def score(self, exptree, constants):
with warnings.catch_warnings():
warnings.simplefilter("ignore")
a, b = fit.sym_fit(exptree, constants, self.X, self.Y, self.guesses)
if b < 0:
return a, float("inf")
return a, b
def physics_fit(prototypes, x_data, y_data, threshold=0, max_terms=5,
fit_tries=12, mul_depth=2):
'''Do a "physicist fit"; expects standard score normalized data
prototypes - list of base functions
x_data, y_data - data to fit
threshold - stop when fit error is below threshold
max_terms - stop when model has this many potototype expressions
mul-depth - generates more prototypes by cross_multipying (unimplemented)
'''
debug_info = []
prototypes = cross_multiply(prototypes, mul_depth)
c0, c1 = sympy.symbols('c0 c1')
# zero order model
opt, cur_err = fit.sym_fit(c0, [c0], x_data, y_data)
zero_order = opt[0]
zero_order_error = cur_err
debug_info.append("Zero order model:")
debug_info.append((zero_order, cur_err))
debug_info.append("prototype scores:")
# calculate base error levels for every function prototype
base_score = []
for func in prototypes:
# multiply by constant for better fitting, rename
func_times_const = c1 * func + c0
constants = func_times_const.free_symbols
constants.remove(x)
constants = list(constants)
# fit data
opt, err = fit.sym_fit(func_times_const, constants, x_data,
y_data, fit_tries * len(constants))
if err < numpy.inf:
base_score.append((err, func))
#debug_info.append((func_times_const.subs(zip(constants, opt)),err))
base_score = sorted(base_score, key=lambda x: x[0], reverse=True)
for i in base_score:
debug_info.append((i[1], i[0]))
debug_info.append("Modeling execution trace:")
# start modeling
model = c0
model_constants = [c0]
for i in range(0, max_terms):
if cur_err < threshold: break
# grab the best_scoring expression
best_expr = base_score.pop()[1]
# rename constants to avoid name collisions
best_expr = rename_constants(best_expr, model_constants)
# every prototype term gets a leading multiplicative constant
model_constants.append(sympy.symbols('c' +
str(len(model_constants))))
best_expr *= model_constants[-1]
# refit
model += best_expr
opt, cur_err = fit.sym_fit(model, model_constants, x_data, y_data,
fit_tries * len(model_constants))
debug_info.append((model.subs(zip(model_constants, opt)), cur_err))
# break if you start doing worse than zero-order model
if cur_err > zero_order_error: break
return debug_info
from sympy import symbols
from fit import sym_fit
import operations as ops
x, c0, c1, c2 = symbols("x c0 c1 c2")
expr = c1 * x ** 2 + c0
# 2 * x^2 + 1
x_data = [0, 1, 2, 3, 4, 5]
y_data = [1, 3, 9, 19, 33, 51] # exact
y_err = [1.1, 3.1, 8.9, 19.8, 33.1, 50] # with some error
print("Attempting to fit c1 * x^2 + c2")
popt, err = sym_fit(expr, [c0, c1], x_data, y_data)
print("Fit to y_data")
print(popt)
print(err)
popt, err = sym_fit(expr, [c0, c1], x_data, y_err)
print("Fit to y_err")
print(popt)
print(err)
print("")
x_data = [1, 2, 3, 4, 5]
y_data = [3, 9, 19, 33, 51]
expr = c0
def score(self, exptree, constants):
return fit.sym_fit(exptree, constants, self.X, self.Y, self.guesses)
