if bool == False:
print('Equation ' + np.str(m+1) + \
' is NOT satisfied. Check for errors!')
# Set iteration number to zero
it_num = 0
# Put all initial mole numbers in y array
y = y_init
# Make y_bar (sum of all y values)
y_bar = np.sum(y)
# Initialize delta variables to 0. (this signifies the first iteration)
delta = np.zeros(i)
delta_bar = np.sum(delta)
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-machine-read.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual.txt'
# Put results into machine readable file
form.output(datadir, header, it_num, speclist, y, y, delta, \
y_bar, y_bar, delta_bar, file, doprint)
# Put results into human readable file
form.fancyout(datadir, it_num, speclist, y, y, delta, y_bar, \
y_bar, delta_bar, file_fancy, doprint)
def lambdacorr(it_num, verb, input, info, save_info=None):
'''
This module applies lambda correction method (Section 4 in the TEA theory
document). When input mole numbers are negative, the code corrects them to
positive values and pass them to the next iteration cycle. The code reads
the values from the last lagrange output, the information from the header
file, performs checks, and starts setting basic equations. It defines a
'smart' range so it can efficiently explore the lambda values from [0,1].
Half of the range is sampled exponentially, and the other half linearly,
totalling 150 points. The code retrieves the last lambda value before first
derivative becomes positive (equation (34) in TEA theory document), and
corrects negative mole numbers to positive.
Parameters
----------
it_num: integer
Iteration number.
verb: Integer
Verbosity level (0=mute, 1=quiet, 2=verbose).
input: List
A list containing the results/data from the previous
calculation in lagrange.py or lambdacorr.py:
the current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
info: list
pressure: atmospheric layer's pressure (bar)
i: Number of species
j: Number of elements
a: Stoichiometric coefficients
b: Elemental mixing fractions
g_RT: Species chemical potential
save_info: List of stuff
If not None, save info to files. The list contains:
[location_out, desc, speclist, temp]
Returns
-------
y: array of floats
The initial guess of molecular species.
x_corr: array of floats
Final mole numbers of molecular species.
delta_corr: array of floats
Array containing change of initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Total initial guess of all molecular species for
current iteration.
x_corr_bar: float
Total sum of the final mole numbers of all molecular species.
detla_corr_bar: float
Change in total number of all species.
verb: Integer
Verbosity level (0=mute, 1=quiet, 2=verbose).
Notes
-----
The code works without adjustments for the temperatures above ~500 K.
For temperatures below 500 K the code produces results with low
precision, thus it is not recommended to use TEA below 500 K.
Setting xtol to 1e-8 and maxinter to 200 is most optimizing.
If higher tolerance level is desired (xtol>1e-8), maxium number
of iterations must be increased. The result can be further improved
with fine adjustments to the lambda exploration variables
'lower' and 'steps' to larger magnitudes
(i.e., lower = -100, steps = 1000). This will lengthen the time
of execution.
'''
# Suppress nan warnings, as they are used for finding valid minima
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
pressure = info[0]
i = info[1]
g_RT = info[5]
# Take final values from last iteration, lagrange.py
y = input[0]
x = input[1]
delta = input[2]
y_bar = input[3]
x_bar = input[4]
delta_bar = input[5]
# Create 'c' value, equation (17) TEA theory document
# c_i = (g/RT)i + ln(P)
c = g_RT + np.log(pressure)
# Create the range of lambda values to explore. To speed up finding
# the correct lambda value to use, the range is split into two
# parts at range_split: the lower exponential range and the
# higher linear range. This helps the system to converge faster.
range_split = 0.5
# Create exponential range, low_range
# Exponent parameter that gives a value close to zero for the start of
# lambda exploration
lower = -50
# Define number of steps to explore exponential range
steps = 100
# Create lower exponential range
low_range = np.exp(np.linspace(lower, 0, steps+1))
# Create linear, evenly spaced range, high_range
high_step = 0.01
high_range = np.arange(0.5, 1 + high_step, high_step)
# Combine the two ranges to create one overall range for lambda exploration
smart_range = np.append(low_range[low_range <= range_split], high_range)
# Set that lambda is not found
lam_not_found = True
# Retrieve last lambda value explored before the minimum energy is passed
for h in smart_range:
val = dF_dlam(h, i, x, y, delta, c, x_bar, y_bar, delta_bar)
if val > 0 or np.isnan(val):
break
# If lambda found, take lambda and set lambda not found to false
lam = h
lam_not_found = False
# If lambda is not found (break), function F (equation (33) in the TEA
# theory document) set the final x mole numbers to the values calculated
# in the last iteration output
if lam_not_found:
x_corr = y
else:
x_corr = y + lam * delta
# Correct x values given this value of lambda
x_corr_bar = np.sum(x_corr)
delta_corr = y - x_corr
delta_corr_bar = x_corr_bar - y_bar
if save_info is not None:
location_out, desc, speclist, temp = save_info
hfolder = location_out + desc + "/headers/"
headerfile = "{:s}/header_{:s}_{:.0f}K_{:.2e}bar.txt".format(
hfolder, desc, temp, pressure)
# Create and name outputs and results directories if they do not exist
datadir = location_out + desc + '/outputs/'
datadir = "{:s}/{:s}_{:.0f}K_{:.2e}bar/".format(
datadir, desc, temp, pressure)
# Export all values into machine and human readable output files
file = '{:s}/lagrange_iteration-{:03d}_machine-read.txt'.format(
datadir, it_num)
form.output(headerfile, it_num, speclist, y, x_corr, delta_corr,
y_bar, x_corr_bar, delta_corr_bar, file, verb)
file = '{:s}/lagrange_iteration-{:03d}_visual.txt'.format(
datadir, it_num)
form.fancyout(it_num, speclist, y, x_corr, delta_corr, y_bar,
x_corr_bar, delta_corr_bar, file, verb)
return y, x_corr, delta_corr, y_bar, x_corr_bar, delta_corr_bar
def lambdacorr(it_num, datadir, doprint, direct):
'''
This module applies lambda correction method (see Section 4 in the TEA theory
document). When input mole numbers are negative, the code corrects them to
positive values and pass them to the next iteration cycle. The code reads
the values from the last lagrange output, the information from the header
file, performs checks, and starts setting basic equations. It defines a
'smart' range so it can efficiently explore the lambda values from [0,1].
