def eval_contour(
model,
var=None,
out=None,
df=None,
levels=None,
n_side=20,
n_levels=5,
):
r"""Generate contours from a model
Generates contours from a model. Evaluates the model on a dense grid, then runs marching squares to generate contours. Supports targeting multiple outputs and handling auxiliary inputs not included in the contour map.
Args:
model (gr.Model): Model to evaluate.
var (list of str): Model inputs to target; must provide exactly two inputs, and both must have finite domain width.
out (list of str): Model output(s) for contour generation.
df (DataFrame or None): Levels for model variables not included in var
(auxiliary inputs). If provided var and model.var contain the same
values, then df may equal None.
levels (dict): Specific output levels for contour generation; overrides n_levels.
n_side (int): Side resolution for grid; n_side**2 total evaluations.
n_levels (int): Number of contour levels.
Returns:
DataFrame: Points along contours, organized by output and auxiliary variable levels.
Examples::
import grama as gr
## Multiple outputs
(
gr.Model()
>> gr.cp_vec_function(
fun=lambda df: gr.df_make(
f=df.x**2 + df.y**2,
g=df.x + df.y,
),
var=["x", "y"],
out=["f", "g"],
)
>> gr.cp_bounds(
x=(-1, +1),
y=(-1, +1),
)
>> gr.ev_contour(
var=["x", "y"],
out=["f", "g"],
)
# Contours with no auxiliary variables can autoplot
>> gr.pt_auto()
)
## Auxiliary inputs
(
gr.Model()
>> gr.cp_vec_function(
fun=lambda df: gr.df_make(
f=df.c * df.x + (1 - df.c) * df.y,
),
var=["x", "y"],
out=["f", "g"],
)
>> gr.cp_bounds(
x=(-1, +1),
y=(-1, +1),
)
>> gr.ev_contour(
var=["x", "y"],
out=["f"],
df=gr.df_make(c=[0, 1])
)
# Contours with auxiliary variables should be manually plotted
>> gr.ggplot(gr.aes("x", "y"))
+ gr.geom_segment(gr.aes(xend="x_end", yend="y_end", group="level", color="c"))
)
"""
## Check invariants
invariants_eval_model(model)
invariants_eval_df(df, acc_none=True)
# Argument given
if var is None:
raise ValueError("No `var` given")
# Correct number of inputs
if len(var) != 2:
raise ValueError("Must provide exactly 2 inputs in `var`.")
# Inputs available
var_diff = set(var).difference(set(model.var))
if len(var_diff) > 0:
raise ValueError(
"`var` must be a subset of model.var; missing: {}".format(
var_diff))
# All inputs supported
var_diff = set(model.var).difference(set(var))
if len(var_diff) > 0:
if df is None:
raise ValueError(
"Must provide values for remaining model variables using df; "
+ "missing values: {}".format(var_diff))
# Drop the swept variables
df = df.drop(columns=var, errors="ignore")
# Check for unsupported inputs
var_diff2 = var_diff.difference(set(df.columns))
if len(var_diff2) > 0:
raise ValueError(
"All model variables need values in provided df; " +
"missing values: {}".format(var_diff2))
if df.shape[0] > 1:
has_aux = True
else:
has_aux = False
else:
has_aux = False
# Finite bound width
if not all([
isfinite(model.domain.get_width(v)) and
(model.domain.get_width(v) > 0) for v in var
]):
raise ValueError(
"All model bounds for `var` must be finite and nonzero")
# Argument given
if out is None:
raise ValueError("No `out` given")
# Outputs available
out_diff = set(out).difference(set(model.out))
if len(out_diff) > 0:
raise ValueError(
"`out` must be a subset of model.out; missing: {}".format(
out_diff))
## Generate data
xv = linspace(*model.domain.get_bound(var[0]), n_side)
yv = linspace(*model.domain.get_bound(var[1]), n_side)
df_x = DataFrame({var[0]: xv})
df_y = DataFrame({var[1]: yv})
df_input = (df_x >> tf_outer(df_outer=df_y))
# Create singleton level if necessary
if df is None:
df = DataFrame({"_foo": [0]})
## Loop over provided auxiliary levels
df_res = DataFrame()
for i in range(df.shape[0]):
df_in_tmp = (df_input >> tf_outer(df_outer=df.iloc[[i]]))
df_out = eval_df(
model,
df=df_in_tmp,
)
## Set output threshold levels
if levels is None:
# Do not overwrite `levels`, to adapt per loop
levels_wk = dict(
zip(out, [
linspace(df_out[o].min(), df_out[o].max(),
n_levels + 2)[1:-1] for o in out
]))
else:
levels_wk = levels
## Run marching squares
# Output quantity
for o in out:
# Reshape data
Data = reshape(df_out[o].values, (n_side, n_side))
# Threshold level
for t in levels_wk[o]:
# Run marching squares
segments = marching_square(xv, yv, Data, t)
sqdata = array(segments).squeeze()
if len(sqdata) > 0:
# Package
df_tmp = DataFrame(
data=sqdata,
columns=[
var[0], var[1], var[0] + "_end", var[1] + "_end"
],
)
df_tmp["out"] = [o] * df_tmp.shape[0]
df_tmp["level"] = [t] * df_tmp.shape[0]
df_tmp = (df_tmp >> tf_outer(df_outer=df.iloc[[i]]))
df_res = concat((df_res, df_tmp), axis=0)
else:
warn("Output {0:} had no contours at level {1:}".format(
o,
t,
))
## Remove dummy column, if present
if "_foo" in df_res.columns:
df_res.drop("_foo", axis=1, inplace=True)
# Drop index
df_res = df_res.reset_index(drop=True)
## Attach metadata
with catch_warnings():
simplefilter("ignore")
df_res._plot_info = {
"type": "contour",
"var": var,
"out": "out",
"level": "level",
"aux": has_aux,
}
## Return the results
return df_res
def eval_form_ria(
model,
limits=None,
cons=None,
df_corr=None,
df_det=None,
append=True,
tol=1e-3,
n_maxiter=25,
n_restart=1,
verbose=False,
):
r"""Tail reliability via FORM RIA
Approximate the desired tail probability using the reliability index approach (RIA) of the first-order reliability method (FORM) [1]. Select limit states to analyze with list input `limits`. Provide confidence levels `cons` and estimator covariance `df_corr` to compute with margin in beta [2].
Note that the reliability index approach (RIA) is generally less stable than the performance measure approach (PMA). Consider using ``gr.eval_form_pma()`` instead, particularly when using FORM to optimize a design.
Args:
model (gr.Model): Model to analyze
limits (list): Target limit states; must be in model.out; limit state assumed to be critical at g == 0.
cons (dict or None): Target confidence levels;
key = limit state name; must be in model.out
value = confidence level, \in (0, 1)
df_corr (DataFrame or None): Sampling distribution covariance entries; parameters with no information assumed to be known exactly.
df_det (DataFrame): Deterministic levels for evaluation; use "nom" for nominal deterministic levels.
n_maxiter (int): Maximum iterations for each optimization run
n_restart (int): Number of restarts (== number of optimization runs)
append (bool): Append MPP results for random values?
verbose (bool): Print optimization results?
Returns:
DataFrame: Results of MPP search
Notes:
Since FORM RIA relies on optimization over the limit state, it is often beneficial to scale your limit state to keep values near unity.
References:
[1] Tu, Choi, and Park, "A new study on reliability-based design optimization," Journal of Mechanical Design, 1999
[2] del Rosario, Fenrich, and Iaccarino, "Fast precision margin with the first-order reliability method," AIAA Journal, 2019
Examples::
import grama as gr
from grama.models import make_cantilever_beam
md_beam = make_cantilever_beam()
## Evaluate the reliability of specified designs
(
md_beam
>> gr.ev_form_ria(
# Specify limit states to analyze
limits=("g_stress", "g_disp"),
# Analyze three different thicknesses
df_det=gr.df_make(t=[2, 3, 4], w=3)
)
)
"""
## Check invariants
invariants_eval_model(model)
invariants_eval_df(df_corr, arg_name="df_corr", acc_none=True)
invariants_eval_df(df_det, arg_name="df_det", valid_str=["nom"])
if limits is None:
raise ValueError(
"Must provide `limits` keyword argument to define reliability targets"
)
if not set(limits).issubset(set(model.out)):
raise ValueError("`limits` must be subset of model.out")
if not cons is None:
if not (set(cons.keys()) == set(limits)):
raise ValueError("cons.keys() must be same as limits")
else:
if df_corr is None:
raise ValueError("Must provide df_corr is using cons")
raise NotImplementedError
df_det = model.var_outer(
DataFrame(data=zeros((1, model.n_var_rand)), columns=model.var_rand),
df_det=df_det,
)
df_det = df_det[model.var_det]
# df_return = DataFrame(columns=model.var_rand + model.var_det + limits)
df_return = DataFrame()
for ind in range(df_det.shape[0]):
## Loop over objectives
for key in limits:
## Temp dataframe
df_inner = df_det.iloc[[ind]].reset_index(drop=True)
## Construct lambdas
def fun_jac(z):
## Squared reliability index
fun = z.dot(z)
jac = 2 * z * length(z)
return (fun, jac)
def con_limit(z):
## Transform: standard normal-to-random variable
df_norm = DataFrame(data=[z], columns=model.var_rand)
df_rand = model.norm2rand(df_norm)
df = model.var_outer(df_rand, df_det=df_inner)
## Eval limit state
df_res = eval_df(model, df=df)
g = df_res[key].iloc[0]
return g
## Use conservative direction for initial guess
signs = array(
[model.density.marginals[k].sign for k in model.var_rand])
if length(signs) > 0:
z0 = signs / length(signs)
else:
z0 = ones(model.n_var_rand) / sqrt(model.n_var_rand)
## Minimize
res_all = []
for jnd in range(n_restart):
res = minimize(
fun_jac,
z0,
args=(),
method="SLSQP",
jac=True,
tol=tol,
options={
"maxiter": n_maxiter,
"disp": False
},
constraints=[{
"type": "eq",
"fun": con_limit
}],
)
# Append only a successful result
if res["status"] == 0:
res_all.append(res)
# Set a random start; repeat
z0 = multivariate_normal([0] * model.n_var_rand,
eye(model.n_var_rand))
z0 = z0 / length(z0)
# Choose value among restarts
n_iter_total = sum([res_all[i].nit for i in range(len(res_all))])
if len(res_all) > 0:
i_star = argmin([res.fun for res in res_all])
x_star = res_all[i_star].x
fun_star = sqrt(res_all[i_star].fun)
if verbose:
print("out = {}: Optimization successful".format(key))
print("n_iter = {}".format(res_all[i_star].nit))
print("n_iter_total = {}".format(n_iter_total))
else:
## WARNING
x_star = [NaN] * model.n_var_rand
fun_star = NaN
if verbose:
print("out = {}: Optimization unsuccessful".format(key))
print("n_iter = {}".format(res_all[i_star].nit))
print("n_iter_total = {}".format(n_iter_total))
## Extract results
if append:
df_inner = concat(
(
df_inner,
model.norm2rand(
DataFrame(data=[x_star], columns=model.var_rand)),
),
axis=1,
sort=False,
)
df_inner["beta_" + key] = [fun_star]
df_return = concat((df_return, df_inner), axis=0, sort=False)
if not append:
df_return = (
df_return.groupby(model.var_det) \
.agg({"beta_" + s: max for s in limits}).reset_index()
)
return df_return
def eval_form_pma(
model,
betas=None,
cons=None,
df_corr=None,
df_det=None,
append=True,
tol=1e-3,
n_maxiter=25,
n_restart=1,
verbose=False,
):
r"""Tail quantile via FORM PMA
Approximate the desired tail quantiles using the performance measure approach (PMA) of the first-order reliability method (FORM) [1]. Select limit states to minimize at desired quantile with `betas`. Provide confidence levels `cons` and estimator covariance `df_corr` to compute with margin in beta [2].
Note that under the performance measure approach, the optimized limit state value `g` is sought to be non-negative $g \geq 0$. This is usually included as a constraint in optimization, which can be accomplished in by using ``gr.eval_form_pnd()` *within* a model definition---see the Examples below for more details.
Args:
model (gr.Model): Model to analyze
betas (dict): Target reliability indices;
key = limit state name; must be in model.out
value = reliability index; beta = Phi^{-1}(reliability)
cons (dict or None): Target confidence levels;
key = limit state name; must be in model.out
value = confidence level, \in (0, 1)
df_corr (DataFrame or None): Sampling distribution covariance entries; parameters with no information assumed to be known exactly.
df_det (DataFrame): Deterministic levels for evaluation; use "nom" for nominal deterministic levels.
n_maxiter (int): Maximum iterations for each optimization run
n_restart (int): Number of restarts (== number of optimization runs)
append (bool): Append MPP results for random values?
verbose (bool): Print optimization results?
Returns:
DataFrame: Results of MPP search
Notes:
Since FORM PMA relies on optimization over the limit state, it is often beneficial to scale your limit state to keep values near unity.
References:
Tu, Choi, and Park, "A new study on reliability-based design optimization," Journal of Mechanical Design, 1999
del Rosario, Fenrich, and Iaccarino, "Fast precision margin with the first-order reliability method," AIAA Journal, 2019
Examples::
import grama as gr
from grama.models import make_cantilever_beam
md_beam = make_cantilever_beam()
## Evaluate the reliability of specified designs
(
md_beam
>> gr.ev_form_pma(
# Specify target reliability
betas=dict(g_stress=3, g_disp=3),
# Analyze three different thicknesses
df_det=gr.df_make(t=[2, 3, 4], w=3)
)
)
## Build a nested model for optimization under uncertainty
md_opt = (
gr.Model("Beam Optimization")
>> gr.cp_vec_function(
fun=lambda df: gr.df_make(c_area=df.w * df.t),
var=["w", "t"],
out=["c_area"],
name="Area objective",
)
>> gr.cp_vec_function(
fun=lambda df: gr.eval_form_pma(
md_beam,
betas=dict(g_stress=3, g_disp=3),
df_det=df,
append=False,
)
var=["w", "t"],
out=["g_stress", "g_disp"],
name="Reliability constraints",
)
>> gr.cp_bounds(w=(2, 4), t=(2, 4))
)
# Run the optimization
(
md_opt
>> gr.ev_min(
out_min="c_area",
out_geq=["g_stress", "g_disp"],
)
)
"""
## Check invariants
invariants_eval_model(model)
invariants_eval_df(df_corr, arg_name="df_corr", acc_none=True)
invariants_eval_df(df_det, arg_name="df_det", valid_str=["nom"])
if betas is None:
raise ValueError(
"Must provide `betas` keyword argument to define reliability targets"
)
if not set(betas.keys()).issubset(set(model.out)):
raise ValueError("betas.keys() must be subset of model.out")
if not cons is None:
if not (set(cons.keys()) == set(betas.keys())):
raise ValueError("cons.keys() must be same as betas.keys()")
else:
if df_corr is None:
raise ValueError("Must provide df_corr is using cons")
raise NotImplementedError
df_det = model.var_outer(
DataFrame(data=zeros((1, model.n_var_rand)), columns=model.var_rand),
df_det=df_det,
)
df_det = df_det[model.var_det]
df_return = DataFrame()
for ind in range(df_det.shape[0]):
## Loop over objectives
for key in betas.keys():
## Temp dataframe
df_inner = df_det.iloc[[ind]].reset_index(drop=True)
## Construct lambdas
def objective(z):
## Transform: standard normal-to-random variable
df_norm = DataFrame(data=[z], columns=model.var_rand)
df_rand = model.norm2rand(df_norm)
df = model.var_outer(df_rand, df_det=df_inner)
df_res = eval_df(model, df=df)
g = df_res[key].iloc[0]
# return (g, jac)
return g
def con_beta(z):
return z.dot(z) - (betas[key])**2
## Use conservative direction for initial guess
signs = array(
[model.density.marginals[k].sign for k in model.var_rand])
if length(signs) > 0:
z0 = betas[key] * signs / length(signs)
else:
z0 = betas[key] * ones(model.n_var_rand) / sqrt(
model.n_var_rand)
## Minimize
res_all = []
for jnd in range(n_restart):
res = minimize(
objective,
z0,
args=(),
method="SLSQP",
jac=False,
tol=tol,
options={
"maxiter": n_maxiter,
"disp": False
},
constraints=[{
"type": "eq",
"fun": con_beta
}],
)
# Append only a successful result
if res["status"] == 0:
res_all.append(res)
# Set a random start; repeat
z0 = multivariate_normal([0] * model.n_var_rand,
eye(model.n_var_rand))
z0 = z0 / length(z0) * betas[key]
# Choose value among restarts
n_iter_total = sum([res_all[i].nit for i in range(len(res_all))])
if len(res_all) > 0:
i_star = argmin([res.fun for res in res_all])
x_star = res_all[i_star].x
fun_star = res_all[i_star].fun
if verbose:
print("out = {}: Optimization successful".format(key))
print("n_iter = {}".format(res_all[i_star].nit))
print("n_iter_total = {}".format(n_iter_total))
else:
## WARNING
x_star = [NaN] * model.n_var_rand
fun_star = NaN
if verbose:
print("out = {}: Optimization unsuccessful".format(key))
print("n_iter = {}".format(res_all[i_star].nit))
print("n_iter_total = {}".format(n_iter_total))
## Extract results
if append:
df_inner = concat(
(
df_inner,
model.norm2rand(
DataFrame(data=[x_star], columns=model.var_rand)),
),
axis=1,
sort=False,
)
df_inner[key] = [fun_star]
df_return = concat((df_return, df_inner), axis=0, sort=False)
if not append:
df_return = (df_return.groupby(model.var_det).agg(
{s: max
for s in betas.keys()}).reset_index())
return df_return
def eval_sinews(
model,
n_density=10,
n_sweeps=3,
seed=None,
df_det=None,
varname="sweep_var",
indname="sweep_ind",
append=True,
skip=False,
):
r"""Sweep study
Perform coordinate sweeps over each model random variable ("sinew" design). Use random starting points drawn from the joint density. Optionally sweep the deterministic variables.
For more expensive models, it can be helpful to tune n_density and n_sweeps to achieve a reasonable runtime.
Use gr.plot_auto() to construct a quick visualization of the output dataframe. Use `skip` version to visualize the design, and non-skipped version to visualize the results.
Args:
model (gr.Model): Model to evaluate
n_density (numeric): Number of points along each sweep
n_sweeps (numeric): Number of sweeps per-random variable
seed (int): Random seed to use
df_det (DataFrame): Deterministic levels for evaluation;
use "nom" for nominal deterministic levels,
use "swp" to sweep deterministic variables
varname (str): Column name to give for sweep variable; default="sweep_var"
indname (str): Column name to give for sweep index; default="sweep_ind"
append (bool): Append results to conservative inputs?
skip (bool): Skip evaluation of the functions?
Returns:
DataFrame: Results of evaluation or unevaluated design
Examples::
import grama as gr
md = gr.make_cantilever_beam()
# Skip evaluation, used to visualize the design (input points)
df_design = md >> gr.ev_sinews(df_det="nom", skip=True)
df_design >> gr.pt_auto()
# Visualize the input-to-output relationships of the model
df_sinew = md >> gr.ev_sinews(df_det="nom")
df_sinew >> gr.pt_auto()
"""
## Common invariant checks
invariants_eval_model(model, skip)
invariants_eval_df(df_det, arg_name="df_det", valid_str=["nom", "swp"])
## Override model if deterministic sweeps desired
if df_det == "swp":
## Collect sweep-able deterministic variables
var_sweep = list(
filter(
lambda v: isfinite(model.domain.get_width(v))
& (model.domain.get_width(v) > 0),
model.var_det,
))
## Generate pseudo-marginals
dicts_var = {}
for v in var_sweep:
dicts_var[v] = {
"dist": "uniform",
"loc": model.domain.get_bound(v)[0],
"scale": model.domain.get_width(v),
}
## Overwrite model
model = comp_marginals(model, **dicts_var)
## Restore flag
df_det = "nom"
## Set seed only if given
if seed is not None:
set_seed(seed)
## Ensure sample count is int
if not isinstance(n_density, Integral):
print("eval_sinews() is rounding n_density...")
n_density = int(n_density)
if not isinstance(n_sweeps, Integral):
print("eval_sinews() is rounding n_sweeps...")
n_sweeps = int(n_sweeps)
## Build quantile sweep data
q_random = tile(random((1, model.n_var_rand, n_sweeps)), (n_density, 1, 1))
q_dense = linspace(0, 1, num=n_density)
Q_all = zeros((n_density * n_sweeps * model.n_var_rand, model.n_var_rand))
C_var = ["tmp"] * (n_density * n_sweeps * model.n_var_rand)
C_ind = [0] * (n_density * n_sweeps * model.n_var_rand)
## Interlace
for i_input in range(model.n_var_rand):
ind_base = i_input * n_density * n_sweeps
for i_sweep in range(n_sweeps):
ind_start = ind_base + i_sweep * n_density
ind_end = ind_base + (i_sweep + 1) * n_density
Q_all[ind_start:ind_end] = q_random[:, :, i_sweep]
Q_all[ind_start:ind_end, i_input] = q_dense
C_var[ind_start:ind_end] = [model.var_rand[i_input]] * n_density
C_ind[ind_start:ind_end] = [i_sweep] * n_density
## Modify endpoints for infinite support
if not isfinite(
model.density.marginals[model.var_rand[i_input]].q(0)):
Q_all[ind_start, i_input] = 1 / n_density / 10
if not isfinite(
model.density.marginals[model.var_rand[i_input]].q(1)):
Q_all[ind_end - 1, i_input] = 1 - 1 / n_density / 10
## Assemble sampling plan
df_pr = DataFrame(data=Q_all, columns=model.var_rand)
df_rand = model.density.pr2sample(df_pr)
df_rand[varname] = C_var
df_rand[indname] = C_ind
## Construct outer-product DOE
df_samp = model.var_outer(df_rand, df_det=df_det)
if skip:
## Evaluation estimate
runtime_est = model.runtime(df_samp.shape[0])
if runtime_est > 0:
print(
"Estimated runtime for design with model ({0:1}):\n {1:4.3} sec"
.format(model.name, runtime_est))
else:
print(
"Design runtime estimates unavailable; model has no timing data."
)
## For autoplot
with catch_warnings():
simplefilter("ignore")
df_samp._plot_info = {
"type": "sinew_inputs",
"var": model.var_rand
}
## Pass-through
return df_samp
## Apply
df_res = eval_df(model, df=df_samp, append=append)
## For autoplot
with catch_warnings():
simplefilter("ignore")
df_res._plot_info = {
"type": "sinew_outputs",
"var": model.var_rand,
"out": model.out,
}
return df_res
def eval_hybrid(
model,
n=1,
plan="first",
df_det=None,
varname="hybrid_var",
seed=None,
append=True,
skip=False,
):
r"""Hybrid points for Sobol' indices
Use the "hybrid point" design (Sobol', 1999) to support estimating Sobol'
indices. Use gr.tran_sobol() to post-process the results and compute
estimates.
Args:
model (gr.Model): Model to evaluate; must have CopulaIndependence
n (numeric): Number of points along each sweep
plan (str): Sobol' index to compute; plan={"first", "total"}
seed (int): Random seed to use
df_det (DataFrame): Deterministic levels for evaluation; use "nom"
for nominal deterministic levels.
varname (str): Column name to give for sweep variable; default="hybrid_var"
append (bool): Append results to conservative inputs?
skip (bool): Skip evaluation of the functions?
Returns:
DataFrame: Results of evaluation or unevaluated design
References:
I.M. Sobol', "Sensitivity Estimates for Nonlinear Mathematical Models" (1999) MMCE, Vol 1.
Examples::
import grama as gr
md = gr.make_cantilever_beam()
## Compute the first-order indices
df_first = md >> gr.ev_hybrid(df_det="nom", plan="first")
df_first >> gr.tf_sobol()
## Compute the total-order indices
df_total = md >> gr.ev_hybrid(df_det="nom", plan="total")
df_total >> gr.tf_sobol()
"""
## Check invariants
invariants_eval_model(model, skip)
invariants_eval_df(df_det, arg_name="df_det", valid_str=["nom"])
if not isinstance(model.density.copula, CopulaIndependence):
raise ValueError(
"model must have CopulaIndependence structure;\n" +
"Sobol' indices only defined for independent variables")
## Set seed only if given
if seed is not None:
set_seed(seed)
if not isinstance(n, Integral):
print("eval_hybrid() is rounding n...")
n = int(n)
## Draw hybrid points
X = random((n, model.n_var_rand))
Z = random((n, model.n_var_rand))
## Reserve space
Q_all = zeros((n * (model.n_var_rand + 1), model.n_var_rand))
Q_all[:n] = X # Base samples
C_var = ["_"] * (n * (model.n_var_rand + 1))
## Interleave samples
for i_in in range(model.n_var_rand):
i_start = (i_in + 1) * n
i_end = (i_in + 2) * n
if plan == "first":
Q_all[i_start:i_end, :] = Z
Q_all[i_start:i_end, i_in] = X[:, i_in]
elif plan == "total":
Q_all[i_start:i_end, :] = X
Q_all[i_start:i_end, i_in] = Z[:, i_in]
else:
raise ValueError("plan must be `first` or `total`")
C_var[i_start:i_end] = [model.var_rand[i_in]] * n
## Construct sampling plan
df_pr = DataFrame(data=Q_all, columns=model.var_rand)
## Convert samples to desired marginals
df_rand = model.density.pr2sample(df_pr)
df_rand[varname] = C_var
## Construct outer-product DOE
df_samp = model.var_outer(df_rand, df_det=df_det)
if skip:
with catch_warnings():
simplefilter("ignore")
df_samp._meta = dict(
type="eval_hybrid",
varname=varname,
plan=plan,
var_rand=model.var_rand,
out=model.out,
)
return df_samp
df_res = eval_df(model, df=df_samp, append=append)
with catch_warnings():
simplefilter("ignore")
df_res._meta = dict(
type="eval_hybrid",
varname=varname,
plan=plan,
var_rand=model.var_rand,
out=model.out,
)
return df_res
def eval_pnd(model, df_train, df_test, signs, n=int(1e4), seed=None, append=True, \
mean_prefix="_mean", sd_prefix="_sd"):
"""Approximate the probability non-dominated (PND)
Approximates the probability non-dominated (PND) for a set of training points given a fitted probabilistic model. Used to rank a set of candidates in the context of multiobjective optimization.
