def test_get_completeness_points(self):
'''
Tests the function get_completeness_points using a synthetic
set of "sigma" derived from a bilinear function with known gradients
and crossover points
'''
crossovers = [20., 50., 80.]
params1 = [-0.5, -1.0, np.log10(crossovers[0]), 1.5]
params2 = [-0.5, -1.3, np.log10(crossovers[1]), 1.0]
params3 = [-0.5, -0.8, np.log10(crossovers[2]), 0.7]
n_years = np.hstack([1., 5., np.arange(10., 110., 10.)])
number_values = len(n_years)
yvals_1 = np.zeros(number_values, dtype=float)
yvals_2 = np.zeros(number_values, dtype=float)
yvals_3 = np.zeros(number_values, dtype=float)
for ival in range(0, number_values):
yvals_1[ival] = 10.**piecewise_linear_scalar(
params1, np.log10(n_years[ival]))
yvals_2[ival] = 10.**piecewise_linear_scalar(
params2, np.log10(n_years[ival]))
yvals_3[ival] = 10.**piecewise_linear_scalar(
params3, np.log10(n_years[ival]))
test_sigma = np.column_stack([yvals_1, yvals_2, yvals_3])
(ntime, nmags) = np.shape(test_sigma)
completeness_time, gradients, _ = \
self.process.get_completeness_points(n_years, test_sigma, nmags,
ntime)
self.assertTrue(fabs(completeness_time[0] - crossovers[0]) < 1.0)
self.assertTrue(fabs(completeness_time[1] - crossovers[1]) < 1.0)
self.assertTrue(fabs(completeness_time[2] - crossovers[2]) < 1.0)
self.assertTrue(fabs(gradients[0] - -1.0) < 0.1)
self.assertTrue(fabs(gradients[1] - -1.3) < 0.1)
self.assertTrue(fabs(gradients[2] - -0.8) < 0.1)
def test_get_completeness_points(self):
'''
Tests the function get_completeness_points using a synthetic
set of "sigma" derived from a bilinear function with known gradients
and crossover points
'''
crossovers = [20., 50., 80.]
params1 = [-0.5, -1.0, np.log10(crossovers[0]), 1.5]
params2 = [-0.5, -1.3, np.log10(crossovers[1]), 1.0]
params3 = [-0.5, -0.8, np.log10(crossovers[2]), 0.7]
n_years = np.hstack([1., 5., np.arange(10., 110., 10.)])
number_values = len(n_years)
yvals_1 = np.zeros(number_values, dtype=float)
yvals_2 = np.zeros(number_values, dtype=float)
yvals_3 = np.zeros(number_values, dtype=float)
for ival in range(0, number_values):
yvals_1[ival] = 10. ** piecewise_linear_scalar(params1,
np.log10(n_years[ival]))
yvals_2[ival] = 10. ** piecewise_linear_scalar(params2,
np.log10(n_years[ival]))
yvals_3[ival] = 10. ** piecewise_linear_scalar(params3,
np.log10(n_years[ival]))
test_sigma = np.column_stack([yvals_1, yvals_2, yvals_3])
(ntime, nmags) = np.shape(test_sigma)
completeness_time, gradients, _ = \
self.process.get_completeness_points(n_years, test_sigma, nmags,
ntime)
self.assertTrue(fabs(completeness_time[0] - crossovers[0]) < 1.0)
self.assertTrue(fabs(completeness_time[1] - crossovers[1]) < 1.0)
self.assertTrue(fabs(completeness_time[2] - crossovers[2]) < 1.0)
self.assertTrue(fabs(gradients[0] - -1.0) < 0.1)
self.assertTrue(fabs(gradients[1] - -1.3) < 0.1)
self.assertTrue(fabs(gradients[2] - -0.8) < 0.1)
def get_bilinear_residuals_stepp(input_params, xvals, yvals, slope1_fit):
'''
Returns the residual sum-of-squares value of a bilinear fit to a data
set - with a segment - 1 gradient fixed by an input value (slope_1_fit)
:param list input_params:
Input parameters for the bilinear model [slope2, crossover_point,
intercept]
:param numpy.ndarray xvals:
x-values of the data to be fit
:param numpy.ndarray yvals:
y-values of the data to be fit
:param float slope1_fit:
Gradient of the first slope
:returns:
Residual sum-of-squares of fit
'''
params = np.hstack([slope1_fit, input_params])
num_x = len(xvals)
y_model = np.zeros(num_x, dtype=float)
residuals = np.zeros(num_x, dtype=float)
for iloc in range(0, num_x):
y_model[iloc] = piecewise_linear_scalar(params, xvals[iloc])
residuals[iloc] = (yvals[iloc] - y_model[iloc]) ** 2.0
return np.sum(residuals)
def setUp(self):
self.xdata = np.arange(0., 11., 1.)
self.params = [2.0, -1.0, 5.0, 1.0]
self.ydata = np.zeros(11, dtype=float)
for ival in range(0, 11):
self.ydata[ival] = piecewise_linear_scalar(self.params,
self.xdata[ival])
def test_fit_bilinear_function(self):
'''
Tests the function to fit a bilinear model to a data set with a
known set of coefficients
'''
self.xdata = np.arange(0., 21., 1.)
