def __init__(self,
storage_climatology,
storage_large_scale,
storage_local,
covariates_descriptor,
insitu_biases=False,
breakpoints_file=None,
global_biases=False,
global_biases_group_list=[],
compute_uncertainties=False,
method='EXACT',
compute_sample=False,
sample_size=definitions.GLOBAL_SAMPLE_SHAPE[3],
compute_prior_sample=False):
super(AnalysisSystem_EUSTACE,
self).__init__(components=[
SpaceTimeComponent(
ClimatologyDefinition(covariates_descriptor),
storage_climatology, True, compute_uncertainties, method,
compute_sample, sample_size, compute_prior_sample),
SpaceTimeComponent(
LargeScaleDefinition(insitu_biases, breakpoints_file),
storage_large_scale, True, compute_uncertainties, method,
compute_sample, sample_size, compute_prior_sample),
SpatialComponent(
LocalDefinition(global_biases, global_biases_group_list),
storage_local, compute_uncertainties, method,
compute_sample, sample_size, compute_prior_sample)
],
observable=ObservationSource.TMEAN)
def run_prior_solve():
componentstorage = TestComponentDefinition()
solutionstorage = SpaceTimeComponentSolutionStorage_InMemory()
printstats=True
compute_uncertainties = False
method='EXACT'
compute_sample=False
sample_size=1
compute_prior_sample=True
component = SpaceTimeComponent(componentstorage, solutionstorage, printstats, compute_uncertainties, method, compute_sample, sample_size, compute_prior_sample)
component_solution = component.component_solution()
component_solution.update()
def test_process_observations_compute_sample(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
number_of_samples = 200
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_sample=True,
sample_size=number_of_samples)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertTrue(s.compute_sample)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
numpy.random.seed(0)
s.update()
# In this case we are considering the last iteration of model solving, hence sample should have been stored
computed_sample = s.solutionstorage.state_sample
self.assertEqual((2, number_of_samples), computed_sample.shape)
numpy.random.seed(0)
variate = scipy.random.normal(0.0, 1.0, (2, number_of_samples))
expected_posterior_precision = numpy.array([[13.25, -16.5],
[-16.5, 80.65]])
# check result
numpy.testing.assert_almost_equal(
numpy.dot(variate.T, variate),
numpy.dot(computed_sample.T,
numpy.dot(expected_posterior_precision,
computed_sample)))
def __init__(self):
# Build analysis system by referencing the global variables
# In distributed computing we would construct these using classes that load from file
super(AnalysisSystem_HadCRUT4_InMemory,
self).__init__(components=[
SpaceTimeComponent(HadCRUT4_InMemory.definition_climatology,
HadCRUT4_InMemory.solution_climatology),
SpaceTimeComponent(HadCRUT4_InMemory.definition_large_scale,
HadCRUT4_InMemory.solution_large_scale),
SpatialComponent(HadCRUT4_InMemory.definition_local,
HadCRUT4_InMemory.solution_local)
],
observable=ObservationSource.TMEAN)
def __init__(self,
storage_climatology,
storage_large_scale,
storage_local_bias,
storage_region_spde,
covariates_descriptor,
insitu_biases=False,
breakpoints_file=None,
global_biases=False,
global_biases_group_list=[],
compute_uncertainties=False,
method='EXACT',
compute_sample=False,
sample_size=definitions.GLOBAL_SAMPLE_SHAPE[3],
neighbourhood_level=0,
region_index=0,
regionspec='LocalSubRegion'):
# initialise the OptimizationSystem
super(RegionOptimizationSystem_EUSTACE,
self).__init__(components=[
SpaceTimeComponent(
ClimatologyDefinition(covariates_descriptor),
storage_climatology, True, compute_uncertainties, method,
compute_sample, sample_size),
SpaceTimeComponent(
LargeScaleDefinition(insitu_biases, breakpoints_file),
storage_large_scale, True, compute_uncertainties, method,
compute_sample, sample_size),
SpatialComponent(
PureBiasComponentDefinition(global_biases,
global_biases_group_list),
storage_local_bias, compute_uncertainties, method,
compute_sample, sample_size),
DelayedSpatialComponent(
LocalViewDefinition(neighbourhood_level, region_index,
regionspec), storage_region_spde,
compute_uncertainties, method, compute_sample,
sample_size)
],
observable=ObservationSource.TMEAN)
def main():
print 'Advanced standard example using a few days of EUSTACE data'
parser = argparse.ArgumentParser(description='Advanced standard example using a few days of EUSTACE data')
parser.add_argument('outpath', help='directory where the output should be redirected')
parser.add_argument('--json_descriptor', default = None, help='a json descriptor containing the covariates to include in the climatology model')
parser.add_argument('--land_biases', action='store_true', help='include insitu land homogenization bias terms')
parser.add_argument('--global_biases', action='store_true', help='include global satellite bias terms')
parser.add_argument('--n_iterations', type=int, default=5, help='number of solving iterations')
args = parser.parse_args()
# Input data path
basepath = os.path.join('/work/scratch/eustace/rawbinary3')
