lib_delay_model module

Library for calculating delays using polynomial models.

Known issues

(!) Delays currently computed w.r.t. the first station, they should computed w.r.t. the center of the Earth instead.

TO DO

Compute absolute delays instead of relative to reference station.

lib_delay_model.apply_offset_coefficients_poly(poly_found, seconds_from_ref)

Apply offset to polynomial, i.e. given a list of polynomial coefficients [p0,p1,p2,...]

from low to high order for f(x), obtain coefficientes for f(x+s) where s is an offset:

q(x)=p(x+s)=p0+p1(x+s)+p2(x+s)^2+p3(x+s)^3+...

The functions returns the list of polynomial coefficients [q0,q1,q2,...] for q(x).

poly_found : list of float

list of polynomial coefficients [p0,p1,p2,...] (LIMIT_POLY_EVAL coefficients).

seconds_from_ref : float

offset in seconds.

poly_found : list of int

list of polynomial coefficients [q0,q1,p2,...] (LIMIT_POLY_FOUND coefficients).

seconds_from_ref : 0

(since this offset has been applied to the polynomial).

Configuration:

LIMIT_POLY_EVAL: maximum order coefficient in input. (e.g.: 5).

LIMIT_POLY_FOUND: maximum order coefficient in output (e.g.: 2).

lib_delay_model.compute_initial_delays(params_array_delay_model, params_array_stations, s_st, s_so, s_delay, mjd_start, seconds_ref_in, tot_steps, step_seconds, seconds_offset=0, v=1, file_ini='')

Main script for computing the initial delays and delay polynomials.

params_array_delay_model : list

information from delay model ini file (see lib_ini_files.py).

params_array_stations : list

information from stations ini file (see lib_ini_files.py).

s_st

configparser handler for stations ini.

s_so

configparser handler for sources ini.

s_delay

configparser handler for delays ini.

mjd_start

MJD for the start of the scan.

seconds_ref_in

seconds for the start of the scan.

tot_steps

number of accumulation periods.

step_seconds

accumulation period duration [s].

seconds_offset

[should be 0, consider removing]

v

verbose if 1.

file_ini

delays.ini output filename.

s_delay

configparser handler to delays.ini output filename.

TO DO:

Check seconds_offset, remove.

lib_delay_model.create_sections_config_delays(s_delay, s_st, s_so)

Add sections to the delay ini file handler.

s_delay

configparser handler for the delays ini file.

s_st

configparser handler for the station ini file.

s_so

configparser handler for the sources ini file.

s_delay : configparserhandler

updated version of input.

pairs_vv : list of str

list with headers, to be accessed using the station and source ids.

lib_delay_model.filter_roots(roots)

Return the real positive smallest delay from a list of complex. To be called after np_roots(pol).

roots : list of complex

roots of a delay polynomial.

min_val : float

result.

lib_delay_model.get_all_polynomials(params_array_delay_model, params_array_stations, s_st, s_so, mjd_start, seconds_ref, seconds_offset, tot_steps, step_seconds, v=0)

Read and pre-process the delay polynomials from the models in the ini files.

params_array_delay_model : list

list with configuration of delay_mode.ini.

params_array_stations : list

list with configuration of stations.ini.

s_st : configparser handler

configparser handler for the station ini file.

s_so : configparser handler

configparser handler for the sources ini file.

mjd_start

MJD for the start of the scan.

seconds_ref

seconds for the start of the scan.

seconds_offset

offset seconds from the start of the scan.

tot_steps

number of accumulation periods.

step_seconds

accumulation period duration.

v

verbose if 1.

seconds_inc_v : 3D list (tot_steps x sources x stations)

offset in seconds since scan start.

max_saved : 2D list (tot_steps x sources)

maximum delay for all stations.

min_saved : 2D list (tot_steps x sources)

minimum delay for all stations.

v_delays : 3D list (tot_steps x sources x stations)

delays in seconds.

v_delay_rates : 3D list (tot_steps x sources x stations)

lists with [poly_delay,seconds_from_ref,poly_station_clock, seconds_diff_clock,result_dr,result_cr,section_in_model] from get_polynomials_interval().

no_offset_total : int

number of times that manual offsets have been applied (based on .ini).

