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CoolProp  6.7.1dev
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Helmholtz.cpp
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1 #include <numeric>
2 #include "Helmholtz.h"
3 
4 #ifdef __ANDROID__
5 # undef _A
6 # undef _B
7 # undef _C
8 # undef _D
9 #endif
10 
11 namespace CoolProp {
12 
13 CoolPropDbl kahanSum(const std::vector<CoolPropDbl>& x) {
14  CoolPropDbl sum = x[0], y, t;
15  CoolPropDbl c = 0.0; //A running compensation for lost low-order bits.
16  for (std::size_t i = 1; i < x.size(); ++i) {
17  y = x[i] - c; //So far, so good: c is zero.
18  t = sum + y; //Alas, sum is big, y small, so low-order digits of y are lost.
19  c = (t - sum) - y; //(t - sum) recovers the high-order part of y; subtracting y recovers -(low part of y)
20  sum = t; //Algebraically, c should always be zero. Beware eagerly optimising compilers!
21  }
22  return sum;
23 }
24 bool wayToSort(CoolPropDbl i, CoolPropDbl j) {
25  return std::abs(i) > std::abs(j);
26 }
27 
28 // define function to be applied coefficient-wise
29 double ramp(double x) {
30  if (x > 0)
31  return x;
32  else
33  return 0;
34 }
35 
36 /*
37 void ResidualHelmholtzGeneralizedExponential::allEigen(const CoolPropDbl &tau, const CoolPropDbl &delta, HelmholtzDerivatives &derivs) throw()
38 {
39  double log_tau = log(tau), log_delta = log(delta),
40  one_over_delta = 1/delta, one_over_tau = 1/tau; // division is much slower than multiplication, so do one division here
41 
42  Eigen::Map<Eigen::ArrayXd> nE(&(n[0]), elements.size());
43  Eigen::Map<Eigen::ArrayXd> dE(&(d[0]), elements.size());
44  Eigen::Map<Eigen::ArrayXd> tE(&(t[0]), elements.size());
45  Eigen::Map<Eigen::ArrayXd> cE(&(c[0]), elements.size());
46  Eigen::Map<Eigen::ArrayXi> l_intE(&(l_int[0]), elements.size());
47  Eigen::Map<Eigen::ArrayXd> l_doubleE(&(l_double[0]), elements.size());
48  Eigen::Map<Eigen::ArrayXd> eta1E(&(eta1[0]), elements.size());
49  Eigen::Map<Eigen::ArrayXd> eta2E(&(eta2[0]), elements.size());
50  Eigen::Map<Eigen::ArrayXd> epsilon1E(&(epsilon1[0]), elements.size());
51  Eigen::Map<Eigen::ArrayXd> epsilon2E(&(epsilon2[0]), elements.size());
52  Eigen::Map<Eigen::ArrayXd> beta1E(&(beta1[0]), elements.size());
53  Eigen::Map<Eigen::ArrayXd> beta2E(&(beta2[0]), elements.size());
54  Eigen::Map<Eigen::ArrayXd> gamma1E(&(gamma1[0]), elements.size());
55  Eigen::Map<Eigen::ArrayXd> gamma2E(&(gamma2[0]), elements.size());
56 
57  // ****************************************
58  // The u part in exp(u) and its derivatives
59  // ****************************************
60 
61  #if defined(EIGEN_VECTORIZE_SSE2)
62  //std::cout << "EIGEN_VECTORIZE_SSE2" << std::endl;
63  #endif
64 
65  // Set the u part of exp(u) to zero
66  uE.fill(0);
67  du_ddeltaE.fill(0);
68  du_dtauE.fill(0);
69  d2u_ddelta2E.fill(0);
70  d2u_dtau2E.fill(0);
71  d3u_ddelta3E.fill(0);
72  d3u_dtau3E.fill(0);
73 
74  if (delta_li_in_u){
75  Eigen::ArrayXd u_increment = -cE*(log_delta*l_doubleE).exp(); //pow(delta,L) -> exp(L*log(delta))
76  uE += u_increment;
77  du_ddeltaE += l_doubleE*u_increment*one_over_delta;
78  d2u_ddelta2E += (l_doubleE-1)*l_doubleE*u_increment*one_over_delta*one_over_delta;
79  d3u_ddelta3E += (l_doubleE-2)*(l_doubleE-1)*l_doubleE*u_increment*one_over_delta*one_over_delta*one_over_delta;
80  }
81 
82 // if (tau_mi_in_u){
83 // CoolPropDbl omegai = el.omega, m_double = el.m_double;
84 // if (std::abs(m_double) > 0){
85 // CoolPropDbl u_increment = -omegai*pow(tau, m_double);
86 // CoolPropDbl du_dtau_increment = m_double*u_increment*one_over_tau;
87 // CoolPropDbl d2u_dtau2_increment = (m_double-1)*du_dtau_increment*one_over_tau;
88 // CoolPropDbl d3u_dtau3_increment = (m_double-2)*d2u_dtau2_increment*one_over_tau;
89 // u += u_increment;
90 // du_dtau += du_dtau_increment;
91 // d2u_dtau2 += d2u_dtau2_increment;
92 // d3u_dtau3 += d3u_dtau3_increment;
93 // }
94 // }
95  if (eta1_in_u){
96  uE += -eta1E*(delta-epsilon1E);
97  du_ddeltaE += -eta1E;
98  }
99  if (eta2_in_u){
100  uE += -eta2E*POW2(delta-epsilon2E);
101  du_ddeltaE += -2*eta2E*(delta-epsilon2E);
102  d2u_ddelta2E += -2*eta2E;
103  }
104  if (beta1_in_u){
105  uE += -beta1E*(tau-gamma1E);
106  du_dtauE += -beta1E;
107  }
108  if (beta2_in_u){
109  uE += -beta2E*POW2(tau-gamma2E);
110  du_dtauE += -2*beta2E*(tau-gamma2E);
111  d2u_dtau2E += -2*beta2E;
112  }
113 
114  Eigen::ArrayXd ndteuE = nE*exp(tE*log_tau + dE*log_delta + uE);
115  Eigen::ArrayXd B_deltaE = delta*du_ddeltaE + dE;
116  Eigen::ArrayXd B_tauE = tau*du_dtauE + tE;
117  Eigen::ArrayXd B_delta2E = POW2(delta)*(d2u_ddelta2E + du_ddeltaE.square()) + 2*dE*delta*du_ddeltaE + dE*(dE-1);
118  Eigen::ArrayXd B_tau2E = POW2(tau)*(d2u_dtau2E + du_dtauE.square()) + 2*tE*tau*du_dtauE + tE*(tE-1);
119  Eigen::ArrayXd B_delta3E = POW3(delta)*d3u_ddelta3E + 3*dE*POW2(delta)*d2u_ddelta2E+3*POW3(delta)*d2u_ddelta2E*du_ddeltaE+3*dE*POW2(delta*du_ddeltaE)+3*dE*(dE-1)*delta*du_ddeltaE+dE*(dE-1)*(dE-2)+POW3(delta*du_ddeltaE);
120  Eigen::ArrayXd B_tau3E = POW3(tau)*d3u_dtau3E + 3*tE*POW2(tau)*d2u_dtau2E+3*POW3(tau)*d2u_dtau2E*du_dtauE+3*tE*POW2(tau*du_dtauE)+3*tE*(tE-1)*tau*du_dtauE+tE*(tE-1)*(tE-2)+POW3(tau*du_dtauE);
121 
122  derivs.alphar += ndteuE.sum();
123  derivs.dalphar_ddelta += (ndteuE*B_deltaE).sum()*one_over_delta;
124  derivs.dalphar_dtau += (ndteuE*B_tauE).sum()*one_over_tau;
125  derivs.d2alphar_ddelta2 += (ndteuE*B_delta2E).sum()*POW2(one_over_delta);
126  derivs.d2alphar_dtau2 += (ndteuE*B_tau2E).sum()*POW2(one_over_tau);
127  derivs.d2alphar_ddelta_dtau += (ndteuE*B_deltaE*B_tauE).sum()*one_over_delta*one_over_tau;
128 
129  derivs.d3alphar_ddelta3 += (ndteuE*B_delta3E).sum()*POW3(one_over_delta);
130  derivs.d3alphar_dtau3 += (ndteuE*B_tau3E).sum()*POW3(one_over_tau);
131  derivs.d3alphar_ddelta2_dtau += (ndteuE*B_delta2E*B_tauE).sum()*POW2(one_over_delta)*one_over_tau;
132  derivs.d3alphar_ddelta_dtau2 += (ndteuE*B_deltaE*B_tau2E).sum()*one_over_delta*POW2(one_over_tau);
133 
134  return;
135 };
136 */
137 void ResidualHelmholtzGeneralizedExponential::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
138  CoolPropDbl log_tau = log(tau), log_delta = log(delta), ndteu, one_over_delta = 1 / delta,
139  one_over_tau = 1 / tau; // division is much slower than multiplication, so do one division here
140 
141  // Maybe split the construction of u and other parts into two separate loops?
142  // If both loops can get vectorized, could be worth it.
143  const std::size_t N = elements.size();
144  for (std::size_t i = 0; i < N; ++i) {
145  ResidualHelmholtzGeneralizedExponentialElement& el = elements[i];
146  CoolPropDbl ni = el.n, di = el.d, ti = el.t;
147 
148  // Set the u part of exp(u) to zero
149  CoolPropDbl u = 0;
150  CoolPropDbl du_ddelta = 0;
151  CoolPropDbl du_dtau = 0;
152  CoolPropDbl d2u_ddelta2 = 0;
153  CoolPropDbl d2u_dtau2 = 0;
154  CoolPropDbl d3u_ddelta3 = 0;
155  CoolPropDbl d3u_dtau3 = 0;
156  CoolPropDbl d4u_ddelta4 = 0;
157  CoolPropDbl d4u_dtau4 = 0;
158 
159  if (delta_li_in_u) {
160  CoolPropDbl ci = el.c, l_double = el.l_double;
161  if (ValidNumber(l_double) && l_double > 0 && std::abs(ci) > DBL_EPSILON) {
162  const CoolPropDbl u_increment = (el.l_is_int) ? -ci * powInt(delta, el.l_int) : -ci * pow(delta, l_double);
163  const CoolPropDbl du_ddelta_increment = l_double * u_increment * one_over_delta;
164  const CoolPropDbl d2u_ddelta2_increment = (l_double - 1) * du_ddelta_increment * one_over_delta;
165  const CoolPropDbl d3u_ddelta3_increment = (l_double - 2) * d2u_ddelta2_increment * one_over_delta;
166  const CoolPropDbl d4u_ddelta4_increment = (l_double - 3) * d3u_ddelta3_increment * one_over_delta;
167  u += u_increment;
168  du_ddelta += du_ddelta_increment;
169  d2u_ddelta2 += d2u_ddelta2_increment;
170  d3u_ddelta3 += d3u_ddelta3_increment;
171  d4u_ddelta4 += d4u_ddelta4_increment;
172  }
173  }
174  if (tau_mi_in_u) {
175  CoolPropDbl omegai = el.omega, m_double = el.m_double;
176  if (std::abs(m_double) > 0) {
177  const CoolPropDbl u_increment = -omegai * pow(tau, m_double);
178  const CoolPropDbl du_dtau_increment = m_double * u_increment * one_over_tau;
179  const CoolPropDbl d2u_dtau2_increment = (m_double - 1) * du_dtau_increment * one_over_tau;
180  const CoolPropDbl d3u_dtau3_increment = (m_double - 2) * d2u_dtau2_increment * one_over_tau;
181  const CoolPropDbl d4u_dtau4_increment = (m_double - 3) * d3u_dtau3_increment * one_over_tau;
182  u += u_increment;
183  du_dtau += du_dtau_increment;
184  d2u_dtau2 += d2u_dtau2_increment;
185  d3u_dtau3 += d3u_dtau3_increment;
186  d4u_dtau4 += d4u_dtau4_increment;
187  }
188  }
189  if (eta1_in_u) {
190  CoolPropDbl eta1 = el.eta1, epsilon1 = el.epsilon1;
191  if (ValidNumber(eta1)) {
192  u += -eta1 * (delta - epsilon1);
193  du_ddelta += -eta1;
194  }
195  }
196  if (eta2_in_u) {
197  CoolPropDbl eta2 = el.eta2, epsilon2 = el.epsilon2;
198  if (ValidNumber(eta2)) {
199  u += -eta2 * POW2(delta - epsilon2);
200  du_ddelta += -2 * eta2 * (delta - epsilon2);
201  d2u_ddelta2 += -2 * eta2;
