pr-adding-tensors

[jbcaillau]

start with going to x[i1, i2 in 1:1, k in 1:1, j] for M(n, 1, R)

• 0:grid_size to 1:grid_size+1 to avoid discrepancy between x and x_m
• [ ] implement operations on x_m instead of x
• at this step, add idoneus subs to replace x(t) or x[rg](g) by x[rg, j] (should work)
• same update can be made for u to allow u(t) -> u[:, j], etc., still with (real) vectors
• vectorise dynamics for exa
• vectorise constraints for exa
•  at this step, re-write some qc tests (with tweaks / macros for matrix / complex values)
• go for tensors (matrix + complex valued)
• for that, use the fact that Julia vectors are indeed n x 1 matrices (v[i] == v[i, 1] for a Vector), consistently with R^n = M(n, 1, R)

NB:

• needed overloads on exa : *, adjoint, dot... (some work, e.g. sum)
• use @def_exa to test
• need some :fun stuff to plot, etc. if going to tensors

[github-actions]

Breakage test results
Date: 2025-12-15 14:25:31

Name	Latest	Stable
OptimalControl	compat: v0.7.2	compat: v0.7.2

[jbcaillau]

• issue: x_m[i, j] ... for j in ... with j that is expected by ExaModels to generate a generator (inside dynamics, constraints...), not an array, as generators (lazy eval, no alloc) are used for SIMD modelling.

fix: don't use x_m but x[i, j] with j generator and i not a generator but a standard index to define a comprehension (then a vector) as below.

so:

• come back to p.x everywhere
• add subs to replace x(t), x[rg](t) by [x[i, j] for i in 1:n / rg] for dynamics, constraints, and costs

julia> g(x) = [x[1] * x[2] + x[3], x[3] * x[4]]
g (generic function with 1 method)

julia> x
Variable

  x ∈ R^{4 × 10}


julia> constraint(c, g([x[i, j] for i in 1:4])[1] for j in 1:10)
Constraint

  s.t. (...)
       g♭ ≤ [g(x,θ,p)]_{p ∈ P} ≤ g♯

  where |P| = 10


julia> for k in 1:2 
       constraint(c, g([x[i, j] for i in 1:4])[k] for j in 1:10)
       end

[jbcaillau]

non scalar dynamics, (nonlinear) constraints:

• use a loop as above
• if the constraint is scalar, use the standard ct convention and treat is as scalar (not length one vector)

[jbcaillau]

• CRITICAL: review all $p.foo$ vs. $(p.foo)$ expressions in onepass.jl
• as a rule: $(p.foo) when the value is a symbol that needs to be interpretated in the (escaped) call context

FTR

julia> n = 6
6

julia> f.x = :n
:n

julia> e = :($(f.x) == 6)
:(n == 6)

julia> eval(e)
true

julia> e = :($f.x == 6)
:((Foo(:n)).x == 6)

julia> eval(e)
false

julia> e = :($(f.x) == 6)
:(n == 6)

julia> f.x = 6
6

julia> e = :($(f.x) == 6)
:(6 == 6)

[jbcaillau]

for vectorised access to state in exa:

• treat x(t) by improving subs2
• update tests (and docstrings), both for subs2...
• ... and dynamics (sum on whole / ranges for state / control, call to user defined functions...)
• same for subs5 (and rename it subs2m)
• remove subs4 from utils tests
• same for constraints and costs

[jbcaillau]

for vectorised access to state in exa:

• treat x(t) by combiningsubs2 and subs
• update tests (and docstrings), both for subs2 and constraints + dynamics + costs
• same for subs5 (and rename it subs2m)
• remove subs4 from utils tests
• same for constraints and costs

[jbcaillau]

• add some with solve on exa backend with and without calling external functions on vectors for dynamics, constraints and cost, all scalar value for now (solve should be the same)

[jbcaillau]

FTR

use case no. 7: mixed vectorisation (CPU, euler)
This is MadNLP version v0.8.12, running with umfpack

Number of nonzeros in constraint Jacobian............:     3758
Number of nonzeros in Lagrangian Hessian.............:     2762

Total number of variables............................:     1255
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        0
                     variables with only upper bounds:        0
Total number of equality constraints.................:      753
Total number of inequality constraints...............:      251
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:      250
        inequality constraints with only upper bounds:        1

EXIT: Invalid number in NLP constraint function detected.