\(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\W}[1]{ \; #1 \; }\)
user_change_grid.py#
View page sourceRemove an Age or Time From a Smoothing#
Purpose#
This examples uses SQL commands to modify a data base. To be specific, it removes one of the age points from a smoothing grid.
Age Table#
The age_table for this example is specified by the code
age_list = [0, 1, 20, 30, 40, 50, 60, 70, 80, 90, 100 ]
Time Table#
The time_table is specified by
time_list = [ 1960, 1995 ]
Parent Smoothing#
The original parent smoothing table contains all of the age and time points.
Value Prior#
The value prior at each (age, time) pair is log-Gaussian with
lower limit 1 e-2 * iota_mean ,
upper limit 1 e +2* iota_mean ,
mean iota mean ,
standard deviation iota_mean ,
and the offset in the log transform 1 e-3 * iota_mean .
Difference Prior#
The forward difference prior at each (age, time) pair is log-Gaussian with
no lower limit,
no upper limit,
mean zero,
standard deviation 1.0 ,
and the offset in the log transform 1e-6 .
Change Parent Smoothing#
Note that the original age grid has 11 points. The last age point, and all the corresponding (age, time) pairs are removed from the smoothing grid with the following SQL commands:
UPDATE smooth SET n_age = 10 WHERE smooth_id == 0;
UPDATE smooth_grid SET smooth_id = WHERE smooth_id == 0 AND age_id == 10;
We refer to this as the modified smoothing.
Fit#
The only variables in this example are the parent rates for iota . Hence the number of variables in the var_table should be the number of grid points in the modified smoothing; i.e., 20. There is no data for this example. Hence the optimal fit is to have iota equal to iota_mean for all the (age, time) paris in the modified smoothing.
Source Code#
# ------------------------------------------------------------------------
iota_mean = 0.01
# ------------------------------------------------------------------------
import sys
import os
test_program = 'example/user/change_grid.py'
if sys.argv[0] != test_program or len(sys.argv) != 1 :
usage = 'python3 ' + test_program + '\n'
usage += 'where python3 is the python 3 program on your system\n'
usage += 'and working directory is the dismod_at distribution directory\n'
sys.exit(usage)
print(test_program)
#
# import dismod_at
local_dir = os.getcwd() + '/python'
if( os.path.isdir( local_dir + '/dismod_at' ) ) :
sys.path.insert(0, local_dir)
import dismod_at
#
# change into the build/example/user directory
if not os.path.exists('build/example/user') :
os.makedirs('build/example/user')
os.chdir('build/example/user')
# ------------------------------------------------------------------------
def example_db (file_name) :
# note that the a, t values are not used for this case
def fun_iota_parent(a, t) :
return ('prior_value', 'prior_diff', 'prior_diff')
import copy
import dismod_at
import math
# ----------------------------------------------------------------------
# age table
age_list = [0, 1, 20, 30, 40, 50, 60, 70, 80, 90, 100 ]
#
# time table
time_list = [ 1960, 1995 ]
#
# integrand table
integrand_table = [
{ 'name':'Sincidence' }
]
# node table
node_table = [
{ 'name':'world', 'parent':'' }
]
#
# weight table:
weight_table = list()
#
# covariate table:
covariate_table = list()
#
# mulcov table
mulcov_table = list()
# ----------------------------------------------------------------------
# data table:
data_table = list()
# ----------------------------------------------------------------------
# prior_table
prior_table = [
{ # prior_diff
'name': 'prior_diff',
'density': 'log_gaussian',
'lower': None,
'upper': None,
'mean': 0.0,
'std': 1.0,
'eta': 1e-6
},{ # prior_value
'name': 'prior_value',
'density': 'log_gaussian',
'lower': 1e-2 * iota_mean,
'upper': 1e+2 * iota_mean,
'mean': iota_mean,
'std': iota_mean,
'eta': 1e-3 * iota_mean
}
]
# ----------------------------------------------------------------------
# smooth table
age_id_list = range( len( age_list ) )
time_id_list = range( len( time_list ) )
smooth_table = [
{ # smooth_rate_parent
'name': 'smooth_rate_parent',
'age_id': age_id_list,
'time_id': time_id_list,
'mulstd_value_prior_name': None,
