Recording - Saving Data Generated for Future Use¶
This tutorial is builds on the Optimization of the Paraboloid Tutorial by demonstrating how to save the data generated for future use. Consider the code below:
from openmdao.api import IndepVarComp, Component, Group, Problem, ScipyOptimizer, SqliteRecorder
class Paraboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
unknowns['f_xy'] = (x - 3.0) ** 2 + x * y + (y + 4.0) ** 2 - 3.0
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = 2.0 * x - 6.0 + y
J['f_xy', 'y'] = 2.0 * y + 8.0 + x
return J
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-50, upper=50)
top.driver.add_desvar('p2.y', lower=-50, upper=50)
top.driver.add_objective('p.f_xy')
recorder = SqliteRecorder('paraboloid')
recorder.options['record_params'] = True
recorder.options['record_metadata'] = True
top.driver.add_recorder(recorder)
top.setup()
top.run()
top.cleanup() # this closes all recorders
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
These next four lines are all it takes to record the state of the problem as the optimizer progresses. Notice that because by default, recorders only record Unknowns, if we also want to record Parameters and metadata, we must set those recording options. (We could also record Resids by using the record_resids option but this problem does not have residuals. )
recorder = SqliteRecorder('paraboloid')
recorder.options['record_params'] = True
recorder.options['record_metadata'] = True
top.driver.add_recorder(recorder)
We initialize a SqliteRecorder by passing it a filename argument. This recorder indirectly uses Python’s sqlite3 module to store the data generated. In this case, sqlite3 will open a database file named ‘paraboloid’ to use as a back-end. Actually, OpenMDAO’s SqliteRecorder makes use of the sqlitedict module because it has a simple, Pythonic dict-like interface to Python’s sqlite3 database.
We then add the recorder to the driver using driver.add_recorder. Depending on your needs, you are able to add more recorders by using additional driver.add_recorder calls. Solvers also have an add_recorder method that is invoked the same way. This allows you to record the evolution of variables at lower levels.
While it might not be an issue, it is good practice to tell the Problem explicitly to clean things up before the program terminates. This will close all recorders and potentially release other operating system resources.
This is simply done in this case by calling:
top.cleanup()
Includes and Excludes¶
Over the course of an analysis or optimization, the model may generate a very large amount of data. Since you may not be interested in the value of every variable at every step, OpenMDAO allows you to filter which variables are recorded through the use of includes and excludes. The recorder will store anything that matches the includes filter and that does not match the exclude filter. By default, the includes are set to [‘*’] and the excludes are set to [], i.e. include everything and exclude nothing.
The includes and excludes filters are set via the options structure in the recorder. If we were only interested in the variable x from our Paraboloid model, we could record that by setting the includes as follows:
recorder = SqliteRecorder('paraboloid')
recorder.options['includes'] = ['x']
top.driver.add_recorder(recorder)
Similarly, if we were interested in everything except the value of f_xy, we could exclude that by doing the following:
recorder = SqliteRecorder('paraboloid')
recorder.options['excludes'] = ['f_xy']
top.driver.add_recorder(recorder)
The includes and excludes filters will accept glob arguments. For example, recorder.options[‘excludes’] = [‘comp1.*’] would exclude any variable that starts with “comp1.”.
Accessing Recorded Data¶
While each recorder stores data differently in order to match the file format, the common theme for accessing data is the iteration coordinate. The iteration coordinate describes where and when in the execution hierarchy the data was collected. Iteration coordinates are strings formatted as pairs of names and iteration numbers separated by ‘|’. For example, ‘rank0:SLSQP|1|root|2|G1|3’ would describe the third iteration of ‘G1’ during the second iteration of ‘root’ during the first iteration of ‘SLSQP’. Some solvers and drivers may have sub-steps that are recorded. In those cases, the iteration number may be of the form ‘1-3’, indicating the third sub-step of the first iteration.
Since our Paraboloid only has a recorder added to the driver, our ‘paraboloid’ SQLite file will contain keys of the form ‘rank0:SLSQP|1’, ‘rank0:SLSQP|2’, etc. To access the data from our run, we can use the following code:
import sqlitedict
from pprint import pprint
db = sqlitedict.SqliteDict( 'paraboloid', 'iterations' )
There are two arguments to create an instance of SqliteDict. The first, ‘paraboloid’, is the name of the SQLite database file. The second, ‘iterations’, is the name of the table in the SQLite database containing the iteration values.
Now, we can access the data using an iteration coordinate. It is not always obvious what are the iteration coordinates. To see what iteration coordinates were recorded, use the keys method on the db object:
print( list( db.keys() ) ) # list() needed for compatibility with Python 3. Not needed for Python 2
which will print out:
['rank0:SLSQP|1', 'rank0:SLSQP|2', 'rank0:SLSQP|3', 'rank0:SLSQP|4', 'rank0:SLSQP|5', 'rank0:SLSQP|6']
Now we can get the values for the first iteration coordinate:
data = db['rank0:SLSQP|1']
This data variable has four keys, ‘timestamp’, ‘Parameters’, ‘Unknowns’, and ‘Residuals’. ‘timestamp’ yields the time at which data was recorded:
p = data['timestamp']
print(p)
The remaining keys will yield a dictionary containing variable names mapped to values. Generally, the variables of interest will be contained in the ‘Unknowns’ key since that will contain the objective function values and the values controlled by the optimizer. For example,
u = data['Unknowns']
pprint(u)
will print out the dictionary:
{'f_xy': -15.0, 'x': 3.0, 'y': -4.0}
You can also access the values for the Parameters:
p = data['Parameters']
pprint(p)
Which will print out the dictionary:
{'p.x': 3.0, 'p.y': -4.0}
Accessing Recorded Metadata¶
Finally, since our code told the recorder to record metadata, we can read that from the file as well. The metadata is only recorded once and is in its own table in the SQLite database. The name of the SQLite table containing the derivatives is called metadata.
