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'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
Copyright (C) 2023 Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''
from math import exp, log
from fluids.numerics import assert_close, assert_close1d, derivative
from fluids.numerics import numpy as np
from fluids.numerics.polynomial_evaluation import (
exp_horner_stable,
exp_horner_stable_and_der,
exp_horner_stable_and_der2,
exp_horner_stable_and_der3,
exp_horner_stable_ln_tau,
exp_horner_stable_ln_tau_and_der,
exp_horner_stable_ln_tau_and_der2,
horner_domain,
horner_log,
horner_stable,
horner_stable_and_der,
horner_stable_and_der2,
horner_stable_and_der3,
horner_stable_and_der4,
horner_stable_ln_tau,
horner_stable_ln_tau_and_der,
horner_stable_ln_tau_and_der2,
horner_stable_ln_tau_and_der3,
horner_stable_log,
)
from fluids.numerics.polynomial_utils import polynomial_offset_scale
def test_horner():
from fluids.numerics.polynomial_evaluation import horner, horner_and_der2, horner_and_der3, horner_and_der4, horner_backwards
assert_close(horner([1.0, 3.0], 2.0), 5.0, rtol=1e-15)
assert_close(horner_backwards(2.0, [1.0, 3.0]), 5.0, rtol=1e-15)
assert_close(horner([3.0], 2.0), 3.0, rtol=1e-15)
poly = [1.12, 432.32, 325.5342, .235532, 32.235]
assert_close1d(horner_and_der2(poly, 3.0), (14726.109396, 13747.040732, 8553.7884), rtol=1e-15)
assert_close1d(horner_and_der3(poly, 3.0), (14726.109396, 13747.040732, 8553.7884, 2674.56), rtol=1e-15)
poly = [1.12, 432.32, 325.5342, .235532, 32.235, 1.01]
assert_close1d(horner_and_der4(poly, 3.0), (44179.338188, 55967.231592, 53155.446664, 33685.04519999999, 10778.880000000001), rtol=1e-15)
assert_close1d(horner_and_der4(poly, 3.0), [np.polyval(np.polyder(poly,o), 3) for o in range(5)])
def test_exp_horner_backwards():
from fluids.numerics.polynomial_evaluation import (
exp_horner_backwards,
exp_horner_backwards_and_der,
exp_horner_backwards_and_der2,
exp_horner_backwards_and_der3,
)
assert_close((exp_horner_backwards(2.0, [1.0, 3.0])), exp(5.0))
# Test the derivatives
coeffs = [1,.2,.03,.0004,.00005]
x = 1.1
val = exp_horner_backwards(x, coeffs)
assert_close(val, 5.853794011493425)
der_num = derivative(lambda x: exp_horner_backwards(x, coeffs), x, dx=x*8e-7, order=7)
der_ana = exp_horner_backwards_and_der(x, coeffs)[1]
assert_close(der_ana, 35.804145691898384, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-10)
der_num = derivative(lambda x: exp_horner_backwards_and_der(x, coeffs)[1], x, dx=x*8e-7, order=7)
der_ana = exp_horner_backwards_and_der2(x, coeffs)[2]
assert_close(der_ana, 312.0678014926728, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-10)
der_num = derivative(lambda x: exp_horner_backwards_and_der2(x, coeffs)[2], x, dx=x*8e-7, order=7)
der_ana = exp_horner_backwards_and_der3(x, coeffs)[3]
assert_close(der_ana, 3208.8680487693714, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-10)
def test_horner_backwards_ln_tau():
from fluids.numerics.polynomial_evaluation import (
horner_backwards_ln_tau,
horner_backwards_ln_tau_and_der,
horner_backwards_ln_tau_and_der2,
horner_backwards_ln_tau_and_der3,
)
coeffs = [9.661381155485653, 224.16316385569456, 2195.419519751738, 11801.26111760343, 37883.05110910901, 74020.46380982929, 87244.40329893673, 69254.45831263301, 61780.155823216155]
Tc = 591.75
val = horner_backwards_ln_tau(500.0, Tc, coeffs)
assert_close(val, 24168.867169087476)
T = 300.0
val = horner_backwards_ln_tau(T, Tc, coeffs)
assert_close(val, 37900.38881665646)
der_num = derivative(lambda T: horner_backwards_ln_tau(T, Tc, coeffs), T, dx=T*8e-7, order=7)
der_ana = horner_backwards_ln_tau_and_der(T, Tc, coeffs)[1]