TO DO:

Check seconds_offset.

lib_delay_model.get_delay_shift_frac(delay, fs, data_type=0)

Compute integer and fractional shift.

delay : float

value for the delay [s].

fs : float

sampling frequency [Hz].

data_type : int

0 for real, 1 for complex.

shift_int : int

offset in number of samples.

fractional_sample_delay : float

fractional sample.

Data type is for being used with complex samples unpacked as a list of integers (in msvf),

otherwise it should be left as zero.

lib_delay_model.get_delay_val(clock_diff, poly_diff, seconds_ref_clock, seconds_ref_poly, seconds, seconds_offset, v=0, diff_pol=1)

Compute delays at seconds_offset+seconds, considering the offsets for each polynomial (seconds_ref_clock and seconds_ref_poly).

clock_diff : list of float

polynomial for station clock delay.

poly_diff : list of float

polynomial for geometric model delay.

seconds_ref_clock : float

offset for the station clock polynomial.

seconds_ref_poly : float

offset for the geometric model polynomial.

seconds : float 1D np.array

seconds (for evaluating polys).

seconds_offset : float

offset to be applied to seconds.

v : int

verbose if 1.

diff_pol : int

1 if using differential polynomials.

r_recalc : float 1D np.array

delays in seconds (model+clock)

m_delay : float 1D np.array

delays in seconds (model)

c_delay : float 1D np.array

delays in seconds (clock)

rate_mc : list of int

[0]

acce_mc : list of int

[0]

Assumptions:

If the four first elements of poly_diff are zero the resulting model delay is zero to avoid calling polyval.

Notes:

simple offset reduces the computation of the offset to only the first value in the timescale provided in seconds.

No correction for retarded baselines.

TO DO:

This needs further work.

Remove rate_mc and acce_mc, no longer used.

Check diff_pol, different behavior ini_exper and lib_fx...

lib_delay_model.get_full_frac_val(r_recalc, fs, diff_frac=0, bypass_correction=0)

Compute total offset in number of samples, and also fractional sample correction.

r_recalc : float

delay.

fs : float

sampling frequency.

diff_frac : 0

[unused] 0 by default.

bypass_correction : int

if 0: corrects the fractional sample correction to be between -0.5 and +0.5.

if 1: returns the fractional sample correction between 0 and 1.

full_fractional_recalc : float

total offset in number of samples, including fractional part.

fractional_recalc : float

fractional sample correction.

Bypass correction used in get_frac_over for simplicity.

lib_delay_model.get_initial_abe(poly_delay, seconds_ref_poly, seconds_offset=0)

Compute delay due to aberration.

lib_delay_model.get_poly_clock(params_array, section_str)

Get list with poly from params array and section string. Clock correction.

params_array : list

information from delay model ini file (see lib_ini_files.py).

section_str : str

section of the ini file associated with a certain station, source and time (see const_ini_files.py)

poly_model : list of float

list of [m-th coeff] with polynomial coefficients for the station clock model with m from zero to max_order-1, in seconds.

lib_delay_model.get_poly_list(params_array, section_str)

Get list with poly from params array and section string.

params_array : list

information from delay model ini file (see lib_ini_files.py).

section_str : str

section of the ini file associated with a certain station, source and time (see const_ini_files.py)

poly_model : list of float

list of [n-th coeff] with polynomial coefficients for the delay model with n from zero to max_order, in seconds.

Configuration (constants):

LIMIT_POLY_EVAL: [2 by default] maximum order coefficient of the polynomial.