self.params = [-0.5, -1.0, 8.0, 10.0]
self.ydata = np.zeros(len(self.xdata), dtype=float)
for ival in range(0, len(self.xdata)):
self.ydata[ival] = piecewise_linear_scalar(self.params,
self.xdata[ival])
# Run analysis
comp_time, gradient, model_line = self.process._fit_bilinear_to_stepp(
self.xdata,
self.ydata,
initial_values = [-0.75, 10.0, 0.0])
# Number of decimal places lowered to allow for uncertainty in
# optimisation results
self.assertAlmostEqual(np.log10(comp_time),
np.log10(100000219.8145678),
places=3)
self.assertAlmostEqual(gradient, -1.000, places=3)
expected_model_line = 10.0 ** (-0.5 * self.xdata + 10.)
for ival in range(0, len(model_line)):
self.assertAlmostEqual(np.log10(model_line[ival]),
np.log10(expected_model_line[ival]),
places=3)
def get_bilinear_residuals_stepp(input_params, xvals, yvals, slope1_fit):
'''
Returns the residual sum-of-squares value of a bilinear fit to a data
set - with a segment - 1 gradient fixed by an input value (slope_1_fit)
:param list input_params:
Input parameters for the bilinear model [slope2, crossover_point,
intercept]
:param numpy.ndarray xvals:
x-values of the data to be fit
:param numpy.ndarray yvals:
y-values of the data to be fit
:param float slope1_fit:
Gradient of the first slope
:returns:
Residual sum-of-squares of fit
'''
params = np.hstack([slope1_fit, input_params])
num_x = len(xvals)
y_model = np.zeros(num_x, dtype=float)
residuals = np.zeros(num_x, dtype=float)
for iloc in range(0, num_x):
y_model[iloc] = piecewise_linear_scalar(params, xvals[iloc])
residuals[iloc] = (yvals[iloc] - y_model[iloc])**2.0
return np.sum(residuals)
def setUp(self):
self.xdata = np.arange(0., 11., 1.)
self.params = [2.0, -1.0, 5.0, 1.0]
self.ydata = np.zeros(11, dtype=float)
for ival in range(0, 11):
self.ydata[ival] = piecewise_linear_scalar(self.params,
self.xdata[ival])
def test_fit_bilinear_function(self):
'''
Tests the function to fit a bilinear model to a data set with a
known set of coefficients
'''
self.xdata = np.arange(0., 21., 1.)
self.params = [-0.5, -1.0, 8.0, 10.0]
self.ydata = np.zeros(len(self.xdata), dtype=float)
for ival in range(0, len(self.xdata)):
self.ydata[ival] = piecewise_linear_scalar(self.params,
self.xdata[ival])
# Run analysis
comp_time, gradient, model_line = self.process._fit_bilinear_to_stepp(
self.xdata, self.ydata, initial_values=[-0.75, 10.0, 0.0])
# Number of decimal places lowered to allow for uncertainty in
# optimisation results
self.assertAlmostEqual(np.log10(comp_time),
np.log10(100000219.8145678),
places=3)
self.assertAlmostEqual(gradient, -1.000, places=3)
expected_model_line = 10.0**(-0.5 * self.xdata + 10.)
for ival in range(0, len(model_line)):
self.assertAlmostEqual(np.log10(model_line[ival]),
np.log10(expected_model_line[ival]),
places=3)
def test_piecewise_linear_function(self):
'''Test the piecewise linear calculator'''
# Good parameter set - 2 segments
params = [2.0, -1.0, 5.0, 0.0]
values = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
expected = [0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 9.0, 8.0, 7.0, 6.0]
for iloc, xval in enumerate(values):
self.assertAlmostEqual(expected[iloc],
utils.piecewise_linear_scalar(params, xval))
# Odd-number of values in parameters - raise value error
params = [2.0, -1.0, 5.0, 0.0, 3.4]
with self.assertRaises(ValueError):
utils.piecewise_linear_scalar(params, 1.0)
# Single segment test
params1seg = [2.0, 0.0]
self.assertAlmostEqual(2.0,
utils.piecewise_linear_scalar(params1seg, 1.0))
# 3- segment test
params = np.array([2.0, -1.0, 3.0, 4.0, 8.0, 0.0])
expected = [0.0, 2.0, 4.0, 6.0, 8.0, 7.0, 6.0, 5.0, 4.0, 7.0]
for iloc, xval in enumerate(values):
self.assertAlmostEqual(expected[iloc],
utils.piecewise_linear_scalar(params, xval))
def test_piecewise_linear_function(self):
'''Test the piecewise linear calculator'''
# Good parameter set - 2 segments
params = [2.0, -1.0, 5.0, 0.0]
values = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0]
expected = [0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 9.0, 8.0, 7.0, 6.0]
for iloc, xval in enumerate(values):
self.assertAlmostEqual(expected[iloc],
utils.piecewise_linear_scalar(params, xval))
# Odd-number of values in parameters - raise value error
params = [2.0, -1.0, 5.0, 0.0, 3.4]
with self.assertRaises(ValueError):
utils.piecewise_linear_scalar(params, 1.0)
# Single segment test
params1seg = [2.0, 0.0]
self.assertAlmostEqual(2.0,
utils.piecewise_linear_scalar(params1seg, 1.0))
# 3- segment test
params = np.array([2.0, -1.0, 3.0, 4.0, 8.0, 0.0])
expected = [0.0, 2.0, 4.0, 6.0, 8.0, 7.0, 6.0, 5.0, 4.0, 7.0]
for iloc, xval in enumerate(values):
self.assertAlmostEqual(expected[iloc],
utils.piecewise_linear_scalar(params, xval))