202  }
203  }
204  if (beta1_in_u) {
205  CoolPropDbl beta1 = el.beta1, gamma1 = el.gamma1;
206  if (ValidNumber(beta1)) {
207  u += -beta1 * (tau - gamma1);
208  du_dtau += -beta1;
209  }
210  }
211  if (beta2_in_u) {
212  CoolPropDbl beta2 = el.beta2, gamma2 = el.gamma2;
213  if (ValidNumber(beta2)) {
214  u += -beta2 * POW2(tau - gamma2);
215  du_dtau += -2 * beta2 * (tau - gamma2);
216  d2u_dtau2 += -2 * beta2;
217  }
218  }
219 
220  ndteu = ni * exp(ti * log_tau + di * log_delta + u);
221 
222  const CoolPropDbl dB_delta_ddelta = delta * d2u_ddelta2 + du_ddelta;
223  const CoolPropDbl d2B_delta_ddelta2 = delta * d3u_ddelta3 + 2 * d2u_ddelta2;
224  const CoolPropDbl d3B_delta_ddelta3 = delta * d4u_ddelta4 + 3 * d3u_ddelta3;
225 
226  const CoolPropDbl B_delta = (delta * du_ddelta + di);
227  const CoolPropDbl B_delta2 = delta * dB_delta_ddelta + (B_delta - 1) * B_delta;
228  const CoolPropDbl dB_delta2_ddelta = delta * d2B_delta_ddelta2 + 2 * B_delta * dB_delta_ddelta;
229  const CoolPropDbl B_delta3 = delta * dB_delta2_ddelta + (B_delta - 2) * B_delta2;
230  const CoolPropDbl dB_delta3_ddelta = delta * delta * d3B_delta_ddelta3 + 3 * delta * B_delta * d2B_delta_ddelta2
231  + 3 * delta * POW2(dB_delta_ddelta) + 3 * B_delta * (B_delta - 1) * dB_delta_ddelta;
232  const CoolPropDbl B_delta4 = delta * dB_delta3_ddelta + (B_delta - 3) * B_delta3;
233 
234  const CoolPropDbl dB_tau_dtau = tau * d2u_dtau2 + du_dtau;
235  const CoolPropDbl d2B_tau_dtau2 = tau * d3u_dtau3 + 2 * d2u_dtau2;
236  const CoolPropDbl d3B_tau_dtau3 = tau * d4u_dtau4 + 3 * d3u_dtau3;
237 
238  const CoolPropDbl B_tau = (tau * du_dtau + ti);
239  const CoolPropDbl B_tau2 = tau * dB_tau_dtau + (B_tau - 1) * B_tau;
240  const CoolPropDbl dB_tau2_dtau = tau * d2B_tau_dtau2 + 2 * B_tau * dB_tau_dtau;
241  const CoolPropDbl B_tau3 = tau * dB_tau2_dtau + (B_tau - 2) * B_tau2;
242  const CoolPropDbl dB_tau3_dtau =
243  tau * tau * d3B_tau_dtau3 + 3 * tau * B_tau * d2B_tau_dtau2 + 3 * tau * POW2(dB_tau_dtau) + 3 * B_tau * (B_tau - 1) * dB_tau_dtau;
244  const CoolPropDbl B_tau4 = tau * dB_tau3_dtau + (B_tau - 3) * B_tau3;
245 
246  derivs.alphar += ndteu;
247 
248  derivs.dalphar_ddelta += ndteu * B_delta;
249  derivs.dalphar_dtau += ndteu * B_tau;
250 
251  derivs.d2alphar_ddelta2 += ndteu * B_delta2;
252  derivs.d2alphar_ddelta_dtau += ndteu * B_delta * B_tau;
253  derivs.d2alphar_dtau2 += ndteu * B_tau2;
254 
255  derivs.d3alphar_ddelta3 += ndteu * B_delta3;
256  derivs.d3alphar_ddelta2_dtau += ndteu * B_delta2 * B_tau;
257  derivs.d3alphar_ddelta_dtau2 += ndteu * B_delta * B_tau2;
258  derivs.d3alphar_dtau3 += ndteu * B_tau3;
259 
260  derivs.d4alphar_ddelta4 += ndteu * B_delta4;
261  derivs.d4alphar_ddelta3_dtau += ndteu * B_delta3 * B_tau;
262  derivs.d4alphar_ddelta2_dtau2 += ndteu * B_delta2 * B_tau2;
263  derivs.d4alphar_ddelta_dtau3 += ndteu * B_delta * B_tau3;
264  derivs.d4alphar_dtau4 += ndteu * B_tau4;
265  }
266  derivs.dalphar_ddelta *= one_over_delta;
267  derivs.dalphar_dtau *= one_over_tau;
268  derivs.d2alphar_ddelta2 *= POW2(one_over_delta);
269  derivs.d2alphar_dtau2 *= POW2(one_over_tau);
270  derivs.d2alphar_ddelta_dtau *= one_over_delta * one_over_tau;
271 
272  derivs.d3alphar_ddelta3 *= POW3(one_over_delta);
273  derivs.d3alphar_dtau3 *= POW3(one_over_tau);
274  derivs.d3alphar_ddelta2_dtau *= POW2(one_over_delta) * one_over_tau;
275  derivs.d3alphar_ddelta_dtau2 *= one_over_delta * POW2(one_over_tau);
276 
277  derivs.d4alphar_ddelta4 *= POW4(one_over_delta);
278  derivs.d4alphar_dtau4 *= POW4(one_over_tau);
279  derivs.d4alphar_ddelta3_dtau *= POW3(one_over_delta) * one_over_tau;
280  derivs.d4alphar_ddelta2_dtau2 *= POW2(one_over_delta) * POW2(one_over_tau);
281  derivs.d4alphar_ddelta_dtau3 *= one_over_delta * POW3(one_over_tau);
282 
283  return;
284 };
285 
286 #if ENABLE_CATCH
287 mcx::MultiComplex<double> ResidualHelmholtzGeneralizedExponential::one_mcx(const mcx::MultiComplex<double>& tau,
288  const mcx::MultiComplex<double>& delta) const {
289  //throw CoolProp::NotImplementedError("Nope");
290  mcx::MultiComplex<double> sum00 = 0.0*tau*delta;
291  auto ln_tau = log(tau);
292  auto ln_delta = log(delta);
293  const std::size_t N = elements.size();
294  for (std::size_t i = 0; i < N; ++i) {
295  const ResidualHelmholtzGeneralizedExponentialElement& el = elements[i];
296 
297  mcx::MultiComplex<double> u = 0.0 * tau * delta;
298  if (delta_li_in_u) {
299  CoolPropDbl ci = el.c, l_double = el.l_double;
300  if (ValidNumber(l_double) && l_double > 0 && std::abs(ci) > DBL_EPSILON) {
301  const auto u_increment = -ci * pow(delta, l_double);
302  u += u_increment;
303  }
304  }
305  if (tau_mi_in_u) {
306  CoolPropDbl omegai = el.omega, m_double = el.m_double;
307  if (std::abs(m_double) > 0) {
308  const auto u_increment = -omegai * pow(tau, m_double);
309  u += u_increment;
310  }
311  }
312  if (eta1_in_u) {
313  CoolPropDbl eta1 = el.eta1, epsilon1 = el.epsilon1;
314  if (ValidNumber(eta1)) {
315  u += -eta1 * (delta - epsilon1);
316  }
317  }
318  if (eta2_in_u) {
319  CoolPropDbl eta2 = el.eta2, epsilon2 = el.epsilon2;
320  if (ValidNumber(eta2)) {
321  u += -eta2 * POW2(delta - epsilon2);
322  }
323  }
324  if (beta1_in_u) {
325  CoolPropDbl beta1 = el.beta1, gamma1 = el.gamma1;
326  if (ValidNumber(beta1)) {
327  u += -beta1 * (tau - gamma1);
328  }
329  }
330  if (beta2_in_u) {
331  CoolPropDbl beta2 = el.beta2, gamma2 = el.gamma2;
332  if (ValidNumber(beta2)) {
333  u += -beta2 * POW2(tau - gamma2);
334  }
335  }
336  sum00 += el.n * exp(el.t * ln_tau + el.d * ln_delta + u);
337  }
338  return sum00;
339 }
340 #endif
341 
342 void ResidualHelmholtzGeneralizedExponential::to_json(rapidjson::Value& el, rapidjson::Document& doc) {
343  el.AddMember("type", "GeneralizedExponential", doc.GetAllocator());
344  cpjson::set_double_array("n", n, el, doc);
345  cpjson::set_double_array("t", t, el, doc);
346  cpjson::set_double_array("d", d, el, doc);
347  cpjson::set_double_array("eta1", eta1, el, doc);
348  cpjson::set_double_array("eta2", eta2, el, doc);
349  cpjson::set_double_array("beta1", beta1, el, doc);
350  cpjson::set_double_array("beta2", beta2, el, doc);
351  cpjson::set_double_array("gamma1", gamma1, el, doc);
352  cpjson::set_double_array("gamma2", gamma2, el, doc);
353  cpjson::set_double_array("epsilon1", epsilon1, el, doc);
354  cpjson::set_double_array("epsilon2", epsilon2, el, doc);
355  cpjson::set_double_array("l_double", l_double, el, doc);
356  cpjson::set_int_array("l_int", l_int, el, doc);
357 }
358 
359 void ResidualHelmholtzNonAnalytic::to_json(rapidjson::Value& el, rapidjson::Document& doc) {
360  el.AddMember("type", "ResidualHelmholtzNonAnalytic", doc.GetAllocator());
361 
362  rapidjson::Value _n(rapidjson::kArrayType), _a(rapidjson::kArrayType), _b(rapidjson::kArrayType), _beta(rapidjson::kArrayType),
363  _A(rapidjson::kArrayType), _B(rapidjson::kArrayType), _C(rapidjson::kArrayType), _D(rapidjson::kArrayType);
364  for (unsigned int i = 0; i <= N; ++i) {
365  ResidualHelmholtzNonAnalyticElement& elem = elements[i];
366  _n.PushBack((double)elem.n, doc.GetAllocator());
367  _a.PushBack((double)elem.a, doc.GetAllocator());
368  _b.PushBack((double)elem.b, doc.GetAllocator());
369  _beta.PushBack((double)elem.beta, doc.GetAllocator());
370  _A.PushBack((double)elem.A, doc.GetAllocator());
371  _B.PushBack((double)elem.B, doc.GetAllocator());
372  _C.PushBack((double)elem.C, doc.GetAllocator());
373  _D.PushBack((double)elem.D, doc.GetAllocator());
374  }
375  el.AddMember("n", _n, doc.GetAllocator());
376  el.AddMember("a", _a, doc.GetAllocator());
377  el.AddMember("b", _b, doc.GetAllocator());
378  el.AddMember("beta", _beta, doc.GetAllocator());
379  el.AddMember("A", _A, doc.GetAllocator());
380  el.AddMember("B", _B, doc.GetAllocator());
381  el.AddMember("C", _C, doc.GetAllocator());
382  el.AddMember("D", _D, doc.GetAllocator());
383 }
384 
385 void ResidualHelmholtzNonAnalytic::all(const CoolPropDbl& tau_in, const CoolPropDbl& delta_in, HelmholtzDerivatives& derivs) throw() {
386  if (N == 0) {
387  return;
388  }
389 
390  // Here we want to hack this function just a tiny bit to avoid evaluation AT the critical point
391  // If we are VERY close to the critical point, just offset us a tiny bit away
392  CoolPropDbl tau = tau_in, delta = delta_in;
393  if (std::abs(tau_in - 1) < 10 * DBL_EPSILON) {
394  tau = 1.0 + 10 * DBL_EPSILON;
395  }
396  if (std::abs(delta_in - 1) < 10 * DBL_EPSILON) {
397  delta = 1.0 + 10 * DBL_EPSILON;
398  }
399 
400  for (unsigned int i = 0; i < N; ++i) {
401  const ResidualHelmholtzNonAnalyticElement& el = elements[i];
402  const CoolPropDbl ni = el.n, ai = el.a, bi = el.b, betai = el.beta;
403  const CoolPropDbl Ai = el.A, Bi = el.B, Ci = el.C, Di = el.D;
404 
405  // Derivatives of theta (all others are zero) (OK - checked)
406  // Do not factor because then when delta = 1 you are dividing by 0
407  const CoolPropDbl theta = (1.0 - tau) + Ai * pow(POW2(delta - 1.0), 1.0 / (2.0 * betai));
408  const CoolPropDbl dtheta_dTau = -1;
409  const CoolPropDbl dtheta_dDelta = Ai / (betai)*pow(POW2(delta - 1), 1 / (2 * betai) - 1) * (delta - 1);
410 
411  const CoolPropDbl d2theta_dDelta2 = Ai / betai * (1 / betai - 1) * pow(POW2(delta - 1), 1 / (2 * betai) - 1);
412  const CoolPropDbl d3theta_dDelta3 = Ai / betai * (2 - 3 / betai + 1 / POW2(betai)) * pow(POW2(delta - 1), 1 / (2 * betai)) / POW3(delta - 1);
413  const CoolPropDbl d4theta_dDelta4 =
414  Ai / betai * (-6 + 11 / betai - 6 / POW2(betai) + 1 / POW3(betai)) * pow(POW2(delta - 1), 1 / (2 * betai) - 2);
415 
416  // Derivatives of PSI (OK - checked)
417  const CoolPropDbl PSI = exp(-Ci * POW2(delta - 1.0) - Di * POW2(tau - 1.0));
418  const CoolPropDbl dPSI_dDelta_over_PSI = -2.0 * Ci * (delta - 1.0);
419  const CoolPropDbl dPSI_dDelta = dPSI_dDelta_over_PSI * PSI;
420  const CoolPropDbl dPSI_dTau_over_PSI = -2.0 * Di * (tau - 1.0);
421  const CoolPropDbl dPSI_dTau = dPSI_dTau_over_PSI * PSI;
422  const CoolPropDbl d2PSI_dDelta2_over_PSI = (2.0 * Ci * POW2(delta - 1.0) - 1.0) * 2.0 * Ci;
423  const CoolPropDbl d2PSI_dDelta2 = d2PSI_dDelta2_over_PSI * PSI;
424  const CoolPropDbl d3PSI_dDelta3 = 2 * Ci * PSI * (-4 * Ci * Ci * POW3(delta - 1) + 6 * Ci * (delta - 1));
425  const CoolPropDbl d4PSI_dDelta4 = 4 * Ci * Ci * PSI * (4 * Ci * Ci * POW4(delta - 1) - 12 * Ci * POW2(delta - 1) + 3);
426  const CoolPropDbl d2PSI_dTau2 = (2.0 * Di * POW2(tau - 1.0) - 1.0) * 2.0 * Di * PSI;
427  const CoolPropDbl d3PSI_dTau3 = 2.0 * Di * PSI * (-4 * Di * Di * POW3(tau - 1) + 6 * Di * (tau - 1));
428  const CoolPropDbl d4PSI_dTau4 = 4 * Di * Di * PSI * (4 * Di * Di * POW4(tau - 1) - 12 * Di * POW2(tau - 1) + 3);
429  const CoolPropDbl d2PSI_dDelta_dTau = dPSI_dDelta * dPSI_dTau_over_PSI;
430  const CoolPropDbl d3PSI_dDelta2_dTau = d2PSI_dDelta2 * dPSI_dTau_over_PSI;
431  const CoolPropDbl d3PSI_dDelta_dTau2 = d2PSI_dTau2 * dPSI_dDelta_over_PSI;
432  const CoolPropDbl d4PSI_dDelta_dTau3 = d3PSI_dTau3 * dPSI_dDelta_over_PSI;
433  const CoolPropDbl d4PSI_dDelta2_dTau2 = d2PSI_dTau2 * d2PSI_dDelta2_over_PSI;
434  const CoolPropDbl d4PSI_dDelta3_dTau = d3PSI_dDelta3 * dPSI_dTau_over_PSI;
435 
436  // Derivatives of DELTA (OK - Checked)
437  const CoolPropDbl DELTA = POW2(theta) + Bi * pow(POW2(delta - 1.0), ai);
438  const CoolPropDbl dDELTA_dTau = 2 * theta * dtheta_dTau;
439  const CoolPropDbl dDELTA_dDelta = 2 * theta * dtheta_dDelta + 2 * Bi * ai * pow(POW2(delta - 1.0), ai - 1.0) * (delta - 1);
440  const CoolPropDbl d2DELTA_dTau2 = 2; // d2theta_dTau2 is zero and (dtheta_dtau)^2 = 1
441  const CoolPropDbl d2DELTA_dDelta_dTau = 2 * dtheta_dTau * dtheta_dDelta; // d2theta_dDelta2 is zero
442  const CoolPropDbl d2DELTA_dDelta2 =
443  2 * (theta * d2theta_dDelta2 + POW2(dtheta_dDelta) + Bi * (2 * ai * ai - ai) * pow(POW2(delta - 1.0), ai - 1.0));
444  const CoolPropDbl d3DELTA_dTau3 = 0;
445  const CoolPropDbl d3DELTA_dDelta_dTau2 = 0;
446  const CoolPropDbl d3DELTA_dDelta2_dTau = 2 * dtheta_dTau * d2theta_dDelta2;
447  const CoolPropDbl d3DELTA_dDelta3 = 2
448  * (theta * d3theta_dDelta3 + 3 * dtheta_dDelta * d2theta_dDelta2
449  + 2 * Bi * ai * (2 * ai * ai - 3 * ai + 1) * pow(POW2(delta - 1.0), ai - 1.0) / (delta - 1));
450 
451  const CoolPropDbl d4DELTA_dTau4 = 0;
452  const CoolPropDbl d4DELTA_dDelta_dTau3 = 0;
453  const CoolPropDbl d4DELTA_dDelta2_dTau2 = 0;
454  const CoolPropDbl d4DELTA_dDelta3_dTau = 2 * dtheta_dTau * d3theta_dDelta3;
455  const CoolPropDbl d4DELTA_dDelta4 = 2
456  * (theta * d4theta_dDelta4 + 4 * dtheta_dDelta * d3theta_dDelta3 + 3 * POW2(d2theta_dDelta2)
457  + 2 * Bi * ai * (4 * ai * ai * ai - 12 * ai * ai + 11 * ai - 3) * pow(POW2(delta - 1.0), ai - 2.0));
458 
459  const CoolPropDbl dDELTAbi_dDelta = bi * pow(DELTA, bi - 1.0) * dDELTA_dDelta;
460  const CoolPropDbl dDELTAbi_dTau = -2.0 * theta * bi * pow(DELTA, bi - 1.0);
461  const CoolPropDbl d2DELTAbi_dDelta2 = bi * (pow(DELTA, bi - 1) * d2DELTA_dDelta2 + (bi - 1.0) * pow(DELTA, bi - 2.0) * pow(dDELTA_dDelta, 2));
462  const CoolPropDbl d3DELTAbi_dDelta3 =
463  bi
464  * (pow(DELTA, bi - 1) * d3DELTA_dDelta3 + d2DELTA_dDelta2 * (bi - 1) * pow(DELTA, bi - 2) * dDELTA_dDelta
465  + (bi - 1)
466  * (pow(DELTA, bi - 2) * 2 * dDELTA_dDelta * d2DELTA_dDelta2
467  + pow(dDELTA_dDelta, 2) * (bi - 2) * pow(DELTA, bi - 3) * dDELTA_dDelta));
468  const CoolPropDbl d2DELTAbi_dDelta_dTau =
469  -Ai * bi * 2.0 / betai * pow(DELTA, bi - 1.0) * (delta - 1.0) * pow(pow(delta - 1.0, 2), 1.0 / (2.0 * betai) - 1.0)
470  - 2.0 * theta * bi * (bi - 1.0) * pow(DELTA, bi - 2.0) * dDELTA_dDelta;
471  const CoolPropDbl d2DELTAbi_dTau2 = 2.0 * bi * pow(DELTA, bi - 1.0) + 4.0 * pow(theta, 2) * bi * (bi - 1.0) * pow(DELTA, bi - 2.0);
472  const CoolPropDbl d3DELTAbi_dTau3 =
473  -12.0 * theta * bi * (bi - 1.0) * pow(DELTA, bi - 2) - 8 * pow(theta, 3) * bi * (bi - 1) * (bi - 2) * pow(DELTA, bi - 3);
474  const CoolPropDbl d3DELTAbi_dDelta_dTau2 = 2 * bi * (bi - 1) * pow(DELTA, bi - 2) * dDELTA_dDelta
475  + 4 * pow(theta, 2) * bi * (bi - 1) * (bi - 2) * pow(DELTA, bi - 3) * dDELTA_dDelta
476  + 8 * theta * bi * (bi - 1) * pow(DELTA, bi - 2) * dtheta_dDelta;
477  const CoolPropDbl d3DELTAbi_dDelta2_dTau =
478  bi
479  * ((bi - 1) * pow(DELTA, bi - 2) * dDELTA_dTau * d2DELTA_dDelta2 + pow(DELTA, bi - 1) * d3DELTA_dDelta2_dTau
480  + (bi - 1)
481  * ((bi - 2) * pow(DELTA, bi - 3) * dDELTA_dTau * pow(dDELTA_dDelta, 2)
482  + pow(DELTA, bi - 2) * 2 * dDELTA_dDelta * d2DELTA_dDelta_dTau));
483 
484  // Fourth partials
485  const CoolPropDbl DELTA_bi = pow(DELTA, bi);
486  const CoolPropDbl d4DELTAbi_dTau4 =
487  bi * DELTA_bi / DELTA
488  * ((POW3(bi) - 6 * POW2(bi) + 11 * bi - 6) * POW4(dDELTA_dTau) / POW3(DELTA)
489  + 6 * (bi * bi - 3 * bi + 2) * POW2(dDELTA_dTau / DELTA) * d2DELTA_dTau2 + 4 * (bi - 1) * dDELTA_dTau / DELTA * d3DELTA_dTau3
490  + 3 * (bi - 1) * POW2(d2DELTA_dTau2) / DELTA + d4DELTA_dTau4);
491  const CoolPropDbl d4DELTAbi_dDelta4 =
492  bi * DELTA_bi / DELTA
493  * ((POW3(bi) - 6 * POW2(bi) + 11 * bi - 6) * POW4(dDELTA_dDelta) / POW3(DELTA)
494  + 6 * (bi * bi - 3 * bi + 2) * POW2(dDELTA_dDelta / DELTA) * d2DELTA_dDelta2 + 4 * (bi - 1) * dDELTA_dDelta / DELTA * d3DELTA_dDelta3
495  + 3 * (bi - 1) * POW2(d2DELTA_dDelta2) / DELTA + d4DELTA_dDelta4);
496  const CoolPropDbl d4DELTAbi_dDelta_dTau3 =
497  bi * (bi - 1) * DELTA_bi / POW2(DELTA) * dDELTA_dDelta
498  * ((bi - 1) * (bi - 2) * POW3(dDELTA_dTau) / POW2(DELTA) + 3 * (bi - 1) * dDELTA_dTau / DELTA * d2DELTA_dTau2 + d3DELTA_dTau3)
499  + bi * DELTA_bi / DELTA
500  * ((bi - 1) * (bi - 2)
501  * (3 * POW2(dDELTA_dTau) / POW2(DELTA) * d2DELTA_dDelta_dTau - 2 * POW3(dDELTA_dTau) / POW3(DELTA) * dDELTA_dDelta)
502  + 3 * (bi - 1)
503  * (dDELTA_dTau / DELTA * d3DELTA_dDelta_dTau2 + d2DELTA_dTau2 / DELTA * d2DELTA_dDelta_dTau
504  - dDELTA_dDelta / POW2(DELTA) * dDELTA_dTau * d2DELTA_dTau2)
505  + d4DELTA_dDelta_dTau3);
506  const CoolPropDbl d4DELTAbi_dDelta3_dTau =
507  bi * (bi - 1) * DELTA_bi / POW2(DELTA) * dDELTA_dTau
508  * ((bi - 1) * (bi - 2) * POW3(dDELTA_dDelta) / POW2(DELTA) + 3 * (bi - 1) * dDELTA_dDelta / DELTA * d2DELTA_dDelta2 + d3DELTA_dDelta3)
509  + bi * DELTA_bi / DELTA
510  * ((bi - 1) * (bi - 2)
511  * (3 * POW2(dDELTA_dDelta) / POW2(DELTA) * d2DELTA_dDelta_dTau - 2 * POW3(dDELTA_dDelta) / POW3(DELTA) * dDELTA_dTau)
512  + 3 * (bi - 1)
513  * (dDELTA_dDelta / DELTA * d3DELTA_dDelta2_dTau + d2DELTA_dDelta2 / DELTA * d2DELTA_dDelta_dTau
514  - dDELTA_dTau / POW2(DELTA) * dDELTA_dDelta * d2DELTA_dDelta2)
515  + d4DELTA_dDelta3_dTau);
516  const CoolPropDbl d4DELTAbi_dDelta2_dTau2 = bi * DELTA_bi / POW4(DELTA)
517  * ((POW3(bi) - 6 * bi * bi + 11 * bi - 6) * POW2(dDELTA_dDelta) * POW2(dDELTA_dTau) // Yellow
518  + (bi - 1) * (bi - 2) * DELTA * POW2(dDELTA_dDelta) * d2DELTA_dTau2 // Orange
519  + (bi - 1) * (bi - 2) * DELTA * POW2(dDELTA_dTau) * d2DELTA_dDelta2 // Pink
520  + 4 * (bi - 1) * (bi - 2) * DELTA * dDELTA_dDelta * dDELTA_dTau * d2DELTA_dDelta_dTau // Green
521  + 2 * (bi - 1) * POW2(DELTA * d2DELTA_dDelta_dTau) // Blue hi
522  + 2 * (bi - 1) * POW2(DELTA) * dDELTA_dTau * d3DELTA_dDelta2_dTau // Blue sharp
523  + 2 * (bi - 1) * POW2(DELTA) * dDELTA_dDelta * d3DELTA_dDelta_dTau2 // Red sharp
524  + (bi - 1) * POW2(DELTA) * d2DELTA_dDelta2 * d2DELTA_dTau2 // black sharp
525  + POW3(DELTA) * d4DELTA_dDelta2_dTau2);
526 
527  derivs.alphar += delta * ni * DELTA_bi * PSI;
528 
529  // First partials
530  derivs.dalphar_dtau += ni * delta * (DELTA_bi * dPSI_dTau + dDELTAbi_dTau * PSI);
531  derivs.dalphar_ddelta += ni * (DELTA_bi * (PSI + delta * dPSI_dDelta) + dDELTAbi_dDelta * delta * PSI);
532 
533  // Second partials
534  derivs.d2alphar_dtau2 += ni * delta * (d2DELTAbi_dTau2 * PSI + 2 * dDELTAbi_dTau * dPSI_dTau + DELTA_bi * d2PSI_dTau2);
535  derivs.d2alphar_ddelta_dtau += ni
536  * (DELTA_bi * (dPSI_dTau + delta * d2PSI_dDelta_dTau) + delta * dDELTAbi_dDelta * dPSI_dTau
537  + dDELTAbi_dTau * (PSI + delta * dPSI_dDelta) + d2DELTAbi_dDelta_dTau * delta * PSI);
538  derivs.d2alphar_ddelta2 += ni
