def test_mini_world_geography_based_mock_data(self):
"""Testing on a simple mock data file, with mock covariate values"""
# GENERATING OBSERVATIONS
# Simulated locations: they will exactly sits on the grid points of the covariate datafile
locations = numpy.array([[0.0, 0.0], [0.0, 0.5], [0.05, 0.0]])
# Simulated measurements: simple linear relation of type: y = 2*x
measurement = numpy.array([2., 2., 2.])
# Simulated errors
uncorrelatederror = 0.1 * numpy.ones(measurement.shape)
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(locations, measurement,
uncorrelatederror)
# Simulate evaluation of this time index
simulated_time_indices = [0]
# GENERATING THE MODEL
# Local component
geography_covariate_element = GeographyBasedElement(
self.covariate_file.name, 'lat', 'lon', 'covariate', 1.0)
geography_covariate_element.load()
geography_based_component = SpatialComponent(
ComponentStorage_InMemory(
geography_covariate_element,
CovariateHyperparameters(-0.5 * numpy.log(10.))),
SpatialComponentSolutionStorage_InMemory())
# GENERATING THE ANALYSIS
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([geography_based_component],
ObservationSource.TMEAN,
log=StringIO())
# Update with data
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[
0].solutionstorage.partial_state_read(0).ravel()
# These are the nodes where observations were put (see SimulatedObservationSource above)
# - check they correspond to within 3 times the stated noise level
self.assertAlmostEqual(2., statevector[0], delta=0.3)
# Also check entire state vector within outer bounds set by obs
self.assertTrue(all(statevector < 2.0))
# And check output corresponds too
# (evaluate result on output structure same as input)
simulated_output_structure = SimulatedObservationStructure(
0, locations, None, None)
result = analysis_system.evaluate_expected_value(
'MAP', simulated_output_structure, flag='POINTWISE')
numpy.testing.assert_almost_equal(
statevector[0] * numpy.ones(len(measurement)), result)
def test_mini_world_local(self):
# Local component
local_component = SpatialComponent(
ComponentStorage_InMemory(
LocalElement(n_triangulation_divisions=1),
LocalHyperparameters(log_sigma=0.0, log_rho=numpy.log(1.0))),
SpatialComponentSolutionStorage_InMemory(),
compute_uncertainties=True,
method='APPROXIMATED')
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([local_component],
ObservationSource.TMEAN,
log=StringIO())
# Simulated inputs
simulated_input_loader = SimulatedInputLoader()
# Simulate evaluation of this time index
simulated_time_indices = [0]
# Update with data
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[
0].solutionstorage.partial_state_read(0).ravel()
# These are the nodes where observations were put (see SimulatedObservationSource above)
# - check they correspond to within 3 times the stated noise level
self.assertAlmostEqual(20.0, statevector[12], delta=0.3)
self.assertAlmostEqual(-15.0, statevector[17], delta=0.3)
self.assertAlmostEqual(5.0, statevector[41], delta=0.3)
# Also check entire state vector within outer bounds set by obs
self.assertTrue(all(statevector < 20.0))
self.assertTrue(all(statevector > -15.0))
# And check output corresponds too
# (evaluate result on output structure same as input)
simulated_output_structure = SimulatedObservationStructure(0)
result = analysis_system.evaluate_expected_value(
'MAP', simulated_output_structure, flag='POINTWISE')
numpy.testing.assert_almost_equal(statevector[[12, 17, 41]], result)
# test output gridding, pointwise limit
outputstructure = OutputRectilinearGridStructure(
2,
epoch_plus_days(2),
latitudes=numpy.linspace(-89.875, 89.875, num=10),
longitudes=numpy.linspace(-179.875, 179.875, num=20))
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], 3)
numpy.testing.assert_array_almost_equal(pointwise_result,
pointwise_limit_result)
def mini_world_spatial():
# Local component
local_component = SpatialComponent(ComponentStorage_InMemory(LocalElement(n_triangulation_divisions=4),
LocalHyperparameters(log_sigma=numpy.log(5.0), log_rho=numpy.log( 15. * numpy.pi / 180. ) )),
SpatialComponentSolutionStorage_InMemory(), compute_uncertainties=False, method='APPROXIMATED', compute_sample = True, sample_size=100)
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([ local_component ], ObservationSource.TMEAN, log=StringIO())
# Simulated inputs
simulated_input_loader = SimulatedInputLoader()