Notes:

Coefficients in the delay model ini file are in microseconds, output polynomials in seconds.

lib_delay_model.get_polynomials_interval(params_array_delay_model, params_array_stations, mjd, seconds_ref, seconds_from_ref, source_id, station_id, v, current_offset=0)

Get the polynomials for the delay and clock models for a given station, source and time:

-day: MJD. -seconds: seconds_ref+seconds_from_ref.

params_array_delay_model : list

information from delay model ini file (see lib_ini_files.py).

params_array_stations : list

information from stations ini file (see lib_ini_files.py).

mjd : int

MJD for the start of the scan.

seconds_ref : int or float

seconds for the start of the scan.

seconds_from_ref : int or float

offset seconds from the start of the scan.

source_id : int

source id.

station_id : int

station id.

v : int

verbose if 1.

result : float

delay [s].

poly_found

polynomial (see get_poly_list() for format).

seconds_from_ref

[check this]

poly_station_clock

polynomial for the station clock.

seconds_diff_clock

seconds between the epoch and the start of the clock.

result_dr

geometric delay [s].

result_cr

station clock delay [s].

error_model : { 0, None}

0 if success, None if error.

section_in_model : str

section in the delay model .ini file (for debugging).

no_offset : int

0 if no offset applied from .ini file [default], 1 otherwise.

Limitations:

Currently single source source_id=0.

Notes:

It returns delay from model ini file.

If no model is available returns None.

Clock polynomial always zero offset with respect to start time, thus no need to offset (unless delta from start).

TO DO:

Organize.

Further testing on precision.

lib_delay_model.get_str_scf(val, tot_dec_pos=16)

Get string representation of float, used for normalization.

lib_delay_model.np_polyder(pol, x, o)

Get derivative of order o at x. Numpy polyval, changing order of polynomial (numpy is decreasing order).

See np_polyval() for more info.

lib_delay_model.np_polyval(pol, x)

Evaluate a polynomial at x. Numpy polyval, changing order of polynomial (numpy is decreasing order).

pol : list of floats

polynomial, leftmost term is zero order.

x : float

value to be evaluated.

out : float

result.

-For numpy polyval the rightmost term is zero order.

(!) –Excerpt from the reference– “Notes:Horner’s scheme [R65] is used to evaluate the polynomial.

Even so, for polynomials of high degree the values may be inaccurate due to rounding errors.

Use carefully.”

lib_delay_model.np_roots(pol)

Get roots of a polynomial. Numpy roots, changing order.

pol : list of floats

polynomial, leftmost term is zero order.

out : list of complex

roots of the polynomial.

lib_delay_model.print_delays(sti, poly_total, poly_clock, t0, t_display=None, v=1)

Print delay information in [us] for debugging.

sti : int

station id.

poly_total : list of floats

polynomial for total delay (leftmost is zero order).

poly_clock : list of floats

polynomial for clock (leftmost is zero order).

t0 : float

time to evaluate polynomials at.

t_display : float

time to be displayed.

v : int

verbose mode if 1.

str_out : str

line with delay information.

lib_delay_model.print_delays_header(v=1)

Print header for summary of delay information.

v : int

verbose mode if 1.

str_out : str

line with header.

lib_delay_model.set_config_delay(s_delay, st_so, seconds_i, a_delay, r_delay, f_delay, poly_diff, clock_diff, clock_abs, seconds_from_ref, seconds_diff_clock, m_delay, c_delay, delta_reference_delay, section_in_model)

Save configuration parameters to delay ini file handler.

s_delay : configparser handler

configparser handler for the delays ini file (to be written).

st_so : str

station - source.

seconds_i : int or float

seconds for the start of this interval since the start of the scan.

a_delay : float

absolute delay [s].

r_delay : float

relative delay (w.r.t. reference station) [s]

f_delay : float

[unused?]

poly_diff : list of float

polynomial for geometric delay.

clock_diff : list of float

polynomial for station clock delay.

clock_abs : float

[unused?] initially for ref station clock.

seconds_from_ref : float

[same as seconds_i ?]

seconds_diff_clock : float

seconds from epoch for the clock (zero if offset).

m_delay : float

geometric-model-only delay.

c_delay : float

clock-only delay.

delta_reference_delay

[unused?]

section_in_model : str

section in delay model (for debugging).

s_delay : configparser handler

updated version of input with added information.