Half of the range is sampled exponentially, and the other half linearly,
totalling 150 points. The code retrieves the last lambda value before first
derivative becomes positive (equation (34) in TEA theory document), and
corrects negative mole numbers to positive.
Parameters
----------
it_num: integer
Iteration number.
datadir: string
Current directory where TEA is run.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
direct: object
Object containing all of the results/data from the previous
calculation in lagrange.py or lambdacorr.py. It is a list
containing current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
Returns
-------
header: string
Name of the header file used.
it_num: integer
Iteration number.
speclist: array of strings
Array containing names of molecular species.
y: array of floats
Array containing initial guess of molecular species for
current iteration.
x_corr: array of floats
Array containing final mole numbers of molecular species for
current iteration.
delta_corr: array of floats
Array containing change of initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Array containing total initial guess of all molecular species for
current iteration.
x_corr_bar: float
Total sum of the final mole numbers of all molecular species.
detla_corr_bar: float
Change in total number of all species.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
Notes
-----
The code works without adjustments and with high precision for the
temperatures above ~600 K. For temperatures below 600 K and
mixing fractions below 10e-14, the code produces results with low
precision. To improve the precision, adjust the lambda exploration
variables 'lower' and 'steps' to larger magnitudes (i.e., lower = -100,
steps = 1000). This will lengthen the time of execution.
'''
# Suppress nan warnings, as they are used for finding valid minima
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
# Read values from last lagrange output
input = direct
# Take the current header file
header = input[0]
# Read values from the header file
pressure, temp, i, j, speclist, a, b, g_RT = form.readheader(header)
# Take final values from last iteration, lagrange.py
y = input[3]
x = input[4]
delta = input[5]
y_bar = input[6]
x_bar = input[7]
delta_bar = input[8]
# Perform checks to be safe
it_num_check = input[1]
speclist_check = input[2]
# Make array of checks
check = np.array(
[it_num_check != it_num, False in (speclist_check == speclist)])
# If iteration number given by iterate.py is not one larger as in 'direct',
# give error
if check[0]:
print("\n\nMAJOR ERROR! Read in file's it_num is not the \
current iteration!\n\n")
# If species names in the header are not the same as in 'direct',
# give error
if check[1]:
print("\n\nMAJOR ERROR! Read in file uses different species \
order/list!\n\n")
# Create 'c' value, equation (17) TEA theory document
# c_i = (g/RT)i + ln(P)
c = g_RT + np.log(pressure)
# Set equation (34) TEA theory document
# dF(lam)/dlam = sum_i delta_i[(g(T)/RT)_i + lnP +
# ln (yi+lam*delta_i)/(y_bar+lam*delta_bar)]
def dF_dlam(s, i, x, y, delta, c, x_bar, y_bar, delta_bar):
dF_dlam = 0
for n in np.arange(i):
dF_dlam += delta[n] * (c[n] + np.log(y[n] + s*delta[n]) - \
np.log(y_bar + s*delta_bar))
return dF_dlam
# Create the range of lambda values to explore. To speed up finding
# the correct lambda value to use, the range is split into two
# parts at range_split: the lower exponential range and the
# higher linear range. This helps the system to converge faster.
range_split = 0.5
# Create exponential range, low_range
# Exponent parameter that gives a value close to zero for the start of
# lambda exploration
lower = -50
# Define number of steps to explore exponential range
steps = 100
# Create lower exponential range
low_range = np.exp(np.linspace(lower, 0, steps + 1))
# Create linear, evenly spaced range, high_range
high_step = 0.01
high_range = np.arange(0.5, 1 + high_step, high_step)
# Combine the two ranges to create one overall range for lambda exploration
smart_range = np.append(low_range[low_range <= range_split], high_range)
# Set that lambda is not found
lam_not_found = True
# Retrieve last lambda value explored before the minimum energy is passed
for h in smart_range:
val = dF_dlam(h, i, x, y, delta, c, x_bar, y_bar, delta_bar)
if val > 0 or np.isnan(val) == True:
break
# If lambda found, take lambda and set lambda not found to false
lam = h
lam_not_found = False
# If lambda is not found (break), function F (equation (33) in the TEA
# theory document) set the final x mole numbers to the values calculated
# in the last iteration output
if lam_not_found:
x_corr = y
else:
x_corr = y + lam * delta
# Correct x values given this value of lambda
x_corr_bar = np.sum(x_corr)
delta_corr = y - x_corr
delta_corr_bar = x_corr_bar - y_bar
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-machine-read.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual.txt'
# Export all values into machine and human readable output files
form.output(datadir, header, it_num, speclist, y, x_corr, delta_corr, \
y_bar, x_corr_bar, delta_corr_bar, file, doprint)
form.fancyout(datadir, it_num, speclist, y, x_corr, delta_corr, y_bar, \
x_corr_bar, delta_corr_bar, file_fancy, doprint)
return [header, it_num, speclist, y, x_corr, delta_corr, y_bar, \
x_corr_bar, delta_corr_bar, doprint]
def lambdacorr(it_num, datadir, doprint, direct):
'''
This module applies lambda correction method (see Section 1.3 in TEA
Document). When input mole numbers are negative, the code corrects them to
positive values and pass them to the next iteration cycle. The code reads
the values from the last lagrange output, the information from the header
file, performs checks, and starts setting basic equations. It sets a smart
range so it can efficiently explore the lambda values from [0,1]. Half of
the range is sampled exponentially, and the other half linearly, totalling
150 points. The code retrieves the last lambda value before first
derivative becomes positive (equation (33) in TEA Document), and corrects
negative mole numbers to positive.
Parameters
----------
it_num: integer
Iteration number.
datadir: string
Current directory where TEA is run.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
direct: object
Object containing all of the results/data from the previous
calculation in lagrange.py or lambdacorr.py. It is a list
containing current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
Returns
-------
header: string
Name of the header file used.
it_num: integer
Iteration number.
speclist: array of strings
Array containing names of molecular species.
y: array of floats
Array containing initial guess of molecular species for
current iteration.
x_corr: array of floats
Array containing final mole numbers of molecular species for
current iteration.
delta_corr: array of floats
Array containing change of initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Array containing total initial guess of all molecular species for
current iteration.
x_corr_bar: float
Total sum of the final mole numbers of all molecular species.
detla_corr_bar: float
Change in total number of all species.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
Notes
-----
The code works without adjustments and with high precision for the
the fractional abundances (mixing fractions) up to 10e-14 and the
temperature range of 1000 - 4000 K. For temperatures below 1000 K and
mixing fractions below 10e-14, the code produces results with low
precision. To improve the precision, adjust the lambda exploration
variables 'lower' and 'steps' to larger magnitudes (i.e., lower = -100,
steps = 1000). This will lengthen the time of execution.
'''
# Suppress nan warnings, as they are used for finding valid minima
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
# Read values from last lagrange output
input = direct
# Take the current header file
header = input[0]
# Read values from the header file
pressure, temp, i, j, speclist, a, b, g_RT = form.readheader(header)
# Take final values from last iteration, lagrange.py
y = input[3]
x = input[4]
delta = input[5]
y_bar = input[6]
x_bar = input[7]
delta_bar = input[8]
# Perform checks to be safe
it_num_check = input[1]
speclist_check = input[2]
# Make array of checks
check = np.array([it_num_check != it_num,
False in (speclist_check == speclist) ])
# If iteration number given by iterate.py is not one larger as in 'direct',
# give error
if check[0]:
print("\n\nMAJOR ERROR! Read in file's it_num is not the \
current iteration!\n\n")
# If species names in the header are not the same as in 'direct',
# give error
if check[1]:
print("\n\nMAJOR ERROR! Read in file uses different species \
order/list!\n\n")
# Create 'c' value, equation (16) TEA Document
# c_i = (g/RT)i + ln(P)
c = g_RT + np.log(pressure)
# Set equation (33) TEA Document
# dF(lam)/dlam = sum_i delta_i[(g(T)/RT)_i + lnP +
# ln (yi+lam*delta_i)/(y_bar+lam*delta_bar)]
def dF_dlam(s, i, x, y, delta, c, x_bar, y_bar, delta_bar):
dF_dlam = 0
for n in np.arange(i):
dF_dlam += delta[n] * (c[n] + np.log(y[n] + s*delta[n]) - \
np.log(y_bar + s*delta_bar))
return dF_dlam
# Create the range of lambda values to explore. To speed up finding
# the correct lambda value to use, the range is split into two
# parts at range_split: the lower exponential range and the
# higher linear range. This helps the system to converge faster.
range_split = 0.5
# Create exponential range, low_range
# Exponent parameter that gives a value close to zero for the start of
# lambda exploration
lower = -50
# Define number of steps to explore exponential range
steps = 100
# Create lower exponential range
low_range = np.exp(np.linspace(lower, 0, steps+1))
# Create linear, evenly spaced range, high_range
high_step = 0.01
high_range = np.arange(0.5, 1 + high_step, high_step)
# Combine the two ranges to create one overall range for lambda exploration
smart_range = np.append(low_range[low_range <= range_split], high_range)
# Set that lambda is not found
lam_not_found = True
# Retrieve last lambda value explored before the minimum energy is passed
for h in smart_range:
val = dF_dlam(h, i, x, y, delta, c, x_bar, y_bar, delta_bar)
if val > 0 or np.isnan(val) == True:
break
# If lambda found, take lambda and set lambda not found to false
lam = h
lam_not_found = False
# If lambda is not found (break), function F (equation (35) in TEA
# Document) set the final x mole numbers to the values calculated
# in the last iteration output
if lam_not_found:
x_corr = y
else:
x_corr = y + lam * delta
# Correct x values given this value of lambda
x_corr_bar = np.sum(x_corr)
delta_corr = y - x_corr
delta_corr_bar = x_corr_bar - y_bar
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-machine-read.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual.txt'
# Export all values into machine and human readable output files
form.output(datadir, header, it_num, speclist, y, x_corr, delta_corr, \
y_bar, x_corr_bar, delta_corr_bar, file, doprint)
form.fancyout(datadir, it_num, speclist, y, x_corr, delta_corr, y_bar, \
x_corr_bar, delta_corr_bar, file_fancy, doprint)
return [header, it_num, speclist, y, x_corr, delta_corr, y_bar, \
x_corr_bar, delta_corr_bar, doprint]
def lagrange(it_num, verb, input, info, save_info=None):
'''
This code applies Lagrange's method and calculates minimum based
on the methodology elaborated in the TEA theory document in
Section (3). Equations in this code contain both references and
an explicitly written definitions.
The program reads the last iteration's output and data from the
last header file, creates variables for the Lagrange equations,
sets up the Lagrange equations, and calculates final x_i mole
numbers for the current iteration cycle. Note that the mole
numbers that result from this function are allowed to be
negative. If negatives are returned, lambda correction
(lambdacorr.py) is necessary. The final x_i values, as well as
x_bar, y_bar, delta, and delta_bar are written into machine- and
human-readable output files. This function is executed by
iterate.py.
Parameters
----------
it_num: integer
Iteration number.
verb: Integer
Verbosity level (0=mute, 1=quiet, 2=verbose).
input: List
The input values/data from the previous
calculation in lagrange.py or lambdacorr.py. It is a list
containing current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
info: List
pressure: atmospheric layer's pressure (bar)
i: Number of species
j: Number of elements
a: Stoichiometric coefficients
b: Elemental mixing fractions
g_RT: Species chemical potential
save_info: string
Current directory where TEA is run.
Returns
-------
y: float array
Input guess of molecular species.
x: float array
Final mole numbers of molecular species.
delta: float array
Array containing change in initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Array containing total sum of initial guesses of all molecular
species for current iteration.
x_bar: float
Total sum of the final mole numbers of all molecular species.
delta_bar: float
Change in total of initial and final mole numbers of molecular
species.
'''
# Read values from the header file
pressure = info[0]
j = info[2]
a = info[3]
b = info[4]
g_RT = info[5]
# Use final values from last iteration (x values) as new initial
y = input[1]
y_bar = input[4]
# ============== CREATE VARIABLES FOR LAGRANGE EQUATION ============== #
# Create 'c' value, equation (18) TEA theory document
# ci = (g/RT)_i + ln(P)
c = g_RT + np.log(pressure)
# Fill in fi(Y) values equation (19) TEA theory document
# fi = x_i * [ci + ln(x_i/x_bar)]
fi_y = y * (c + np.log(y / y_bar))
# Allocate value of u, equation (28) TEA theory document
# List all unknowns in the above set of equations
unknowns = [None] * (j + 1)
# Allocate pi_j, where j is element index
for m in np.arange(j):
unknowns[m] = Symbol('pi_' + str(m + 1))
unknowns[j] = Symbol('u')
# ================= SET SYSTEM OF EQUATIONS ======================= #
# Total number of equations is j + 1
# Create first j'th equations equation (27) TEA theory document
# r_1j*pi_1 + r_2j*pi_2 + ... + r_jj*pi_j + b_j*u = sum_i[a_ij * fi(Y)]
system = np.zeros((j + 1, j + 2))
# Fill out values of r_ij, equation (26) TEA theory document
# rjk = rkj = sum_i(a_ij * a_ik) * y_i
for l in np.arange(j):
for m in np.arange(j):
system[m, l] = np.sum(a[:, m] * a[:, l] * y)
# Last column, b_j*u:
system[:j, j] = b
# Set up a_ij * fi(Y) summations equation (27) TEA theory document
# sum_i[a_ij * fi(Y)]
system[:j, j + 1] = np.sum(a.T * fi_y, axis=1)
# Last (j+1)th equation (27) TEA theory document
# b_1*pi_1 + b_2*pi_2 + ... + b_m*pi_m = sum_i[fi(Y)]
system[j, :j] = b
system[j, j + 1] = np.sum(fi_y)
# Solve final system of j+1 equations
fsol = solve_linear_system(Matrix(system), *unknowns)
# Make array of pi values
pi_f = np.zeros(j, np.double)
for m in np.arange(j):
pi_f[m] = fsol[unknowns[m]]
fsolu = fsol[unknowns[j]]
# ============ CALCULATE xi VALUES FOR CURRENT ITERATION ============ #
# Calculate x_bar from solution to get 'u', eq (28) TEA theory document
# u = -1. + (x_bar/y_bar), where fsolu is u
x_bar = (fsolu + 1.0) * y_bar
# Apply Lagrange solution for final set of x_i values for this iteration
# equation (23) TEA theory document
# x_i = -fi(Y) + (y_i/y_bar) * x_bar + [sum_j(pi_j * a_ij)] * y_i
sum_pi_aij = np.sum(pi_f * a, axis=1)
x = np.array(-fi_y + (y / y_bar) * x_bar + sum_pi_aij * y, np.double)
# Calculate other variables of interest
x_bar = np.sum(x) # sum of all x_i
delta = x - y # difference between initial and final values
delta_bar = x_bar - y_bar # difference between sum of initial and
# final values
# Name output files with corresponding iteration number name
if save_info:
location_out, desc, speclist, temp = save_info
hfolder = location_out + desc + "/headers/"
headerfile = "{:s}/header_{:s}_{:.0f}K_{:.2e}bar.txt".format(
hfolder, desc, temp, pressure)
# Create and name outputs and results directories if they do not exist
datadir = location_out + desc + '/outputs/'
datadir = "{:s}/{:s}_{:.0f}K_{:.2e}bar/".format(
datadir, desc, temp, pressure)
if not os.path.exists(datadir):
os.makedirs(datadir)
# Export all values into machine and human readable output files
file = '{:s}/lagrange_iteration-{:03d}_machine-read-nocorr.txt'.format(
datadir, it_num)
form.output(headerfile, it_num, speclist, y, x, delta, y_bar, x_bar,
delta_bar, file, verb)
file = '{:s}/lagrange_iteration-{:03d}_visual-nocorr.txt'.format(
datadir, it_num)
form.fancyout(it_num, speclist, y, x, delta, y_bar, x_bar, delta_bar,
file, verb)
return y, x, delta, y_bar, x_bar, delta_bar
def lagrange(it_num, datadir, doprint, direct):
'''
This code applies Lagrange's method and calculates minimum based on the
methodology elaborated in the TEA theory document in Section (3). Equations in
this code contain both references and an explicitly written definitions.
The program reads the last iteration's output and data from the last header
file, creates variables for the Lagrange equations, sets up the Lagrange
equations, and calculates final x_i mole numbers for the current iteration
cycle. Note that the mole numbers that result from this function are
allowed to be negative. If negatives are returned, lambda correction
(lambdacorr.py) is necessary. The final x_i values, as well as x_bar,
y_bar, delta, and delta_bar are written into machine- and human-readable
output files. This function is executed by iterate.py.
Parameters
----------
it_num: integer
Iteration number.
datadir: string
Current directory where TEA is run.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
direct: object
Object containing all of the results/data from the previous
calculation in lagrange.py or lambdacorr.py. It is a list
containing current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
Returns
-------
header: string
Name of the header file used.
it_num: integer
Iteration number.
speclist: string array
Array containing names of molecular species.
y: float array
Array containing initial guess of molecular species for
current iteration.
x: float array
Array containing final mole numbers of molecular species for
current iteration.
delta: float array
Array containing change in initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Array containing total sum of initial guesses of all molecular
species for current iteration.
x_bar: float
Total sum of the final mole numbers of all molecular species.
delta_bar: float
Change in total of initial and final mole numbers of molecular
species.
'''
# Read values from last iteration
input = direct
# Take the current header file
header = input[0]
# Read values from the header file
pressure, temp, i, j, speclist, a, b, g_RT = form.readheader(header)
# Use final values from last iteration (x values) as new initial
y = input[4]
y_bar = input[7]
# Perform checks to be safe
it_num_check = input[1]
speclist_check = input[2]
# Make array of checks
check = np.array([it_num_check != it_num - 1,
False in (speclist_check == speclist) ])
# If iteration number given by iterate.py is not one larger as in 'direct',
# give error
if check[0]:
print("\n\nMAJOR ERROR! Read in file's it_num is not the most \
recent iteration!\n\n")
# If species names in the header are not the same as in 'direct',
# give error
if check[1]:
print("\n\nMAJOR ERROR! Read in file uses different species \
order/list!\n\n")
# ============== CREATE VARIABLES FOR LAGRANGE EQUATION ============== #
# Create 'c' value, equation (18) TEA theory document
# ci = (g/RT)_i + ln(P)
c = g_RT + np.log(pressure)
# Allocates array of fi(Y) over different values of i (species)
fi_y = np.zeros(i)
# Fill in fi(Y) values equation (19) TEA theory document
# fi = x_i * [ci + ln(x_i/x_bar)]
for n in np.arange(i):
y_frac = np.float(y[n] / y_bar)
fi_y[n] = y[n] * ( c[n] + np.log(y_frac) )
