def cost_fun(x, *args):
thresh = x[0]
ts, capacity, bounds, costs = args
integral = clipped_area(ts, thresh=thresh)
cost = (integral - capacity) ** 2
cost /= ((thresh - bounds[0] + sum(bounds))**2)**0.5
cost /= ((thresh - bounds[1] + sum(bounds))**2)**0.5
costs += [(thresh, cost, integral)]
return cost
def cost_fun(x, *args):
thresh = x[0]
ts, capacity, bounds, costs = args
integral = clipped_area(ts, thresh=thresh)
cost = (integral - capacity)**2
cost /= ((thresh - bounds[0] + sum(bounds))**2)**0.5
cost /= ((thresh - bounds[1] + sum(bounds))**2)**0.5
costs += [(thresh, cost, integral)]
return cost
def cost_fun(x, *args):
thresh = x[0]
ts, capacity, bounds, costs, weights = args
integral = util.clipped_area(ts, thresh=thresh)
cost = 0
terms = np.array([(100. * (integral - capacity) / capacity) ** 2,
1. / (((thresh - bounds[0]) / max(bounds))**2)**0.5,
1. / (((thresh - bounds[1]) / max(bounds))**2)**0.5,
1.1 ** (integral / capacity)])
cost = np.sum(weights * terms)
costs += [(thresh, cost, integral)]
return cost
def test_optimal_threshold(self):
"""
Test using scipy.optimize.minimize on a bumpy data set to find the clipping threshold
"""
return
t = ['2014-12-09T00:00', '2014-12-09T00:15', '2014-12-09T00:30', '2014-12-09T00:45', '2014-12-09T01:00', '2014-12-09T01:15', '2014-12-09T01:30', '2014-12-09T01:45']
ts = pd.Series([217, 234, 235, 231, 219, 219, 231, 232], index=pd.to_datetime(t))
thresh=234
capacity=562.5
util.clipped_area(ts, thresh=thresh)
pd.DataFrame({'ts': ts, 'thresh': pd.Series(thresh*np.ones(len(ts)), index=ts.index)}).plot()
# invest.util.clipping_params()
ts.index = ts.index.astype(np.int64)
costs = []
weights = np.ones(4)
def cost_fun(x, *args):
thresh = x[0]
ts, capacity, bounds, costs, weights = args
integral = util.clipped_area(ts, thresh=thresh)
cost = 0
terms = np.array([(100. * (integral - capacity) / capacity) ** 2,
1. / (((thresh - bounds[0]) / max(bounds))**2)**0.5,
1. / (((thresh - bounds[1]) / max(bounds))**2)**0.5,
1.1 ** (integral / capacity)])
cost = np.sum(weights * terms)
costs += [(thresh, cost, integral)]
return cost
bounds = (ts.min(), ts.max())
thresh0 = 0.4*bounds[1] + 0.6*bounds[0]
optimum = minimize(fun=cost_fun, x0=[thresh0], bounds=[bounds], args=(ts, capacity, bounds, costs, weights))
thresh = optimum.x[0]
integral = util.clipped_area(ts, thresh=thresh)
self.assertGreater(capacity, integral)
self.assertLess((capacity-integral)/capacity, 0.01)
from pug.invest.util import clipped_area
# from scipy.optimize import minimize
import pandas as pd
from matplotlib import pyplot as plt
np = pd.np
t = ['2014-12-09T00:00', '2014-12-09T00:15', '2014-12-09T00:30', '2014-12-09T00:45', '2014-12-09T01:00', '2014-12-09T01:15', '2014-12-09T01:30', '2014-12-09T01:45']
ts = pd.Series([217, 234, 235, 231, 219, 219, 231, 232], index=pd.to_datetime(t))
thresh=234
capacity=562.5 # barely enough to do anything
clipped_area(ts, thresh=thresh)
pd.DataFrame({'ts': ts, 'thresh': pd.Series(thresh*np.ones(len(ts)), index=ts.index)}).plot()
# invest.util.clipping_params()
ts.index = ts.index.astype(np.int64)
costs = []
def cost_fun(x, *args):
thresh = x[0]
ts, capacity, bounds, costs = args
integral = clipped_area(ts, thresh=thresh)
cost = (integral - capacity) ** 2
cost /= ((thresh - bounds[0] + sum(bounds))**2)**0.5
cost /= ((thresh - bounds[1] + sum(bounds))**2)**0.5
costs += [(thresh, cost, integral)]
return cost
bounds = (ts.min(), ts.max())
# thresh0 = 0.9*bounds[1] + 0.1*bounds[0]
# optimum = minimize(fun=cost_fun, x0=[thresh0], bounds=[bounds], args=(ts, capacity, bounds, costs))
]
ts = pd.Series([217, 234, 235, 231, 219, 219, 231, 232],
index=pd.to_datetime(t))
thresh = 234
capacity = 562.5 # barely enough to do anything
bounds = (ts.min(), ts.max())
# thresh0 = 0.9*bounds[1] + 0.1*bounds[0]
# optimum = minimize(fun=cost_fun, x0=[thresh0], bounds=[bounds], args=(ts, capacity, bounds, costs))
# thresh = optimum.x[0]
# integral = clipped_area(ts, thresh=thresh)
rows = []
threshes = np.arange(bounds[0] * .9, 1.1 * bounds[1],
(1.1 * bounds[1] - .9 * bounds[0]) / 1000.)
for thresh in threshes:
integral = clipped_area(ts, thresh=thresh)
terms = np.array([(10. * (integral - capacity) / capacity)**2,
2. / 0.1**((bounds[0] - thresh) * capacity / bounds[0]),
2. / 0.1**((thresh - bounds[1]) * capacity / bounds[1]),
1.2**(integral / capacity)])
row = [thresh, integral] + list(terms) + [np.sum(terms)]
rows += [row]
labels = [
'threshold', 'integral', 'capacity-error-term', 'lower-bound-term',
'upper-bound-term', 'exponential-capacity-term', 'total-cost'
]
df = pd.DataFrame(rows, columns=labels)
df2 = pd.DataFrame(df[[c for c in df.columns if c[-1] == 'm' or c[-1] == 't']])
df2.index = df['threshold']
df2.plot(logy=True)