assert_close(der_ana, -54.63227984184944, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-10)
der_num = derivative(lambda T: horner_backwards_ln_tau_and_der(T, Tc, coeffs)[1], T, dx=T*8e-7, order=7)
der_ana = horner_backwards_ln_tau_and_der2(T, Tc, coeffs)[2]
assert_close(der_ana, 0.037847046150971016, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-8)
der_num = derivative(lambda T: horner_backwards_ln_tau_and_der2(T, Tc, coeffs)[2], T, dx=T*160e-7, order=7)
der_ana = horner_backwards_ln_tau_and_der3(T, Tc, coeffs)[3]
assert_close(der_ana, -0.001920502581912092, rtol=1e-10)
assert_close(der_num,der_ana, rtol=1e-10)
assert 0 == horner_backwards_ln_tau(600.0, Tc, coeffs)
assert_close1d(horner_backwards_ln_tau_and_der(600.0, Tc, coeffs), (0.0, 0.0))
assert_close1d(horner_backwards_ln_tau_and_der2(600.0, Tc, coeffs), (0.0, 0.0, 0.0))
assert_close1d(horner_backwards_ln_tau_and_der3(600.0, Tc, coeffs), (0.0, 0.0, 0.0, 0.0))
def test_exp_horner_backwards_ln_tau():
from fluids.numerics.polynomial_evaluation import exp_horner_backwards_ln_tau, exp_horner_backwards_ln_tau_and_der, exp_horner_backwards_ln_tau_and_der2
# Coefficients for water from REFPROP, fit
cs=[-1.2616237655927602e-05, -0.0004061873638525952, -0.005563382112542401, -0.04240531802937599, -0.19805733513004808, -0.5905741856310869, -1.1388001144550794, -0.1477584393673108, -2.401287527958821]
Tc = 647.096
T = 300.0
expect = 0.07175344047522199
val = exp_horner_backwards_ln_tau(T, Tc, cs)
assert_close(val, expect, rtol=1e-9)
assert 0 == exp_horner_backwards_ln_tau(Tc, Tc, cs)
expect_der = -0.000154224581713238
val, der = exp_horner_backwards_ln_tau_and_der(T, Tc, cs)
assert_close(der, expect_der, rtol=1e-13)
assert_close(val, expect, rtol=1e-9)
val, der, der2 = exp_horner_backwards_ln_tau_and_der2(T, Tc, cs)
assert_close(der, expect_der, rtol=1e-13)
assert_close(val, expect, rtol=1e-9)
expect_der2 = -5.959538970287795e-07
assert_close(der2, expect_der2, rtol=1e-13)
assert 0 == exp_horner_backwards_ln_tau(Tc+1, Tc, cs)
assert_close1d(exp_horner_backwards_ln_tau_and_der(1000.0, Tc, cs), (0.0, 0.0))
assert_close1d(exp_horner_backwards_ln_tau_and_der2(1000.0, Tc, cs), (0.0, 0.0, 0.0))
def test_horner_domain():
test_stable_coeffs = [28.0163226043884, 24.92038363551981, -7.469247118451516, 16.400149851861975, 67.52558234042988, 176.7837155284216]
xmin, xmax = (162.0, 570.0)
x = 300
expect = 157.0804912518053
calc = horner_domain(x, test_stable_coeffs, xmin, xmax)
assert_close(calc, expect, rtol=1e-14)
def test_horner_stable():
x = 300
test_stable_coeffs = [28.0163226043884, 24.92038363551981, -7.469247118451516, 16.400149851861975, 67.52558234042988, 176.7837155284216]
xmin, xmax = (162.0, 570.0)
expect = 157.0804912518053
offset, scale = polynomial_offset_scale(xmin, xmax)
calc = horner_stable(x, test_stable_coeffs, offset, scale)
assert_close(calc, expect, rtol=1e-14)
der_num = derivative(horner_stable, x, args=(test_stable_coeffs, offset, scale), dx=x*1e-7)
der_analytical = horner_stable_and_der(x, test_stable_coeffs, offset, scale)[1]
assert_close(der_analytical, 0.25846754626830115, rtol=1e-14)
assert_close(der_num, der_analytical, rtol=1e-7)
der_num = derivative(lambda *args: horner_stable_and_der(*args)[1], x,
args=(test_stable_coeffs, offset, scale), dx=x*1e-7)
der_analytical = horner_stable_and_der2(x, test_stable_coeffs, offset, scale)[2]
assert_close(der_analytical, 0.0014327609525395784, rtol=1e-14)
assert_close(der_num, der_analytical, rtol=1e-7)
der_num = derivative(lambda *args: horner_stable_and_der2(*args)[-1], x,
args=(test_stable_coeffs, offset, scale), dx=x*1e-7)