# Allocate values of rjk. Both j and k goes from 1 to m.
k = j
rjk = np.zeros((j,k))
# Fill out values of rjk, equation (26) TEA theory document
# rjk = rkj = sum_i(a_ij * a_ik) * y_i
for l in np.arange(k):
for m in np.arange(j):
r_sum = 0.0
for n in np.arange(i):
r_sum += a[n, m] * a[n, l] * y[n]
rjk[m, l] = r_sum
# Allocate value of u, equation (28) TEA theory document
u = Symbol('u')
# Allocate pi_j variables, where j is element index
# Example: pi_2 is Lagrange multiplier of N (j = 2)
pi = []
for m in np.arange(j):
name = 'pi_' + np.str(m+1)
pi = np.append(pi, Symbol(name))
# Allocate rjk * pi_j summations, equation (27) TEA theory document
# There will be j * k terms of rjk * pi_j
sq_pi = [pi]
for m in np.arange(j-1):
# Make square array of pi values with shape j * k
sq_pi = np.append(sq_pi, [pi], axis = 0)
# Multiply rjk * sq_pi to get array of rjk * pi_j
# equation (27) TEA theory document
rpi = rjk * sq_pi
# ======================= SET FINAL EQUATIONS ======================= #
# Total number of equations is j + 1
# Set up a_ij * fi(Y) summations equation (27) TEA theory document
# sum_i[a_ij * fi(Y)]
aij_fiy = np.zeros((j))
for m in np.arange(j):
rhs = 0.0
for n in np.arange(i):
rhs += a[n,m] * fi_y[n]
aij_fiy[m] = rhs
# Create first j'th equations equation (27) TEA theory document
# r_1m*pi_1 + r_2m*pi_2 + ... + r_mm*pi_m + b_m*u = sum_i[a_im * fi(Y)]
for m in np.arange(j):
if m == 0:
equations = np.array([np.sum(rpi[m]) + b[m]*u - aij_fiy[m]])
else:
lagrange_eq = np.array([np.sum(rpi[m]) + b[m]*u - aij_fiy[m]])
equations = np.append(equations, lagrange_eq)
# Last (j+1)th equation (27) TEA theory document
# b_1*pi_1 + b_2*pi_2 + ... + b_m*pi_m + 0*u = sum_i[fi(Y)]
bpi = b * pi
lagrange_eq_last = np.array([np.sum(bpi) - np.sum(fi_y)])
equations = np.append(equations, lagrange_eq_last)
# List all unknowns in the above set of equations
unknowns = list(pi)
unknowns.append(u)
# Solve final system of j+1 equations
fsol = solve(list(equations), unknowns, rational=False)
# ============ CALCULATE xi VALUES FOR CURRENT ITERATION ============ #
# Make array of pi values
pi_f = []
for m in np.arange(j):
pi_f = np.append(pi_f, [fsol[pi[m]]])
# Calculate x_bar from solution to get 'u', equation (28) TEA theory document
# u = -1. + (x_bar/y_bar)
u_f = fsol[u]
x_bar = (u_f + 1.) * y_bar
# Initiate array for x values of size i
x = np.zeros(i)
# Apply Lagrange solution for final set of x_i values for this iteration
# equation (23) TEA theory document
# x_i = -fi(Y) + (y_i/y_bar) * x_bar + [sum_j(pi_j * a_ij)] * y_i
for n in np.arange(i):
sum_pi_aij = 0.0
for m in np.arange(j):
sum_pi_aij += pi_f[m] * a[n, m]
x[n] = - fi_y[n] + (y[n]/y_bar) * x_bar + sum_pi_aij * y[n]
# Calculate other variables of interest
x_bar = np.sum(x) # sum of all x_i
delta = x - y # difference between initial and final values
delta_bar = x_bar - y_bar # difference between sum of initial and
# final values
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'machine-read-nocorr.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual-nocorr.txt'
# Export all values into machine and human readable output files
form.output(datadir, header, it_num, speclist, y, x, \
delta, y_bar, x_bar, delta_bar, file, doprint)
form.fancyout(datadir, it_num, speclist, y, x, delta,\
y_bar, x_bar, delta_bar, file_fancy, doprint)
return [header, it_num, speclist, y, x, delta, y_bar, x_bar, delta_bar]
def lagrange(it_num, datadir, doprint, direct):
'''
This code applies Lagrange's method and calculates minimum based on the
methodology elaborated in the TEA theory document in Section (3). Equations in
this code contain both references and an explicitly written definitions.
The program reads the last iteration's output and data from the last header
file, creates variables for the Lagrange equations, sets up the Lagrange
equations, and calculates final x_i mole numbers for the current iteration
cycle. Note that the mole numbers that result from this function are
allowed to be negative. If negatives are returned, lambda correction
(lambdacorr.py) is necessary. The final x_i values, as well as x_bar,
y_bar, delta, and delta_bar are written into machine- and human-readable
output files. This function is executed by iterate.py.
Parameters
----------
it_num: integer
Iteration number.
datadir: string
Current directory where TEA is run.
doprint: string
Parameter in configuration file that allows printing for
debugging purposes.
direct: object
Object containing all of the results/data from the previous
calculation in lagrange.py or lambdacorr.py. It is a list
containing current header directory, current iteration
number, array of species names, array of initial guess,
array of non-corrected Lagrange values, and array of
lambdacorr corrected values.
Returns
-------
header: string
Name of the header file used.
it_num: integer
Iteration number.
speclist: string array
Array containing names of molecular species.
y: float array
Array containing initial guess of molecular species for
current iteration.
x: float array
Array containing final mole numbers of molecular species for
current iteration.
delta: float array
Array containing change in initial and final mole numbers of
molecular species for current iteration.
y_bar: float
Array containing total sum of initial guesses of all molecular
species for current iteration.
x_bar: float
Total sum of the final mole numbers of all molecular species.
delta_bar: float
Change in total of initial and final mole numbers of molecular
species.
