- Jupyter Notebook
- ipysankeywidget
Code in this section uses the CE solar model
from solar.solar import *
Vehicle = Aircraft(Npod=3, sp=True)
M = Mission(Vehicle, latitude=[20])
M.cost = M[M.aircraft.Wtotal]
sol = M.localsolve("mosek_cli")
from gpkit.interactive.sankey import Sankey
Sankey
diagrams can be used to
visualize sensitivity structure in a model. A blue flow from a constraint to its parent
indicates that the sensitivity of the chosen variable (or of making the
constraint easier, if no variable is given) is negative; that
is, the objective of the overall model would improve if that variable's
value were increased in that constraint alone. Red indicates a
positive sensitivity: the objective and the the constraint 'want' that
variable's value decreased. Gray flows indicate a sensitivity whose
absolute value is below 1e-2, i.e. a constraint that is inactive for
that variable. Where equal red and blue flows meet, they cancel each
other out to gray.
In a Sankey diagram of a variable, the variable is on the right with its final sensitivity; to the left of it are all constraints that variable is in.
Free variables have an overall sensitivity of 0, so this visualization shows how the various pressures on that variable in all its constraints cancel each other out; this can get quite complex, as in this diagram of the pressures on wingspan (right-click and open in a new tab to see it more clearly):
Sankey(sol, M, "SolarMission").diagram(M.aircraft.wing.planform.b, showconstraints=False)
Gray lines in this diagram indicate constraints or constraint sets that the variable is in
but which have no net sensitivity to it. Note that the showconstraints
argument can be used to hide constraints if you
wish to see more of the model hierarchy with the same number of links.
Variable in the cost function, have a "[cost function]" node on the diagram like so:
Sankey(sol, M, "SolarMission").diagram(M.aircraft.Wtotal)
Fixed variables can have a nonzero overall sensitivity. Sankey diagrams can how that sensitivity comes together:
Sankey(sol, M, "SolarMission").diagram(M.variables_byname("tmin")[0], left=100)
Note that the left= syntax is used to reduce the left margin in this plot.
Similar arguments exist for the right, top, and bottom margins:
all arguments are in pixels.
The only difference between free and fixed variables from this perspective
is their final sensitivity; for example Nprop, the number of propellers on the
plane, has almost zero sensitivity, much like the wingspan b, above.
Sankey(sol, M, "SolarMission").diagram(M["Nprop"])
When created without a variable, the diagram shows the sensitivity of every named model to becoming locally easier. Because derivatives are additive, these sensitivities are too: a model's sensitivity is equal to the sum of its constraints' sensitivities and the magnitude of its fixed-variable sensitivities. Gray lines in this diagram indicate models without any tight constraints or sensitive fixed variables.
Sankey(sol, M, "SolarMission").diagram(maxlinks=30, showconstraints=False, height=700)
Note that in addition to the showconstraints syntax introduced above,
this uses two additional arguments you may find useful when visualizing large models:
height sets the height of the diagram in pixels (similarly for width),
while maxlinks increases the maximum number of links (default 20), making
a more detailed plot. Plot construction time goes approximately as the square
of the number of links, so be careful when increasing maxlinks!
With some different arguments, the model looks like this:
Sankey(sol, M).diagram(minsenss=1, maxlinks=30, left=130, showconstraints=False)
The only piece of unexplained syntax in this is minsenss. Perhaps
unsurprisingly, this just limits the links shown to only those whose sensitivity
exceeds that minimum; it's quite useful for exploring a large model.
Methods exist to facilitate creating, solving, and plotting the results of a single-variable sweep (see :ref:`Sweeps` for details). Example usage is as follows:
.. literalinclude:: examples/plot_sweep1d.py
Which results in:
