def select_block_size_rf(nruns, group_type, loc_dict, Cvar_dict, idw_example_grid, shapefile,\
file_path_elev, idx_list, cluster_num1, cluster_num2, cluster_num3,
expand_area, boreal_shapefile):
'''Evaluate the standard deviation of MAE values based on consective runs of the cross-valiation,
in order to select the block/cluster size
Parameters
----------
nruns : int
number of repetitions
group_type : string
whether using 'clusters' or 'blocks'
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
idw_example_grid : ndarray
used for reference of study area grid size
shapefile : string
path to the study area shapefile
file_path_elev : string
path to the elevation lookup file
idx_list : int
position of the elevation column in the lookup file
cluster_num1-3 : int
three cluster numbers to test, for blocking this must be one of three:25, 16, 9
you can enter 'None' and it will automatically test 25, 16, 9
expand_area : bool
expand area by 200km
boreal_shapefile : string
path to shapefile with the boreal zone
Returns
----------
int
- block/cluster number with lowest stdev
float
- average MAE of all the runs for that cluster/block number
'''
# Get group dictionaries
if group_type == 'blocks':
folds25 = mbk.make_block(idw_example_grid, 25)
dictionaryGroups25 = mbk.sorting_stations(folds25, shapefile,
Cvar_dict)
folds16 = mbk.make_block(idw_example_grid, 16)
dictionaryGroups16 = mbk.sorting_stations(folds16, shapefile,
Cvar_dict)
folds9 = mbk.make_block(idw_example_grid, 9)
dictionaryGroups9 = mbk.sorting_stations(folds9, shapefile, Cvar_dict)
elif group_type == 'clusters':
if expand_area:
inBoreal = GD.is_station_in_boreal(loc_dict, Cvar_dict,
boreal_shapefile)
# Overwrite cvar_dict
Cvar_dict = {k: v for k, v in Cvar_dict.items() if k in inBoreal}
dictionaryGroups25 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num1,
file_path_elev, idx_list,
False, False, False)
dictionaryGroups16 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num2,
file_path_elev, idx_list,
False, False, False)
dictionaryGroups9 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num3,
file_path_elev, idx_list,
False, False, False)
else:
dictionaryGroups25 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num1,
file_path_elev, idx_list,
False, False, False)
dictionaryGroups16 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num2,
file_path_elev, idx_list,
False, False, False)
dictionaryGroups9 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, cluster_num3,
file_path_elev, idx_list,
False, False, False)
else:
print('Thats not a valid group type')
sys.exit()
block25_error = []
block16_error = []
block9_error = []
if nruns <= 1:
print('That is not enough runs to calculate the standard deviation!')
sys.exit()
for n in range(0, nruns):