Args:
model (gr.model): predictive model to evaluate
df_train (DataFrame): dataframe with training data
df_test (DataFrame): dataframe with test data
signs (dict): dict with the variables you would like to use and
minimization or maximization parameter for each
append (bool): Append df_test to pnd algorithm outputs
Kwargs:
n (int): Number of draws for importance sampler
seed (int): declarble seed value for reproducibility
Returns:
DataFrame: Results of predictive model going through a PND algorithm.
Conatians both values and their scores.
References:
del Rosario, Zachary, et al. "Assessing the frontier: Active learning, model accuracy, and multi-objective candidate discovery and optimization." The Journal of Chemical Physics 153.2 (2020): 024112.
Examples::
import grama as gr
## Define a ground-truth model
md_true = gr.make_pareto_random()
df_data = (
md_true
>> gr.ev_sample(n=2e3, seed=101, df_det="nom")
)
## Generate test/train data
df_train = (
df_data
>> gr.tf_sample(n=10)
)
df_test = (
df_data
>> gr.anti_join(
df_train,
by = ["x1","x2"]
)
>> gr.tf_sample(n=200)
)
## Fit a model to training data
md_fit = (
df_train
>> gr.ft_gp(
var=["x1","x2"]
out=["y1","y2"]
)
)
## Rank training points by PND algorithm
df_pnd = (
md_fit
>> gr.ev_pnd(
df_train,
df_test,
signs = {"y1":1, "y2":1},
seed = 101
)
>> gr.tf_arrange(gr.desc(DF.pr_scores))
)
"""
invariants_eval_model(model)
invariants_eval_df(df_train, arg_name="df_train")
invariants_eval_df(df_test, arg_name="df_test")
# Check content
if len(model.out)/2 < 2:
raise ValueError('Given Model needs multiple outputs')
if not set(model.var).issubset(set(df_train.columns)):
raise ValueError("model.var must be subset of df_train.columns")
if not set(model.var).issubset(set(df_test.columns)):
raise ValueError("model.var must be subset of df_test.columns")
for key in signs.keys():
if key+mean_prefix not in model.out:
raise ValueError(f"signs.{key} implies output {key+mean_prefix}, which is not found in provided md.out")
if key+sd_prefix not in model.out:
raise ValueError(f"signs{key} implies output {key+sd_prefix}, which is not found in provided sd.out")
## Compute predictions and predicted uncertainties
df_pred = (
df_test
>> tf_md(md=model)
)
## Setup for reshaping
means = []
sds = []
columns = df_train.columns.values
length = int(len(signs.keys()))
outputs = [key for key in signs.keys() if key in columns]
signs = [value for value in signs.values()]
## append mean and sd prefixes
for i, value in enumerate(outputs):
means.append(value+mean_prefix)
sds.append(value+sd_prefix)
## Remove extra columns from df_test
df_pred = df_pred[means + sds]
## Reshape data for PND algorithm
X_pred = df_pred[means].values # Predicted response values
X_sig = df_pred[sds].values # Predictive uncertainties
X_train = df_train[outputs].values # Training
### Create covariance matrices
X_cov = zeros((X_sig.shape[0], length, length))
for l in range(length):
for i in range(X_sig.shape[0]):
X_cov[i, l, l] = X_sig[i, l]
### Apply pnd
pr_scores, var_values = approx_pnd(
X_pred,
X_cov,
X_train,
signs = signs,
n = n,
seed = seed
)
### Package outputs
df_pnd = DataFrame(
{
"pr_scores": pr_scores,
"var_values": var_values,
}
)
if append:
return df_test.reset_index(drop=True).merge(df_pnd, left_index=True, right_index=True)
return df_pnd
def eval_min(
model,
out_min=None,
out_geq=None,
out_leq=None,
out_eq=None,
method="SLSQP",
tol=1e-6,
n_restart=1,
n_maxiter=50,
seed=None,
df_start=None,
):
r"""Constrained minimization using functions from a model
Perform constrained minimization using functions from a model. Model must
have deterministic variables only.
Wrapper for scipy.optimize.minimize
Args:
model (gr.Model): Model to analyze. All model variables must be
deterministic.
out_min (str): Output to use as minimization objective.
out_geq (None OR list of str): Outputs to use as geq constraints; out >= 0
out_leq (None OR list of str): Outputs to use as leq constraints; out <= 0
out_eq (None OR list of str): Outputs to use as equality constraints; out == 0
method (str): Optimization method; see the documentation for
scipy.optimize.minimize for options.
tol (float): Optimization objective convergence tolerance
n_restart (int): Number of restarts; beyond n_restart=1 random
restarts are used.
df_start (None or DataFrame): Specific starting values to use; overrides
n_restart if non None provided.
Returns:
DataFrame: Results of optimization
Examples::
import grama as gr
## Define a model with objective and constraints
md = (
gr.Model("Constrained Rosenbrock")
>> gr.cp_function(
fun=lambda x: (1 - x[0])**2 + 100*(x[1] - x[0]**2)**2,
var=["x", "y"],
out=["c"],
)
>> gr.cp_function(
fun=lambda x: (x[0] - 1)**3 - x[1] + 1,
var=["x", "y"],
out=["g1"],
)
>> gr.cp_function(
fun=lambda x: x[0] + x[1] - 2,
var=["x", "y"],
out=["g2"],
)
>> gr.cp_bounds(
x=(-1.5, +1.5),
y=(-0.5, +2.5),
)
)
## Run the optimizer
md >> gr.ev_min(
out_min="c",
out_leq=["g1", "g2"]
)
"""
## Common invariant checks
invariants_eval_model(model)
invariants_eval_df(df_start, arg_name="df_start", acc_none=True)
## Check that model has only deterministic variables
if model.n_var_rand > 0:
raise ValueError("model must have no random variables")
## Check that objective is in model
if not (out_min in model.out):
raise ValueError("model must contain out_min")
## Check that constraints are in model
if not (out_geq is None):
out_diff = set(out_geq).difference(set(model.out))
if len(out_diff) > 0:
raise ValueError(
"model must contain each out_geq; missing {}".format(out_diff))
if not (out_leq is None):
out_diff = set(out_leq).difference(set(model.out))
if len(out_diff) > 0:
raise ValueError(
"model must contain each out_leq; missing {}".format(out_diff))
if not (out_eq is None):
out_diff = set(out_eq).difference(set(model.out))
if len(out_diff) > 0:
raise ValueError(
"model must contain each out_eq; missing {}".format(out_diff))
## Formulate initial guess
df_nom = eval_nominal(model, df_det="nom", skip=True)
if df_start is None:
df_start = df_nom[model.var]
if n_restart > 1:
if not (seed is None):
setseed(seed)
## Collect sweep-able deterministic variables
var_sweep = list(
filter(
lambda v: isfinite(model.domain.get_width(v))
& (model.domain.get_width(v) > 0),
model.var_det,
))
## Generate pseudo-marginals
dicts_var = {}
for v in var_sweep:
dicts_var[v] = {
"dist": "uniform",
"loc": model.domain.get_bound(v)[0],
"scale": model.domain.get_width(v),
}
## Overwrite model
md_sweep = comp_marginals(model, **dicts_var)
md_sweep = comp_copula_independence(md_sweep)
## Generate random start points
df_rand = eval_sample(
md_sweep,
n=n_restart - 1,
df_det="nom",
skip=True,
)
df_start = concat((df_start, df_rand[model.var]),
axis=0).reset_index(drop=True)
else:
n_restart = df_start.shape[0]
## Factory for wrapping model's output
def make_fun(out, sign=+1):
def fun(x):
df = DataFrame([x], columns=model.var)
df_res = eval_df(model, df)
return sign * df_res[out]
return fun
## Create helper functions for constraints
constraints = []
if not (out_geq is None):
for out in out_geq:
constraints.append({
"type": "ineq",
"fun": make_fun(out),
})
if not (out_leq is None):
for out in out_leq:
constraints.append({
"type": "ineq",
"fun": make_fun(out, sign=-1),
})
if not (out_eq is None):
for out in out_eq:
constraints.append({
"type": "eq",
"fun": make_fun(out),
})
## Parse the bounds for minimize
bounds = list(map(lambda k: model.domain.bounds[k], model.var))
## Run optimization
df_res = DataFrame()
for i in range(n_restart):
x0 = df_start[model.var].iloc[i].values
res = minimize(
make_fun(out_min),
x0,
args=(),
method=method,
jac=False,
tol=tol,
options={
"maxiter": n_maxiter,
"disp": False
},
constraints=constraints,
bounds=bounds,
)
df_opt = df_make(
**dict(zip(model.var, res.x)),
**dict(zip(map(lambda s: s + "_0", model.var), x0)),
)
df_tmp = eval_df(model, df=df_opt)
df_tmp["success"] = [res.success]
df_tmp["message"] = [res.message]
df_tmp["n_iter"] = [res.nit]
df_res = concat((df_res, df_tmp), axis=0).reset_index(drop=True)
return df_res
def eval_nls(
model,
df_data=None,
out=None,
var_fix=None,
df_init=None,
append=False,
tol=1e-6,
ftol=1e-9,
gtol=1e-5,
n_maxiter=100,
n_restart=1,
n_process=1,
method="L-BFGS-B",
seed=None,
verbose=True,
):
r"""Estimate with Nonlinear Least Squares (NLS)
Estimate best-fit variable levels with nonlinear least squares (NLS).
Args:
model (gr.Model): Model to analyze. All model variables
selected for fitting must be bounded or random. Deterministic
variables may have semi-infinite bounds.
df_data (DataFrame): Data for estimating parameters. Variables not
found in df_data optimized in fitting.
out (list or None): Output contributions to consider in computing MSE.
Assumed to be model.out if left as None.
var_fix (list or None): Variables to fix to nominal levels. Note that
variables with domain width zero will automatically be fixed.
df_init (DataFrame or None): Initial guesses for parameters; overrides
n_restart
append (bool): Append metadata? (Initial guess, MSE, optimizer status)
tol (float): Optimizer convergence tolerance
n_maxiter (int): Optimizer maximum iterations
n_restart (int): Number of restarts; beyond n_restart=1 random
restarts are used.
seed (int OR None): Random seed for restarts
verbose (bool): Print messages to console?