539  * (DELTA_bi * (2.0 * dPSI_dDelta + delta * d2PSI_dDelta2) + 2.0 * dDELTAbi_dDelta * (PSI + delta * dPSI_dDelta)
540  + d2DELTAbi_dDelta2 * delta * PSI);
541 
542  // Third partials
543  derivs.d3alphar_dtau3 +=
544  ni * delta * (d3DELTAbi_dTau3 * PSI + 3 * d2DELTAbi_dTau2 * dPSI_dTau + 3 * dDELTAbi_dTau * d2PSI_dTau2 + DELTA_bi * d3PSI_dTau3);
545  derivs.d3alphar_ddelta_dtau2 +=
546  ni * delta
547  * (d2DELTAbi_dTau2 * dPSI_dDelta + d3DELTAbi_dDelta_dTau2 * PSI + 2 * dDELTAbi_dTau * d2PSI_dDelta_dTau
548  + 2.0 * d2DELTAbi_dDelta_dTau * dPSI_dTau + DELTA_bi * d3PSI_dDelta_dTau2 + dDELTAbi_dDelta * d2PSI_dTau2)
549  + ni * (d2DELTAbi_dTau2 * PSI + 2.0 * dDELTAbi_dTau * dPSI_dTau + DELTA_bi * d2PSI_dTau2);
550  derivs.d3alphar_ddelta3 +=
551  ni
552  * (DELTA_bi * (3 * d2PSI_dDelta2 + delta * d3PSI_dDelta3) + 3 * dDELTAbi_dDelta * (2 * dPSI_dDelta + delta * d2PSI_dDelta2)
553  + 3 * d2DELTAbi_dDelta2 * (PSI + delta * dPSI_dDelta) + d3DELTAbi_dDelta3 * PSI * delta);
554  CoolPropDbl Line1 =
555  DELTA_bi * (2 * d2PSI_dDelta_dTau + delta * d3PSI_dDelta2_dTau) + dDELTAbi_dTau * (2 * dPSI_dDelta + delta * d2PSI_dDelta2);
556  CoolPropDbl Line2 = 2 * dDELTAbi_dDelta * (dPSI_dTau + delta * d2PSI_dDelta_dTau) + 2 * d2DELTAbi_dDelta_dTau * (PSI + delta * dPSI_dDelta);
557  CoolPropDbl Line3 = d2DELTAbi_dDelta2 * delta * dPSI_dTau + d3DELTAbi_dDelta2_dTau * delta * PSI;
558  derivs.d3alphar_ddelta2_dtau += ni * (Line1 + Line2 + Line3);
559 
560  // Fourth partials
561  derivs.d4alphar_dtau4 += ni * delta
562  * (DELTA_bi * d4PSI_dTau4 + 4 * dDELTAbi_dTau * d3PSI_dTau3 + 6 * d2DELTAbi_dTau2 * d2PSI_dTau2
563  + 4 * d3DELTAbi_dTau3 * dPSI_dTau + PSI * d4DELTAbi_dTau4);
564  derivs.d4alphar_ddelta4 +=
565  ni
566  * (delta * DELTA_bi * d4PSI_dDelta4 + delta * PSI * d4DELTAbi_dDelta4 + 4 * delta * dDELTAbi_dDelta * d3PSI_dDelta3
567  + 4 * delta * dPSI_dDelta * d3DELTAbi_dDelta3 + 6 * delta * d2DELTAbi_dDelta2 * d2PSI_dDelta2 + 4 * DELTA_bi * d3PSI_dDelta3
568  + 4 * PSI * d3DELTAbi_dDelta3 + 12 * dDELTAbi_dDelta * d2PSI_dDelta2 + 12 * dPSI_dDelta * d2DELTAbi_dDelta2);
569 
570  derivs.d4alphar_ddelta_dtau3 +=
571  ni
572  * (delta * DELTA_bi * d4PSI_dDelta_dTau3 + delta * PSI * d4DELTAbi_dDelta_dTau3 + delta * dDELTAbi_dDelta * d3PSI_dTau3
573  + 3 * delta * dDELTAbi_dTau * d3PSI_dDelta_dTau2 + delta * dPSI_dDelta * d3DELTAbi_dTau3 + 3 * delta * dPSI_dTau * d3DELTAbi_dDelta_dTau2
574  + 3 * delta * d2DELTAbi_dDelta_dTau * d2PSI_dTau2 + 3 * delta * d2DELTAbi_dTau2 * d2PSI_dDelta_dTau + DELTA_bi * d3PSI_dTau3
575  + PSI * d3DELTAbi_dTau3 + 3 * dDELTAbi_dTau * d2PSI_dTau2 + 3 * dPSI_dTau * d2DELTAbi_dTau2);
576  derivs.d4alphar_ddelta3_dtau +=
577  ni
578  * (delta * DELTA_bi * d4PSI_dDelta3_dTau + delta * PSI * d4DELTAbi_dDelta3_dTau + 3 * delta * dDELTAbi_dDelta * d3PSI_dDelta2_dTau
579  + delta * dDELTAbi_dTau * d3PSI_dDelta3 + 3 * delta * dPSI_dDelta * d3DELTAbi_dDelta2_dTau + delta * dPSI_dTau * d3DELTAbi_dDelta3
580  + 3 * delta * d2DELTAbi_dDelta2 * d2PSI_dDelta_dTau + 3 * delta * d2DELTAbi_dDelta_dTau * d2PSI_dDelta2
581  + 3 * DELTA_bi * d3PSI_dDelta2_dTau + 3 * PSI * d3DELTAbi_dDelta2_dTau + 6 * dDELTAbi_dDelta * d2PSI_dDelta_dTau
582  + 3 * dDELTAbi_dTau * d2PSI_dDelta2 + 6 * dPSI_dDelta * d2DELTAbi_dDelta_dTau + 3 * dPSI_dTau * d2DELTAbi_dDelta2);
583  derivs.d4alphar_ddelta2_dtau2 +=
584  ni
585  * (delta * DELTA_bi * d4PSI_dDelta2_dTau2 + delta * PSI * d4DELTAbi_dDelta2_dTau2 + 2 * delta * dDELTAbi_dDelta * d3PSI_dDelta_dTau2
586  + 2 * delta * dDELTAbi_dTau * d3PSI_dDelta2_dTau + 2 * delta * dPSI_dDelta * d3DELTAbi_dDelta_dTau2
587  + 2 * delta * dPSI_dTau * d3DELTAbi_dDelta2_dTau + delta * d2DELTAbi_dDelta2 * d2PSI_dTau2
588  + 4 * delta * d2DELTAbi_dDelta_dTau * d2PSI_dDelta_dTau + delta * d2DELTAbi_dTau2 * d2PSI_dDelta2 + 2 * DELTA_bi * d3PSI_dDelta_dTau2
589  + 2 * PSI * d3DELTAbi_dDelta_dTau2 + 2 * dDELTAbi_dDelta * d2PSI_dTau2 + 4 * dDELTAbi_dTau * d2PSI_dDelta_dTau
590  + 2 * dPSI_dDelta * d2DELTAbi_dTau2 + 4 * dPSI_dTau * d2DELTAbi_dDelta_dTau);
591  }
592 }
593 
594 #if ENABLE_CATCH
595 mcx::MultiComplex<double> ResidualHelmholtzNonAnalytic::one_mcx(const mcx::MultiComplex<double>& tau,
596  const mcx::MultiComplex<double>& delta) const {
597 
598  mcx::MultiComplex<double> sum00 = 0.0 * tau * delta;
599  for (unsigned int i = 0; i < N; ++i) {
600  const ResidualHelmholtzNonAnalyticElement& el = elements[i];
601  const CoolPropDbl ni = el.n, ai = el.a, bi = el.b, betai = el.beta;
602  const CoolPropDbl Ai = el.A, Bi = el.B, Ci = el.C, Di = el.D;
603 
604  const auto theta = (1.0 - tau) + Ai * pow(POW2(delta - 1.0), 1.0 / (2.0 * betai));
605  const auto PSI = exp(-Ci * POW2(delta - 1.0) - Di * POW2(tau - 1.0));
606  const auto DELTA = POW2(theta) + Bi * pow(POW2(delta - 1.0), ai);
607  const auto DELTA_bi = pow(DELTA, bi);
608 
609  sum00 += delta * ni * DELTA_bi * PSI;
610  }
611  return sum00;
612 }
613 #endif
614 
615 void ResidualHelmholtzGeneralizedCubic::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
616  if (!enabled) {
617  return;
618  }
619 
620  derivs.alphar += m_abstractcubic->alphar(tau, delta, z, 0, 0);
621 
622  derivs.dalphar_ddelta += m_abstractcubic->alphar(tau, delta, z, 0, 1);
623  derivs.dalphar_dtau += m_abstractcubic->alphar(tau, delta, z, 1, 0);
624 
625  derivs.d2alphar_ddelta2 += m_abstractcubic->alphar(tau, delta, z, 0, 2);
626  derivs.d2alphar_ddelta_dtau += m_abstractcubic->alphar(tau, delta, z, 1, 1);
627  derivs.d2alphar_dtau2 += m_abstractcubic->alphar(tau, delta, z, 2, 0);
628 
629  derivs.d3alphar_ddelta3 += m_abstractcubic->alphar(tau, delta, z, 0, 3);
630  derivs.d3alphar_ddelta2_dtau += m_abstractcubic->alphar(tau, delta, z, 1, 2);
631  derivs.d3alphar_ddelta_dtau2 += m_abstractcubic->alphar(tau, delta, z, 2, 1);
632  derivs.d3alphar_dtau3 += m_abstractcubic->alphar(tau, delta, z, 3, 0);
633 
634  derivs.d4alphar_ddelta4 += m_abstractcubic->alphar(tau, delta, z, 0, 4);
635  derivs.d4alphar_ddelta3_dtau += m_abstractcubic->alphar(tau, delta, z, 1, 3);
636  derivs.d4alphar_ddelta2_dtau2 += m_abstractcubic->alphar(tau, delta, z, 2, 2);
637  derivs.d4alphar_ddelta_dtau3 += m_abstractcubic->alphar(tau, delta, z, 3, 1);
638  derivs.d4alphar_dtau4 += m_abstractcubic->alphar(tau, delta, z, 4, 0);
639 }
640 
665 void ResidualHelmholtzGaoB::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
666  if (!enabled) {
667  return;
668  }
669 
670  CoolPropDbl Ftau = 0, Fdelta = 0, taudFtaudtau = 0, tau2d2Ftaudtau2 = 0, tau3d3Ftaudtau3 = 0, tau4d4Ftaudtau4 = 0, deltadFdeltaddelta = 0,
671  delta2d2Fdeltaddelta2 = 0, delta3d3Fdeltaddelta3 = 0, delta4d4Fdeltaddelta4 = 0;
672 
673  for (int i = 0; i < static_cast<int>(n.size()); ++i) {
674 
675  const CoolPropDbl n = this->n[i], t = this->t[i], d = this->d[i], eta = this->eta[i], beta = this->beta[i], gamma = this->gamma[i],
676  epsilon = this->epsilon[i], b = this->b[i];
677 
678  Ftau = pow(tau, t) * exp(1.0 / (b + beta * pow(-gamma + tau, 2)));
679  Fdelta = pow(delta, d) * exp(eta * pow(delta - epsilon, 2));
680  taudFtaudtau = (2 * beta * pow(tau, t + 1) * (gamma - tau) + t * pow(tau, t) * pow(b + beta * pow(gamma - tau, 2), 2))
681  * exp(1.0 / (b + beta * pow(gamma - tau, 2))) / pow(b + beta * pow(gamma - tau, 2), 2);
682  tau2d2Ftaudtau2 = pow(tau, t)
683  * (4 * beta * t * tau * pow(b + beta * pow(gamma - tau, 2), 2) * (gamma - tau)
684  + 2 * beta * pow(tau, 2)
685  * (4 * beta * (b + beta * pow(gamma - tau, 2)) * pow(gamma - tau, 2) + 2 * beta * pow(gamma - tau, 2)
686  - pow(b + beta * pow(gamma - tau, 2), 2))
687  + t * pow(b + beta * pow(gamma - tau, 2), 4) * (t - 1))
688  * exp(1.0 / (b + beta * pow(gamma - tau, 2))) / pow(b + beta * pow(gamma - tau, 2), 4);
689  tau3d3Ftaudtau3 =
690  pow(tau, t)
691  * (4 * pow(beta, 2) * pow(tau, 3) * (gamma - tau)
692  * (12 * beta * (b + beta * pow(gamma - tau, 2)) * pow(gamma - tau, 2) + 2 * beta * pow(gamma - tau, 2)
693  - 6 * pow(b + beta * pow(gamma - tau, 2), 3) + pow(b + beta * pow(gamma - tau, 2), 2) * (12 * beta * pow(gamma - tau, 2) - 3))
694  + 6 * beta * t * pow(tau, 2) * pow(b + beta * pow(gamma - tau, 2), 2)
695  * (4 * beta * (b + beta * pow(gamma - tau, 2)) * pow(gamma - tau, 2) + 2 * beta * pow(gamma - tau, 2)
696  - pow(b + beta * pow(gamma - tau, 2), 2))
697  + 6 * beta * t * tau * pow(b + beta * pow(gamma - tau, 2), 4) * (gamma - tau) * (t - 1)
698  + t * pow(b + beta * pow(gamma - tau, 2), 6) * (pow(t, 2) - 3 * t + 2))
699  * exp(1.0 / (b + beta * pow(gamma - tau, 2))) / pow(b + beta * pow(gamma - tau, 2), 6);
700  tau4d4Ftaudtau4 =
701  pow(tau, t)
702  * (16 * pow(beta, 2) * t * pow(tau, 3) * pow(b + beta * pow(gamma - tau, 2), 2) * (gamma - tau)
703  * (12 * beta * (b + beta * pow(gamma - tau, 2)) * pow(gamma - tau, 2) + 2 * beta * pow(gamma - tau, 2)
704  - 6 * pow(b + beta * pow(gamma - tau, 2), 3) + pow(b + beta * pow(gamma - tau, 2), 2) * (12 * beta * pow(gamma - tau, 2) - 3))
705  + pow(beta, 2) * pow(tau, 4)
706  * (pow(beta, 2) * (192 * b + 192 * beta * pow(gamma - tau, 2)) * pow(gamma - tau, 4) + 16 * pow(beta, 2) * pow(gamma - tau, 4)
707  + 96 * beta * pow(b + beta * pow(gamma - tau, 2), 3) * pow(gamma - tau, 2) * (4 * beta * pow(gamma - tau, 2) - 3)
708  + 48 * beta * pow(b + beta * pow(gamma - tau, 2), 2) * pow(gamma - tau, 2) * (12 * beta * pow(gamma - tau, 2) - 1)
709  + 24 * pow(b + beta * pow(gamma - tau, 2), 5) + pow(b + beta * pow(gamma - tau, 2), 4) * (-288 * beta * pow(gamma - tau, 2) + 12))
710  + 12 * beta * t * pow(tau, 2) * pow(b + beta * pow(gamma - tau, 2), 4) * (t - 1)
711  * (4 * beta * (b + beta * pow(gamma - tau, 2)) * pow(gamma - tau, 2) + 2 * beta * pow(gamma - tau, 2)
712  - pow(b + beta * pow(gamma - tau, 2), 2))
713  + 8 * beta * t * tau * pow(b + beta * pow(gamma - tau, 2), 6) * (gamma - tau) * (pow(t, 2) - 3 * t + 2)
714  + t * pow(b + beta * pow(gamma - tau, 2), 8) * (pow(t, 3) - 6 * pow(t, 2) + 11 * t - 6))
715  * exp(1.0 / (b + beta * pow(gamma - tau, 2))) / pow(b + beta * pow(gamma - tau, 2), 8);
716  deltadFdeltaddelta = (d * pow(delta, d) + 2 * pow(delta, d + 1) * eta * (delta - epsilon)) * exp(eta * pow(delta - epsilon, 2));
717  delta2d2Fdeltaddelta2 =
718  pow(delta, d) * (4 * d * delta * eta * (delta - epsilon) + d * (d - 1) + 2 * pow(delta, 2) * eta * (2 * eta * pow(delta - epsilon, 2) + 1))
719  * exp(eta * pow(delta - epsilon, 2));
720  delta3d3Fdeltaddelta3 =
721  pow(delta, d)
722  * (6 * d * pow(delta, 2) * eta * (2 * eta * pow(delta - epsilon, 2) + 1) + 6 * d * delta * eta * (d - 1) * (delta - epsilon)
723  + d * (pow(d, 2) - 3 * d + 2) + 4 * pow(delta, 3) * pow(eta, 2) * (delta - epsilon) * (2 * eta * pow(delta - epsilon, 2) + 3))
724  * exp(eta * pow(delta - epsilon, 2));
725  delta4d4Fdeltaddelta4 =
726  pow(delta, d)
727  * (16 * d * pow(delta, 3) * pow(eta, 2) * (delta - epsilon) * (2 * eta * pow(delta - epsilon, 2) + 3)
728  + 12 * d * pow(delta, 2) * eta * (d - 1) * (2 * eta * pow(delta - epsilon, 2) + 1)
729  + 8 * d * delta * eta * (delta - epsilon) * (pow(d, 2) - 3 * d + 2) + d * (pow(d, 3) - 6 * pow(d, 2) + 11 * d - 6)
730  + pow(delta, 4) * pow(eta, 2) * (16 * pow(eta, 2) * pow(delta - epsilon, 4) + 48 * eta * pow(delta - epsilon, 2) + 12))
731  * exp(eta * pow(delta - epsilon, 2));
732 
733  derivs.alphar += n * Ftau * Fdelta;
734 
735  derivs.dalphar_ddelta += n * Ftau * deltadFdeltaddelta / delta;
736  derivs.dalphar_dtau += n * Fdelta * taudFtaudtau / tau;
737 
738  derivs.d2alphar_ddelta2 += n * Ftau * delta2d2Fdeltaddelta2 / POW2(delta);
739  derivs.d2alphar_ddelta_dtau += n * taudFtaudtau * deltadFdeltaddelta / tau / delta;
740  derivs.d2alphar_dtau2 += n * Fdelta * tau2d2Ftaudtau2 / POW2(tau);
741 
742  derivs.d3alphar_ddelta3 += n * Ftau * delta3d3Fdeltaddelta3 / POW3(delta);
743  derivs.d3alphar_ddelta2_dtau += n * taudFtaudtau * delta2d2Fdeltaddelta2 / POW2(delta) / tau;
744  derivs.d3alphar_ddelta_dtau2 += n * tau2d2Ftaudtau2 * deltadFdeltaddelta / POW2(tau) / delta;
745  derivs.d3alphar_dtau3 += n * Fdelta * tau3d3Ftaudtau3 / POW3(tau);
746 
747  derivs.d4alphar_ddelta4 += n * Ftau * delta4d4Fdeltaddelta4 / POW4(delta);
748  derivs.d4alphar_ddelta3_dtau += n * taudFtaudtau * delta3d3Fdeltaddelta3 / POW3(delta) / tau;
749  derivs.d4alphar_ddelta2_dtau2 += n * tau2d2Ftaudtau2 * delta2d2Fdeltaddelta2 / POW2(delta) / POW2(tau);
750  derivs.d4alphar_ddelta_dtau3 += n * tau3d3Ftaudtau3 * deltadFdeltaddelta / POW3(tau) / delta;
751  derivs.d4alphar_dtau4 += n * Fdelta * tau4d4Ftaudtau4 / POW4(tau);
752  }
753 }
754 
755 
756 #if ENABLE_CATCH
757 mcx::MultiComplex<double> ResidualHelmholtzGaoB::one_mcx(const mcx::MultiComplex<double>& tau, const mcx::MultiComplex<double>& delta) const {
758  mcx::MultiComplex<double> sum00 = 0.0;
759  for (std::size_t i = 0; i < static_cast<int>(n.size()); ++i) {
760  auto u = b[i] + beta[i] * (tau-gamma[i])*(tau-gamma[i]);
761  auto Ftau = pow(tau, t[i]) * exp(1.0 / u);
762  auto Fdelta = pow(delta, d[i]) * exp(eta[i] * pow(delta - epsilon[i], 2));
763  sum00 += n[i] * Ftau * Fdelta;
764  }
765  return sum00;
766 }
767 #endif
768 
769 ResidualHelmholtzXiangDeiters::ResidualHelmholtzXiangDeiters(const CoolPropDbl Tc, const CoolPropDbl pc, const CoolPropDbl rhomolarc,
770  const CoolPropDbl acentric, const CoolPropDbl R)
771  : Tc(Tc), pc(pc), rhomolarc(rhomolarc), acentric(acentric), R(R) {
772  double Zc = pc / (R * Tc * rhomolarc);
773  theta = POW2(Zc - 0.29);
774 
775  // From Xiang & Deiters, doi:10.1016/j.ces.2007.11.029
776  double _d[] = {1, 1, 1, 2, 3, 7, 1, 1, 2, 5, 1, 1, 4, 2};
777  std::vector<CoolPropDbl> d(_d, _d + sizeof(_d) / sizeof(double));
778  double _t[] = {0.25, 1.25, 1.5, 1.375, 0.25, 0.875, 0, 2.375, 2, 2.125, 3.5, 6.5, 4.75, 12.5};
779  std::vector<CoolPropDbl> t(_t, _t + sizeof(_t) / sizeof(double));
780  double _l[] = {0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3};
781  std::vector<CoolPropDbl> l(_l, _l + sizeof(_l) / sizeof(double));
782  double _g[] = {0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1};
783  std::vector<CoolPropDbl> g(_g, _g + sizeof(_g) / sizeof(double));
784  double _a0[] = {8.5740489E-01, -3.2863233E+00, 1.6480939E+00, -5.4524817E-02, 6.1623592E-02, 2.7389266E-04, -6.0655087E-02,
785  -3.1811852E-02, -1.1550422E-01, -1.8610466E-02, -1.8348671E-01, 5.5071325E-03, -1.2268039E-02, -5.0433436E-03};
786  std::vector<CoolPropDbl> a0(_a0, _a0 + sizeof(_a0) / sizeof(double));
787  double _a1[] = {5.6200117E-01, 3.2439544E+00, -4.9628768E+00, -2.2132851E-01, 9.3388356E-02, 2.4940171E-05, -1.7519204E-01,
788  8.9325660E-01, 2.9886613E+00, 1.0881387E-01, -6.7166746E-01, 1.4477326E-01, -2.8716809E-01, -1.1478402E-01};
789  std::vector<CoolPropDbl> a1(_a1, _a1 + sizeof(_a1) / sizeof(double));
790  double _a2[] = {-8.1680511E+01, 4.6384732E+02, -2.7970850E+02, 2.9317364E+01, -2.2324825E+01, -5.0932691E-02, -7.2836590E+00,
791  -2.2063100E+02, -3.0435126E+02, 5.8514719E+00, 1.7995451E+02, -1.0178400E+02, 4.0848053E+01, 1.2411984E+01};
792  std::vector<CoolPropDbl> a2(_a2, _a2 + sizeof(_a2) / sizeof(double));
793 
794  phi0.add_Exponential(a0, d, t, g, l);
795  phi1.add_Exponential(a1, d, t, g, l);
796  phi2.add_Exponential(a2, d, t, g, l);
797 
798  enabled = true;
799 };
800 
801 void ResidualHelmholtzXiangDeiters::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
802  if (!enabled) {
803  return;
804  }
805 
806  HelmholtzDerivatives derivs0, derivs1, derivs2;
807 
808  // Calculate each of the derivative terms
809  phi0.all(tau, delta, derivs0);
810  phi1.all(tau, delta, derivs1);
811  phi2.all(tau, delta, derivs2);
812 
813  // Add up the contributions
814  derivs = derivs + derivs0 + derivs1 * acentric + derivs2 * theta;
815 }
816 #if ENABLE_CATCH
817 mcx::MultiComplex<double> ResidualHelmholtzXiangDeiters::one_mcx(const mcx::MultiComplex<double>& tau, const mcx::MultiComplex<double>& delta) const {
818 
819  return phi0.one_mcx(tau, delta) + phi1.one_mcx(tau, delta) * acentric + phi2.one_mcx(tau, delta) * theta;
820 }
821 #endif
822 
823 void ResidualHelmholtzSAFTAssociating::to_json(rapidjson::Value& el, rapidjson::Document& doc) {
824  el.AddMember("type", "ResidualHelmholtzSAFTAssociating", doc.GetAllocator());
825  el.AddMember("a", a, doc.GetAllocator());
826  el.AddMember("m", m, doc.GetAllocator());
827  el.AddMember("epsilonbar", epsilonbar, doc.GetAllocator());
828  el.AddMember("vbarn", vbarn, doc.GetAllocator());
829  el.AddMember("kappabar", kappabar, doc.GetAllocator());
830 }
831 CoolPropDbl ResidualHelmholtzSAFTAssociating::Deltabar(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
832  return this->g(this->eta(delta)) * (exp(this->epsilonbar * tau) - 1) * this->kappabar;
833 }
834 CoolPropDbl ResidualHelmholtzSAFTAssociating::dDeltabar_ddelta__consttau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
835  return this->dg_deta(this->eta(delta)) * (exp(this->epsilonbar * tau) - 1) * this->kappabar * this->vbarn;
836 }
837 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2Deltabar_ddelta2__consttau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
838  return this->d2g_deta2(this->eta(delta)) * (exp(this->epsilonbar * tau) - 1) * this->kappabar * pow(this->vbarn, (int)2);
839 }
840 CoolPropDbl ResidualHelmholtzSAFTAssociating::dDeltabar_dtau__constdelta(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
841  return this->g(this->eta(delta)) * this->kappabar * exp(this->epsilonbar * tau) * this->epsilonbar;
842 }
843 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2Deltabar_dtau2__constdelta(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
844  return this->g(this->eta(delta)) * this->kappabar * exp(this->epsilonbar * tau) * pow(this->epsilonbar, (int)2);
845 }
846 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2Deltabar_ddelta_dtau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
847  return this->dg_deta(this->eta(delta)) * exp(this->epsilonbar * tau) * this->epsilonbar * this->kappabar * this->vbarn;
848 }
849 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3Deltabar_dtau3__constdelta(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
850  return this->g(this->eta(delta)) * this->kappabar * exp(this->epsilonbar * tau) * pow(this->epsilonbar, (int)3);
851 }
852 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3Deltabar_ddelta_dtau2(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
853  return this->dg_deta(this->eta(delta)) * this->kappabar * exp(this->epsilonbar * tau) * pow(this->epsilonbar, (int)2) * this->vbarn;
854 }
855 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3Deltabar_ddelta2_dtau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
856  return this->d2g_deta2(this->eta(delta)) * exp(this->epsilonbar * tau) * this->epsilonbar * this->kappabar * pow(this->vbarn, (int)2);
857 }
858 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3Deltabar_ddelta3__consttau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
859  return this->d3g_deta3(this->eta(delta)) * (exp(this->epsilonbar * tau) - 1) * this->kappabar * pow(this->vbarn, (int)3);
860 }
861 
862 CoolPropDbl ResidualHelmholtzSAFTAssociating::X(const CoolPropDbl& delta, const CoolPropDbl& Deltabar) const {
863  return 2 / (sqrt(1 + 4 * Deltabar * delta) + 1);
864 }
865 CoolPropDbl ResidualHelmholtzSAFTAssociating::dX_dDeltabar__constdelta(const CoolPropDbl& delta, const CoolPropDbl& Deltabar) const {
866  CoolPropDbl X = this->X(delta, Deltabar);
867  return -delta * X * X / (2 * Deltabar * delta * X + 1);
868 }
869 CoolPropDbl ResidualHelmholtzSAFTAssociating::dX_ddelta__constDeltabar(const CoolPropDbl& delta, const CoolPropDbl& Deltabar) const {
870  CoolPropDbl X = this->X(delta, Deltabar);
871  return -Deltabar * X * X / (2 * Deltabar * delta * X + 1);
872 }
873 CoolPropDbl ResidualHelmholtzSAFTAssociating::dX_dtau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
874  CoolPropDbl Deltabar = this->Deltabar(tau, delta);
875  return this->dX_dDeltabar__constdelta(delta, Deltabar) * this->dDeltabar_dtau__constdelta(tau, delta);
876 }
877 CoolPropDbl ResidualHelmholtzSAFTAssociating::dX_ddelta(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
878  CoolPropDbl Deltabar = this->Deltabar(tau, delta);
879  return (this->dX_ddelta__constDeltabar(delta, Deltabar)
880  + this->dX_dDeltabar__constdelta(delta, Deltabar) * this->dDeltabar_ddelta__consttau(tau, delta));
881 }
882 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2X_dtau2(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
883  CoolPropDbl Deltabar = this->Deltabar(tau, delta);
884  CoolPropDbl X = this->X(delta, Deltabar);
885  CoolPropDbl beta = this->dDeltabar_dtau__constdelta(tau, delta);
886  CoolPropDbl d_dXdtau_dbeta = -delta * X * X / (2 * Deltabar * delta * X + 1);
887  CoolPropDbl d_dXdtau_dDeltabar = 2 * delta * delta * X * X * X / pow(2 * Deltabar * delta * X + 1, 2) * beta;
888  CoolPropDbl d_dXdtau_dX = -2 * beta * delta * X * (Deltabar * delta * X + 1) / pow(2 * Deltabar * delta * X + 1, 2);
889  CoolPropDbl dbeta_dtau = this->d2Deltabar_dtau2__constdelta(tau, delta);
890  CoolPropDbl dX_dDeltabar = this->dX_dDeltabar__constdelta(delta, Deltabar);
891  return d_dXdtau_dX * dX_dDeltabar * beta + d_dXdtau_dDeltabar * beta + d_dXdtau_dbeta * dbeta_dtau;
892 }
893 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2X_ddeltadtau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
894  CoolPropDbl Deltabar = this->Deltabar(tau, delta);
895  CoolPropDbl X = this->X(delta, Deltabar);
896  CoolPropDbl alpha = this->dDeltabar_ddelta__consttau(tau, delta);
897  CoolPropDbl beta = this->dDeltabar_dtau__constdelta(tau, delta);
898  CoolPropDbl dalpha_dtau = this->d2Deltabar_ddelta_dtau(tau, delta);
899  CoolPropDbl d_dXddelta_dDeltabar = X * X * (2 * delta * delta * X * alpha - 1) / pow(2 * Deltabar * delta * X + 1, 2);
900  CoolPropDbl d_dXddelta_dalpha = -delta * X * X / (2 * Deltabar * delta * X + 1);
901  CoolPropDbl d_dXddelta_dX = -(Deltabar + delta * alpha) * 2 * (Deltabar * delta * X * X + X) / pow(2 * Deltabar * delta * X + 1, 2);
902  CoolPropDbl dX_dDeltabar = this->dX_dDeltabar__constdelta(delta, Deltabar);
903  return d_dXddelta_dX * dX_dDeltabar * beta + d_dXddelta_dDeltabar * beta + d_dXddelta_dalpha * dalpha_dtau;
904 }
905 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2X_ddelta2(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
906  CoolPropDbl Deltabar = this->Deltabar(tau, delta);
907  CoolPropDbl X = this->X(delta, Deltabar);
908  CoolPropDbl alpha = this->dDeltabar_ddelta__consttau(tau, delta);
909  CoolPropDbl dalpha_ddelta = this->d2Deltabar_ddelta2__consttau(tau, delta);
910 
911  CoolPropDbl dX_ddelta_constall = X * X * (2 * Deltabar * Deltabar * X - alpha) / pow(2 * Deltabar * delta * X + 1, 2);
912  CoolPropDbl d_dXddelta_dX = -(Deltabar + delta * alpha) * 2 * (Deltabar * delta * X * X + X) / pow(2 * Deltabar * delta * X + 1, 2);
913  CoolPropDbl d_dXddelta_dDeltabar = X * X * (2 * delta * delta * X * alpha - 1) / pow(2 * Deltabar * delta * X + 1, 2);
914  CoolPropDbl d_dXddelta_dalpha = -delta * X * X / (2 * Deltabar * delta * X + 1);
915 
916  CoolPropDbl dX_dDeltabar = this->dX_dDeltabar__constdelta(delta, Deltabar);
917  CoolPropDbl dX_ddelta = this->dX_ddelta__constDeltabar(delta, Deltabar);
918 
919  CoolPropDbl val = (dX_ddelta_constall + d_dXddelta_dX * dX_ddelta + d_dXddelta_dX * dX_dDeltabar * alpha + d_dXddelta_dDeltabar * alpha
920  + d_dXddelta_dalpha * dalpha_ddelta);
921  return val;
922 }
923 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3X_dtau3(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
924  CoolPropDbl Delta = this->Deltabar(tau, delta);
925  CoolPropDbl X = this->X(delta, Delta);
926  CoolPropDbl dX_dDelta = this->dX_dDeltabar__constdelta(delta, Delta);
927  CoolPropDbl Delta_t = this->dDeltabar_dtau__constdelta(tau, delta);
928  CoolPropDbl Delta_tt = this->d2Deltabar_dtau2__constdelta(tau, delta);
929  CoolPropDbl Delta_ttt = this->d3Deltabar_dtau3__constdelta(tau, delta);
930  CoolPropDbl dXtt_dX = 2 * X * delta
931  * (-6 * Delta * pow(Delta_t, 2) * pow(X, 2) * pow(delta, 2) * (Delta * X * delta + 1)
932  + 3 * pow(Delta_t, 2) * X * delta * (2 * Delta * X * delta + 1) - Delta_tt * pow(2 * Delta * X * delta + 1, 3)
933  + X * delta * (Delta * Delta_tt + 3 * pow(Delta_t, 2)) * pow(2 * Delta * X * delta + 1, 2))
934  / pow(2 * Delta * X * delta + 1, 4);
935  CoolPropDbl dXtt_dDelta = 2 * pow(X, 3) * pow(delta, 2)
936  * (-6 * pow(Delta_t, 2) * X * delta * (Delta * X * delta + 1)
937  - 3 * pow(Delta_t, 2) * X * delta * (2 * Delta * X * delta + 1) + Delta_tt * pow(2 * Delta * X * delta + 1, 2))
938  / pow(2 * Delta * X * delta + 1, 4);
939  CoolPropDbl dXtt_dDelta_t = 4 * Delta_t * pow(X, 3) * pow(delta, 2) * (3 * Delta * X * delta + 2) / pow(2 * Delta * X * delta + 1, 3);
940  CoolPropDbl dXtt_dDelta_tt = -pow(X, 2) * delta / (2 * Delta * X * delta + 1);
941  return dXtt_dX * dX_dDelta * Delta_t + dXtt_dDelta * Delta_t + dXtt_dDelta_t * Delta_tt + dXtt_dDelta_tt * Delta_ttt;
942 }
943 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3X_ddeltadtau2(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
944  CoolPropDbl Delta = this->Deltabar(tau, delta);
945  CoolPropDbl X = this->X(delta, Delta);
946  CoolPropDbl dX_ddelta = this->dX_ddelta__constDeltabar(delta, Delta);
947  CoolPropDbl dX_dDelta = this->dX_dDeltabar__constdelta(delta, Delta);
948  CoolPropDbl Delta_t = this->dDeltabar_dtau__constdelta(tau, delta);
949  CoolPropDbl Delta_d = this->dDeltabar_ddelta__consttau(tau, delta);
950  CoolPropDbl Delta_dt = this->d2Deltabar_ddelta_dtau(tau, delta);
951  CoolPropDbl Delta_tt = this->d2Deltabar_dtau2__constdelta(tau, delta);
952  CoolPropDbl Delta_dtt = this->d3Deltabar_ddelta_dtau2(tau, delta);
953  CoolPropDbl dXtt_ddelta =
954  pow(X, 2)
955  * (-12 * Delta * pow(Delta_t, 2) * pow(X, 2) * pow(delta, 2) * (Delta * X * delta + 1)
956  + 2 * pow(Delta_t, 2) * X * delta * (-Delta * X * delta + 2) * (2 * Delta * X * delta + 1) - Delta_tt * pow(2 * Delta * X * delta + 1, 3)
957  + 2 * X * delta * (Delta * Delta_tt + 2 * pow(Delta_t, 2)) * pow(2 * Delta * X * delta + 1, 2))
958  / pow(2 * Delta * X * delta + 1, 4);
959  CoolPropDbl dXtt_dX = 2 * X * delta
960  * (-6 * Delta * pow(Delta_t, 2) * pow(X, 2) * pow(delta, 2) * (Delta * X * delta + 1)
961  + 3 * pow(Delta_t, 2) * X * delta * (2 * Delta * X * delta + 1) - Delta_tt * pow(2 * Delta * X * delta + 1, 3)
962  + X * delta * (Delta * Delta_tt + 3 * pow(Delta_t, 2)) * pow(2 * Delta * X * delta + 1, 2))
963  / pow(2 * Delta * X * delta + 1, 4);
964  CoolPropDbl dXtt_dDelta = 2 * pow(X, 3) * pow(delta, 2)
965  * (-6 * pow(Delta_t, 2) * X * delta * (Delta * X * delta + 1)
966  - 3 * pow(Delta_t, 2) * X * delta * (2 * Delta * X * delta + 1) + Delta_tt * pow(2 * Delta * X * delta + 1, 2))
967  / pow(2 * Delta * X * delta + 1, 4);
968  CoolPropDbl dXtt_dDelta_t = 4 * Delta_t * pow(X, 3) * pow(delta, 2) * (3 * Delta * X * delta + 2) / pow(2 * Delta * X * delta + 1, 3);
969  CoolPropDbl dXtt_dDelta_tt = -pow(X, 2) * delta / (2 * Delta * X * delta + 1);
970  return dXtt_ddelta + dXtt_dX * dX_ddelta + dXtt_dX * dX_dDelta * Delta_d + dXtt_dDelta * Delta_d + dXtt_dDelta_t * Delta_dt
971  + dXtt_dDelta_tt * Delta_dtt;
972 }
973 