# We want same number of stations selected for each cluster number
# We need to calculate, 5 folds x 25 clusters = 125 stations; 8 folds x 16 clusters = 128 stations, etc.
# What is 30% of the stations
target_stations = len(Cvar_dict.keys()) * 0.3
fold_num1 = int(round(target_stations / cluster_num1))
fold_num2 = int(round(target_stations / cluster_num2))
fold_num3 = int(round(target_stations / cluster_num3))
block25 = spatial_groups_rf(idw_example_grid, loc_dict, Cvar_dict,
shapefile, cluster_num1, fold_num1, True,
dictionaryGroups25, file_path_elev,
idx_list, expand_area)
block25_error.append(block25)
block16 = spatial_groups_rf(idw_example_grid, loc_dict, Cvar_dict,
shapefile, cluster_num2, fold_num2, True,
dictionaryGroups16, file_path_elev,
idx_list, expand_area)
block16_error.append(block16)
block9 = spatial_groups_rf(idw_example_grid, loc_dict, Cvar_dict,
shapefile, cluster_num3, fold_num3, True,
dictionaryGroups9, file_path_elev, idx_list,
expand_area)
block9_error.append(block9)
stdev25 = statistics.stdev(block25_error)
stdev16 = statistics.stdev(block16_error)
stdev9 = statistics.stdev(block9_error)
list_stdev = [stdev25, stdev16, stdev9]
list_block_name = [cluster_num1, cluster_num2, cluster_num3]
list_error = [block25_error, block16_error, block9_error]
index_min = list_stdev.index(min(list_stdev))
lowest_stdev = statistics.stdev(list_error[index_min])
ave_MAE = sum(list_error[index_min]) / len(list_error[index_min])
cluster_select = list_block_name[index_min]
print(list_error[index_min])
print(ave_MAE)
print(lowest_stdev)
print(cluster_select)
return cluster_select, ave_MAE, lowest_stdev
def spatial_kfold_rf(idw_example_grid, loc_dict, Cvar_dict, shapefile, file_path_elev, elev_array, idx_list,\
block_num, blocking_type, return_error):
'''Spatially blocked k-fold cross-validation procedure for RF
Parameters
----------
idw_example_grid : ndarray
used for reference of study area grid size
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
shapefile : string
path to the study area shapefile
file_path_elev : string
path to the elevation lookup file
elev_array : ndarray
array for elevation, create using IDEW interpolation (this is a trick to speed up code)
idx_list : int
position of the elevation column in the lookup file
block_num : int
number of blocks/clusters
blocking_type : string
whether to use clusters or blocks
return_error : bool
whether or not to return the error dictionary
Returns
----------
float
- MAE estimate for entire surface
int
- Return the block number just so we can later write it into the file to keep track
dictionary
- if return_error = True, a dictionary of the absolute error at each fold when it was left out
'''
groups_complete = [
] # If not using replacement, keep a record of what we have done
error_dictionary = {}
x_origin_list = []
y_origin_list = []
absolute_error_dictionary = {}
projected_lat_lon = {}
# Selecting blocknum
if blocking_type == 'cluster':
cluster = c3d.spatial_cluster(loc_dict, Cvar_dict, shapefile,
block_num, file_path_elev, idx_list,
False, False, False)
elif blocking_type == 'block':
# Get the numpy array that delineates the blocks
np_array_blocks = mbk.make_block(idw_example_grid, block_num)
cluster = mbk.sorting_stations(np_array_blocks, shapefile, loc_dict,
Cvar_dict) # Now get the dictionary
else:
print('That is not a valid blocking method')
sys.exit()
for group in cluster.values():
if group not in groups_complete:
station_list = [k for k, v in cluster.items() if v == group]
groups_complete.append(group)
for station_name in Cvar_dict.keys():
if station_name in loc_dict.keys():
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
Plat, Plon = pyproj.Proj('esri:102001')(longitude, latitude)
Plat = float(Plat)
Plon = float(Plon)
projected_lat_lon[station_name] = [Plat, Plon]
lat = []
lon = []
Cvar = []
for station_name in sorted(Cvar_dict.keys()):
if station_name in loc_dict.keys():
if station_name not in station_list:
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
cvar_val = Cvar_dict[station_name]
lat.append(float(latitude))
lon.append(float(longitude))
Cvar.append(cvar_val)
else:
pass
y = np.array(lat)
x = np.array(lon)
z = np.array(Cvar)
na_map = gpd.read_file(shapefile)
bounds = na_map.bounds
xmax = bounds['maxx']
xmin = bounds['minx']
ymax = bounds['maxy']
ymin = bounds['miny']
pixelHeight = 10000
pixelWidth = 10000
num_col = int((xmax - xmin) / pixelHeight)
num_row = int((ymax - ymin) / pixelWidth)
# We need to project to a projected system before making distance matrix
source_proj = pyproj.Proj(proj='latlong', datum='NAD83')
xProj, yProj = pyproj.Proj('esri:102001')(x, y)
df_trainX = pd.DataFrame({'xProj': xProj, 'yProj': yProj, 'var': z})
yProj_extent = np.append(yProj, [bounds['maxy'], bounds['miny']])
xProj_extent = np.append(xProj, [bounds['maxx'], bounds['minx']])
Yi = np.linspace(np.min(yProj_extent), np.max(yProj_extent), num_row)
Xi = np.linspace(np.min(xProj_extent), np.max(xProj_extent), num_col)
Xi, Yi = np.meshgrid(Xi, Yi)
Xi, Yi = Xi.flatten(), Yi.flatten()
maxmin = [
np.min(yProj_extent),
np.max(yProj_extent),
np.max(xProj_extent),
np.min(xProj_extent)
]
# Elevation
# Preparing the coordinates to send to the function that will get the elevation grid
concat = np.array((Xi.flatten(), Yi.flatten())).T
send_to_list = concat.tolist()
# The elevation function takes a tuple
send_to_tuple = [tuple(x) for x in send_to_list]
Xi1_grd = []
Yi1_grd = []
elev_grd = []
# Get the elevations from the lookup file
elev_grd_dict = GD.finding_data_frm_lookup(send_to_tuple, file_path_elev,
idx_list)
for keys in elev_grd_dict.keys(): # The keys are each lat lon pair
x = keys[0]
y = keys[1]
Xi1_grd.append(x)
Yi1_grd.append(y)
# Append the elevation data to the empty list
elev_grd.append(elev_grd_dict[keys])
elev_array = np.array(elev_grd) # make an elevation array
elev_dict = GD.finding_data_frm_lookup(
zip(xProj, yProj), file_path_elev,
idx_list) # Get the elevations for the stations
xProj_input = []
yProj_input = []
e_input = []
for keys in zip(
xProj,
yProj): # Repeat process for just the stations not the whole grid
x = keys[0]
y = keys[1]
xProj_input.append(x)
yProj_input.append(y)
e_input.append(elev_dict[keys])
source_elev = np.array(e_input)
Xi1_grd = np.array(Xi1_grd)
Yi1_grd = np.array(Yi1_grd)
df_trainX = pd.DataFrame({
'xProj': xProj,
'yProj': yProj,
'elevS': source_elev,
'var': z
})
df_testX = pd.DataFrame({'Xi': Xi1_grd, 'Yi': Yi1_grd, 'elev': elev_array})
reg = RandomForestRegressor(n_estimators=100,
max_features='sqrt',
random_state=1)
y = np.array(df_trainX['var']).reshape(-1, 1)
X_train = np.array(df_trainX[['xProj', 'yProj', 'elevS']])
X_test = np.array(df_testX[['Xi', 'Yi', 'elev']])
reg.fit(X_train, y)
Zi = reg.predict(X_test)
rf_grid = Zi.reshape(num_row, num_col)
# Calc the RMSE, MAE at the pixel loc
# Delete at a certain point
for statLoc in station_list:
coord_pair = projected_lat_lon[statLoc]
x_orig = int(
(coord_pair[0] - float(bounds['minx'])) / pixelHeight) # lon
y_orig = int(
(coord_pair[1] - float(bounds['miny'])) / pixelWidth) # lat
x_origin_list.append(x_orig)
y_origin_list.append(y_orig)
interpolated_val = rf_grid[y_orig][x_orig]
original_val = Cvar_dict[statLoc]
absolute_error = abs(interpolated_val - original_val)
absolute_error_dictionary[statLoc] = absolute_error
# average of all the withheld stations
MAE = sum(absolute_error_dictionary.values()) / \
len(absolute_error_dictionary.values())
if return_error:
return block_num, MAE, absolute_error_dictionary
else:
return block_num, MAE
def select_block_size_IDEW(nruns, group_type, loc_dict, Cvar_dict,
idw_example_grid, shapefile, file_path_elev,
idx_list, elev_array, d):
'''Evaluate the standard deviation of MAE values based on consective runs of the cross-valiation,
in order to select the block/cluster size
Parameters
----------
nruns : int
number of repetitions
group_type : string
whether using 'clusters' or 'blocks'
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
idw_example_grid : ndarray
used for reference of study area grid size
shapefile : string
path to the study area shapefile
file_path_elev : string
path to the elevation lookup file
idx_list : int
position of the elevation column in the lookup file
elev_array : ndarray
array for elevation, create using IDEW interpolation (this is a trick to speed up code)
d : int
the weighting for IDW interpolation
Returns
----------
int
- block/cluster number with lowest stdev
float
- average MAE of all the runs for that cluster/block number
'''
# Get group dictionaries
if group_type == 'blocks':
folds25 = mbk.make_block(idw_example_grid, 25)
dictionaryGroups25 = mbk.sorting_stations(folds25, shapefile,
Cvar_dict)
folds16 = mbk.make_block(idw_example_grid, 16)
dictionaryGroups16 = mbk.sorting_stations(folds16, shapefile,
Cvar_dict)
folds9 = mbk.make_block(idw_example_grid, 9)
dictionaryGroups9 = mbk.sorting_stations(folds9, shapefile, Cvar_dict)
elif group_type == 'clusters':
dictionaryGroups25 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, 25, file_path_elev,
idx_list, False, False, False)
dictionaryGroups16 = c3d.spatial_cluster(loc_dict, Cvar_dict,
shapefile, 16, file_path_elev,
idx_list, False, False, False)
dictionaryGroups9 = c3d.spatial_cluster(loc_dict, Cvar_dict, shapefile,
9, file_path_elev, idx_list,
False, False, False)
else:
print('Thats not a valid group type')
sys.exit()
block25_error = []
block16_error = []
block9_error = []
if nruns <= 1:
print('That is not enough runs to calculate the standard deviation!')
sys.exit()
for n in range(0, nruns):
block25 = spatial_groups_IDEW(idw_example_grid, loc_dict, Cvar_dict,
shapefile, d, 25, 5, True,
dictionaryGroups25, file_path_elev,
idx_list, elev_array)
block25_error.append(block25)
block16 = spatial_groups_IDEW(idw_example_grid, loc_dict, Cvar_dict,
shapefile, d, 16, 8, True,
dictionaryGroups16, file_path_elev,
idx_list, elev_array)
block16_error.append(block16)
block9 = spatial_groups_IDEW(idw_example_grid, loc_dict, Cvar_dict,
shapefile, d, 9, 14, True,
dictionaryGroups9, file_path_elev,
idx_list, elev_array)
block9_error.append(block9)
stdev25 = statistics.stdev(block25_error)
stdev16 = statistics.stdev(block16_error)
stdev9 = statistics.stdev(block9_error)
list_stdev = [stdev25, stdev16, stdev9]
list_block_name = [25, 16, 9]
list_error = [block25_error, block16_error, block9_error]
index_min = list_stdev.index(min(list_stdev))
lowest_stdev = list_block_name[index_min]
ave_MAE = sum(list_error[index_min]) / len(list_error[index_min])
print(lowest_stdev)
print(ave_MAE)
return lowest_stdev, ave_MAE
def spatial_kfold_IDEW(loc_dict, Cvar_dict, shapefile, file_path_elev,
elev_array, idx_list, d, block_num, blocking_type):
'''Spatially blocked k-folds cross-validation procedure for IDEW
Parameters
----------
idw_example_grid : ndarray
used for reference of study area grid size
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
shapefile : string
path to the study area shapefile
d : int
the weighting for IDW interpolation
file_path_elev : string
path to the elevation lookup file
elev_array : ndarray
array for elevation, create using IDEW interpolation (this is a trick to speed up code)
idx_list : int
position of the elevation column in the lookup file
block_num : int
number of blocks/clusters
blocking_type : string
whether to use clusters or blocks
Returns
----------
float
- MAE estimate for entire surface
int
- Return the block number just so we can later write it into the file to keep track
'''
groups_complete = [
] # If not using replacement, keep a record of what we have done
error_dictionary = {}
x_origin_list = []
y_origin_list = []
absolute_error_dictionary = {}
projected_lat_lon = {}
if blocking_type == 'cluster':
cluster = c3d.spatial_cluster(loc_dict, Cvar_dict, shapefile,
block_num, file_path_elev, idx_list,
False, False, False)
elif blocking_type == 'block':
# Get the numpy array that delineates the blocks
np_array_blocks = mbk.make_block(idw_example_grid, block_num)
cluster = mbk.sorting_stations(np_array_blocks, shapefile, loc_dict,
Cvar_dict) # Now get the dictionary
else:
print('That is not a valid blocking method')
sys.exit()
for group in cluster.values():
if group not in groups_complete:
station_list = [k for k, v in cluster.items() if v == group]
groups_complete.append(group)
for station_name in Cvar_dict.keys():
if station_name in loc_dict.keys():
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
Plat, Plon = pyproj.Proj('esri:102001')(longitude, latitude)
Plat = float(Plat)
Plon = float(Plon)
projected_lat_lon[station_name] = [Plat, Plon]
lat = []
lon = []
Cvar = []
for station_name in sorted(Cvar_dict.keys()):
if station_name in loc_dict.keys():
if station_name not in station_list:
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
cvar_val = Cvar_dict[station_name]
lat.append(float(latitude))
lon.append(float(longitude))
Cvar.append(cvar_val)
else:
pass
y = np.array(lat)
x = np.array(lon)
# what if we add the bounding locations to the array??? ==> that would be extrapolation not interpolation?
z = np.array(Cvar)
na_map = gpd.read_file(shapefile)
bounds = na_map.bounds
xmax = bounds['maxx']
xmin = bounds['minx']
ymax = bounds['maxy']
ymin = bounds['miny']
pixelHeight = 10000
pixelWidth = 10000
num_col = int((xmax - xmin) / pixelHeight)
num_row = int((ymax - ymin) / pixelWidth)
# We need to project to a projected system before making distance matrix
# We dont know but assume
source_proj = pyproj.Proj(proj='latlong', datum='NAD83')
xProj, yProj = pyproj.Proj('esri:102001')(x, y)
yProj_extent = np.append(yProj, [bounds['maxy'], bounds['miny']])
xProj_extent = np.append(xProj, [bounds['maxx'], bounds['minx']])
Yi = np.linspace(np.min(yProj_extent), np.max(yProj_extent), num_row)
Xi = np.linspace(np.min(xProj_extent), np.max(xProj_extent), num_col)
Xi, Yi = np.meshgrid(Xi, Yi)
Xi, Yi = Xi.flatten(), Yi.flatten()
maxmin = [
np.min(yProj_extent),
np.max(yProj_extent),
np.max(xProj_extent),
np.min(xProj_extent)
]
vals = np.vstack((xProj, yProj)).T
interpol = np.vstack((Xi, Yi)).T
# Length of the triangle side from the cell to the point with data
dist_not = np.subtract.outer(vals[:, 0], interpol[:, 0])
# Length of the triangle side from the cell to the point with data
dist_one = np.subtract.outer(vals[:, 1], interpol[:, 1])
# euclidean distance, getting the hypotenuse
distance_matrix = np.hypot(dist_not, dist_one)
# what if distance is 0 --> np.inf? have to account for the pixel underneath
weights = 1 / (distance_matrix**d)
# Making sure to assign the value of the weather station above the pixel directly to the pixel underneath
weights[np.where(np.isinf(weights))] = 1 / (1.0E-50)
weights /= weights.sum(axis=0)
Zi = np.dot(weights.T, z)
idw_grid = Zi.reshape(num_row, num_col)
elev_dict = GD.finding_data_frm_lookup(zip(xProj, yProj), file_path_elev,
idx_list)
xProj_input = []
yProj_input = []
e_input = []
for keys in zip(
xProj,
yProj): # in case there are two stations at the same lat\lon
x = keys[0]
y = keys[1]
xProj_input.append(x)
yProj_input.append(y)
e_input.append(elev_dict[keys])
source_elev = np.array(e_input)
vals2 = np.vstack(source_elev).T
interpol2 = np.vstack(elev_array).T
dist_not2 = np.subtract.outer(vals2[0], interpol2[0])
dist_not2 = np.absolute(dist_not2)
weights2 = 1 / (dist_not2**d)
weights2[np.where(np.isinf(weights2))] = 1
weights2 /= weights2.sum(axis=0)
fin = 0.8 * np.dot(weights.T, z) + 0.2 * np.dot(weights2.T, z)
fin = fin.reshape(num_row, num_col)
# Calc the RMSE, MAE, NSE, and MRAE at the pixel loc
# Delete at a certain point
for statLoc in station_list:
coord_pair = projected_lat_lon[statLoc]
x_orig = int(
(coord_pair[0] - float(bounds['minx'])) / pixelHeight) # lon
y_orig = int(
(coord_pair[1] - float(bounds['miny'])) / pixelWidth) # lat
x_origin_list.append(x_orig)
y_origin_list.append(y_orig)
interpolated_val = fin[y_orig][x_orig]
original_val = Cvar_dict[statLoc]
absolute_error = abs(interpolated_val - original_val)
absolute_error_dictionary[statLoc] = absolute_error
# average of all the withheld stations
MAE = sum(absolute_error_dictionary.values()) / \
len(absolute_error_dictionary.values())
return block_num, MAE
def spatial_kfold_idw(idw_example_grid, loc_dict, Cvar_dict, shapefile, d,
file_path_elev, idx_list, block_num, blocking_type, return_error):
'''Spatially blocked k-fold cross-validation procedure for IDW
Parameters
----------
idw_example_grid : ndarray
used for reference of study area grid size
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
shapefile : string
path to the study area shapefile
d : int
the weighting for IDW interpolation
file_path_elev : string
path to the elevation lookup file
idx_list : int
position of the elevation column in the lookup file
block_num : int
number of blocks/clusters
blocking_type : string
whether to use clusters or blocks
return_error : bool
whether or not to return the error dictionary
Returns
----------
float
- MAE estimate for entire surface
int
- Return the block number just so we can later write it into the file to keep track
dictionary
- if return_error = True, a dictionary of the absolute error at each fold when it was left out
'''
groups_complete = []
error_dictionary = {}
x_origin_list = []
y_origin_list = []
absolute_error_dictionary = {}
projected_lat_lon = {}
if blocking_type == 'cluster':
cluster = c3d.spatial_cluster(
loc_dict, Cvar_dict, shapefile, block_num, file_path_elev, idx_list, False, False, False)
elif blocking_type == 'block':
# Get the numpy array that delineates the blocks
np_array_blocks = mbk.make_block(idw_example_grid, block_num)
cluster = mbk.sorting_stations(
np_array_blocks, shapefile, loc_dict, Cvar_dict) # Now get the dictionary
else:
print('That is not a valid blocking method')
sys.exit()
for group in cluster.values():
if group not in groups_complete:
station_list = [k for k, v in cluster.items() if v == group]
groups_complete.append(group)
for station_name in Cvar_dict.keys():
if station_name in loc_dict.keys():
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
Plat, Plon = pyproj.Proj('esri:102001')(longitude, latitude)
Plat = float(Plat)
Plon = float(Plon)
projected_lat_lon[station_name] = [Plat, Plon]
lat = []
lon = []
Cvar = []
for station_name in sorted(Cvar_dict.keys()):
if station_name in loc_dict.keys():
if station_name not in station_list: # This is the step where we hold back the fold
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
cvar_val = Cvar_dict[station_name]
lat.append(float(latitude))
lon.append(float(longitude))
Cvar.append(cvar_val)
else:
pass # Skip the station
y = np.array(lat)
x = np.array(lon)
z = np.array(Cvar)
na_map = gpd.read_file(shapefile)
bounds = na_map.bounds
xmax = bounds['maxx']
xmin = bounds['minx']
ymax = bounds['maxy']
ymin = bounds['miny']
pixelHeight = 10000
pixelWidth = 10000
num_col = int((xmax - xmin) / pixelHeight)
num_row = int((ymax - ymin) / pixelWidth)
# We need to project to a projected system before making distance matrix
# We dont know but assume
source_proj = pyproj.Proj(proj='latlong', datum='NAD83')
xProj, yProj = pyproj.Proj('esri:102001')(x, y)
yProj_extent = np.append(yProj, [bounds['maxy'], bounds['miny']])
xProj_extent = np.append(xProj, [bounds['maxx'], bounds['minx']])
Yi = np.linspace(np.min(yProj_extent), np.max(yProj_extent), num_row)
Xi = np.linspace(np.min(xProj_extent), np.max(xProj_extent), num_col)
Xi, Yi = np.meshgrid(Xi, Yi)
Xi, Yi = Xi.flatten(), Yi.flatten()
maxmin = [np.min(yProj_extent), np.max(yProj_extent),
np.max(xProj_extent), np.min(xProj_extent)]
