def __init__(self, problem, dims, w=0.2):
"""
Arguments
---------
problem : Problem
Pointer to the Problem object being wrapped.
dims : int or list/tuple of ints
Either the number of dimensions or a list of the dimension indices that this
problem uses.
w : float
The value to use for all unaccounted for inputs where 0/1 is lower/upper bound.
"""
self.problem = problem
self.w = w
if isinstance(dims, int):
self.dims = np.arange(dims)
assert dims <= problem.options["ndim"]
elif isinstance(dims, (list, tuple, np.ndarray)):
self.dims = np.array(dims, int)
assert np.max(dims) < problem.options["ndim"]
else:
raise ValueError("dims is invalid")
self.options = OptionsDictionary()
self.options.declare("ndim", len(self.dims), types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name",
"R_" + self.problem.options["name"],
types=str)
self.xlimits = np.zeros((self.options["ndim"], 2))
for idim, idim_reduced in enumerate(self.dims):
self.xlimits[idim, :] = problem.xlimits[idim_reduced, :]
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the problem being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> import numpy as np
>>> from smt.sampling_methods import Random
>>> sampling = Random(xlimits=np.arange(2).reshape((1, 2)))
"""
self.options = OptionsDictionary()
self.options.declare(
"xlimits",
types=np.ndarray,
desc=
"The interval of the domain in each dimension with shape nx x 2 (required)",
)
self._initialize()
self.options.update(kwargs)
def __init__(self, problem, dims, w=0.2):
"""
Arguments
---------
problem : Problem
Pointer to the Problem object being wrapped.
dims : int or list/tuple of ints
Either the number of dimensions or a list of the dimension indices of problem
that this problem uses.
w : float
The value to use for all unaccounted for inputs where 0/1 is lower/upper bound.
"""
self.problem = problem
self.w = w
if isinstance(dims, int):
self.dims = np.arange(dims)
assert dims <= problem.options['ndim']
elif isinstance(dims, (list, tuple)):
self.dims = np.array(dims, int)
assert numpy.max(dims) < problem.options['ndim']
else:
raise ValueError('dims is invalid')
self.options = OptionsDictionary()
self.options.declare('ndim', len(self.dims), types=int)
self.options.declare('name',
'R_' + self.problem.options['name'],
types=str)
self.xlimits = np.zeros((self.options['ndim'], 2))
for idim in self.dims:
self.xlimits[idim, :] = problem.xlimits[self.dims[idim], :]
class Sampling(object):
def __init__(self, **kwargs):
self.options = OptionsDictionary()
self.options.declare('xlimits', types=np.ndarray)
self._declare_options()
self.options.update(kwargs)
def _declare_options(self):
pass
def __call__(self, n):
"""
Compute the requested number of sampling points.
Arguments
---------
n : int
Number of points requested.
Returns
-------
ndarray[n, nx]
The sampling locations in the input space.
"""
xlimits = self.options['xlimits']
nx = xlimits.shape[0]
x = self._compute(n)
for kx in range(nx):
x[:,
kx] = xlimits[kx,
0] + x[:, kx] * (xlimits[kx, 1] - xlimits[kx, 0])
return x
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the problem being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.problems import Sphere
>>> prob = Sphere(ndim=3)
"""
self.options = OptionsDictionary()
self.options.declare("ndim", 1, types=int)
self.options.declare("return_complex", False, types=bool)
self._initialize()
self.options.update(kwargs)
self.xlimits = np.zeros((self.options["ndim"], 2))
self._setup()
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the surrogate model being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.surrogate_models import RBF
>>> sm = RBF(print_global=False)
"""
self.options = OptionsDictionary()
self.supports = supports = {}
supports["training_derivatives"] = False
supports["derivatives"] = False
supports["output_derivatives"] = False
supports["adjoint_api"] = False
supports["variances"] = False
declare = self.options.declare
declare(
"print_global",
True,
types=bool,
desc="Global print toggle. If False, all printing is suppressed",
)
declare(
"print_training",
True,
types=bool,
desc="Whether to print training information",
)
declare(
"print_prediction",
True,
types=bool,
desc="Whether to print prediction information",
)
declare(
"print_problem",
True,
types=bool,
desc="Whether to print problem information",
)
declare("print_solver",
True,
types=bool,
desc="Whether to print solver information")
self._initialize()
self.options.update(kwargs)
self.training_points = defaultdict(dict)
self.printer = Printer()
class SurrogateBasedApplication:
if compiled_available:
_surrogate_type = {
"KRG": KRG,
"LS": LS,
"QP": QP,
"KPLS": KPLS,
"KPLSK": KPLSK,
"GEKPLS": GEKPLS,
"RBF": RBF,
"RMTC": RMTC,
"RMTB": RMTB,
"IDW": IDW,
"MGP": MGP,
}
else:
_surrogate_type = {
"KRG": KRG,
"LS": LS,
"QP": QP,
"KPLS": KPLS,
"KPLSK": KPLSK,
"GEKPLS": GEKPLS,
"MGP": MGP,
}
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the surrogate model being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.applications import VFM
>>> extension = VFM(type_bridge = 'Additive', name_model_LF = QP, name_model_bridge =
LS, X_LF = xLF, y_LF = yLF, X_HF = xHF, y_HF = yHF, options_LF =
dictOptionLFModel, options_bridge = dictOptionBridgeModel)
"""
self.options = OptionsDictionary()
self._initialize()
self.options.update(kwargs)
def _initialize(self):
"""
Implemented by the application to declare options and declare what they support (optional).
Examples
--------
self.options.declare('option_name', default_value, types=(bool, int), desc='description')
"""
pass
class Extensions(object):
if compiled_available:
_surrogate_type = {
'KRG': KRG,'LS': LS,'QP': QP,'KPLS':KPLS,'KPLSK':KPLSK,'GEKPLS':GEKPLS,
'RBF':RBF,'RMTC':RMTC,'RMTB':RMTB,'IDW':IDW}
else:
_surrogate_type = {
'KRG': KRG,'LS': LS,'QP': QP,'KPLS':KPLS,'KPLSK':KPLSK,'GEKPLS':GEKPLS}
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the surrogate model being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.extensions import VFM
>>> extension = VFM(type_bridge = 'Additive', name_model_LF = QP, name_model_bridge =
LS, X_LF = xLF, y_LF = yLF, X_HF = xHF, y_HF = yHF, options_LF =
dictOptionLFModel, options_bridge = dictOptionBridgeModel)
"""
self.options = OptionsDictionary()
self._initialize()
self.options.update(kwargs)
def _initialize(self):
"""
Implemented by the application to declare options and declare what they support (optional).
Examples
--------
self.options.declare('option_name', default_value, types=(bool, int), desc='description')
"""
pass
def apply_method(self):
"""
Run the complete algorithm of the SMT application; e.g.: VFM, ME, EGO...
"""
self._apply()
def analyse_results(self, **kwargs):
"""
Get the final results; e.g., for VFM, two possible analysis are available:
- kwargs = {x = x, operation = 'predict_values'}
- kwargs = {x = x, operation = 'predict_derivatives, kx = i}
"""
return self._analyse_results(**kwargs)
def __init__(self, ndim=1, width=10.0):
self.problem = TensorProduct(ndim=ndim, func="tanh", width=width)
self.options = OptionsDictionary()
self.options.declare("ndim", ndim, types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name", "NdimStepFunction", types=str)
self.xlimits = self.problem.xlimits
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(CantileverBeam(ndim=3*ndim), np.arange(1, 3*ndim, 3), w=w)
self.options = OptionsDictionary()
self.options.declare('ndim', ndim, types=int)
self.options.declare('return_complex', False, types=bool)
self.options.declare('name', 'NdimCantileverBeam', types=str)
self.xlimits = self.problem.xlimits
def __init__(self, **kwargs):
self.mtx = None
self.rhs = None
self.options = OptionsDictionary()
self.options.declare("print_init", True, types=bool)
self.options.declare("print_solve", True, types=bool)
self._initialize()
self.options.update(kwargs)
def __init__(self, **kwargs):
self.mtx = None
self.rhs = None
self.options = OptionsDictionary()
self.options.declare('print_init', True, types=bool)
self.options.declare('print_solve', False, types=bool)
self._declare_options()
self.options.update(kwargs)
def __init__(self, **kwargs):
self.options = OptionsDictionary()
self.options.declare('ndim', 1, types=int)
self._declare_options()
self.options.update(kwargs)
self.xlimits = np.zeros((self.options['ndim'], 2))
self._initialize()
def __init__(self, ndim=1, width=10.0):
self.problem = TensorProduct(ndim=ndim, func='tanh', width=width)
self.options = OptionsDictionary()
self.options.declare('ndim', ndim, types=int)
self.options.declare('return_complex', False, types=bool)
self.options.declare('name', 'NdimStepFunction', types=str)
self.xlimits = self.problem.xlimits
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(RobotArm(ndim=2 * (ndim + 1)),
np.arange(3, 2 * (ndim + 1), 2),
w=w)
self.options = OptionsDictionary()
self.options.declare('ndim', ndim, types=int)
self.options.declare('return_complex', False, types=bool)
self.options.declare('name', 'NdimRobotArm', types=str)
self.xlimits = self.problem.xlimits
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(Rosenbrock(ndim=ndim + 1),
np.arange(1, ndim + 1),
w=w)
self.options = OptionsDictionary()
self.options.declare("ndim", ndim, types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name", "NdimRosenbrock", types=str)
self.xlimits = self.problem.xlimits
class NdimRosenbrock(Problem):
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(Rosenbrock(ndim=ndim + 1),
np.arange(1, ndim + 1),
w=w)
self.options = OptionsDictionary()
self.options.declare('ndim', ndim, types=int)
self.options.declare('return_complex', False, types=bool)
self.options.declare('name', 'NdimRosenbrock', types=str)
self.xlimits = self.problem.xlimits
def _evaluate(self, x, kx):
return self.problem._evaluate(x, kx)
def __init__(self, **kwargs):
'''
Constructor.
Arguments
---------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
'''
self.options = OptionsDictionary()
self._declare_options()
self.options.update(kwargs)
self.training_pts = {'exact': {}}
self.printer = Printer()
class Problem(object):
def __init__(self, **kwargs):
self.options = OptionsDictionary()
self.options.declare('ndim', 1, types=int)
self._declare_options()
self.options.update(kwargs)
self.xlimits = np.zeros((self.options['ndim'], 2))
self._initialize()
def _declare_options(self):
pass
def _initialize(self):
pass
def __call__(self, x, kx=None):
"""
Arguments
---------
x : ndarray[ne, nx]
Evaluation points.
kx : int or None
Index of derivative (0-based) to return values with respect to.
None means return function value rather than derivative.
Returns
-------
ndarray[ne, 1]
Functions values if kx=None or derivative values if kx is an int.
"""
if not isinstance(x, np.ndarray) or len(x.shape) != 2:
raise TypeError('x should be a rank-2 array.')
elif x.shape[1] != self.options['ndim']:
raise ValueError('The second dimension of x should be %i' %
self.options['ndim'])
if kx is not None:
if not isinstance(kx, int) or kx < 0:
raise TypeError('kx should be None or a non-negative int.')
return self._evaluate(x, kx)
def __init__(self, **kwargs):
"""
Examples
--------
>>> from methods import localGEKPLS
>>> local1 = localGEKPLS(para_file='data/local1.npy')
"""
self.options = OptionsDictionary()
declare = self.options.declare
declare(
'para_file',
values=None,
types=str,
desc=
'Directory for loading / saving cached data; None means do not save or load'
)
self.options.update(kwargs)
self._readPara()
def globalSurrogateModel(data, pr):
pr.callingFunction = "globalSurrogate"
data["prediction"] = pr.predict(data)
ttdE = testTrainData(data, pr, encoded=True)
ttdNE = testTrainData(data, pr, encoded=False)
options = OptionsDictionary()
options.declare("ndim", 1.0, types=float)
options.declare("return_complex", False, types=bool)
xlimits = np.zeros((int(options["ndim"]), 4))
xlimits[:, 0] = -2.0
xlimits[:, 1] = 2.0
funXLimits = xlimits
ndim = 4
# models retrieved from https://github.com/SMTorg/smt/blob/master/tutorial/SMT_Tutorial.ipynb
models = pd.Series()
models["linear"] = Model(linearModel, ttdE)
models["quadratic"] = Model(quadraticModel, ttdE)
# models["kriging"] = Model(kriging, ttdE, ndim=ndim)
# models["KPLSK"] = Model(kPLSK, ttdE)
models["IDW"] = Model(iDW, ttdE)
models["RBF"] = Model(rBF, ttdE)
#models["RMTBSimba"] = Model(rMTBSimba, ttdNE, xL = funXLimits)
#models["GEKPLS"] = Model(gEKPLS, ttdNE, xL = funXLimits, ndim = ndim)
#models["DEKPLS"] = Model(dEKPLS, ttdNE, xL = funXLimits, ndim = ndim)
for model in models:
compareToOrig(model.t, model.title, model.xtest, model.ytest)
class LinearSolver(object):
def __init__(self, **kwargs):
self.mtx = None
self.rhs = None
self.options = OptionsDictionary()
self.options.declare("print_init", True, types=bool)
self.options.declare("print_solve", True, types=bool)
self._initialize()
self.options.update(kwargs)
def _initialize(self):
pass
def _setup(self, mtx, printer, mg_matrices=[]):
pass
def _solve(self, rhs, sol=None, ind_y=0):
pass
def _clone(self):
clone = self.__class__()
clone.options.update(clone.options._dict)
return clone
@contextlib.contextmanager
def _active(self, active):
orig_active = self.printer.active
self.printer.active = self.printer.active and active
yield self.printer
self.printer.active = orig_active
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the surrogate model being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.applications import VFM
>>> extension = VFM(type_bridge = 'Additive', name_model_LF = QP, name_model_bridge =
LS, X_LF = xLF, y_LF = yLF, X_HF = xHF, y_HF = yHF, options_LF =
dictOptionLFModel, options_bridge = dictOptionBridgeModel)
"""
self.options = OptionsDictionary()
self._initialize()
self.options.update(kwargs)
def __init__(self, **kwargs):
"""
Examples
--------
>>> from methods import localGEKPLS
>>> clmodel = MoE(func='cl',nlocal=20)
"""
self.options = OptionsDictionary()
declare = self.options.declare
declare('func',
values=('Cl', 'Cd', 'Cm'),
types=str,
desc='Which model to construct')
declare('nlocal',
values=None,
types=int,
desc='How many local models to use')
self.options.update(kwargs)
self.models = []
self.posteriors = []
self._setup()
class NdimRobotArm(Problem):
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(RobotArm(ndim=2 * (ndim + 1)),
np.arange(3, 2 * (ndim + 1), 2),
w=w)
self.options = OptionsDictionary()
self.options.declare("ndim", ndim, types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name", "NdimRobotArm", types=str)
self.xlimits = self.problem.xlimits
def _evaluate(self, x, kx):
return self.problem._evaluate(x, kx)
class NdimCantileverBeam(Problem):
def __init__(self, ndim=1, w=0.2):
self.problem = ReducedProblem(CantileverBeam(ndim=3 * ndim),
np.arange(1, 3 * ndim, 3),
w=w)
self.options = OptionsDictionary()
self.options.declare("ndim", ndim, types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name", "NdimCantileverBeam", types=str)
self.xlimits = self.problem.xlimits
def _evaluate(self, x, kx):
return self.problem._evaluate(x, kx)
class SurrogateModel(object):
"""
Base class for all surrogate models.
Attributes
----------
options : OptionsDictionary
Dictionary of options. Options values can be set on this attribute directly
or they can be passed in as keyword arguments during instantiation.
supports : dict
Dictionary containing information about what this surrogate model supports.
Examples
--------
>>> from smt.surrogate_models import RBF
>>> sm = RBF(print_training=False)
>>> sm.options['print_prediction'] = False
"""
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the surrogate model being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.surrogate_models import RBF
>>> sm = RBF(print_global=False)
"""
self.options = OptionsDictionary()
self.supports = supports = {}
supports["training_derivatives"] = False
supports["derivatives"] = False
supports["output_derivatives"] = False
supports["adjoint_api"] = False
supports["variances"] = False
declare = self.options.declare
declare(
"print_global",
True,
types=bool,
desc="Global print toggle. If False, all printing is suppressed",
)
declare(
"print_training",
True,
types=bool,
desc="Whether to print training information",
)
declare(
"print_prediction",
True,
types=bool,
desc="Whether to print prediction information",
)
declare(
"print_problem",
True,
types=bool,
desc="Whether to print problem information",
)
declare("print_solver",
True,
types=bool,
desc="Whether to print solver information")
self._initialize()
self.options.update(kwargs)
self.training_points = defaultdict(dict)
self.printer = Printer()
def set_training_values(self, xt, yt, name=None):
"""
Set training data (values).
Parameters
----------
xt : np.ndarray[nt, nx] or np.ndarray[nt]
The input values for the nt training points.
yt : np.ndarray[nt, ny] or np.ndarray[nt]
The output values for the nt training points.
name : str or None
An optional label for the group of training points being set.
This is only used in special situations (e.g., multi-fidelity applications).
"""
xt = check_2d_array(xt, "xt")
yt = check_2d_array(yt, "yt")
if xt.shape[0] != yt.shape[0]:
raise ValueError(
"the first dimension of xt and yt must have the same length")
self.nt = xt.shape[0]
self.nx = xt.shape[1]
self.ny = yt.shape[1]
kx = 0
self.training_points[name][kx] = [np.array(xt), np.array(yt)]
def update_training_values(self, yt, name=None):
"""
Update the training data (values) at the previously set input values.
Parameters
----------
yt : np.ndarray[nt, ny] or np.ndarray[nt]
The output values for the nt training points.
name : str or None
An optional label for the group of training points being set.
This is only used in special situations (e.g., multi-fidelity applications).
"""
yt = check_2d_array(yt, "yt")
kx = 0
if kx not in self.training_points[name]:
raise ValueError(
"The training points must be set first with set_training_values "
+ "before calling update_training_values.")
xt = self.training_points[name][kx][0]
if xt.shape[0] != yt.shape[0]:
raise ValueError(
"The number of training points does not agree with the earlier call of "
+ "set_training_values.")
self.training_points[name][kx][1] = np.array(yt)
def set_training_derivatives(self, xt, dyt_dxt, kx, name=None):
"""
Set training data (derivatives).
Parameters
----------
xt : np.ndarray[nt, nx] or np.ndarray[nt]
The input values for the nt training points.
dyt_dxt : np.ndarray[nt, ny] or np.ndarray[nt]
The derivatives values for the nt training points.
kx : int
0-based index of the derivatives being set.
name : str or None
An optional label for the group of training points being set.
This is only used in special situations (e.g., multi-fidelity applications).
"""
check_support(self, "training_derivatives")
xt = check_2d_array(xt, "xt")
dyt_dxt = check_2d_array(dyt_dxt, "dyt_dxt")
if xt.shape[0] != dyt_dxt.shape[0]:
raise ValueError(
"the first dimension of xt and dyt_dxt must have the same length"
)
if not isinstance(kx, int):
raise ValueError("kx must be an int")
self.training_points[name][kx + 1] = [np.array(xt), np.array(dyt_dxt)]
def update_training_derivatives(self, dyt_dxt, kx, name=None):
"""
Update the training data (values) at the previously set input values.
Parameters
----------
dyt_dxt : np.ndarray[nt, ny] or np.ndarray[nt]
The derivatives values for the nt training points.
kx : int
0-based index of the derivatives being set.
name : str or None
An optional label for the group of training points being set.
This is only used in special situations (e.g., multi-fidelity applications).
