def test_correlation_small_uncertainty(self):
imt = SA(period=1.5, damping=5)
cormo = HM2018CorrelationModel(uncertainty_multiplier=0)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
cormo2 = HM2018CorrelationModel(uncertainty_multiplier=1E-30)
corma2 = cormo2._get_correlation_matrix(self.SITECOL, imt)
self.assertTrue((corma == corma2).all())
def test_correlation_with_uncertainty(self):
Nsim = 100000
cormo = HM2018CorrelationModel(uncertainty_multiplier=1)
imt = SA(period=3, damping=5)
corma_3d = numpy.zeros((len(self.SITECOL), len(self.SITECOL), Nsim))
# For each simulation, construct a new correlation matrix
for isim in range(0, Nsim):
corma_3d[0:, 0:, isim] = \
cormo._get_correlation_matrix(self.SITECOL, imt)
# Mean and Coefficient of Variation (COV) of correlation matrix
MEANcorMa = corma_3d.mean(2)
COVcorma = numpy.divide(corma_3d.std(2), MEANcorMa)
aaae(MEANcorMa,[[1.0000000, 0.3766436, 1.0000000, 0.3766436,],
[0.3766436, 1.0000000, 0.3766436, 0.2534904,],
[1.0000000, 0.3766436, 1.0000000, 0.3766436,],
[0.3766436, 0.2534904, 0.3766436, 1.00000,]], 2)
aaae(COVcorma,[[0.0000000, 0.4102512, 0.0000000, 0.4102512,],
[0.4102512, 0.0000000, 0.4102512, 0.5636907,],
[0.0000000, 0.4102512, 0.0000000, 0.4102512,],
[0.4102512, 0.5636907, 0.4102512, 0.00000,]], 2)
def test_pga_no_uncertainty(self):
sa = SA(period=1e-50, damping=5)
pga = PGA()
cormo = HM2018CorrelationModel(uncertainty_multiplier=0)
corma = cormo._get_correlation_matrix(self.SITECOL, sa)
corma2 = cormo._get_correlation_matrix(self.SITECOL, pga)
self.assertTrue((corma == corma2).all())
def test_correlation_no_uncertainty(self):
cormo = HM2018CorrelationModel(uncertainty_multiplier=0)
imt = SA(period=0.1, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.3981537, 1.0000000, 0.3981537],
[0.3981537, 1.0000000, 0.3981537, 0.2596809],
[1.0000000, 0.3981537, 1.0000000, 0.3981537],
[0.3981537, 0.2596809, 0.3981537, 1.0000000]])
imt = SA(period=0.5, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.3809173, 1.0000000, 0.3809173],
[0.3809173, 1.0000000, 0.3809173, 0.2433886],
[1.0000000, 0.3809173, 1.0000000, 0.3809173],
[0.3809173, 0.2433886, 0.3809173, 1.0000000]])
imt = SA(period=1, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.3906193, 1.0000000, 0.3906193],
[0.3906193, 1.0000000, 0.3906193, 0.2525181],
[1.0000000, 0.3906193, 1.0000000, 0.3906193],
[0.3906193, 0.2525181, 0.3906193, 1.0000000]])
imt = SA(period=2, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.4011851, 1.0000000, 0.4011851],
[0.4011851, 1.0000000, 0.4011851, 0.2625807],
[1.0000000, 0.4011851, 1.0000000, 0.4011851],
[0.4011851, 0.2625807, 0.4011851, 1.0000000]])
imt = SA(period=4, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.3522765, 1.0000000, 0.3522765],
[0.3522765, 1.0000000, 0.3522765, 0.2170695],
[1.0000000, 0.3522765, 1.0000000, 0.3522765],
[0.3522765, 0.2170695, 0.3522765, 1.0000000]])
imt = SA(period=6, damping=5)
corma = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(corma, [[1.0000000, 0.3159779, 1.0000000, 0.3159779],
[0.3159779, 1.0000000, 0.3159779, 0.1851206],
[1.0000000, 0.3159779, 1.0000000, 0.3159779],
[0.3159779, 0.1851206, 0.3159779, 1.0000000]])
def test_with_uncertainty(self):
numpy.random.seed(1)
Nsim = 100000
imt = SA(period=3.0, damping=5)
stddev_intra = numpy.array([0.3, 0.6, 0.9])
cormo = HM2018CorrelationModel(uncertainty_multiplier=1)
intra_residuals_sampled = numpy.random.multivariate_normal(
numpy.zeros(3), numpy.diag(stddev_intra ** 2), Nsim).\
transpose(1, 0)
intra_residuals_correlated = cormo.apply_correlation(
self.SITECOL, imt, intra_residuals_sampled, stddev_intra)
inferred_corrcoef = numpy.corrcoef(intra_residuals_correlated)
mean = intra_residuals_correlated.mean(1)
std = intra_residuals_correlated.std(1)
aaae(numpy.squeeze(numpy.asarray(mean)), numpy.zeros(3), 2)
aaae(numpy.squeeze(numpy.asarray(std)), stddev_intra, 2)
aaae(inferred_corrcoef, [[1., 0.3807, 0.5066], [0.3807, 1., 0.3075],
[0.5066, 0.3075, 1.]], 2)
def test_no_uncertainty(self):
numpy.random.seed(1)
Nsim = 100000
imt = SA(period=2.0, damping=5)
stddev_intra = numpy.array([0.5, 0.6, 0.7])
cormo = HM2018CorrelationModel(uncertainty_multiplier=0)
intra_residuals_sampled = numpy.random.multivariate_normal(
numpy.zeros(3), numpy.diag(stddev_intra ** 2), Nsim).\
transpose(1, 0)
intra_residuals_correlated = cormo.apply_correlation(
self.SITECOL, imt, intra_residuals_sampled, stddev_intra)
inferred_corrcoef = numpy.corrcoef(intra_residuals_correlated)
mean = intra_residuals_correlated.mean(1)
std = intra_residuals_correlated.std(1)
aaae(numpy.squeeze(numpy.asarray(mean)), numpy.zeros(3), 2)
aaae(numpy.squeeze(numpy.asarray(std)), stddev_intra, 2)
actual_corrcoef = cormo._get_correlation_matrix(self.SITECOL, imt)
aaae(inferred_corrcoef, actual_corrcoef, 2)