Returns:
DataFrame: Results of estimation
Examples::
import grama as gr
from grama.data import df_trajectory_full
from grama.models import make_trajectory_linear
md_trajectory = make_trajectory_linear()
df_fit = (
md_trajectory
>> gr.ev_nls(df_data=df_trajectory_full)
)
print(df_fit)
"""
## Common invariant checks
invariants_eval_model(model)
invariants_eval_df(df_data, arg_name="df_data")
invariants_eval_df(df_init, arg_name="df_init", acc_none=True)
## Check `out` invariants
if out is None:
out = model.out
if verbose:
print("... eval_nls setting out = {}".format(out))
set_diff = set(out).difference(set(df_data.columns))
if len(set_diff) > 0:
raise ValueError("out must be subset of df_data.columns\n" +
"difference = {}".format(set_diff))
## Determine variables to be fixed
if var_fix is None:
var_fix = set()
else:
var_fix = set(var_fix)
for var in model.var_det:
wid = model.domain.get_width(var)
if wid == 0:
var_fix.add(var)
if verbose:
print("... eval_nls setting var_fix = {}".format(list(var_fix)))
var_fix = list(var_fix)
## Determine variables for evaluation
var_feat = set(model.var).intersection(set(df_data.columns))
if verbose:
print("... eval_nls setting var_feat = {}".format(var_feat))
var_feat = list(var_feat)
## Determine variables for fitting
var_fit = set(model.var).difference(set(var_fix).union(set(var_feat)))
if len(var_fit) == 0:
raise ValueError("No var selected for fitting!\n" +
"Try checking model bounds and df_data.columns.")
var_fit = list(var_fit)
## Separate var_fit into det and rand
var_fit_det = list(set(model.var_det).intersection(var_fit))
var_fit_rand = list(set(model.var_rand).intersection(var_fit))
## Construct bounds, fix var_fit order
var_fit = var_fit_det + var_fit_rand
bounds = []
var_prob = []
for var in var_fit_det:
if not isfinite(model.domain.get_nominal(var)):
var_prob.append(var)
bounds.append(model.domain.get_bound(var))
if len(var_prob) > 0:
raise ValueError(
"all variables to be fitted must finite nominal value\n" +
"offending var = {}".format(var_prob))
for var in var_fit_rand:
bounds.append((
model.density.marginals[var].q(0),
model.density.marginals[var].q(1),
))
## Determine initial guess points
df_nom = eval_nominal(model, df_det="nom", skip=True)
## Use specified initial guess(es)
if not (df_init is None):
# Check invariants
set_diff = list(set(var_fit).difference(set(df_init.columns)))
if len(set_diff) > 0:
raise ValueError("var_fit must be subset of df_init.columns\n" +
"difference = {}".format(set_diff))
# Pull n_restart
n_restart = df_init.shape[0]
## Generate initial guess(es)
else:
df_init = df_nom[var_fit]
if n_restart > 1:
if not (seed is None):
setseed(seed)
## Collect sweep-able deterministic variables
var_sweep = list(
filter(
lambda v: isfinite(model.domain.get_width(v))
& (model.domain.get_width(v) > 0),
model.var_det,
))
## Generate pseudo-marginals
dicts_var = {}
for v in var_sweep:
dicts_var[v] = {
"dist": "uniform",
"loc": model.domain.get_bound(v)[0],
"scale": model.domain.get_width(v),
}
## Overwrite model
md_sweep = comp_marginals(model, **dicts_var)
md_sweep = comp_copula_independence(md_sweep)
## Generate random start points
df_rand = eval_sample(
md_sweep,
n=n_restart - 1,
df_det="nom",
skip=True,
)
df_init = concat((df_init, df_rand[var_fit]),
axis=0).reset_index(drop=True)
## Iterate over initial guesses
df_res = DataFrame()
def fun_mp(i):
x0 = df_init[var_fit].iloc[i].values
## Build evaluator
def objective(x):
"""x = [var_fit]"""
## Evaluate model
df_var = tran_outer(
df_data[var_feat],
concat(
(df_nom[var_fix].iloc[[0]],
df_make(**dict(zip(var_fit, x)))),
axis=1,
),
)
df_tmp = eval_df(model, df=df_var)
## Compute joint MSE
return ((df_tmp[out].values - df_data[out].values)**2).mean()
## Run optimization
res = minimize(
objective,
x0,
args=(),
method=method,
jac=False,
tol=tol,
options={
"maxiter": n_maxiter,
"disp": False,
"ftol": ftol,
"gtol": gtol,
},
bounds=bounds,
)
df_tmp = df_make(
**dict(zip(var_fit, res.x)),
**dict(zip(map(lambda s: s + "_0", var_fit), x0)),
)
df_tmp["success"] = [res.success]
df_tmp["message"] = [res.message]
df_tmp["n_iter"] = [res.nit]
df_tmp["mse"] = [res.fun]
return df_tmp
df_res = DataFrame()
for i in range(n_restart):
df_tmp = fun_mp(i)
df_res = concat((df_res, df_tmp), axis=0).reset_index(drop=True)
## Post-process
if append:
return df_res
return df_res[var_fit]