Overview

Overview#

In Getting Started you installed linopy, built a first scalar model, and saw N-D variables on coordinates. The User Guide reopens each of those pieces in depth and adds the rest of the modelling surface.

Each page is a runnable Jupyter notebook — read it top to bottom, or use it as a reference once you know what you’re looking for.

Core building blocks#

The four notebooks below cover the model object you’ll interact with most. Read them in order the first time; come back to them whenever you’re unsure what a particular operator or argument does.

  • Creating Variables — declaring decision variables, with bounds and coordinates. Continuous, integer, binary, and semi-continuous.

  • Creating Expressions — combining variables into linear (and quadratic) expressions; arithmetic, broadcasting, sum, groupby, rolling, where.

  • Creating Constraints — turning expressions into ≤ / ≥ / == constraints, and the CSRConstraint memory-efficient alternative.

  • Coordinate Alignment — how linopy lines up operands that live on different coordinates, and how to control it with join.

After these four you can build any LP/MIP/QP linopy supports.

Numerical scaling#

Large or very small coefficients can make mathematical programs harder for solvers to process. Linopy therefore accepts optional positive, finite scaling factors when adding variables, constraints, and the objective.

For continuous and semi-continuous variables, scaling=s means the solver-side column represents s * x. Bounds are multiplied by s, and coefficients that reference x are divided by s. Binary and integer variable scaling is stored and round-tripped, but their solver columns remain ordinary discrete columns.

For constraints, scaling=s multiplies both the left-hand-side coefficients and the right-hand side by s. Objective scaling is row-like: scaling=s multiplies linear and quadratic objective coefficients by s. Primal values, dual values, and objective values are transformed back to the original user units after solving.

Equivalently, for constraint matrix A, right-hand side b, linear objective coefficients c, variable scaling matrix Sx, constraint scaling matrix Sc, and scalar objective scaling so, linopy exports y = Sx x and A_solver = Sc A Sx^-1, b_solver = Sc b, and c_solver = so c Sx^-1. Quadratic objective coefficients receive the inverse variable scaling once for each variable factor and the scalar objective scaling once globally.

x = m.add_variables(lower=0, scaling=1e3, name="x")
m.add_constraints(2 * x >= 10, scaling=10, name="demand")
m.add_objective(5 * x, scaling=100)

For a worked example that builds a badly-scaled model and applies each of the three variants step by step, see the Numerical Scaling tutorial.

Working with an existing model#

Once you’ve built a model, you’ll often want to inspect it, change a bound, swap a constraint, or copy it for what-if analysis.

  • Modifying Models — modifying or removing variables and constraints in place; Model.copy(); fix / relax for variables.

Where to go next#