'''
# Read values from last iteration
input = direct
# Take the current header file
header = input[0]
# Read values from the header file
pressure, temp, i, j, speclist, a, b, g_RT = form.readheader(header)
# Use final values from last iteration (x values) as new initial
y = input[4]
y_bar = input[7]
# Perform checks to be safe
it_num_check = input[1]
speclist_check = input[2]
# Make array of checks
check = np.array([it_num_check != it_num - 1,
False in (speclist_check == speclist) ])
# If iteration number given by iterate.py is not one larger as in 'direct',
# give error
if check[0]:
print("\n\nMAJOR ERROR! Read in file's it_num is not the most \
recent iteration!\n\n")
# If species names in the header are not the same as in 'direct',
# give error
if check[1]:
print("\n\nMAJOR ERROR! Read in file uses different species \
order/list!\n\n")
# ============== CREATE VARIABLES FOR LAGRANGE EQUATION ============== #
# Create 'c' value, equation (18) TEA theory document
# ci = (g/RT)_i + ln(P)
c = g_RT + np.log(pressure)
# Allocates array of fi(Y) over different values of i (species)
fi_y = np.zeros(i)
# Fill in fi(Y) values equation (19) TEA theory document
# fi = x_i * [ci + ln(x_i/x_bar)]
for n in np.arange(i):
y_frac = np.float(y[n] / y_bar)
fi_y[n] = y[n] * ( c[n] + np.log(y_frac) )
# Allocate values of rjk. Both j and k goes from 1 to m.
k = j
rjk = np.zeros((j,k))
# Fill out values of rjk, equation (26) TEA theory document
# rjk = rkj = sum_i(a_ij * a_ik) * y_i
for l in np.arange(k):
for m in np.arange(j):
r_sum = 0.0
for n in np.arange(i):
r_sum += a[n, m] * a[n, l] * y[n]
rjk[m, l] = r_sum
# Allocate value of u, equation (28) TEA theory document
u = Symbol('u')
# Allocate pi_j variables, where j is element index
# Example: pi_2 is Lagrange multiplier of N (j = 2)
pi = []
for m in np.arange(j):
name = 'pi_' + np.str(m+1)
pi = np.append(pi, Symbol(name))
# Allocate rjk * pi_j summations, equation (27) TEA theory document
# There will be j * k terms of rjk * pi_j
sq_pi = [pi]
for m in np.arange(j-1):
# Make square array of pi values with shape j * k
sq_pi = np.append(sq_pi, [pi], axis = 0)
# Multiply rjk * sq_pi to get array of rjk * pi_j
# equation (27) TEA theory document
rpi = rjk * sq_pi
# ======================= SET FINAL EQUATIONS ======================= #
# Total number of equations is j + 1
# Set up a_ij * fi(Y) summations equation (27) TEA theory document
# sum_i[a_ij * fi(Y)]
aij_fiy = np.zeros((j))
for m in np.arange(j):
rhs = 0.0
for n in np.arange(i):
rhs += a[n,m] * fi_y[n]
aij_fiy[m] = rhs
# Create first j'th equations equation (27) TEA theory document
# r_1m*pi_1 + r_2m*pi_2 + ... + r_mm*pi_m + b_m*u = sum_i[a_im * fi(Y)]
for m in np.arange(j):
if m == 0:
equations = np.array([np.sum(rpi[m]) + b[m]*u - aij_fiy[m]])
else:
lagrange_eq = np.array([np.sum(rpi[m]) + b[m]*u - aij_fiy[m]])
equations = np.append(equations, lagrange_eq)
# Last (j+1)th equation (27) TEA theory document
# b_1*pi_1 + b_2*pi_2 + ... + b_m*pi_m + 0*u = sum_i[fi(Y)]
bpi = b * pi
lagrange_eq_last = np.array([np.sum(bpi) - np.sum(fi_y)])
equations = np.append(equations, lagrange_eq_last)
# List all unknowns in the above set of equations
unknowns = list(pi)
unknowns.append(u)
# Solve final system of j+1 equations
fsol = solve(list(equations), unknowns, rational=False)
# ============ CALCULATE xi VALUES FOR CURRENT ITERATION ============ #
# Make array of pi values
pi_f = []
for m in np.arange(j):
pi_f = np.append(pi_f, [fsol[pi[m]]])
# Calculate x_bar from solution to get 'u', equation (28) TEA theory document
# u = -1. + (x_bar/y_bar)
u_f = fsol[u]
x_bar = (u_f + 1.) * y_bar
# Initiate array for x values of size i
x = np.zeros(i)
# Apply Lagrange solution for final set of x_i values for this iteration
# equation (23) TEA theory document
# x_i = -fi(Y) + (y_i/y_bar) * x_bar + [sum_j(pi_j * a_ij)] * y_i
for n in np.arange(i):
sum_pi_aij = 0.0
for m in np.arange(j):
sum_pi_aij += pi_f[m] * a[n, m]
x[n] = - fi_y[n] + (y[n]/y_bar) * x_bar + sum_pi_aij * y[n]
# Calculate other variables of interest
x_bar = np.sum(x) # sum of all x_i
delta = x - y # difference between initial and final values
delta_bar = x_bar - y_bar # difference between sum of initial and
# final values
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'machine-read-nocorr.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual-nocorr.txt'
# Export all values into machine and human readable output files
form.output(datadir, header, it_num, speclist, y, x, \
delta, y_bar, x_bar, delta_bar, file, doprint)
form.fancyout(datadir, it_num, speclist, y, x, delta,\
y_bar, x_bar, delta_bar, file_fancy, doprint)
return [header, it_num, speclist, y, x, delta, y_bar, x_bar, delta_bar]
print('Equation ' + np.str(m+1) + \
' is NOT satisfied. Check for errors!')