974 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3X_ddelta2dtau(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
975  CoolPropDbl Delta = this->Deltabar(tau, delta);
976  CoolPropDbl X = this->X(delta, Delta);
977  CoolPropDbl dX_dDelta = this->dX_dDeltabar__constdelta(delta, Delta);
978  CoolPropDbl Delta_t = this->dDeltabar_dtau__constdelta(tau, delta);
979  CoolPropDbl Delta_d = this->dDeltabar_ddelta__consttau(tau, delta);
980  CoolPropDbl Delta_dd = this->d2Deltabar_ddelta2__consttau(tau, delta);
981  CoolPropDbl Delta_dt = this->d2Deltabar_ddelta_dtau(tau, delta);
982  CoolPropDbl Delta_ddt = this->d3Deltabar_ddelta2_dtau(tau, delta);
983  CoolPropDbl dXdd_dX =
984  2 * X
985  * (-6 * Delta * pow(X, 2) * delta * pow(Delta + Delta_d * delta, 2) * (Delta * X * delta + 1)
986  - Delta_dd * delta * pow(2 * Delta * X * delta + 1, 3)
987  + 2 * X * (2 * Delta * X * delta + 1)
988  * (-Delta * Delta_d * delta * (2 * Delta_d * X * pow(delta, 2) - 1) - Delta * delta * (2 * pow(Delta, 2) * X - Delta_d)
989  + Delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1) + Delta_d * delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1))
990  + pow(2 * Delta * X * delta + 1, 2)
991  * (3 * pow(Delta, 2) * X + Delta * Delta_dd * X * pow(delta, 2) + Delta * X * (Delta + Delta_d * delta)
992  + pow(Delta_d, 2) * X * pow(delta, 2) + Delta_d * X * delta * (Delta + Delta_d * delta)
993  + Delta_d * (2 * Delta_d * X * pow(delta, 2) - 1) - Delta_d))
994  / pow(2 * Delta * X * delta + 1, 4);
995  CoolPropDbl dXdd_dDelta = pow(X, 3)
996  * (-8 * pow(Delta, 2) * Delta_d * pow(X, 2) * pow(delta, 3) + 8 * pow(Delta, 2) * Delta_dd * pow(X, 2) * pow(delta, 4)
997  + 10 * pow(Delta, 2) * X * delta - 24 * Delta * pow(Delta_d, 2) * pow(X, 2) * pow(delta, 4)
998  + 8 * Delta * Delta_d * X * pow(delta, 2) + 8 * Delta * Delta_dd * X * pow(delta, 3) + 8 * Delta
999  - 18 * pow(Delta_d, 2) * X * pow(delta, 3) + 12 * Delta_d * delta + 2 * Delta_dd * pow(delta, 2))
1000  / (16 * pow(Delta, 4) * pow(X, 4) * pow(delta, 4) + 32 * pow(Delta, 3) * pow(X, 3) * pow(delta, 3)
1001  + 24 * pow(Delta, 2) * pow(X, 2) * pow(delta, 2) + 8 * Delta * X * delta + 1);
1002  CoolPropDbl dXdd_dDelta_d =
1003  2 * pow(X, 2)
1004  * (2 * X * delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1) + (2 * Delta * X * delta + 1) * (2 * Delta_d * X * pow(delta, 2) - 1))
1005  / pow(2 * Delta * X * delta + 1, 3);
1006  CoolPropDbl dXdd_dDelta_dd = -pow(X, 2) * delta / (2 * Delta * X * delta + 1);
1007 
1008  return dXdd_dX * dX_dDelta * Delta_t + dXdd_dDelta * Delta_t + dXdd_dDelta_d * Delta_dt + dXdd_dDelta_dd * Delta_ddt;
1009 }
1010 
1011 double Xdd(double X, double delta, double Delta, double Delta_d, double Delta_dd) {
1012  return Delta * pow(X, 2) * (2 * Delta + 2 * Delta_d * delta) * (Delta * pow(X, 2) * delta + X) / pow(2 * Delta * X * delta + 1, 3)
1013  + Delta_d * pow(X, 2) * delta * (2 * Delta + 2 * Delta_d * delta) * (Delta * pow(X, 2) * delta + X) / pow(2 * Delta * X * delta + 1, 3)
1014  + Delta_d * pow(X, 2) * (2 * Delta_d * X * pow(delta, 2) - 1) / pow(2 * Delta * X * delta + 1, 2)
1015  - Delta_dd * pow(X, 2) * delta / (2 * Delta * X * delta + 1)
1016  + pow(X, 2) * (2 * pow(Delta, 2) * X - Delta_d) / pow(2 * Delta * X * delta + 1, 2);
1017 }
1018 
1019 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3X_ddelta3(const CoolPropDbl& tau, const CoolPropDbl& delta) const {
1020  CoolPropDbl Delta = this->Deltabar(tau, delta);
1021  CoolPropDbl X = this->X(delta, Delta);
1022  CoolPropDbl dX_ddelta = this->dX_ddelta__constDeltabar(delta, Delta);
1023  CoolPropDbl dX_dDelta = this->dX_dDeltabar__constdelta(delta, Delta);
1024  CoolPropDbl Delta_d = this->dDeltabar_ddelta__consttau(tau, delta);
1025  CoolPropDbl Delta_dd = this->d2Deltabar_ddelta2__consttau(tau, delta);
1026  CoolPropDbl Delta_ddd = this->d3Deltabar_ddelta3__consttau(tau, delta);
1027 
1028  CoolPropDbl dXdd_dX =
1029  2 * X
1030  * (-6 * Delta * pow(X, 2) * delta * pow(Delta + Delta_d * delta, 2) * (Delta * X * delta + 1)
1031  - Delta_dd * delta * pow(2 * Delta * X * delta + 1, 3)
1032  + 2 * X * (2 * Delta * X * delta + 1)
1033  * (-Delta * Delta_d * delta * (2 * Delta_d * X * pow(delta, 2) - 1) - Delta * delta * (2 * pow(Delta, 2) * X - Delta_d)
1034  + Delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1) + Delta_d * delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1))
1035  + pow(2 * Delta * X * delta + 1, 2)
1036  * (3 * pow(Delta, 2) * X + Delta * Delta_dd * X * pow(delta, 2) + Delta * X * (Delta + Delta_d * delta)
1037  + pow(Delta_d, 2) * X * pow(delta, 2) + Delta_d * X * delta * (Delta + Delta_d * delta)
1038  + Delta_d * (2 * Delta_d * X * pow(delta, 2) - 1) - Delta_d))
1039  / pow(2 * Delta * X * delta + 1, 4);
1040  CoolPropDbl dXdd_ddelta = pow(X, 2)
1041  * (-24 * pow(Delta, 4) * pow(X, 3) * delta - 8 * pow(Delta, 3) * Delta_d * pow(X, 3) * pow(delta, 2)
1042  - 18 * pow(Delta, 3) * pow(X, 2) + 8 * pow(Delta, 2) * Delta_d * pow(X, 2) * delta
1043  - 4 * pow(Delta, 2) * Delta_dd * pow(X, 2) * pow(delta, 2) + 10 * Delta * pow(Delta_d, 2) * pow(X, 2) * pow(delta, 2)
1044  + 12 * Delta * Delta_d * X - 4 * Delta * Delta_dd * X * delta + 8 * pow(Delta_d, 2) * X * delta - Delta_dd)
1045  / (16 * pow(Delta, 4) * pow(X, 4) * pow(delta, 4) + 32 * pow(Delta, 3) * pow(X, 3) * pow(delta, 3)
1046  + 24 * pow(Delta, 2) * pow(X, 2) * pow(delta, 2) + 8 * Delta * X * delta + 1);
1047  CoolPropDbl dXdd_dDelta = pow(X, 3)
1048  * (-8 * pow(Delta, 2) * Delta_d * pow(X, 2) * pow(delta, 3) + 8 * pow(Delta, 2) * Delta_dd * pow(X, 2) * pow(delta, 4)
1049  + 10 * pow(Delta, 2) * X * delta - 24 * Delta * pow(Delta_d, 2) * pow(X, 2) * pow(delta, 4)
1050  + 8 * Delta * Delta_d * X * pow(delta, 2) + 8 * Delta * Delta_dd * X * pow(delta, 3) + 8 * Delta
1051  - 18 * pow(Delta_d, 2) * X * pow(delta, 3) + 12 * Delta_d * delta + 2 * Delta_dd * pow(delta, 2))
1052  / (16 * pow(Delta, 4) * pow(X, 4) * pow(delta, 4) + 32 * pow(Delta, 3) * pow(X, 3) * pow(delta, 3)
1053  + 24 * pow(Delta, 2) * pow(X, 2) * pow(delta, 2) + 8 * Delta * X * delta + 1);
1054  CoolPropDbl dXdd_dDelta_d =
1055  2 * pow(X, 2)
1056  * (2 * X * delta * (Delta + Delta_d * delta) * (Delta * X * delta + 1) + (2 * Delta * X * delta + 1) * (2 * Delta_d * X * pow(delta, 2) - 1))
1057  / pow(2 * Delta * X * delta + 1, 3);
1058  CoolPropDbl dXdd_dDelta_dd = -pow(X, 2) * delta / (2 * Delta * X * delta + 1);
1059 
1060  return dXdd_ddelta + dXdd_dX * (dX_ddelta + dX_dDelta * Delta_d) + dXdd_dDelta * Delta_d + dXdd_dDelta_d * Delta_dd + dXdd_dDelta_dd * Delta_ddd;
1061 }
1062 CoolPropDbl ResidualHelmholtzSAFTAssociating::g(const CoolPropDbl& eta) const {
1063  return 0.5 * (2 - eta) / pow(1 - eta, (int)3);
1064 }
1065 CoolPropDbl ResidualHelmholtzSAFTAssociating::dg_deta(const CoolPropDbl& eta) const {
1066  return 0.5 * (5 - 2 * eta) / pow(1 - eta, (int)4);
1067 }
1068 CoolPropDbl ResidualHelmholtzSAFTAssociating::d2g_deta2(const CoolPropDbl& eta) const {
1069  return 3 * (3 - eta) / pow(1 - eta, (int)5);
1070 }
1071 CoolPropDbl ResidualHelmholtzSAFTAssociating::d3g_deta3(const CoolPropDbl& eta) const {
1072  return 6 * (7 - 2 * eta) / pow(1 - eta, (int)6);
1073 }
1074 CoolPropDbl ResidualHelmholtzSAFTAssociating::eta(const CoolPropDbl& delta) const {
1075  return this->vbarn * delta;
1076 }
1077 
1078 void ResidualHelmholtzSAFTAssociating::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& deriv) throw() {
1079  if (disabled) {
1080  return;
1081  }
1082  CoolPropDbl X = this->X(delta, this->Deltabar(tau, delta));
1083  CoolPropDbl X_t = this->dX_dtau(tau, delta);
1084  CoolPropDbl X_d = this->dX_ddelta(tau, delta);
1085  CoolPropDbl X_tt = this->d2X_dtau2(tau, delta);
1086  CoolPropDbl X_dd = this->d2X_ddelta2(tau, delta);
1087  CoolPropDbl X_dt = this->d2X_ddeltadtau(tau, delta);
1088  CoolPropDbl X_ttt = this->d3X_dtau3(tau, delta);
1089  CoolPropDbl X_dtt = this->d3X_ddeltadtau2(tau, delta);
1090  CoolPropDbl X_ddt = this->d3X_ddelta2dtau(tau, delta);
1091  CoolPropDbl X_ddd = this->d3X_ddelta3(tau, delta);
1092 
1093  deriv.alphar += this->m * this->a * ((log(X) - X / 2.0 + 0.5));
1094  deriv.dalphar_ddelta += this->m * this->a * (1 / X - 0.5) * this->dX_ddelta(tau, delta);
1095  deriv.dalphar_dtau += this->m * this->a * (1 / X - 0.5) * this->dX_dtau(tau, delta);
1096  deriv.d2alphar_dtau2 += this->m * this->a * ((1 / X - 0.5) * X_tt - pow(X_t / X, 2));
1097  deriv.d2alphar_ddelta2 += this->m * this->a * ((1 / X - 0.5) * X_dd - pow(X_d / X, 2));
1098  deriv.d2alphar_ddelta_dtau += this->m * this->a * ((-X_t / X / X) * X_d + X_dt * (1 / X - 0.5));
1099  deriv.d3alphar_dtau3 += this->m * this->a
1100  * ((1 / X - 1.0 / 2.0) * X_ttt + (-X_t / pow(X, (int)2)) * X_tt
1101  - 2 * (pow(X, (int)2) * (X_t * X_tt) - pow(X_t, (int)2) * (X * X_t)) / pow(X, (int)4));
1102  deriv.d3alphar_ddelta_dtau2 += this->m * this->a
1103  * ((1 / X - 1.0 / 2.0) * X_dtt - X_d / pow(X, (int)2) * X_tt
1104  - 2 * (pow(X, (int)2) * (X_t * X_dt) - pow(X_t, (int)2) * (X * X_d)) / pow(X, (int)4));
1105  deriv.d3alphar_ddelta2_dtau += this->m * this->a
