Fixes for examples and solutions notebook

[mmcky]

This branch is applying fixes for broken examples and solutions notebooks.

Broken

1. examples/paths_and_hist.py
2. examples/robust_monopolist.oy
3. examples/lakemodel_example.py
4. solutions/lakemodel_solutions.ipynb

Fixed

1. examples/lakemodel_example.py => Added lakemodel.py to quantecon library for use by this example and the related solutions notebook.
2. solutions/lakemodel_solutions.ipynb => Same as above.

In addition this PR improves the reporting on the command line.

[mmcky]

@cc7768 Any ideas why robust_monopolist.py is failing to converge? I looked at the history of the robust_monopolist.py but it isn't immediately apparent to me.

Traceback (most recent call last):
  File "robust_monopolist.py", line 130, in <module>
    Po, Fo, do = optimal_lq.stationary_values()
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/lqcontrol.py", line 209, in stationary_values
    P = solve_discrete_riccati(A0, B0, R, Q, N)
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/matrix_eqn.py", line 197, in solve_discrete_riccati
    raise ValueError(fail_msg.format(i))
ValueError: Convergence failed after 501 iterations.

[cc7768]

@mmcky I looked around, but nothing changed within that file should break it -- At some point we may have changed the order of arguments for solve_discrete_riccati. Could that be it?

Notice:

• In the LQ class we call https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/lqcontrol.py#L209
• But we call them different things in solve_discrete_riccati https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/matrix_eqn.py#L100

This may have been on purpose; I don't remember whether Q and R are the same in LQ and solve_discrete_riccati (I remember being confused at one point about them). Off the top of my head that's best suggestion I have. I can look into it more later if it turns out to not be the problem.

[mmcky]

@cc7768 That is a little odd. I had a quick look into this and tried swapping them but then you get a linalg problem. So it doesn't immedietly seem like a quick fix.

Traceback (most recent call last):
  File "examples/robust_monopolist.py", line 130, in <module>
    Po, Fo, do = optimal_lq.stationary_values()
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/lqcontrol.py", line 209, in stationary_values
    P = solve_discrete_riccati(A0, B0, Q, R, N)
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/quantecon/matrix_eqn.py", line 166, in solve_discrete_riccati
    Q_tilde = - Q + dot(N.T, solve(Z, N + gamma * BTA)) + gamma * I
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 381, in solve
    r = gufunc(a, b, signature=signature, extobj=extobj)
  File "/home/matthewmckay/anaconda/lib/python2.7/site-packages/numpy/linalg/linalg.py", line 90, in _raise_linalgerror_singular
    raise LinAlgError("Singular matrix")
numpy.linalg.linalg.LinAlgError: Singular matrix

[mmcky]

Introduced dimension checking on input for lss.py picked up two other files where the C vector should be column and not row. Fixes for tsh_hg.py and paths_and_stationarity.py submitted.

[mmcky]

With only one example left to fix example/robust_monopolist.py I propose we merge this branch to incorporate current fixes and open an issue to track the last item.

[jstac]

@mmcky Many thanks.