"""
check_support(self, "training_derivatives")
dyt_dxt = check_2d_array(dyt_dxt, "dyt_dxt")
if kx not in self.training_points[name]:
raise ValueError(
"The training points must be set first with set_training_values "
+ "before calling update_training_values.")
xt = self.training_points[name][kx][0]
if xt.shape[0] != dyt_dxt.shape[0]:
raise ValueError(
"The number of training points does not agree with the earlier call of "
+ "set_training_values.")
self.training_points[name][kx + 1][1] = np.array(dyt_dxt)
def train(self):
"""
Train the model
"""
n_exact = self.training_points[None][0][0].shape[0]
self.printer.active = self.options["print_global"]
self.printer._line_break()
self.printer._center(self.name)
self.printer.active = (self.options["print_global"]
and self.options["print_problem"])
self.printer._title("Problem size")
self.printer(" %-25s : %i" % ("# training points.", n_exact))
self.printer()
self.printer.active = (self.options["print_global"]
and self.options["print_training"])
if self.name == "MixExp":
# Mixture of experts model
self.printer._title("Training of the Mixture of experts")
else:
self.printer._title("Training")
# Train the model using the specified model-method
with self.printer._timed_context("Training", "training"):
self._train()
def predict_values(self, x):
"""
Predict the output values at a set of points.
Parameters
----------
x : np.ndarray[nt, nx] or np.ndarray[nt]
Input values for the prediction points.
Returns
-------
y : np.ndarray[nt, ny]
Output values at the prediction points.
"""
x = check_2d_array(x, "x")
check_nx(self.nx, x)
n = x.shape[0]
self.printer.active = (self.options["print_global"]
and self.options["print_prediction"])
if self.name == "MixExp":
# Mixture of experts model
self.printer._title("Evaluation of the Mixture of experts")
else:
self.printer._title("Evaluation")
self.printer(" %-12s : %i" % ("# eval points.", n))
self.printer()
# Evaluate the unknown points using the specified model-method
with self.printer._timed_context("Predicting", key="prediction"):
y = self._predict_values(x)
time_pt = self.printer._time("prediction")[-1] / n
self.printer()
self.printer("Prediction time/pt. (sec) : %10.7f" % time_pt)
self.printer()
return y.reshape((n, self.ny))
def predict_derivatives(self, x, kx):
"""
Predict the dy_dx derivatives at a set of points.
Parameters
----------
x : np.ndarray[nt, nx] or np.ndarray[nt]
Input values for the prediction points.
kx : int
The 0-based index of the input variable with respect to which derivatives are desired.
Returns
-------
dy_dx : np.ndarray[nt, ny]
Derivatives.
"""
check_support(self, "derivatives")
x = check_2d_array(x, "x")
check_nx(self.nx, x)
n = x.shape[0]
self.printer.active = (self.options["print_global"]
and self.options["print_prediction"])
if self.name == "MixExp":
# Mixture of experts model
self.printer._title("Evaluation of the Mixture of experts")
else:
self.printer._title("Evaluation")
self.printer(" %-12s : %i" % ("# eval points.", n))
self.printer()
# Evaluate the unknown points using the specified model-method
with self.printer._timed_context("Predicting", key="prediction"):
y = self._predict_derivatives(x, kx)
time_pt = self.printer._time("prediction")[-1] / n
self.printer()
self.printer("Prediction time/pt. (sec) : %10.7f" % time_pt)
self.printer()
return y.reshape((n, self.ny))
def predict_output_derivatives(self, x):
"""
Predict the derivatives dy_dyt at a set of points.
Parameters
----------
x : np.ndarray[nt, nx] or np.ndarray[nt]
Input values for the prediction points.
Returns
-------
dy_dyt : dict of np.ndarray[nt, nt]
Dictionary of output derivatives.
Key is None for derivatives wrt yt and kx for derivatives wrt dyt_dxt.
"""
check_support(self, "output_derivatives")
check_nx(self.nx, x)
dy_dyt = self._predict_output_derivatives(x)
return dy_dyt
def predict_variances(self, x):
"""
Predict the variances at a set of points.
Parameters
----------
x : np.ndarray[nt, nx] or np.ndarray[nt]
Input values for the prediction points.
