gpkit: Auto-breakdowns

A feature I discussed with @mtwichan.

Anecdotally, a lot of GP(kit) constraints take the form y > x1 + x2 + x3 + ... + xn (e.g. mass rollup, cost rollup, energy rollup etc.). What’s more, those x1, x2 etc. are often themselves constrained by rollups.

I often want to see/understand/plot/fetch the values of the constituent parts that make up y, i.e. the values of x1...n.

To do this in a semi-automatic way, I currently access the (known) constraint’s varkeys, with something like:

mass_rollup = constraints[4]
masses = mass_rollup.right.varkeys
some_plotting_function(sol, masses)

However, given that the pattern is relatively prevalent and that it would be nice to be able to visualize any arbitrary rollup, I think it could be useful (and not too tricky) to have a native breakdown generator built into GPkit that takes a model (or a solution!) and a variable (in this case y) as an input and returns the rollup.

I think there are ~three~ four possible tiers of functionality, maybe implementation stepping stones.

Bronze

Returns a list of varkeys given an input varkey

# for the constraint y >= x1 + x2 + x3
m.breakdown_search("y") --> [x1, x2, x3]

Silver

Returns a dict of lists given an input varkey

# y >= x1 + x2 + x3
# x1 >= v1 + v2
# x2 >= v3
# x3 >= b*t**3 + a*t**2
m.breakdown_search("y") --> {x1: [v1, v2], x2: [v3], x3: x3}

Gold

Returns a nested dict of dicts for a SolutionArray given an input varkey. This is particularly appealing because I often want to dig into a solution without needing to re-generate the model object from which to derive the rollup (which breaks if the model has rollup has diverged from the rollup used to generate the solution).

# y >= x1 + x2 + x3
# x1 >= v1 + v2           # v2 has optimal value 5
# v1 >= u2 + u2           # u1 has optimal value 1, u2 has optimal value 2
# x2 >= v3 + v4           # v3 has optimal value 2, v4 has optimal value 1
# x3 >= b*t**3 + a*t**2   # x3 has optimal value 10
sol.breakdown("y") --> {x1: {v1: {u1: 1, u2: 2}, v2: 5},
                        x2: {v3: 2, v4: 1},
                        x3: 10}

Platinum

Returns a JSON string for creating an icicle plot (the D3 syntax is just one option – I’m biased because it’s the one I use)

# y >= x1 + x2 + x3
# x1 >= v1 + v2           # v2 has optimal value 5
# v1 >= u2 + u2           # u1 has optimal value 1, u2 has optimal value 2
# x2 >= v3 + v4           # v3 has optimal value 2, v4 has optimal value 1
# x3 >= b*t**3 + a*t**2   # x3 has optimal value 10
sol.breakdown("y", units="MUSD") -->
"""
{"name": "y",                                                                    
 "children": [                                                                   
  {"name": "x1",                                                                 
   "children": [                                                                 
    {"name": "v1":                                                               
     "children": [                                                               
      {"name": "u1",                                                             
       "size": 1,                                                                
       "label": "1 MUSD",                                                        
      },                                                                         
      {"name": "u2",                                                             
       "size": 2,                                                                
       "label": "0.002 MUSD",                                                    
      },                                                                         
    },                                                                           
    {"name": v2"                                                                 
     "size": 5,                                                                  
     "label": "5 MUSD",                                                          
    },                                                                           
   ]                                                                             
  },                                                                             
  {"name": x2",                                                                  
   "children": [                                                                 
    {"name": "v3",                                                               
     "size": 2,                                                                  
     "label": "2 MUSD",                                                          
    },                                                                           
    {"name": v4,                                                                 
     "size": 1,                                                                  
     "label": "1 MUSD",                                                          
    },                                                                           
   ],                                                                            
  },                                                                             
  {"name": "x3",                                                                 
   "size": 10,                                                                   
   "label": "0.01 MUSD",                                                         
  },                                                                             
 ]                                                                               
} # I'm sure I made some mistake but you get the point
"""

@bqpd what do you think about these various proposals?