# Set iteration number to zero
it_num = 0
# Put all initial mole numbers in y array
y = y_init
# Make y_bar (sum of all y values)
y_bar = np.sum(y)
# Initialize delta variables to 0. (this signifies the first iteration)
delta = np.zeros(i)
delta_bar = np.sum(delta)
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-machine-read.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual.txt'
# Put results into machine readable file
form.output(datadir, header, it_num, speclist, y, y, delta, \
y_bar, y_bar, delta_bar, file, doprint)
# Put results into human readable file
form.fancyout(datadir, it_num, speclist, y, y, delta, y_bar, \
y_bar, delta_bar, file_fancy, doprint)
def balanceFunction(head, destination, location_out):
if location_out[-1] != '/':
location_out += '/'
header = head # Name of header file
desc = destination # Directory name
# Create and name outputs and results directories if they do not exist
datadir = location_out + desc + '/outputs/' + 'transient/'
# If output directory does not exist already, make it
if not os.path.exists(datadir): os.makedirs(datadir)
# Read in values from header file
pressure, temp, i, j, speclist, a, b, c = form.readheader(header)
# Print b values for debugging purposes
if doprint:
print("b values: " + str(b))
# Find chunk of ai_j array that will allow the corresponding yi values
# to be free variables such that all elements are considered
for n in np.arange(i - j + 1):
# Get lower and upper indices for chunk of ai_j array to check
lower = n
upper = n + j
# Retrieve chunk of ai_j that would contain free variables
a_chunk = a[lower:upper]
# Sum columns to get total of ai_j in chunk for each species 'j'
check = map(sum,zip(*a_chunk))
# Look for zeros in check. If a zero is found, this chunk of data can't
# be used for free variables, as this signifies an element is ignored
has_zero = 0 in check
# If zero not found, create list of free variables' indices
if has_zero == False:
free_id = []
for m in np.arange(j):
if doprint == True:
print('Using y_' + np.str(n + m + 1) + ' as a free variable')
free_id = np.append(free_id, n + m)
break
# Set initial guess of non-free y_i
scale = 0.1
# Assume that all or some y_i are negative or zeros
nofit = True
# Loop until all y_i are non-zero positive
while nofit:
# Set up list of 'known' initial mole numbers before and after free chunk
pre_free = np.zeros(free_id[0]) + scale
post_free = np.zeros(i - free_id[-1] - 1) + scale
# Set up list of free variables
free = []
for m in np.arange(j):
name = 'y_unknown_' + np.str(m)
free = np.append(free, Symbol(name))
# Combine free and 'known' to make array of y_initial mole numbers
y_init = np.append(pre_free, free)
y_init = np.append( y_init, post_free)
# Make 'j' equations satisfying mass balance equation (17) in TEA theory doc:
# sum_i(ai_j * y_i) = b_j
eq = [[]]
for m in np.arange(j):
rhs = 0
for n in np.arange(i):
rhs += a[n, m] * y_init[n]
rhs -= b[m]
eq = np.append(eq, rhs)
# Solve system of linear equations to get free y_i variables
result = solve(list(eq), list(free), rational=False)
# Correct for no-solution-found results.
# If no solution found, decrease scale size.
if result == []:
scale /= 10
if doprint:
print("Correcting initial guesses for realistic mass. \
Trying " + str(scale) + "...")
# Correct for negative-mass results. If found, decrease scale size.
else:
# Assume no negatives and check
hasneg = False
for m in np.arange(j):
if result[free[m]] < 0:
hasneg = True
# If negatives found, decrease scale size
if hasneg:
scale /= 10
if doprint:
print("Negative numbers found in fit.")
print("Correcting initial guesses for realistic mass. \
Trying " + str(scale) + "...")
# If no negatives found, exit the loop (good fit is found)
else:
nofit = False
if doprint:
print(str(scale) + " provided a viable initial guess.")
# Gather the results
fit = []
for m in np.arange(j):
fit = np.append(fit, result[free[m]])
# Put the result into the final y_init array
y_init[free_id[0]:free_id[j-1]+1] = fit
# This part of the code is only for debugging purposes
# It rounds the values and checks whether the balance equation is satisfied
# No values are changed and this serves solely as a check
if doprint == True:
print('\nCHECKS:')
for m in np.arange(j):
bool = round((sum(a[:,m] * y_init[:])), 2) == round(b[m], 2)
if bool == True:
if doprint == True:
print('Equation ' + np.str(m+1) + ' is satisfied.')
if bool == False:
print('Equation ' + np.str(m+1) + \
' is NOT satisfied. Check for errors!')
# Set iteration number to zero
it_num = 0
# Put all initial mole numbers in y array
y = y_init
# Make y_bar (sum of all y values)
y_bar = np.sum(y)
# Initialize delta variables to 0. (this signifies the first iteration)
delta = np.zeros(i)
delta_bar = np.sum(delta)
# Name output files with corresponding iteration number name
file = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-machine-read.txt'
file_fancy = datadir + '/lagrange-iteration-' + np.str(it_num) + \
'-visual.txt'
# Put results into machine readable file
form.output(datadir, header, it_num, speclist, y, y, delta, \
y_bar, y_bar, delta_bar, file, doprint)
# Put results into human readable file
form.fancyout(datadir, it_num, speclist, y, y, delta, y_bar, \
y_bar, delta_bar, file_fancy, doprint)