Returns
-------
s2 : np.ndarray[nt, ny]
Variances.
"""
check_support(self, "variances")
check_nx(self.nx, x)
n = x.shape[0]
s2 = self._predict_variances(x)
return s2.reshape((n, self.ny))
def _initialize(self):
"""
Implemented by surrogate models to declare options and declare what they support (optional).
Examples
--------
self.options.declare('option_name', default_value, types=(bool, int), desc='description')
self.supports['derivatives'] = True
"""
pass
def _train(self):
"""
Implemented by surrogate models to perform training (optional, but typically implemented).
"""
pass
def _predict_values(self, x):
"""
Implemented by surrogate models to predict the output values.
Parameters
----------
x : np.ndarray[nt, nx]
Input values for the prediction points.
Returns
-------
y : np.ndarray[nt, ny]
Output values at the prediction points.
"""
raise Exception("This surrogate model is incorrectly implemented")
def _predict_derivatives(self, x, kx):
"""
Implemented by surrogate models to predict the dy_dx derivatives (optional).
If this method is implemented, the surrogate model should have
::
self.supports['derivatives'] = True
in the _initialize() implementation.
Parameters
----------
x : np.ndarray[nt, nx]
Input values for the prediction points.
kx : int
The 0-based index of the input variable with respect to which derivatives are desired.
Returns
-------
dy_dx : np.ndarray[nt, ny]
Derivatives.
"""
check_support(self, "derivatives", fail=True)
def _predict_output_derivatives(self, x):
"""
Implemented by surrogate models to predict the dy_dyt derivatives (optional).
If this method is implemented, the surrogate model should have
::
self.supports['output_derivatives'] = True
in the _initialize() implementation.
Parameters
----------
x : np.ndarray[nt, nx]
Input values for the prediction points.
Returns
-------
dy_dyt : dict of np.ndarray[nt, nt]
Dictionary of output derivatives.
Key is None for derivatives wrt yt and kx for derivatives wrt dyt_dxt.
"""
check_support(self, "output_derivatives", fail=True)
def _predict_variances(self, x):
"""
Implemented by surrogate models to predict the variances at a set of points (optional).
If this method is implemented, the surrogate model should have
::
self.supports['variances'] = True
in the _initialize() implementation.
Parameters
----------
x : np.ndarray[nt, nx]
Input values for the prediction points.
Returns
-------
s2 : np.ndarray[nt, ny]
Variances.
"""
check_support(self, "variances", fail=True)
class ReducedProblem(Problem):
def __init__(self, problem, dims, w=0.2):
"""
Arguments
---------
problem : Problem
Pointer to the Problem object being wrapped.
dims : int or list/tuple of ints
Either the number of dimensions or a list of the dimension indices that this
problem uses.
w : float
The value to use for all unaccounted for inputs where 0/1 is lower/upper bound.
"""
self.problem = problem
self.w = w
if isinstance(dims, int):
self.dims = np.arange(dims)
assert dims <= problem.options["ndim"]
elif isinstance(dims, (list, tuple, np.ndarray)):
self.dims = np.array(dims, int)
assert np.max(dims) < problem.options["ndim"]
else:
raise ValueError("dims is invalid")
self.options = OptionsDictionary()
self.options.declare("ndim", len(self.dims), types=int)
self.options.declare("return_complex", False, types=bool)
self.options.declare("name",
"R_" + self.problem.options["name"],
types=str)
self.xlimits = np.zeros((self.options["ndim"], 2))
for idim, idim_reduced in enumerate(self.dims):
self.xlimits[idim, :] = problem.xlimits[idim_reduced, :]
def _evaluate(self, x, kx):
"""
Arguments
---------
x : ndarray[ne, nx]
Evaluation points.
kx : int or None
Index of derivative (0-based) to return values with respect to.
None means return function value rather than derivative.
Returns
-------
ndarray[ne, 1]
Functions values if kx=None or derivative values if kx is an int.