# Simulate evaluation of this time index
simulated_time_indices = [ 0 ]
# Update with data
analysis_system.update([ simulated_input_loader ], simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[0].solutionstorage.partial_state_read(0)
return analysis_system, statevector
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_altitude_with_latitude(self):
"""Testing using altitude as a covariate"""
# GENERATING OBSERVATIONS
# Simulated locations: they will exactly sits on the grid points of the covariate datafile
DEM = Dataset(self.altitude_datafile)
latitude = DEM.variables['lat'][:]
longitude = DEM.variables['lon'][:]
altitude = DEM.variables['dem'][:]
indices = numpy.stack(
(numpy.array([1, 3, 5, 7, 8, 9, 10, 11
]), numpy.array([0, 0, 0, 0, 0, 0, 0, 0])),
axis=1)
selected_location = []
altitude_observations = []
for couple in indices:
selected_location.append([
latitude[couple[0], couple[1]], longitude[couple[0], couple[1]]
])
altitude_observations.append(altitude[couple[0], couple[1]])
DEM.close()
locations = numpy.array(selected_location)
# Simulated model is y = z + a*cos(2x) + c*cos(4*x) + b*sin(2x) + d*sin(4*x), with z = altitude, x = latitude, a=b=c=d=0
slope = 1e-3
measurement = slope * numpy.array(altitude_observations)
# Simulated errors
uncorrelatederror = 0.1 * numpy.ones(measurement.shape)
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(locations, measurement,
uncorrelatederror)
# Simulate evaluation of this time index
simulated_time_indices = [0]
# GENERATING THE MODEL
# Local component
geography_covariate_element = GeographyBasedElement(
self.altitude_datafile, 'lat', 'lon', 'dem', 1.0)
geography_covariate_element.load()
combined_element = CombinationElement(
[geography_covariate_element,
LatitudeHarmonicsElement()])
combined_hyperparamters = CombinationHyperparameters([
CovariateHyperparameters(-0.5 * numpy.log(10.)),
CombinationHyperparameters([
CovariateHyperparameters(-0.5 * numpy.log(p))
for p in [10.0, 10.0, 10.0, 10.0]
])
])
combined_component = SpatialComponent(
ComponentStorage_InMemory(combined_element,
combined_hyperparamters),
SpatialComponentSolutionStorage_InMemory())
# GENERATING THE ANALYSIS
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([combined_component],
ObservationSource.TMEAN,
log=StringIO())
# Update with data
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[
0].solutionstorage.partial_state_read(0).ravel()
# These are the nodes where observations were put (see SimulatedObservationSource above)
# - check they correspond to within 3 times the stated noise level
self.assertAlmostEqual(slope, statevector[0], delta=0.3)
self.assertAlmostEqual(0., statevector[1], delta=0.3)
self.assertAlmostEqual(0., statevector[2], delta=0.3)
self.assertAlmostEqual(0., statevector[3], delta=0.3)
self.assertAlmostEqual(0., statevector[4], delta=0.3)
# And check output corresponds too
# (evaluate result on output structure same as input)
simulated_output_structure = SimulatedObservationStructure(
0, locations, None, None)
result = analysis_system.evaluate_expected_value(
'MAP', simulated_output_structure, flag='POINTWISE')
expected = statevector[0]*numpy.array(altitude_observations)\
+ statevector[1]*LatitudeFunction(numpy.cos, 2.0).compute(locations[:,0]).ravel()\
+ statevector[2]*LatitudeFunction(numpy.sin, 2.0).compute(locations[:,0]).ravel()\
+ statevector[3]*LatitudeFunction(numpy.cos, 4.0).compute(locations[:,0]).ravel()\
+ statevector[4]*LatitudeFunction(numpy.sin, 2.0).compute(locations[:,0]).ravel()
numpy.testing.assert_almost_equal(expected, result)
# 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_altitude(self):
"""Testing using altitude as a covariate"""
# GENERATING OBSERVATIONS
# Simulated locations: they will exactly sits on the grid points of the covariate datafile
DEM = Dataset(self.altitude_datafile)
latitude = DEM.variables['lat'][:]
longitude = DEM.variables['lon'][:]
altitude = DEM.variables['dem'][:]
indices = numpy.stack(
(numpy.array([1, 3, 267, 80, 10, 215, 17, 120]),
numpy.array([2, 256, 9, 110, 290, 154, 34, 151])),
axis=1)
selected_location = []
altitude_observations = []
for couple in indices:
selected_location.append([
latitude[couple[0], couple[1]], longitude[couple[0], couple[1]]
])
altitude_observations.append(altitude[couple[0], couple[1]])
DEM.close()
locations = numpy.array(selected_location)