# Days to process
time_indices = range(int(days_since_epoch(datetime(2006, 2, 1))), int(days_since_epoch(datetime(2006, 2, 2))))
# Sources to use
sources = [ 'surfaceairmodel_land', 'surfaceairmodel_ocean', 'surfaceairmodel_ice', 'insitu_land', 'insitu_ocean' ]
#SETUP
# setup for the seasonal core: climatology covariates setup read from file
seasonal_setup = {'n_triangulation_divisions':5,
'n_harmonics':4,
'n_spatial_components':6,
'amplitude':2.,
'space_length_scale':5., # length scale in units of degrees
}
grandmean_amplitude = 15.0
# setup for the large scale component
spacetime_setup = {'n_triangulation_divisions':2,
'alpha':2,
'starttime':0,
'endtime':10.,
'n_nodes':2,
'overlap_factor':2.5,
'H':1,
'amplitude':1.,
'space_lenght_scale':15.0, # length scale in units of degrees
'time_length_scale':15.0 # length scal in units of days
}
bias_amplitude = .9
# setup for the local component
local_setup = {'n_triangulation_divisions':6,
'amplitude':2.,
'space_length_scale':2. # length scale in units of degrees
}
globalbias_amplitude = 15.0
# CLIMATOLOGY COMPONENT: combining the seasonal core along with latitude harmonics, altitude and coastal effects
if args.json_descriptor is not None:
loader = LoadCovariateElement(args.json_descriptor)
loader.check_keys()
covariate_elements, covariate_hyperparameters = loader.load_covariates_and_hyperparameters()
print('The following fields have been added as covariates of the climatology model')
print(loader.data.keys())
else:
covariate_elements, covariate_hyperparameters = [], []
climatology_element = CombinationElement( [SeasonalElement(n_triangulation_divisions=seasonal_setup['n_triangulation_divisions'],
n_harmonics=seasonal_setup['n_harmonics'],
include_local_mean=True),
GrandMeanElement()]+covariate_elements)
climatology_hyperparameters = CombinationHyperparameters( [SeasonalHyperparameters(n_spatial_components=seasonal_setup['n_spatial_components'],
common_log_sigma=numpy.log(seasonal_setup['amplitude']),
common_log_rho=numpy.log(numpy.radians(seasonal_setup['space_length_scale']))),
CovariateHyperparameters(numpy.log(grandmean_amplitude))] + covariate_hyperparameters )
climatology_component = SpaceTimeComponent(ComponentStorage_InMemory(climatology_element, climatology_hyperparameters), SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True, method='APPROXIMATED',
compute_sample=True, sample_size=definitions.GLOBAL_SAMPLE_SHAPE[3])
# LARGE SCALE (kronecker product) COMPONENT: combining large scale trends with bias terms accounting for homogeneization effects
if args.land_biases:
bias_element, bias_hyperparameters = [InsituLandBiasElement(BREAKPOINTS_FILE)], [CovariateHyperparameters(numpy.log(bias_amplitude))]
print('Adding bias terms for insitu land homogenization')
else:
bias_element, bias_hyperparameters = [], []
large_scale_element = CombinationElement( [SpaceTimeKroneckerElement(n_triangulation_divisions=spacetime_setup['n_triangulation_divisions'],
alpha=spacetime_setup['alpha'],
starttime=spacetime_setup['starttime'],
endtime=spacetime_setup['endtime'],
n_nodes=spacetime_setup['n_nodes'],
overlap_factor=spacetime_setup['overlap_factor'],
H=spacetime_setup['H'])] + bias_element)
large_scale_hyperparameters = CombinationHyperparameters( [SpaceTimeSPDEHyperparameters(space_log_sigma=numpy.log(spacetime_setup['amplitude']),
space_log_rho=numpy.log(numpy.radians(spacetime_setup['space_lenght_scale'])),
time_log_rho=numpy.log(spacetime_setup['time_length_scale']))] + bias_hyperparameters)
large_scale_component = SpaceTimeComponent(ComponentStorage_InMemory(large_scale_element, large_scale_hyperparameters), SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True, method='APPROXIMATED',
compute_sample=True, sample_size=definitions.GLOBAL_SAMPLE_SHAPE[3])
# LOCAL COMPONENT: combining local scale variations with global satellite bias terms
if args.global_biases:
bias_elements = [BiasElement(groupname, 1) for groupname in GLOBAL_BIASES_GROUP_LIST]
bias_hyperparameters = [CovariateHyperparameters(numpy.log(globalbias_amplitude)) for index in range(len(GLOBAL_BIASES_GROUP_LIST))]
print('Adding global bias terms for all the surfaces')
else:
bias_elements, bias_hyperparameters = [], []
local_scale_element = CombinationElement([LocalElement(n_triangulation_divisions=local_setup['n_triangulation_divisions'])] + bias_elements)
local_scale_hyperparameters = CombinationHyperparameters([LocalHyperparameters(log_sigma=numpy.log(local_setup['amplitude']),
log_rho=numpy.log(numpy.radians(local_setup['space_length_scale'])))] + bias_hyperparameters)
local_component = SpatialComponent(ComponentStorage_InMemory(local_scale_element, local_scale_hyperparameters), SpatialComponentSolutionStorage_InMemory(),
compute_uncertainties=True, method='APPROXIMATED',
compute_sample=True, sample_size=definitions.GLOBAL_SAMPLE_SHAPE[3])
# Analysis system using the specified components, for the Tmean observable
print 'Analysing inputs'
analysis_system = AnalysisSystem(