vals = np.vstack((xProj, yProj)).T
interpol = np.vstack((Xi, Yi)).T
# Length of the triangle side from the cell to the point with data
dist_not = np.subtract.outer(vals[:, 0], interpol[:, 0])
# Length of the triangle side from the cell to the point with data
dist_one = np.subtract.outer(vals[:, 1], interpol[:, 1])
# euclidean distance, getting the hypotenuse
distance_matrix = np.hypot(dist_not, dist_one)
# what if distance is 0 --> np.inf? have to account for the pixel underneath
weights = 1 / (distance_matrix**d)
# Making sure to assign the value of the weather station above the pixel directly to the pixel underneath
weights[np.where(np.isinf(weights))] = 1 / (1.0E-50)
weights /= weights.sum(axis=0)
Zi = np.dot(weights.T, z)
idw_grid = Zi.reshape(num_row, num_col)
# Compare at a certain point
for statLoc in station_list:
coord_pair = projected_lat_lon[statLoc]
x_orig = int(
(coord_pair[0] - float(bounds['minx']))/pixelHeight) # lon
y_orig = int(
(coord_pair[1] - float(bounds['miny'])) / pixelWidth) # lat
x_origin_list.append(x_orig)
y_origin_list.append(y_orig)
interpolated_val = idw_grid[y_orig][x_orig]
original_val = Cvar_dict[statLoc]
absolute_error = abs(interpolated_val - original_val)
absolute_error_dictionary[statLoc] = absolute_error
# average of all the withheld stations
MAE = sum(absolute_error_dictionary.values()) / \
len(absolute_error_dictionary.values())
if return_error:
return block_num, MAE, absolute_error_dictionary
else:
return block_num, MAE
def spatial_kfold_tps(idw_example_grid, loc_dict, Cvar_dict, shapefile, phi,
file_path_elev, idx_list, block_num, blocking_type,
return_error, calc_phi):
'''Spatially blocked k-folds cross-validation procedure for thin plate splines
Parameters
----------
idw_example_grid : ndarray
used for reference of study area grid size
loc_dict : dictionary
the latitude and longitudes of the daily/hourly stations
Cvar_dict : dictionary
dictionary of weather variable values for each station
shapefile : string
path to the study area shapefile
phi : float
smoothing parameter for the thin plate spline, if 0 no smoothing
file_path_elev : string
path to the elevation lookup file
idx_list : int
position of the elevation column in the lookup file
block_num : int
number of blocks/clusters
blocking_type : string
whether to use clusters or blocks
return_error : bool
whether or not to return the error dictionary
calc_phi : bool
whether to calculate phi in the function, if True, phi can = None
Returns
----------
float
- MAE estimate for entire surface
int
- Return the block number just so we can later write it into the file to keep track
dictionary
- if return_error = True, a dictionary of the absolute error at each fold when it was left out
'''
groups_complete = [
] # If not using replacement, keep a record of what we have done
error_dictionary = {}
absolute_error_dictionary = {} # for plotting
station_name_list = []
projected_lat_lon = {}
if blocking_type == 'cluster':
cluster = c3d.spatial_cluster(loc_dict, Cvar_dict, shapefile,
block_num, file_path_elev, idx_list,
False, False, False)
elif blocking_type == 'block':
# Get the numpy array that delineates the blocks
np_array_blocks = mbk.make_block(idw_example_grid, block_num)
cluster = mbk.sorting_stations(np_array_blocks, shapefile, loc_dict,