"""
ne, nx = x.shape
nx_prob = self.problem.options["ndim"]
x_prob = np.zeros((ne, nx_prob), complex)
for ix in range(nx_prob):
x_prob[:, ix] = (1 - self.w) * self.problem.xlimits[
ix, 0] + self.w * self.problem.xlimits[ix, 1]
for ix in range(nx):
x_prob[:, self.dims[ix]] = x[:, ix]
if kx is None:
y = self.problem._evaluate(x_prob, None)
else:
y = self.problem._evaluate(x_prob, self.dims[kx])
return y
class Problem(object):
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the problem being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> from smt.problems import Sphere
>>> prob = Sphere(ndim=3)
"""
self.options = OptionsDictionary()
self.options.declare("ndim", 1, types=int)
self.options.declare("return_complex", False, types=bool)
self._initialize()
self.options.update(kwargs)
self.xlimits = np.zeros((self.options["ndim"], 2))
self._setup()
def _initialize(self):
"""
Implemented by problem to declare options (optional).
Examples
--------
self.options.declare('option_name', default_value, types=(bool, int), desc='description')
"""
pass
def _setup(self):
pass
def __call__(self, x, kx=None):
"""
Evaluate the function.
Parameters
----------
x : ndarray[n, nx] or ndarray[n]
Evaluation points where n is the number of evaluation points.
kx : int or None
Index of derivative (0-based) to return values with respect to.
None means return function value rather than derivative.
Returns
-------
ndarray[n, 1]
Functions values if kx=None or derivative values if kx is an int.
"""
x = ensure_2d_array(x, "x")
if x.shape[1] != self.options["ndim"]:
raise ValueError("The second dimension of x should be %i" %
self.options["ndim"])
if kx is not None:
if not isinstance(kx, int) or kx < 0:
raise TypeError("kx should be None or a non-negative int.")
y = self._evaluate(x, kx)
if self.options["return_complex"]:
return y
else:
return np.real(y)
def _evaluate(self, x, kx=None):
"""
Implemented by surrogate models to evaluate the function.
Parameters
----------
x : ndarray[n, nx]
Evaluation points where n is the number of evaluation points.
kx : int or None
Index of derivative (0-based) to return values with respect to.
None means return function value rather than derivative.
Returns
-------
ndarray[n, 1]
Functions values if kx=None or derivative values if kx is an int.
"""
raise Exception("This problem has not been implemented correctly")
class SamplingMethod(object):
def __init__(self, **kwargs):
"""
Constructor where values of options can be passed in.
For the list of options, see the documentation for the problem being used.
Parameters
----------
**kwargs : named arguments
Set of options that can be optionally set; each option must have been declared.
Examples
--------
>>> import numpy as np
>>> from smt.sampling_methods import Random
>>> sampling = Random(xlimits=np.arange(2).reshape((1, 2)))
"""
self.options = OptionsDictionary()
self.options.declare(
"xlimits",
types=np.ndarray,
desc=
"The interval of the domain in each dimension with shape nx x 2 (required)",
)
self._initialize()
self.options.update(kwargs)
def _initialize(self):
"""
Implemented by sampling methods to declare options (optional).
Examples
--------
self.options.declare('option_name', default_value, types=(bool, int), desc='description')
"""
pass
def __call__(self, nt):
"""
Compute the requested number of sampling points.
The number of dimensions (nx) is determined based on `xlimits.shape[0]`.
Arguments
---------
nt : int
Number of points requested.
Returns
-------
ndarray[nt, nx]
The sampling locations in the input space.
"""
xlimits = self.options["xlimits"]
nx = xlimits.shape[0]
x = self._compute(nt)
for kx in range(nx):
x[:,
kx] = xlimits[kx,
0] + x[:, kx] * (xlimits[kx, 1] - xlimits[kx, 0])
return x
def _compute(self, nt):
"""
Implemented by sampling methods to compute the requested number of sampling points.
The number of dimensions (nx) is determined based on `xlimits.shape[0]`.
Arguments
---------
nt : int
Number of points requested.
Returns
-------
ndarray[nt, nx]
The sampling locations in the input space.
"""
raise Exception(
"This sampling method has not been implemented correctly")