[ climatology_component, large_scale_component, local_component ],
ObservationSource.TMEAN)
# Object to load raw binary inputs at time indices
inputloaders = [ AnalysisSystemInputLoaderRawBinary_Sources(basepath, source, time_indices) for source in sources ]
for iteration in range(args.n_iterations):
message = 'Iteration {}'.format(iteration)
print(message)
# Update with data
analysis_system.update(inputloaders, time_indices)
print 'Computing outputs'
# Produce an output for each time index
for time_index in time_indices:
# Get date for output
outputdate = inputloaders[0].datetime_at_time_index(time_index)
print 'Evaluating output grid: ', outputdate
#Configure output grid
outputstructure = OutputRectilinearGridStructure(
time_index, outputdate,
latitudes=numpy.linspace(-90.+definitions.GLOBAL_FIELD_RESOLUTION/2., 90.-definitions.GLOBAL_FIELD_RESOLUTION/2., num=definitions.GLOBAL_FIELD_SHAPE[1]),
longitudes=numpy.linspace(-180.+definitions.GLOBAL_FIELD_RESOLUTION/2., 180.-definitions.GLOBAL_FIELD_RESOLUTION/2., num=definitions.GLOBAL_FIELD_SHAPE[2]))
# Evaluate expected value at these locations
for field in ['MAP', 'post_STD']:
print 'Evaluating: ',field
result_expected_value = analysis_system.evaluate_expected_value('MAP', outputstructure, 'GRID_CELL_AREA_AVERAGE', [1,1], 1000)
result_expected_uncertainties = analysis_system.evaluate_expected_value('post_STD', outputstructure, 'GRID_CELL_AREA_AVERAGE', [1,1], 1000)
print 'Evaluating: climatology fraction'
climatology_fraction = analysis_system.evaluate_climatology_fraction(outputstructure, [1,1], 1000)
print 'Evaluating: the sample'
sample = analysis_system.evaluate_projected_sample(outputstructure)
# Make output filename
pathname = 'eustace_example_output_{0:04d}{1:02d}{2:02d}.nc'.format(outputdate.year, outputdate.month, outputdate.day)
pathname = os.path.join(args.outpath, pathname)
print 'Saving: ', pathname
# Save results
filebuilder = FileBuilderGlobalField(
pathname,
time_index,
'Infilling Example',
'UNVERSIONED',
definitions.TAS.name,
'',
'Example data only',
'eustace.analysis.advanced_standard.examples.example_eustace_few_days',
'')
filebuilder.add_global_field(definitions.TAS, result_expected_value.reshape(definitions.GLOBAL_FIELD_SHAPE))
filebuilder.add_global_field(definitions.TASUNCERTAINTY, result_expected_uncertainties.reshape(definitions.GLOBAL_FIELD_SHAPE))
filebuilder.add_global_field(definitions.TAS_CLIMATOLOGY_FRACTION, climatology_fraction.reshape(definitions.GLOBAL_FIELD_SHAPE))
for index in range(definitions.GLOBAL_SAMPLE_SHAPE[3]):
variable = copy.deepcopy(definitions.TASENSEMBLE)
variable.name = variable.name + '_' + str(index)
selected_sample = sample[:,index].ravel()+result_expected_value
filebuilder.add_global_field(variable, selected_sample.reshape(definitions.GLOBAL_FIELD_SHAPE))
filebuilder.save_and_close()
print 'Complete'
def test_mini_world_large_and_local(self):
# Use a number of time steps
number_of_simulated_time_steps = 30
# Large-scale spatial variability
simulated_large_variation = 10.0
# Local variability
simulated_local_variation = 1.0
# Iterations to use
number_of_solution_iterations = 5
# Build system
# Large-scale factor
element_large = SpaceTimeKroneckerElement(
n_triangulation_divisions=1,
alpha=2,
starttime=0,
endtime=number_of_simulated_time_steps + 1,
n_nodes=number_of_simulated_time_steps + 2,
overlap_factor=2.5,
H=1)
initial_hyperparameters_large = SpaceTimeSPDEHyperparameters(
space_log_sigma=0.0,
space_log_rho=numpy.log(numpy.radians(5.0)),
time_log_rho=numpy.log(1.0 / 365.0))
component_large = SpaceTimeComponent(
ComponentStorage_InMemory(element_large,
initial_hyperparameters_large),
SpaceTimeComponentSolutionStorage_InMemory())
# And a local process
component_local = SpatialComponent(
ComponentStorage_InMemory(
LocalElement(n_triangulation_divisions=3),
LocalHyperparameters(log_sigma=0.0,
log_rho=numpy.log(numpy.radians(5.0)))),
SpatialComponentSolutionStorage_InMemory())
analysis_system = AnalysisSystem([component_large, component_local],
ObservationSource.TMEAN,
log=StringIO())
# analysis_system = AnalysisSystem([ component_large ], ObservationSource.TMEAN)
# analysis_system = AnalysisSystem([ component_local ], ObservationSource.TMEAN)
# use fixed locations from icosahedron
fixed_locations = cartesian_to_polar2d(
MeshIcosahedronSubdivision.build(3).points)
# random measurement at each location
numpy.random.seed(8976)
field_basis = simulated_large_variation * numpy.random.randn(
fixed_locations.shape[0])
# some time function that varies over a year
time_basis = numpy.cos(
numpy.linspace(0.1, 1.75 * numpy.pi,
number_of_simulated_time_steps))
# kronecker product of the two
large_scale_process = numpy.kron(field_basis,
numpy.expand_dims(time_basis, 1))
# Random local changes where mean change at each time is zero
# local_process = simulated_local_variation * numpy.random.randn(large_scale_process.shape[0], large_scale_process.shape[1])
# local_process -= numpy.tile(local_process.mean(axis=1), (local_process.shape[1], 1)).T
local_process = numpy.zeros(large_scale_process.shape)
somefield = simulated_local_variation * numpy.random.randn(
1, large_scale_process.shape[1])
somefield -= somefield.ravel().mean()
local_process[10, :] = somefield
local_process[11, :] = -somefield
# Add the two processes
measurement = large_scale_process + local_process
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(fixed_locations,
measurement, 0.001)
# Simulate evaluation of this time index
simulated_time_indices = range(number_of_simulated_time_steps)
# All systems linear so single update should be ok
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Get all results
result = numpy.zeros(measurement.shape)
for t in range(number_of_simulated_time_steps):
result[t, :] = analysis_system.evaluate_expected_value(
'MAP',
SimulatedObservationStructure(t, fixed_locations, None, None),
flag='POINTWISE')
disparity_large_scale = (numpy.abs(result -
large_scale_process)).ravel().max()
# print 'large scale disparity: ', disparity_large_scale
disparity_overall = (numpy.abs(result - measurement)).ravel().max()
# print 'overall disparity: ', disparity_overall
numpy.testing.assert_almost_equal(result, measurement, decimal=4)
self.assertTrue(disparity_overall < 1E-4)
def test_mini_world_noiseless(self):
number_of_simulated_time_steps = 1
# Build system
element = SeasonalElement(n_triangulation_divisions=3,
n_harmonics=5,
include_local_mean=True)
hyperparameters = SeasonalHyperparameters(n_spatial_components=6,
common_log_sigma=0.0,
common_log_rho=0.0)
component = SpaceTimeComponent(
ComponentStorage_InMemory(element, hyperparameters),
SpaceTimeComponentSolutionStorage_InMemory())
analysis_system = AnalysisSystem([component],
ObservationSource.TMEAN,
log=StringIO())
# use fixed locations from icosahedron
fixed_locations = cartesian_to_polar2d(
MeshIcosahedronSubdivision.build(3).points)
# random measurement at each location
numpy.random.seed(8976)
field_basis = numpy.random.randn(fixed_locations.shape[0])
#print(field_basis.shape)
#time_basis = numpy.array(harmonics_list)
# some time function that varies over a year
#decimal_years = numpy.array([datetime_to_decimal_year(epoch_plus_days(step)) for step in range(number_of_simulated_time_steps)])
time_basis = numpy.cos(
numpy.linspace(0.1, 1.75 * numpy.pi,
number_of_simulated_time_steps))
# kronecker product of the two
#print(numpy.expand_dims(time_basis, 1))
measurement = numpy.kron(field_basis, numpy.expand_dims(
time_basis, 1)) #numpy.expand_dims(time_basis, 1))
#print(measurement.shape)
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(fixed_locations,
measurement, 0.0001)
# Simulate evaluation of this time index
simulated_time_indices = range(number_of_simulated_time_steps)
# Iterate
for iteration in range(5):
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Get all results
result = numpy.zeros(measurement.shape)
for t in range(number_of_simulated_time_steps):
result[t, :] = analysis_system.evaluate_expected_value(
'MAP',
SimulatedObservationStructure(t, fixed_locations, None, None),
flag='POINTWISE')
# Should be very close to original because specified noise is low
numpy.testing.assert_almost_equal(result, measurement)
max_disparity = (numpy.abs(result - measurement)).ravel().max()
self.assertTrue(max_disparity < 1E-5)
# test output gridding, pointwise limit
outputstructure = OutputRectilinearGridStructure(
2,
epoch_plus_days(2),
latitudes=numpy.linspace(-60., 60., num=5),
longitudes=numpy.linspace(-90., 90, num=10))
pointwise_result = analysis_system.evaluate_expected_value(
'MAP', outputstructure, 'POINTWISE')
pointwise_limit_result = analysis_system.evaluate_expected_value(
'MAP', outputstructure, 'GRID_CELL_AREA_AVERAGE', [1, 1], 10)
numpy.testing.assert_array_almost_equal(pointwise_result,
pointwise_limit_result)
def test_mini_world_noiseless(self):
# Use a number of time steps
number_of_simulated_time_steps = 1
# Build system
element = SpaceTimeFactorElement(
n_triangulation_divisions=3,
alpha=2,
starttime=0,
endtime=number_of_simulated_time_steps + 1,
n_nodes=number_of_simulated_time_steps + 2,
overlap_factor=2.5,
H=1)
initial_hyperparameters = SpaceTimeSPDEHyperparameters(
space_log_sigma=0.0,
space_log_rho=numpy.log(numpy.radians(45.0)),
time_log_rho=numpy.log(3.0 / 365.0))
component = SpaceTimeComponent(
ComponentStorage_InMemory(element, initial_hyperparameters),
SpaceTimeComponentSolutionStorage_InMemory())
analysis_system = AnalysisSystem([component],
ObservationSource.TMEAN,
log=StringIO())
# use fixed locations from icosahedron
fixed_locations = cartesian_to_polar2d(
MeshIcosahedronSubdivision.build(3).points)
# random measurement at each location
numpy.random.seed(8976)
field_basis = 10.0 * numpy.random.randn(fixed_locations.shape[0])
# some time function that varies over a year
time_basis = numpy.cos(
numpy.linspace(0.1, 1.75 * numpy.pi,
number_of_simulated_time_steps))
# kronecker product of the two
measurement = numpy.kron(field_basis, numpy.expand_dims(time_basis, 1))
