptions)  # ['cost_is_never_negative', 'curve_complete', 'curve_curvature', 'curve_increasing']
isinstance(program.assumptions['curve_increasing'], Assumption)  # True
message = assumption_message('curve_increasing', program.assumptions['curve_increasing'])
message  # "assumption 'curve_increasing' does not hold for the data bound to 'bp_x' — piecewise 'curve': method: convex requires strictly increasing breakpoints in 'bp_x' along 'bp'"
written = assumption_message('cost_is_never_negative', program.assumptions['cost_is_never_negative'])
written  # "assumption 'cost_is_never_negative' does not hold for the data bound to 'bp_y' — a negative cost is a gain the objective would chase"

Nodes and masks#

The node classes live in math_spec.program, for isinstance tests and field reads. children() walks an expression node's operands, and where_children() walks a predicate's. walk() yields every node under an expression, parents first. walk_regions() yields each node with the cases: regions it stands inside, outermost first.

A Named stands where an expressions: entry is used. Its body is the entry's expression, the same object that program.expressions[name].expression holds, and its value is the body's value. children() steps into the body, so a walk reads through it.

Every where arrives as a Mask. Its .root is the resolved predicate. The mask also answers four questions:

  • .conjuncts flattens the AND spine, and stops at an OR or a NOT.
  • .names_read gives the declarations the mask names.
  • .atoms gives its leaves, with the connectives removed.
  • .dims gives the dimensions the mask is read at.

A comparison of expressions arrives as an ExpressionComparison. Its two sides are program expressions like a constraint's, and its dims are every dimension either side carries. Its names_read are every parameter and relation the sides read, the relation a grouping reads through included.

A name compared against a literal does not arrive this way. p_max > 5 is a ParameterComparison and 1 * p_max > 5 is an ExpressionComparison, though both mask the same coordinates.

Three predicates read another predicate rather than a declaration. A CountComparison carries the mask it counts and the dimension it counts away. A TranslatedPredicate carries the mask it reads at a neighbouring coordinate. A PulledBackPredicate carries the mask it reads through a relation, and the Direction it reads in. Each holds that mask as a Mask, where a connective holds a bare predicate, so the walk recurses through a connective and stops at these. .names_read and .dims see through all three, and the relation a PulledBackPredicate reads is in its .names_read.

Mask(predicate) answers the same four questions of any resolved predicate, and ~, & and | combine masks into a mask. A mask folds as it is built, so a boolean literal stands at a mask's root or nowhere. A Region's when is a Mask too.

Asking what a program uses#

program.footprint says which of the language's constructs one model uses. It answers for the rows the program holds. A curve still on the program is not a row, so its constructs count on the program of the expansion:

footprint = rows.footprint

sorted(footprint.quadratic)  # []
sorted(footprint.domains)  # ['continuous']
sorted(footprint.sos_types)  # []
sorted(kind.__name__ for kind in footprint.kinds)  # ['Constant', 'Multiply', 'Parameter', 'Sum', 'Variable']

Every field is a set, and an empty field means the model does not use the construct. Whether a solver takes a construct is the engine's question (what counts as language). Convexity is not reported: it depends on the numbers.

Asking whether an axis can be cut#

program.separability says, per axis, whether every row of the model fits inside one window along it: a storage balance that reads the previous snapshot does, and an annual emissions cap does not. Like the footprint, it answers for the rows the program holds. The curve's rows sum over bp, so only the rows show that tie:

program.separability['bp'].windowable  # True
rows.separability['bp'].windowable  # False
rows.separability['generator'].linking_rows  # ('target',)
rows.separability['generator'].linking_columns  # ()
tied = rows.separability['generator'].coupled["constraint 'target'"]
tied.partition(' — ')[0]  # 'sums over generator'
'sum_back(window=n)' in tied  # True

Every declared axis has an entry. A coupling that a piecewise: expansion introduced is named under the declaration the expansion emitted.

  • coupled names each declaration that ties the whole axis together: a sum over the axis in a constraint, a grouping that consumes the axis, a wrapped shift, or a set. After the dash, each entry names the one change that would remove the tie.
  • undecided lists each read whose reach only the data can say, as a Reach: the declaration, the parameter or relation it reads, and the kind of read. A caller that holds the data hands the smallest value of each named parameter to resolved, which returns the report with those reads decided.
  • restarts names each declaration that counts a position() along the axis.
  • linking_rows names each constraint that no single window holds.
  • linking_columns names each variable the axis does not index, whose column every window reads.
  • ahead is how many coordinates a window must see past its last row: 0 where every row is pointwise, and 2 for a shift of -2.
  • windowable is false while anything is coupled or undecided.

A sum over the axis in the objective ties nothing. The report says nothing about whether the windowed answer equals the whole-horizon answer.

Writing a spec back out#

spec.to_dict() returns the spec as plain data, and spec.to_yaml() returns that data as a file. Both round-trip, so to_spec(spec.to_dict()) == spec.

to_yaml() writes every value and omits every absence. domain: continuous is written out. A null and an empty section are left out. dims: [] is written, because it says the declaration is a scalar.