der_analytical = horner_stable_and_der3(x, test_stable_coeffs, offset, scale)[-1]
assert_close(der_analytical, -7.345952769973301e-06, rtol=1e-14)
assert_close(der_num, der_analytical, rtol=1e-7)
der_num = derivative(lambda *args: horner_stable_and_der3(*args)[-1], x,
args=(test_stable_coeffs, offset, scale), dx=x*1e-7)
der_analytical = horner_stable_and_der4(x, test_stable_coeffs, offset, scale)[-1]
assert_close(der_analytical, -2.8269861583547557e-07, rtol=1e-14)
assert_close(der_num, der_analytical, rtol=1e-7)
five_vals = horner_stable_and_der4(x, test_stable_coeffs, offset, scale)
assert_close1d(five_vals, (157.0804912518053, 0.25846754626830115, 0.0014327609525395784, -7.345952769973301e-06, -2.8269861583547557e-07), rtol=1e-14)
four_vals = horner_stable_and_der3(x, test_stable_coeffs, offset, scale)
assert_close1d(four_vals, (157.0804912518053, 0.25846754626830115, 0.0014327609525395784, -7.345952769973301e-06), rtol=1e-14)
three_vals = horner_stable_and_der2(x, test_stable_coeffs, offset, scale)
assert_close1d(three_vals, (157.0804912518053, 0.25846754626830115, 0.0014327609525395784), rtol=1e-14)
two_vals = horner_stable_and_der(x, test_stable_coeffs, offset, scale)
assert_close1d(two_vals, (157.0804912518053, 0.25846754626830115), rtol=1e-14)
def test_stablepoly_ln_tau():
Tmin, Tmax, Tc = 178.18, 591.74, 591.75
coeffs = [-0.00854738149791956, 0.05600738152861595, -0.30758192972280085, 1.6848304651211947, -8.432931053161155, 37.83695791102946, -150.87603890354512, 526.4891248463246, -1574.7593541151946, 3925.149223414621, -7826.869059381197, 11705.265444382389, -11670.331914006258, 5817.751307862842]
expect = 24498.131947494512
expect_d, expect_d2, expect_d3 = -100.77476796035525, -0.6838185833621794, -0.012093191888904656
xmin, xmax = log(1-Tmin/Tc), log(1-Tmax/Tc)
offset, scale = polynomial_offset_scale(xmin, xmax)
T = 500.0
calc = horner_stable_ln_tau(T, Tc, coeffs, offset, scale)
assert_close(expect, calc)
assert_close(horner_stable_ln_tau(700.0, Tc, coeffs, offset, scale), 0.0)
calc2 = horner_stable_ln_tau_and_der(T, Tc, coeffs, offset, scale)
assert_close(expect, calc2[0])
assert_close(expect_d, calc2[1])
assert_close1d(horner_stable_ln_tau_and_der(700.0, Tc, coeffs, offset, scale), (0.0, 0.0))
calc3 = horner_stable_ln_tau_and_der2(T, Tc, coeffs, offset, scale)
assert_close(expect, calc3[0])
assert_close(expect_d, calc3[1])
assert_close(expect_d2, calc3[2])
assert_close1d(horner_stable_ln_tau_and_der2(700.0, Tc, coeffs, offset, scale), (0.0, 0.0, 0.0))
calc4 = horner_stable_ln_tau_and_der3(T, Tc, coeffs, offset, scale)
assert_close(expect, calc4[0])
assert_close(expect_d, calc4[1])
assert_close(expect_d2, calc4[2])
assert_close(expect_d3, calc4[3])
assert_close1d(horner_stable_ln_tau_and_der3(700.0, Tc, coeffs, offset, scale), (0.0, 0.0, 0.0, 0.0))
def test_exp_stablepoly_fit():
xmin, xmax = 309.0, 591.72
coeffs = [0.008603558174828078, 0.007358688688856427, -0.016890323025782954, -0.005289197721114957, -0.0028824712174469625, 0.05130960832946553, -0.12709896610233662, 0.37774977659528036, -0.9595325030688526, 2.7931528759840174, 13.10149649770156]
x = 400
offset, scale = polynomial_offset_scale(xmin, xmax)
expect = 157191.01706242564
calc = exp_horner_stable(x, coeffs, offset, scale)
assert_close(calc, expect, rtol=1e-14)
der_num = derivative(exp_horner_stable, x, args=(coeffs, offset, scale), dx=x*1e-7)
der_analytical = exp_horner_stable_and_der(x, coeffs, offset, scale)[1]
assert_close(der_num, der_analytical, rtol=1e-7)
assert_close(der_analytical, 4056.436943642117, rtol=1e-14)
der_num = derivative(lambda *args: exp_horner_stable_and_der(*args)[1], x,