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(fixed_locations,
measurement, 0.01)
# Simulate evaluation of this time index
simulated_time_indices = range(number_of_simulated_time_steps)
# Iterate
for iteration in range(5):
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Get all results
result = numpy.zeros(measurement.shape)
for t in range(number_of_simulated_time_steps):
result[t, :] = analysis_system.evaluate_expected_value(
'MAP',
SimulatedObservationStructure(t, fixed_locations, None, None),
flag='POINTWISE')
# Should be very close to original because specified noise is low
numpy.testing.assert_almost_equal(result, measurement)
max_disparity = (numpy.abs(result - measurement)).ravel().max()
self.assertTrue(max_disparity < 1E-5)
def main():
print 'EUSTACE example using HadCRUT4 monthly data'
# Input data path
input_basepath = os.path.join(WORKSPACE_PATH, 'data/incoming/HadCRUT4.5.0.0')
# Input filenames
input_filenames = [
'hadcrut4_median_netcdf.nc',
'hadcrut4_uncorrelated_supplementary.nc',
'hadcrut4_blended_uncorrelated.nc' ]
# Months to process
time_indices = range(2)
# Climatology component
climatology_component = SpaceTimeComponent(ComponentStorage_InMemory(SeasonalElement(n_triangulation_divisions=5, n_harmonics=5, include_local_mean=True),
SeasonalHyperparameters(n_spatial_components=6, common_log_sigma=1.0, common_log_rho=0.0)),
SpaceTimeComponentSolutionStorage_InMemory())
# Number of factors for large scale (factor analysis) component and initial hyperparameters
n_factors = 5
factors = [ ]
factor_hyperparameters = [ ]
for factor_index in range(n_factors):
factor_hyperparameters.append( SpaceTimeSPDEHyperparameters(
space_log_sigma=0.0,
space_log_rho=numpy.log(10.0 * numpy.pi/180 + 25.0 * numpy.pi/180 *(n_factors - factor_index) / n_factors),
time_log_rho=numpy.log(1/12.0 + 6/12.0*(n_factors - factor_index) / n_factors)) )
factors.append( SpaceTimeFactorElement(n_triangulation_divisions=5, alpha=2, starttime=0, endtime=36, overlap_factor=2.5, H=1) )
# Large scale (factor analysis) component
large_scale_component = SpaceTimeComponent(ComponentStorage_InMemory(CombinationElement(factors), CombinationHyperparameters(factor_hyperparameters)),
SpaceTimeComponentSolutionStorage_InMemory())
# Local component
local_component = SpatialComponent(ComponentStorage_InMemory(LocalElement(n_triangulation_divisions=4),
LocalHyperparameters(log_sigma=0.0, log_rho=numpy.log(10.0 * numpy.pi/180))),
SpatialComponentSolutionStorage_InMemory())
print 'Analysing inputs'
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem(
[ climatology_component, large_scale_component, local_component ],
ObservationSource.TMEAN)
# Make filelist
input_filelist = [ os.path.join(input_basepath, filename) for filename in input_filenames ]
# Object to load HadCRUT4 inputs at time indices
inputloader = AnalysisSystemInputLoaderHadCRUT4(input_filelist)
# Update with data
analysis_system.update([ inputloader ], time_indices)
print 'Computing outputs'
# Produce an output for each time index
for time_index in time_indices:
# Make output filename
outputdate = inputloader.datetime_at_time_index(time_index)
pathname = 'example_output_{0:04d}{1:02d}.nc'.format(outputdate.year, outputdate.month)
print 'Saving: ', pathname
# Configure output grid
outputstructure = OutputRectilinearGridStructure(
time_index, outputdate,
latitudes=numpy.linspace(-87.5, 87.5, num=36),
longitudes=numpy.linspace(-177.5, 177.5, num=72))
# Evaluate expected value at these locations
result_expected_value = analysis_system.evaluate_expected_value(outputstructure)
# Save results
filebuilder = FileBuilderHadCRUT4ExampleOutput(pathname, outputstructure)
filebuilder.add_global_field(TAS_ANOMALY, result_expected_value.reshape(1,36,72))
filebuilder.save_and_close()
print 'Complete'
def test_process_observations_no_uncertainties(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
sample_size=666)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertFalse(s.compute_uncertainties)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
s.update()
numpy.testing.assert_almost_equal(
s.solutionstorage.state, numpy.array([-0.60697861, 1.78530506]))
# No marginal variances should have been computed at all, same for the sample
self.assertEqual(None, s.solutionstorage.state_marginal_std)
self.assertEqual(None, s.solutionstorage.state_sample)
for time, expected_array in zip([21, 532], [
numpy.array([-1.5 * -0.60697861 + 2.2 * 1.78530506]),
numpy.array([3.3 * 1.78530506])
]):
# Observation at time t=t* should be design matrix for that time multiplied by expected state
numpy.testing.assert_almost_equal(
s.solution_observation_expected_value(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
expected_array)
# In this case we are considering a generical model solving iteration for the model, no marginal variances stored, hence we expect 0. as observation uncertainties
numpy.testing.assert_array_equal(
s.solution_observation_expected_uncertainties(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
0.)
# check samples are zero
numpy.testing.assert_array_equal(
0.,
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(t=time)))
# check default number of samples
self.assertEqual(
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(
t=time)).shape[1], 666)
def test_process_observations_compute_uncertainties(self):
# Our test system is:
#
# ( [ 2.0 0.0 ] + [ -1.5 0.0 ] [ 5.0 0.0 ] [ -1.5 2.2 ] ) x = [ -1.5 0.0 ] [ 10.0 3.0 ] [ 7.0 - 2.0 ]
# ( [ 0.0 2.0 ] [ 2.2 3.3 ] [ 0.0 5.0 ] [ 0.0 3.3 ] ) [ 2.2 3.3 ] [ 3.0 10.0 ] [ 9.0 - 3.0 ]
#
# [ 13.25 -16.5 ] x = [ -37.5 ]
# [-16.5 80.65 ] [ 154.0 ]
#
# => x = [ -0.60697861 ]
# [ 1.78530506 ]
#
c = SpaceTimeComponent(ComponentStorage_InMemory(
TestSpaceTimeComponentSolution.TestElement(),
CovariateHyperparameters(-0.5 * numpy.log(2.0))),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True)
s = c.component_solution()
self.assertIsInstance(s, SpaceTimeComponentSolution)
self.assertTrue(s.compute_uncertainties)
test_offset = numpy.array([2.0, 3.0])
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=21),
test_offset[0:1])
s.update_time_step()
s.process_observations(
TestSpaceTimeComponentSolution.TestObservations(t=532),
test_offset[1:2])
s.update_time_step()
s.update()
# No sample should have been computed at all
self.assertEqual(None, s.solutionstorage.state_sample)
# In this case we are considering the last iteration of model solving, hence marginal variances should have been stored
expected_marginal_std = numpy.sqrt(
numpy.diag(
numpy.linalg.inv(numpy.array([[13.25, -16.5], [-16.5,
80.65]]))))
numpy.testing.assert_array_almost_equal(
s.solutionstorage.state_marginal_std, expected_marginal_std)
# Now we compute the projection of marginal variances onto the given observations
for time in [532]:
# Observation at time t=t* should be design matrix for that time multiplied by expected state
expected_projection = TestSpaceTimeComponentSolution.TestDesign(
t=time).design_function(expected_marginal_std)
numpy.testing.assert_almost_equal(
s.solution_observation_expected_uncertainties(
TestSpaceTimeComponentSolution.TestObservations(t=time)),
expected_projection)
# check samples are zero
numpy.testing.assert_array_equal(
0.,
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(t=time)))
# check default number of samples
self.assertEqual(
s.solution_observation_projected_sample(
TestSpaceTimeComponentSolution.TestObservations(
t=time)).shape[1], 1)
def main():
print 'Advanced standard example using a few days of EUSTACE data'
parser = argparse.ArgumentParser(
description='Advanced standard example using a few days of EUSTACE data'
)
parser.add_argument('outpath',
help='directory where the output should be redirected')
parser.add_argument(
'--json_descriptor',
default=None,
help=
'a json descriptor containing the covariates to include in the climatology model'
)
parser.add_argument('--land_biases',
action='store_true',
help='include insitu land homogenization bias terms')
parser.add_argument('--global_biases',
action='store_true',
help='include global satellite bias terms')
parser.add_argument('--n_iterations',
type=int,
default=5,
help='number of solving iterations')
args = parser.parse_args()
# Input data path
basepath = os.path.join('/work/scratch/eustace/rawbinary3')
# Days to process
#time_indices = range(int(days_since_epoch(datetime(2006, 2, 1))), int(days_since_epoch(datetime(2006, 2, 2))))
#time_indices = range(int(days_since_epoch(datetime(1906, 2, 1))), int(days_since_epoch(datetime(1906, 2, 2))))
date_list = [
datetime(2006, 1, 1) + relativedelta(days=k) for k in range(3)
]
#backwards_list = [date_list[i] for i in range(11, -1, -1)]
#date_list = backwards_list
time_indices = [int(days_since_epoch(date)) for date in date_list]
# Sources to use
sources = [
'surfaceairmodel_land', 'surfaceairmodel_ocean', 'surfaceairmodel_ice',
'insitu_land', 'insitu_ocean'
]
sources = ['insitu_land', 'insitu_ocean']
#sources = [ 'surfaceairmodel_land' ]
# CLIMATOLOGY COMPONENT: combining the seasonal core along with latitude harmonics, altitude and coastal effects
if args.json_descriptor is not None:
loader = LoadCovariateElement(args.json_descriptor)
loader.check_keys()
covariate_elements, covariate_hyperparameters = loader.load_covariates_and_hyperparameters(
)
print(
'The following fields have been added as covariates of the climatology model'
)
print(loader.data.keys())
else:
covariate_elements, covariate_hyperparameters = [], []
#climatology_element = CombinationElement( [SeasonalElement(n_triangulation_divisions=2, n_harmonics=2, include_local_mean=False), GrandMeanElement()]+covariate_elements)
#climatology_hyperparameters = CombinationHyperparameters( [SeasonalHyperparameters(n_spatial_components=2, common_log_sigma=0.0, common_log_rho=0.0), CovariateHyperparameters(numpy.log(15.0))] + covariate_hyperparameters )
climatology_element = CombinationElement([
GrandMeanElement(),
] + covariate_elements)
climatology_hyperparameters = CombinationHyperparameters([
CovariateHyperparameters(numpy.log(15.0)),
] + covariate_hyperparameters)
#climatology_element =SeasonalElement(n_triangulation_divisions=2, n_harmonics=2, include_local_mean=False)
#climatology_hyperparameters = SeasonalHyperparameters(n_spatial_components=2, common_log_sigma=0.0, common_log_rho=0.0)
climatology_component = SpaceTimeComponent(