'mulstd_dage_prior_name': None,
'mulstd_dtime_prior_name': None,
'fun': fun_iota_parent
}
]
# ----------------------------------------------------------------------
# rate table
rate_table = [ {
'name': 'iota',
'parent_smooth': 'smooth_rate_parent'
} ]
# ----------------------------------------------------------------------
# option_table
option_table = [
{ 'name':'parent_node_name', 'value':'world' },
{ 'name':'ode_step_size', 'value':'10.0' },
{ 'name':'random_seed', 'value':'0' },
{ 'name':'rate_case', 'value':'iota_pos_rho_zero' },
{ 'name':'quasi_fixed', 'value':'true' },
{ 'name':'derivative_test_fixed', 'value':'none' },
{ 'name':'max_num_iter_fixed', 'value':'50' },
{ 'name':'print_level_fixed', 'value':'0' },
{ 'name':'tolerance_fixed', 'value':'1e-10' },
{ 'name':'derivative_test_random', 'value':'second-order' },
{ 'name':'max_num_iter_random', 'value':'50' },
{ 'name':'print_level_random', 'value':'0' },
{ 'name':'tolerance_random', 'value':'1e-10' }
]
# ----------------------------------------------------------------------
# avgint table: empty
avgint_table = list()
# ----------------------------------------------------------------------
# nslist_dict:
nslist_dict = dict()
# ----------------------------------------------------------------------
# subgroup_table
subgroup_table = [ { 'subgroup':'world', 'group':'world' } ]
# ----------------------------------------------------------------------
# create database
dismod_at.create_database(
file_name,
age_list,
time_list,
integrand_table,
node_table,
subgroup_table,
weight_table,
covariate_table,
avgint_table,
data_table,
prior_table,
smooth_table,
nslist_dict,
rate_table,
mulcov_table,
option_table
)
# ----------------------------------------------------------------------
#
file_name = 'example.db'
example_db(file_name)
# ===========================================================================
# remove one age from the original smoothing
# ===========================================================================
#
connection = dismod_at.create_connection(
file_name, new = False, readonly = False
)
age_table = dismod_at.get_table_dict(connection, 'age')
n_age = len( age_table )
#
# change number of ages in the smooth table
command = 'UPDATE smooth SET n_age = ' + str(n_age - 1) + ' '
command += 'WHERE smooth_id == 0;'
dismod_at.sql_command(connection, command)
#
# Remove the last grid point. Note that there is a new last age and the
# corresponding dage priors are not used (even though they are not null).
remove_index = int( n_age - 1 )
command = 'UPDATE smooth_grid SET smooth_id = null '
command += 'WHERE smooth_id == 0 AND age_id == ' + str(remove_index) + ';'
dismod_at.sql_command(connection, command)
#
# ===========================================================================
# do a fit and check results
# ===========================================================================
program = '../../devel/dismod_at'
dismod_at.system_command_prc([ program, file_name, 'init' ])
dismod_at.system_command_prc([ program, file_name, 'fit', 'both' ])
#
# Results for fitting with no noise
age_table = dismod_at.get_table_dict(connection, 'age')
time_table = dismod_at.get_table_dict(connection, 'time')
var_table = dismod_at.get_table_dict(connection, 'var')
fit_var_table = dismod_at.get_table_dict(connection, 'fit_var')
#
n_age = len( age_table )
n_time = len( time_table )
n_var = len( var_table )
assert n_var == (n_age - 1 ) * n_time
#
parent_node_id = 0
eps = 1e-4
#
# check parent rates values
iota_rate_id = 1
max_err = 0.0;
age_id_list = range( n_age )
for var_id in range( n_var ) :
row = var_table[var_id]
value = fit_var_table[var_id]['fit_var_value']
assert row['var_type'] == 'rate'
assert row['node_id'] == parent_node_id
assert row['rate_id'] == iota_rate_id
assert row['age_id'] in age_id_list
assert row['age_id'] != remove_index
max_err = max(max_err, abs( value / iota_mean - 1.0 ) )
assert abs(value / iota_mean - 1.0 ) <= 1e-2
# -----------------------------------------------------------------------------
print('change_grid.py: OK')
# -----------------------------------------------------------------------------