import sqlitedict
from pprint import pprint
db = sqlitedict.SqliteDict( 'paraboloid', 'metadata' )
u_meta = db['Unknowns']
pprint(u_meta)
p_meta = db['Parameters']
pprint(p_meta)
print(db['format_version'])
This code prints out the following:
{'p.f_xy': {'is_objective': True,
'pathname': 'p.f_xy',
'shape': 1,
'size': 1,
'top_promoted_name': 'p.f_xy',
'val': 0.0},
'p1.x': {'_canset_': True,
'is_desvar': True,
'pathname': 'p1.x',
'shape': 1,
'size': 1,
'top_promoted_name': 'p1.x',
'val': 3.0},
'p2.y': {'_canset_': True,
'is_desvar': True,
'pathname': 'p2.y',
'shape': 1,
'size': 1,
'top_promoted_name': 'p2.y',
'val': -4.0}}
{'p.x': {'pathname': 'p.x',
'shape': 1,
'size': 1,
'top_promoted_name': 'p.x',
'val': 0.0},
'p.y': {'pathname': 'p.y',
'shape': 1,
'size': 1,
'top_promoted_name': 'p.y',
'val': 0.0}}
4
Accessing Recorded Derivatives¶
Sometimes it is useful for debugging purposes to look at the derivatives computed. If the user has turned on recording using the option:
recorder.options['record_derivs'] = True
then the derivatives are also recorded to the case recording file.
import sqlitedict
from pprint import pprint
db = sqlitedict.SqliteDict( 'paraboloid', 'derivs' )
The name of the SQLite table containing the derivatives is called derivs.
Just like before, we can access the data using an iteration coordinate. The derivative value can either be an ndarray or a dict, depending on the optimizer being used.
data = db['rank0:SLSQP|1']
u = data['Derivatives']
pprint(u)
will print out:
array([[-4., 3.]])
The CaseReader¶
The SqliteCaseRecorder and HDF5CaseRecorder are the two main ways to save data from an OpenMDAO run. Accessing the data, as the previous section shows, requires some knowledge of the structure of the recorded file, which is a function of the recorder used. Furthermore, finding the key of the desired iteration coordinate is a process that needs to be repeated each time recorded data is loaded.
In an effort to make this process independent of the recorder used, the CaseReader class gives the user a common interface to recorded data, regardless of format. Iteration coordinates are accessible by both their coordinate string descriptor, or as a standard python index.
class Paraboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
unknowns['f_xy'] = (x - 3.0) ** 2 + x * y + (y + 4.0) ** 2 - 3.0
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = 2.0 * x - 6.0 + y
J['f_xy', 'y'] = 2.0 * y + 8.0 + x
return J
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-50, upper=50)
top.driver.add_desvar('p2.y', lower=-50, upper=50)
top.driver.add_objective('p.f_xy')
recorder = SqliteRecorder('paraboloid')
recorder.options['record_params'] = True
recorder.options['record_metadata'] = True
top.driver.add_recorder(recorder)
top.setup()
top.run()
top.cleanup() # this closes all recorders
A CaseReader instance contains two main sets of data: metadata for the parameters and unknowns, and data from each case. The metadata is accessed via the properties parameters and unknowns. For instance, in the following code
from openmdao.api import CaseReader
cr = CaseReader('paraboloid')
cr.unknowns
cr will contain a dictionary:
:: {‘p1.x’: {‘val’: 3.0, ‘is_desvar’: True, ‘shape’: 1, ‘pathname’: ‘p1.x’, ‘top_promoted_name’: ‘p1.x’, ‘_canset_’: True, ‘size’: 1}, ‘p.f_xy’: {‘is_objective’: True, ‘val’: 0.0, ‘shape’: 1, ‘pathname’: ‘p.f_xy’, ‘top_promoted_name’: ‘p.f_xy’, ‘size’: 1}, ‘p2.y’: {‘val’: -4.0, ‘is_desvar’: True, ‘shape’: 1, ‘pathname’: ‘p2.y’, ‘top_promoted_name’: ‘p2.y’, ‘_canset_’: True, ‘size’: 1}}
To show the case iteration coordinates in the recorded file:
print(cr.list_cases())
which outputs:
('rank0:SLSQP|1', 'rank0:SLSQP|2', 'rank0:SLSQP|3', 'rank0:SLSQP|4', 'rank0:SLSQP|5', 'rank0:SLSQP|6')
It’s common to only care about the final case (the solution) of the optimization. To load the data from the final case we can either access it via its case iteration coordinate:
last_case = cr.get_case('rank0:SLSQP|6')
or, simply use an index (where -1 is the Pythonic way for accessing the last index of a list)
last_case = cr.get_case(-1)
The get_case method returns a Case object, which has properties for parameters, unkowns, derivs, and resids. Each of these is a dictionary, in which the path of the appropriate variable returns the respective value of the param, unknown, deriv, or resid. In general, the most commonly accessed information are the unknowns. If we access the case as a dictionary where unknown variables are the keys, it will return values of those unknowns. For instance, we can access the values of x, y, and f at the solution of the paraboloid using:
x = last_case['p1.x']
y = last_case['p2.y']
f_xy = last_case['p.f_xy']
print('Minimum is {0:7.4f} at x={1:7.4f} and y={2:7.4f}'.format(f_xy, x, y))
which outputs
Minimum is -27.3333 at x= 6.6667 and y=-7.3333