ComponentStorage_InMemory(climatology_element,
climatology_hyperparameters),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True,
method='APPROXIMATED')
# LARGE SCALE (kronecker product) COMPONENT: combining large scale trends with bias terms accounting for homogeneization effects
if args.land_biases:
bias_element, bias_hyperparameters = [
InsituLandBiasElement(BREAKPOINTS_FILE)
], [CovariateHyperparameters(numpy.log(.9))]
print('Adding bias terms for insitu land homogenization')
else:
bias_element, bias_hyperparameters = [], []
large_scale_element = CombinationElement([
SpaceTimeKroneckerElement(n_triangulation_divisions=2,
alpha=2,
starttime=-30,
endtime=365 * 1 + 30,
n_nodes=12 * 1 + 2,
overlap_factor=2.5,
H=1)
] + bias_element)
large_scale_hyperparameters = CombinationHyperparameters([
SpaceTimeSPDEHyperparameters(space_log_sigma=0.0,
space_log_rho=numpy.log(
numpy.radians(15.0)),
time_log_rho=numpy.log(15.0))
] + bias_hyperparameters)
large_scale_component = SpaceTimeComponent(
ComponentStorage_InMemory(large_scale_element,
large_scale_hyperparameters),
SpaceTimeComponentSolutionStorage_InMemory(),
compute_uncertainties=True,
method='APPROXIMATED')
# LOCAL COMPONENT: combining local scale variations with global satellite bias terms
if args.global_biases:
bias_elements = [
BiasElement(groupname, 1) for groupname in GLOBAL_BIASES_GROUP_LIST
]
bias_hyperparameters = [
CovariateHyperparameters(numpy.log(15.0)) for index in range(3)
]
print('Adding global bias terms for all the surfaces')
else:
bias_elements, bias_hyperparameters = [], []
n_triangulation_divisions_local = 7
local_log_sigma = numpy.log(5)
local_log_rho = numpy.log(numpy.radians(5.0))
local_element = NonStationaryLocal(
n_triangulation_divisions=n_triangulation_divisions_local)
n_local_nodes = local_element.spde.n_latent_variables()
local_scale_element = CombinationElement([local_element] + bias_elements)
local_hyperparameters = ExpandedLocalHyperparameters(
log_sigma=numpy.repeat(local_log_sigma, n_local_nodes),
log_rho=numpy.repeat(local_log_rho, n_local_nodes))
local_scale_hyperparameters = CombinationHyperparameters(
[local_hyperparameters] + bias_hyperparameters)
local_component = DelayedSpatialComponent(
ComponentStorage_InMemory(local_scale_element,
local_scale_hyperparameters),
SpatialComponentSolutionStorage_InMemory(),
compute_uncertainties=True,
method='APPROXIMATED')
print "hyperparameter storage:", local_component.storage.hyperparameters
print 'Analysing inputs'
# Analysis system using the specified components, for the Tmean observable
##analysis_system = AnalysisSystem(
## [ climatology_component, large_scale_component, local_component ],
## ObservationSource.TMEAN)
analysis_system = OptimizationSystem(
[climatology_component, local_component], ObservationSource.TMEAN)
# Object to load raw binary inputs at time indices
inputloaders = [
AnalysisSystemInputLoaderRawBinary_Sources(basepath, source,
time_indices)
for source in sources
]
for iteration in range(args.n_iterations):
message = 'Iteration {}'.format(iteration)
print(message)
# Update with data
analysis_system.update(inputloaders, time_indices)
##################################################
# Optimize local model hyperparameters
# Loop over local regions, generate optimization systems, fit hyperparameters and save
# split spde and bias models for local component into two components
global_spde_sub_component_definition = ComponentStorage_InMemory(
CombinationElement([local_element]),
CombinationHyperparameters([local_hyperparameters]))
global_spde_sub_component_storage_solution = SpatialComponentSolutionStorage_InMemory(
)
global_spde_sub_component = DelayedSpatialComponent(
global_spde_sub_component_definition,
global_spde_sub_component_storage_solution)
bias_sub_component_definition = ComponentStorage_InMemory(
CombinationElement(bias_elements),
CombinationHyperparameters(bias_hyperparameters))
bias_sub_component_storage_solution = SpatialComponentSolutionStorage_InMemory(
)
bias_sub_component = DelayedSpatialComponent(
bias_sub_component_definition, bias_sub_component_storage_solution)
element_optimisation_flags = [True, False, False,
False] # one spde, three biases
for time_key in time_indices:
split_states_time(local_component, global_spde_sub_component,
bias_sub_component, element_optimisation_flags,
time_key)
# Define subregions and extract their states
neighbourhood_level = 1
n_subregions = global_spde_sub_component.storage.element_read(
).combination[0].spde.n_triangles_at_level(neighbourhood_level)
hyperparameter_file_template = "local_hyperparameters.%i.%i.%i.npy"
fit_hyperparameters = True
optimization_component_index = 2
if fit_hyperparameters:
for region_index in range(n_subregions):
# Setup model for local subregion of neighours with super triangle
view_flags = [
True,
]
region_element = CombinationElement([
LocalSubRegion(n_triangulation_divisions_local,
neighbourhood_level, region_index)
])
region_hyperparameters = ExtendedCombinationHyperparameters([
LocalHyperparameters(log_sigma=local_log_sigma,
log_rho=local_log_rho)
])
region_component_storage_solution = SpatialComponentSolutionStorage_InMemory(
)
region_sub_component = DelayedSpatialComponent(
ComponentStorage_InMemory(region_element,
region_hyperparameters),
region_component_storage_solution)
for time_key in time_indices:
print "region_index, time_key:", region_index, time_key
extract_local_view_states_time(global_spde_sub_component,
region_sub_component,
view_flags, time_key)
print "running optimization for region:", region_index
region_optimization_system = OptimizationSystem([
climatology_component, bias_sub_component, region_sub_component
], ObservationSource.TMEAN)
for time_key in time_indices:
region_optimization_system.update_component_time(
inputloaders, optimization_component_index, time_key)
# commented version that works for few days inputs
#region_optimization_system.components[optimization_component_index].component_solution().optimize()
#region_optimization_system.components[optimization_component_index].storage.hyperparameters.get_array()
#hyperparameter_file = os.path.join(args.outpath, hyperparameter_file_template % (n_triangulation_divisions_local, neighbourhood_level, region_index) )
#region_sub_component.storage.hyperparameters.values_to_npy_savefile( hyperparameter_file )
# replaced with version for full processing based json dump of input files - need to generate the input_descriptor dict
hyperparameter_file = os.path.join(
args.outpath, hyperparameter_file_template %
(n_triangulation_divisions_local, neighbourhood_level,
region_index))
region_optimization_system.process_inputs(
input_descriptor, optimization_component_index, time_indices)
region_optimization_system.optimize_component(
optimization_component_index,
hyperparameter_storage_file=hyperparameter_file)
fitted_hyperparameters_converted = region_sub_component.storage.hyperparameters.get_array(
)
fitted_hyperparameters_converted[0] = numpy.exp(
fitted_hyperparameters_converted[0])
fitted_hyperparameters_converted[1] = numpy.exp(
fitted_hyperparameters_converted[1]) * 180.0 / numpy.pi
print 'fitted_hyperparameters_converted:', fitted_hyperparameters_converted
# Setup model for the super triangle without neighbours for hyperparameter merging
region_spdes = []
region_hyperparameter_values = []
for region_index in range(n_subregions):
# Redefine the region sub component as a supertriangle rather than a neighbourhood
region_element = CombinationElement([
LocalSuperTriangle(n_triangulation_divisions_local,
neighbourhood_level, region_index)
])
region_hyperparameters = ExtendedCombinationHyperparameters([
LocalHyperparameters(log_sigma=local_log_sigma,
log_rho=local_log_rho)
])
region_component_storage_solution = SpatialComponentSolutionStorage_InMemory(
)
region_sub_component = DelayedSpatialComponent(
ComponentStorage_InMemory(region_element, region_hyperparameters),
region_component_storage_solution)
# Read the optimized hyperparameters
hyperparameter_file = os.path.join(
args.outpath,
hyperparameter_file_template % (n_triangulation_divisions_local,
neighbourhood_level, region_index))
region_sub_component.storage.hyperparameters.values_from_npy_savefile(
hyperparameter_file)
# Append the spde model and hyperparameters to their lists for merging
region_spdes.append(region_element.combination[0].spde)
region_hyperparameter_values.append(
region_sub_component.storage.hyperparameters.get_array())
# merge and save hyperparameters
full_spde = local_element.spde
new_hyperparameter_values, global_sigma_design, global_rho_design = full_spde.merge_local_parameterisations(
region_spdes, region_hyperparameter_values, merge_method='exp_average')
local_hyperparameters.set_array(new_hyperparameter_values)
hyperparameter_file_merged = "merged_hyperparameters.%i.%i.npy" % (
n_triangulation_divisions_local, neighbourhood_level)
local_hyperparameters.values_to_npy_savefile(
os.path.join(args.outpath, hyperparameter_file_merged))
# Refit local model with the optimized hyperparameters
analysis_system.update_component(inputloaders, 1, time_indices)
##################################################
print 'Computing outputs'
# Produce an output for each time index
for time_index in time_indices:
# Get date for output
outputdate = inputloaders[0].datetime_at_time_index(time_index)
print 'Evaluating output grid: ', outputdate
#Configure output grid
outputstructure = OutputRectilinearGridStructure(
time_index,
outputdate,
latitudes=numpy.linspace(-89.875,
89.875,
num=definitions.GLOBAL_FIELD_SHAPE[1]),
longitudes=numpy.linspace(-179.875,
179.875,
num=definitions.GLOBAL_FIELD_SHAPE[2]))
# print 'Size of grid : ', outputstructure.number_of_observations()
# Evaluate expected value at these locations
result_expected_value = analysis_system.evaluate_expected_value(
'MAP', outputstructure, 'POINTWISE')
result_expected_uncertainties = analysis_system.evaluate_expected_value(
'post_STD', outputstructure, 'POINTWISE')
# Make output filename
pathname = 'eustace_example_output_{0:04d}{1:02d}{2:02d}.nc'.format(
outputdate.year, outputdate.month, outputdate.day)
pathname = os.path.join(args.outpath, pathname)
print 'Saving: ', pathname
# Save results
filebuilder = FileBuilderGlobalField(
pathname, time_index, 'Infilling Example', 'UNVERSIONED',
definitions.TAS.name, '', 'Example data only',
'eustace.analysis.advanced_standard.examples.example_eustace_few_days',
'')
filebuilder.add_global_field(
definitions.TAS,
result_expected_value.reshape(definitions.GLOBAL_FIELD_SHAPE))
filebuilder.add_global_field(
definitions.TASUNCERTAINTY,
result_expected_uncertainties.reshape(
definitions.GLOBAL_FIELD_SHAPE))
filebuilder.save_and_close()
print 'Complete'