#!/usr/bin/env python
# coding: utf-8

# # Solver Parameters Tutorial
# 
# For instructions on how to run these tutorial notebooks, please see the [README](./README.md) in this folder.

# ## Setting solver parameters
# Many solvers allow the users to adjust the parameters. When calling `Solve()` function, Drake will use the default parameters for the solver (iterations, optimality tolerance, etc). You could modify these parameters in two ways, by either calling `MathematicalProgram::SetSolverOption`, or pass a `SolverOptions` argument to the `Solve()` function.

# ### Calling MathematicalProgram::SetSolverOption
# By calling `MathematicalProgram::SetSolverOption(solver_id, option_name, option_value)`, you can set a parameter for a specific solver (with the matching `solver_id`). The `option_name` is specific to that solver (for example, [here](https://www.coin-or.org/Ipopt/documentation/node40.html) is a list of IPOPT parameters). Note that `MathematicalProgram` object will store this solver parameter, and this parameter will be applied in the `Solve()` call, if that specific solver (with the matching `solver_id`) is invoked.
# 
# In the following code snippet, we show an example of setting the options of IPOPT.

# In[ ]:


from pydrake.solvers.mathematicalprogram import MathematicalProgram, SolverOptions, Solve
from pydrake.solvers.ipopt import IpoptSolver
import numpy as np
prog = MathematicalProgram()
x = prog.NewContinuousVariables(2)
prog.AddCost(x[0]**2 + x[1] ** 2)
prog.AddConstraint(x[0] + x[1] == 1)

# Set the maximum iteration for IPOPT to be 1.
# max_iter is a parameter of IPOPT solver, explained in
# https://www.coin-or.org/Ipopt/documentation/node42.html
prog.SetSolverOption(IpoptSolver().solver_id(), "max_iter", 1)
solver = IpoptSolver()
result = solver.Solve(prog, np.array([10, 1]), None)
# With fewer maximum iteration, IPOPT hasn't converged to optimality yet (The true optimal is [0.5, 0.5])
print("Success? ", result.is_success())
print(result.get_solution_result())
print("IPOPT x*= ", result.GetSolution(x))


# Also note that setting the parameter of a solver **doesn't** mean that `result = Solve(prog)` will invoke that solver. The invoked solver is determined by Drake, to choose whichever solver it thinks most appropriate.
# 
# In the following snippet, although we set the solver options for IPOPT, Drake chooses another solver (which can solve this particular problem in the closed form.)

# In[ ]:


prog.SetSolverOption(IpoptSolver().solver_id(), "max_iter", 1)
result = Solve(prog)
print(result.get_solver_id().name())


# ### Passing a SolverOptions to Solve function
# Another way of setting the solver options is to pass in a `SolverOptions` object as an argument to `Solve` function. `MathematicalProgram` will *not* store this `SolverOptions` object.
# 
# In the following example, in the first `Solve` call, it uses the `SolverOptions` object to set the parameter for IPOPT; in the second `Solve` call, it uses the default IPOPT parameters, hence we get different results from two `Solve` calls.

# In[ ]:


prog = MathematicalProgram()
x = prog.NewContinuousVariables(2)
prog.AddCost(x[0]**2 + x[1] ** 2)
prog.AddConstraint(x[0] + x[1] == 1)

solver_options = SolverOptions()
solver_options.SetOption(IpoptSolver().solver_id(), "max_iter", 1)
solver = IpoptSolver()

# Call Solve with solver_options, IPOPT will use `max_iter` = 1
result = solver.Solve(prog, np.array([10, 1]), solver_options)
print("Success? ", result.is_success())
print(result.get_solution_result())
# Call Solve without solver_options, IPOPT will use the default options.
result = solver.Solve(prog, np.array([10, 1]), None)
print("Success? ", result.is_success())
print(result.get_solution_result())