def fit_time_func(model, date_list, ts_dis, unit_fac=100, G_fit=None, conf_level=0.95, seconds=0):
"""Fit a suite of fime functions to the time series.
Equations: Gm = d
Parameters: model - dict of time functions, check utils.time_func.estimate_time_func() for details.
date_list - list of dates in YYYYMMDD format
ts_dis - 1D np.ndarray, displacement time series
unit_fac - float, scaling factor due to different data and display units
G_fit - 2D np.ndarray, design matrix for the dense time series prediction plot
conf_level - float in [0,1], confidence level of the plotted confidence intervals
Returns: m_strs - dict, dictionary in {ds_name: ds_value}
ts_fit - 1D np.ndarray, dense time series fit for plotting
ts_fit_lim - list of 1D np.ndarray, the lower and upper
boundaries of dense time series fit for plotting
"""
# init output
m_strs = []
ts_fit = None
ts_fit_lim = None
if np.all(np.isnan(ts_dis)):
return m_strs, ts_fit, ts_fit_lim
# 1.1 estimate time func parameter via least squares (OLS)
G, m, e2 = time_func.estimate_time_func(
model=model,
date_list=date_list,
dis_ts=ts_dis,
seconds=seconds)
# 1.2 calc the precision of time func parameters
# using the OLS estimation residues e2 = sum((d - Gm) ** 2)
# assuming obs errors following normal distribution in time
num_obs = len(date_list)
num_param = G.shape[1]
G_inv = linalg.inv(np.dot(G.T, G))
m_var_sum = e2.flatten() / (num_obs - num_param)
m_std = np.sqrt(np.dot(np.diag(G_inv).reshape(-1, 1), m_var_sum))
# 1.3 translate estimation result into HDF5 ready datasets
# AND compose list of strings for printout
m_dict = ts2vel.model2hdf5_dataset(model, m, m_std)[0]
m_strs = get_model_param_str(model, m_dict, unit_fac=unit_fac)
# 2. reconstruct the fine resolution function
if G_fit is not None:
ts_fit = np.matmul(G_fit, m)
ts_fit_std = np.sqrt(np.diag(G_fit.dot(np.diag(m_std**2)).dot(G_fit.T)))
# calc confidence interval
# references:
# 1. Exercise 6.4 OMT: Interpretation from Hanssen et al. (2017) EdX online course.
# Hanssen, R., Verhagen, S. and Samiei-Esfahany, S., (2017) Observation Theory: Estimating the Unknown,
# Available at: https://www.edx.org/course/observation-theory-estimating-the-unknown
# 2. https://stackoverflow.com/questions/20626994
alpha = 1 - conf_level # level of significance
conf_int_scale = stats.norm.ppf(1 - alpha / 2) # scaling factor for confidence interval
ts_fit_lim = [ts_fit - conf_int_scale * ts_fit_std,
ts_fit + conf_int_scale * ts_fit_std]
return m_strs, ts_fit, ts_fit_lim
def get_model_param_str(model, ds_dict, unit_fac=100):
"""Summary model parameters in a str paragraph.
Parameters: model - dict, model dictionary
ds_dict - dict, est. time func. param
unit_fac - float, unit scaling factor, to determine the unit
Returns: ds_strs - list of strings, each to summary the result of one time func
"""
# dataset unit dict
ds_unit_dict = ts2vel.model2hdf5_dataset(model)[2]
# update unit based on unit_fac
for ds_name, ds_unit in ds_unit_dict.items():
units = ds_unit.split('/')
if units[0] == 'm':
if unit_fac == 1000 : units[0] = 'mm'
elif unit_fac == 100 : units[0] = 'cm'
elif unit_fac == 10 : units[0] = 'dm'
elif unit_fac == 1 : units[0] = 'm'
elif unit_fac == 0.001: units[0] = 'km'
ds_unit_dict[ds_name] = '/'.join(units)
# list of dataset names
ds_names = [x for x in ds_dict.keys() if not x.endswith('Std')]
w_key = max([len(x) for x in ds_names])
w_val = max([len('{:.2f}'.format(x[0])) for x in ds_dict.values()])
ds_strs = []
for ds_name in ds_names:
# get param info
ds_value = ds_dict[ds_name]
ds_unit = ds_unit_dict[ds_name]
ds_std_value = ds_dict.get(ds_name+'Std', None)
# compose string
ds_str = f'{ds_name:<{w_key}}: {ds_value[0]:>{w_val}.2f}'
ds_str += f' +/- {ds_std_value[0]:>{w_val}.2f}' if ds_std_value is not None else ''
ds_str += f' {ds_unit}'
ds_strs.append(ds_str)
return ds_strs
def get_model_param_str(model, ds_dict, disp_unit='cm'):
"""Summary model parameters in a str paragraph.
Parameters: model - dict, model dictionary
ds_dict - dict, est. time func. param
disp_unit - float, display unit for length, which can be scaled
Returns: ds_strs - list of strings, each to summary the result of one time func
"""
# dataset unit dict
ds_unit_dict = ts2vel.model2hdf5_dataset(model)[2]
ds_names = list(ds_unit_dict.keys())
# update ds_unit_dict based on disp_unit
for ds_name in ds_names:
units = ds_unit_dict[ds_name].split('/')
if units[0] == 'm' and disp_unit != 'm':
units[0] = disp_unit
ds_unit_dict[ds_name] = '/'.join(units)
# list of dataset names
ds_names = [x for x in ds_dict.keys() if not x.endswith('Std')]
w_key = max([len(x) for x in ds_names])
w_val = max([len('{:.2f}'.format(x[0])) for x in ds_dict.values()])
ds_strs = []
for ds_name in ds_names:
# get param info
ds_value = ds_dict[ds_name]
ds_unit = ds_unit_dict[ds_name]
ds_std_value = ds_dict.get(ds_name + 'Std', None)
# compose string
ds_str = f'{ds_name:<{w_key}}: {ds_value[0]:>{w_val}.2f}'
ds_str += f' +/- {ds_std_value[0]:>{w_val}.2f}' if ds_std_value is not None else ''
ds_str += f' {ds_unit}'
ds_strs.append(ds_str)
return ds_strs