# Simulated measurements: simple linear relation of type: y = PI*x
measurement = numpy.pi * numpy.array(altitude_observations)
# Simulated errors
uncorrelatederror = 0.1 * numpy.ones(measurement.shape)
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(locations, measurement,
uncorrelatederror)
# Simulate evaluation of this time index
simulated_time_indices = [0]
# GENERATING THE MODEL
# Local component
geography_covariate_element = GeographyBasedElement(
self.altitude_datafile, 'lat', 'lon', 'dem', 1.0)
geography_covariate_element.load()
geography_based_component = SpatialComponent(
ComponentStorage_InMemory(
geography_covariate_element,
CovariateHyperparameters(-0.5 * numpy.log(10.))),
SpatialComponentSolutionStorage_InMemory())
# GENERATING THE ANALYSIS
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([geography_based_component],
ObservationSource.TMEAN,
log=StringIO())
# Update with data
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[
0].solutionstorage.partial_state_read(0).ravel()
# These are the nodes where observations were put (see SimulatedObservationSource above)
# - check they correspond to within 3 times the stated noise level
self.assertAlmostEqual(numpy.pi, statevector[0], delta=0.3)
# Also check entire state vector within outer bounds set by obs
self.assertTrue(all(statevector < numpy.pi))
# And check output corresponds too
# (evaluate result on output structure same as input)
simulated_output_structure = SimulatedObservationStructure(
0, locations, None, None)
result = analysis_system.evaluate_expected_value(
'MAP', simulated_output_structure, flag='POINTWISE')
numpy.testing.assert_almost_equal(
statevector[0] * numpy.array(altitude_observations), result)
def test_mini_world_latitude_harmonics(self):
"""Testing on a simple mock data file using latitude harmonics"""
# GENERATING OBSERVATIONS
# Simulated locations: they will exactly sits on the grid points of the covariate datafile
locations = numpy.array([[0.0, 0.0], [0.25, 0.5], [0.5, 0.0]])
# Simulated model is y = a*cos(2x) + c*cos(4*x) + b*sin(2x) + d*sin(4*x) with x = latitude, so we expect a=c=1, c=d=0
measurement = LatitudeFunction(numpy.cos, 2.0).compute(
locations[:, 0]).ravel() + LatitudeFunction(
numpy.cos, 4.0).compute(locations[:, 0]).ravel()
# Simulated errors
uncorrelatederror = 0.1 * numpy.ones(measurement.shape)
# Simulated inputs
simulated_input_loader = SimulatedInputLoader(locations, measurement,
uncorrelatederror)
# Simulate evaluation of this time index
simulated_time_indices = [0]
latitude_harmonics_component = SpatialComponent(
ComponentStorage_InMemory(
LatitudeHarmonicsElement(),
CombinationHyperparameters([
CovariateHyperparameters(-0.5 * numpy.log(p))
for p in [10.0, 10.0, 10.0, 10.0]
])), SpatialComponentSolutionStorage_InMemory())
# Analysis system using the specified components, for the Tmean observable
analysis_system = AnalysisSystem([latitude_harmonics_component],
ObservationSource.TMEAN,
log=StringIO())
# GENERATING THE ANALYSIS
# Update with data
analysis_system.update([simulated_input_loader],
simulated_time_indices)
# Check state vector directly
statevector = analysis_system.components[
0].solutionstorage.partial_state_read(0).ravel()
# These are the nodes where observations were put (see SimulatedObservationSource above)
# - check they correspond to within 3 times the stated noise level
self.assertAlmostEqual(1., statevector[0], delta=0.3)
self.assertAlmostEqual(1., statevector[2], delta=0.3)
self.assertAlmostEqual(0., statevector[1], delta=0.3)
self.assertAlmostEqual(0., statevector[3], delta=0.3)
# Also check entire state vector within outer bounds set by obs
self.assertTrue(all(statevector < 1.0))
# And check output corresponds too
# (evaluate result on output structure same as input)
simulated_output_structure = SimulatedObservationStructure(
0, locations, None, None)
result = analysis_system.evaluate_expected_value(
'MAP', simulated_output_structure, flag='POINTWISE')
expected = statevector[0]*LatitudeFunction(numpy.cos, 2.0).compute(locations[:,0]).ravel() + statevector[1]*LatitudeFunction(numpy.sin, 2.0).compute(locations[:,0]).ravel()\
+ statevector[2] *LatitudeFunction(numpy.cos, 4.0).compute(locations[:,0]).ravel()+ statevector[3]*LatitudeFunction(numpy.sin, 4.0).compute(locations[:,0]).ravel()
numpy.testing.assert_almost_equal(expected, result)
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'