args=(coeffs, offset, scale), dx=x*1e-7)
der_analytical = exp_horner_stable_and_der2(x, coeffs, offset, scale)[-1]
assert_close(der_analytical, 81.32645570045084, rtol=1e-14)
assert_close(der_num, der_analytical, rtol=1e-7)
der_num = derivative(lambda *args: exp_horner_stable_and_der2(*args)[-1], x,
args=(coeffs, offset, scale), dx=x*1e-7)
der_analytical = exp_horner_stable_and_der3(x, coeffs, offset, scale)[-1]
assert_close(der_num, der_analytical, rtol=1e-7)
assert_close(der_analytical, 1.103603650822488, rtol=1e-14)
vals = exp_horner_stable_and_der3(x, coeffs, offset, scale)
assert_close1d(vals, (157191.01706242564, 4056.436943642117, 81.32645570045084, 1.103603650822488), rtol=1e-14)
vals = exp_horner_stable_and_der2(x, coeffs, offset, scale)
assert_close1d(vals, (157191.01706242564, 4056.436943642117, 81.32645570045084), rtol=1e-14)
vals = exp_horner_stable_and_der(x, coeffs, offset, scale)
assert_close1d(vals, (157191.01706242564, 4056.436943642117), rtol=1e-14)
def test_exp_stablepoly_fit_ln_tau():
coeffs = [0.011399360373616219, -0.014916568994522095, -0.06881296308711171, 0.0900153056718409, 0.19066633691545576, -0.24937350547406822, -0.3148389292182401, 0.41171834646956995, 0.3440581845934503, -0.44989947455906076, -0.2590532901358529, 0.33869134876113094, 0.1391329435696207, -0.18195230788023764, -0.050437145563137165, 0.06583166394466389, 0.01685157036382634, -0.022266583863000733, 0.003539388708205138, -0.005171064606571463, 0.012264455189935575, -0.018085676249990357, 0.026950795197264732, -0.04077120220662778, 0.05786417011592615, -0.07222889554773304, 0.07433570330647113, -0.05829288696590232, -3.7182636506596722, -5.844828481765601]
Tmin, Tmax, Tc = 233.22, 646.15, 647.096
xmin, xmax = log(1-Tmin/Tc), log(1-Tmax/Tc)
offset, scale = polynomial_offset_scale(xmin, xmax)
T = 500
expect = 0.03126447402046822
expect_d, expect_d2 = -0.0002337992205182661, -1.0453011134030858e-07
calc = exp_horner_stable_ln_tau(T, Tc, coeffs, offset, scale)
assert_close(expect, calc)
assert 0 == exp_horner_stable_ln_tau(700, Tc, coeffs, offset, scale)
calc2 = exp_horner_stable_ln_tau_and_der(T, Tc, coeffs, offset, scale)
assert (0,0) == exp_horner_stable_ln_tau_and_der(700, Tc, coeffs, offset, scale)
assert_close(expect, calc2[0])
assert_close(expect_d, calc2[1])
calc3 = exp_horner_stable_ln_tau_and_der2(T, Tc, coeffs, offset, scale)
assert (0,0, 0) == exp_horner_stable_ln_tau_and_der2(700, Tc, coeffs, offset, scale)
assert_close(expect, calc3[0])
assert_close(expect_d, calc3[1])
assert_close(expect_d2, calc3[2])
def test_horner_log():
coeffs = [1.0, 2.0, 3.0]
calc = horner_log(coeffs, 5.3, 4.5)
expect = 40.22161020291425
assert_close(calc, expect, rtol=1e-13)
def test_horner_stable_log():
# Have yet to be able to get coeffs for horner_stable_log directly
# Would work with mpmath for sure though
int_T_stable_coeffs = [3.2254691548856482, 6.923549962582991, 1.5349425170308109, -1.2154278928596742, 0.2691917024300867, 0.08207134574884214, -0.00891350763588927, -0.14463666181618448, 0.20857726049059955, -0.16593159587411, 0.034375567510854466, 0.0906937625089119, -0.0049590621229368415, -0.11605604886860361, -0.23898450392809112, 0.5368870089626024, 0.1796614633975993, -0.7638508609027873, -0.07854882554664272, 0.7411591719079632, -0.06004401012118543, -0.45423261676213483, 0.13111045246315745, 0.11263751330617959, -0.04919816763192376]
int_T_log_coeff = 33.94307866530405
offset = -1.2872369320147412
scale= 0.0011436184660073706
calc = horner_stable_log(300, int_T_stable_coeffs, offset, scale, int_T_log_coeff)
assert_close(calc, 193.51466126959178)
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