Cvar_dict) # Now get the dictionary
else:
print('That is not a valid blocking method')
sys.exit()
for group in cluster.values():
if group not in groups_complete:
station_list = [k for k, v in cluster.items() if v == group]
groups_complete.append(group)
for station_name in Cvar_dict.keys():
if station_name in loc_dict.keys():
station_name_list.append(station_name)
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
Plat, Plon = pyproj.Proj('esri:102001')(longitude, latitude)
Plat = float(Plat)
Plon = float(Plon)
projected_lat_lon[station_name] = [Plat, Plon]
lat = []
lon = []
Cvar = []
# For preparing the empty grid w/ the values inserted for the rbf function
x_origin_list = []
y_origin_list = []
z_origin_list = []
na_map = gpd.read_file(shapefile)
bounds = na_map.bounds
pixelHeight = 10000
pixelWidth = 10000
for station_name in sorted(Cvar_dict.keys()):
if station_name in loc_dict.keys():
if station_name not in station_list:
loc = loc_dict[station_name]
latitude = loc[0]
longitude = loc[1]
cvar_val = Cvar_dict[station_name]
lat.append(float(latitude))
lon.append(float(longitude))
Cvar.append(cvar_val)
coord_pair = projected_lat_lon[station_name]
x_orig = int((coord_pair[0] - float(bounds['minx'])) /
pixelHeight) # lon
y_orig = int((coord_pair[1] - float(bounds['miny'])) /
pixelWidth) # lat
x_origin_list.append(x_orig)
y_origin_list.append(y_orig)
z_origin_list.append(Cvar_dict[station_name])
else:
pass
y = np.array(lat)
x = np.array(lon)
z = np.array(Cvar)
na_map = gpd.read_file(shapefile)
bounds = na_map.bounds
xmax = bounds['maxx']
xmin = bounds['minx']
ymax = bounds['maxy']
ymin = bounds['miny']
pixelHeight = 10000
pixelWidth = 10000
num_col = int((xmax - xmin) / pixelHeight)
num_row = int((ymax - ymin) / pixelWidth)
# We need to project to a projected system before making distance matrix
# We dont know but assume
source_proj = pyproj.Proj(proj='latlong', datum='NAD83')
xProj, yProj = pyproj.Proj('esri:102001')(x, y)
yProj_extent = np.append(yProj, [bounds['maxy'], bounds['miny']])
xProj_extent = np.append(xProj, [bounds['maxx'], bounds['minx']])
Yi = np.linspace(np.min(yProj_extent), np.max(yProj_extent), num_row)
Xi = np.linspace(np.min(xProj_extent), np.max(xProj_extent), num_col)
Xi, Yi = np.meshgrid(Xi, Yi)
empty_grid = np.empty((
num_row,
num_col,
)) * np.nan
for x, y, z in zip(x_origin_list, y_origin_list, z_origin_list):
empty_grid[y][x] = z
vals = ~np.isnan(empty_grid)
func = interpolate.Rbf(Xi[vals],
Yi[vals],
empty_grid[vals],
function='thin_plate',
smooth=phi)
thin_plate = func(Xi, Yi)
spline = thin_plate.reshape(num_row, num_col)
# Calc the RMSE, MAE, at the pixel loc
# Delete at a certain point
for statLoc in station_list:
coord_pair = projected_lat_lon[statLoc]
x_orig = int(
(coord_pair[0] - float(bounds['minx'])) / pixelHeight) # lon
y_orig = int(
(coord_pair[1] - float(bounds['miny'])) / pixelWidth) # lat
interpolated_val = spline[y_orig][x_orig]
original_val = Cvar_dict[statLoc]
absolute_error = abs(interpolated_val - original_val)
absolute_error_dictionary[statLoc] = absolute_error
# average of all the withheld stations
MAE = sum(absolute_error_dictionary.values()) / \
len(absolute_error_dictionary.values())
if return_error:
return block_num, MAE, absolute_error_dictionary
else:
return block_num, MAE