1106  * ((1 / X - 1.0 / 2.0) * X_ddt - X_t / pow(X, (int)2) * X_dd
1107  - 2 * (pow(X, (int)2) * (X_d * X_dt) - pow(X_d, (int)2) * (X * X_t)) / pow(X, (int)4));
1108  deriv.d3alphar_ddelta3 += this->m * this->a
1109  * ((1 / X - 1.0 / 2.0) * X_ddd - X_d / pow(X, (int)2) * X_dd
1110  - 2 * (pow(X, (int)2) * (X_d * X_dd) - pow(X_d, (int)2) * (X * X_d)) / pow(X, (int)4));
1111 }
1112 
1113 #if ENABLE_CATCH
1114 mcx::MultiComplex<double> IdealHelmholtzCP0PolyT::one_mcx(const mcx::MultiComplex<double>& tau,
1115  const mcx::MultiComplex<double>& delta) const {
1116  mcx::MultiComplex<double> sum = 0.0;
1117  for (std::size_t i = 0; i < N; ++i) {
1118  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1119  sum += c[i] - c[i] * tau / tau0 + c[i] * log(tau / tau0);
1120  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1121  sum += c[i] * tau / Tc * log(tau0 / tau) + c[i] / Tc * (tau - tau0);
1122  } else {
1123  sum += -c[i] * pow(Tc, t[i]) * pow(tau, -t[i]) / (t[i] * (t[i] + 1)) - c[i] * pow(T0, t[i] + 1) * tau / (Tc * (t[i] + 1))
1124  + c[i] * pow(T0, t[i]) / t[i];
1125  }
1126  }
1127  return sum;
1128 }
1129 #endif
1130 
1131 void IdealHelmholtzCP0PolyT::to_json(rapidjson::Value& el, rapidjson::Document& doc) {
1132  el.AddMember("type", "IdealGasCP0Poly", doc.GetAllocator());
1133 
1134  rapidjson::Value _c(rapidjson::kArrayType), _t(rapidjson::kArrayType);
1135  for (std::size_t i = 0; i < N; ++i) {
1136  _c.PushBack(static_cast<double>(c[i]), doc.GetAllocator());
1137  _t.PushBack(static_cast<double>(t[i]), doc.GetAllocator());
1138  }
1139  el.AddMember("c", _c, doc.GetAllocator());
1140  el.AddMember("t", _t, doc.GetAllocator());
1141  el.AddMember("Tc", static_cast<double>(Tc), doc.GetAllocator());
1142  el.AddMember("T0", static_cast<double>(T0), doc.GetAllocator());
1143 }
1144 
1145 void IdealHelmholtzLead::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1146  if (!enabled) {
1147  return;
1148  }
1149  derivs.alphar += log(delta) + a1 + a2 * tau;
1150  derivs.dalphar_ddelta += 1.0 / delta;
1151  derivs.dalphar_dtau += a2;
1152  derivs.d2alphar_ddelta2 += -1.0 / delta / delta;
1153  derivs.d3alphar_ddelta3 += 2 / delta / delta / delta;
1154  derivs.d4alphar_ddelta4 += -6 / POW4(delta);
1155 }
1156 void IdealHelmholtzEnthalpyEntropyOffset::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1157  if (!enabled) {
1158  return;
1159  }
1160  derivs.alphar += a1 + a2 * tau;
1161  derivs.dalphar_dtau += a2;
1162 }
1163 void IdealHelmholtzLogTau::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1164 
1165  if (!enabled) {
1166  return;
1167  }
1168  derivs.alphar += a1 * log(tau);
1169  derivs.dalphar_dtau += a1 / tau;
1170  derivs.d2alphar_dtau2 += -a1 / tau / tau;
1171  derivs.d3alphar_dtau3 += 2 * a1 / tau / tau / tau;
1172  derivs.d4alphar_dtau4 += -6 * a1 / POW4(tau);
1173 }
1174 void IdealHelmholtzPower::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1175  if (!enabled) {
1176  return;
1177  }
1178  {
1179  CoolPropDbl s = 0;
1180  for (std::size_t i = 0; i < N; ++i) {
1181  s += n[i] * pow(tau, t[i]);
1182  }
1183  derivs.alphar += s;
1184  }
1185  {
1186  CoolPropDbl s = 0;
1187  for (std::size_t i = 0; i < N; ++i) {
1188  s += n[i] * t[i] * pow(tau, t[i] - 1);
1189  }
1190  derivs.dalphar_dtau += s;
1191  }
1192  {
1193  CoolPropDbl s = 0;
1194  for (std::size_t i = 0; i < N; ++i) {
1195  s += n[i] * t[i] * (t[i] - 1) * pow(tau, t[i] - 2);
1196  }
1197  derivs.d2alphar_dtau2 += s;
1198  }
1199  {
1200  CoolPropDbl s = 0;
1201  for (std::size_t i = 0; i < N; ++i) {
1202  s += n[i] * t[i] * (t[i] - 1) * (t[i] - 2) * pow(tau, t[i] - 3);
1203  }
1204  derivs.d3alphar_dtau3 += s;
1205  }
1206  {
1207  CoolPropDbl s = 0;
1208  for (std::size_t i = 0; i < N; ++i) {
1209  s += n[i] * t[i] * (t[i] - 1) * (t[i] - 2) * (t[i] - 3) * pow(tau, t[i] - 4);
1210  }
1211  derivs.d4alphar_dtau4 += s;
1212  }
1213 }
1214 void IdealHelmholtzPlanckEinsteinGeneralized::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1215  // First pre-calculate exp(theta[i]*tau) for each contribution; used in each term
1216  std::vector<double> expthetatau(N);
1217  for (std::size_t i = 0; i < N; ++i) {
1218  expthetatau[i] = exp(theta[i] * tau);
1219  }
1220 
1221  if (!enabled) {
1222  return;
1223  }
1224  {
1225  CoolPropDbl s = 0;
1226  for (std::size_t i = 0; i < N; ++i) {
1227  s += n[i] * log(c[i] + d[i] * expthetatau[i]);
1228  }
1229  derivs.alphar += s;
1230  }
1231  {
1232  CoolPropDbl s = 0;
1233  for (std::size_t i = 0; i < N; ++i) {
1234  s += n[i] * theta[i] * d[i] * expthetatau[i] / (c[i] + d[i] * expthetatau[i]);
1235  }
1236  derivs.dalphar_dtau += s;
1237  }
1238  {
1239  CoolPropDbl s = 0;
1240  for (std::size_t i = 0; i < N; ++i) {
1241  s += n[i] * POW2(theta[i]) * c[i] * d[i] * expthetatau[i] / pow(c[i] + d[i] * expthetatau[i], 2);
1242  }
1243  derivs.d2alphar_dtau2 += s;
1244  }
1245  {
1246  CoolPropDbl s = 0;
1247  for (std::size_t i = 0; i < N; ++i) {
1248  s += n[i] * POW3(theta[i]) * c[i] * d[i] * (c[i] - d[i] * expthetatau[i]) * expthetatau[i] / pow(c[i] + d[i] * expthetatau[i], 3);
1249  }
1250  derivs.d3alphar_dtau3 += s;
1251  }
1252  {
1253  CoolPropDbl s = 0;
1254  for (std::size_t i = 0; i < N; ++i) {
1255  const CoolPropDbl para = c[i] + d[i] * expthetatau[i];
1256  const CoolPropDbl bracket = 6 * POW3(d[i]) * POW3(expthetatau[i]) - 12 * d[i] * d[i] * para * POW2(expthetatau[i])
1257  + 7 * d[i] * POW2(para) * expthetatau[i] - POW3(para);
1258  s += -n[i] * d[i] * pow(theta[i], 4) * bracket * expthetatau[i] / pow(c[i] + d[i] * expthetatau[i], 4);
1259  }
1260  derivs.d4alphar_dtau4 += s;
1261  }
1262 }
1263 void IdealHelmholtzCP0Constant::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1264  if (!enabled) {
1265  return;
1266  }
1267  derivs.alphar += cp_over_R - cp_over_R * tau / tau0 + cp_over_R * log(tau / tau0);
1268  derivs.dalphar_dtau += cp_over_R / tau - cp_over_R / tau0;
1269  derivs.d2alphar_dtau2 += -cp_over_R / (tau * tau);
1270  derivs.d3alphar_dtau3 += 2 * cp_over_R / (tau * tau * tau);
1271  derivs.d4alphar_dtau4 += -6 * cp_over_R / POW4(tau);
1272 }
1273 void IdealHelmholtzCP0PolyT::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1274  if (!enabled) {
1275  return;
1276  }
1277  {
1278  double sum = 0;
1279  for (std::size_t i = 0; i < N; ++i) {
1280  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1281  sum += c[i] - c[i] * tau / tau0 + c[i] * log(tau / tau0);
1282  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1283  sum += c[i] * tau / Tc * log(tau0 / tau) + c[i] / Tc * (tau - tau0);
1284  } else {
1285  sum += -c[i] * pow(Tc, t[i]) * pow(tau, -t[i]) / (t[i] * (t[i] + 1)) - c[i] * pow(T0, t[i] + 1) * tau / (Tc * (t[i] + 1))
1286  + c[i] * pow(T0, t[i]) / t[i];
1287  }
1288  }
1289  derivs.alphar += sum;
1290  }
1291  {
1292  double sum = 0;
1293  for (std::size_t i = 0; i < N; ++i) {
1294  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1295  sum += c[i] / tau - c[i] / tau0;
1296  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1297  sum += c[i] / Tc * log(tau0 / tau);
1298  } else {
1299  sum += c[i] * pow(Tc, t[i]) * pow(tau, -t[i] - 1) / (t[i] + 1) - c[i] * pow(Tc, t[i]) / (pow(tau0, t[i] + 1) * (t[i] + 1));
1300  }
1301  }
1302  derivs.dalphar_dtau += sum;
1303  }
1304  {
1305  double sum = 0;
1306  for (std::size_t i = 0; i < N; ++i) {
1307  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1308  sum += -c[i] / (tau * tau);
1309  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1310  sum += -c[i] / (tau * Tc);
1311  } else {
1312  sum += -c[i] * pow(Tc / tau, t[i]) / (tau * tau);
1313  }
1314  }
1315  derivs.d2alphar_dtau2 += sum;
1316  }
1317  {
1318  double sum = 0;
1319  for (std::size_t i = 0; i < N; ++i) {
1320  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1321  sum += 2 * c[i] / (tau * tau * tau);
1322  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1323  sum += c[i] / (tau * tau * Tc);
1324  } else {
1325  sum += c[i] * pow(Tc / tau, t[i]) * (t[i] + 2) / (tau * tau * tau);
1326  }
1327  }
1328  derivs.d3alphar_dtau3 += sum;
1329  }
1330  {
1331  double sum = 0;
1332  for (std::size_t i = 0; i < N; ++i) {
1333  if (std::abs(t[i]) < 10 * DBL_EPSILON) {
1334  sum += -6 * c[i] / POW4(tau);
1335  } else if (std::abs(t[i] + 1) < 10 * DBL_EPSILON) {
1336  sum += -3 * c[i] / (POW3(tau) * Tc);
1337  } else {
1338  sum += -c[i] * (t[i] + 2) * (t[i] + 3) * pow(Tc / tau, t[i]) / (tau * tau * tau * tau);
1339  }
1340  }
1341  derivs.d4alphar_dtau4 += sum;
1342  }
1343 }
1344 
1345 void IdealHelmholtzGERG2004Sinh::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1346  if (!enabled) {
1347  return;
1348  }
1349  // Check that the reducing temperature value is provided
1350  CoolPropDbl T_red = _HUGE;
1351  if (ValidNumber(_Tr)) {
1352  T_red = _Tr; // Primarily useful for testing
1353  } else if (ValidNumber(derivs.T_red)) {
1354  T_red = derivs.T_red;
1355  } else {
1356  throw ValueError("T_red needs to be stored somewhere for GERG2004Sinh");
1357  }
1358  CoolPropDbl Tci_over_Tr = Tc / T_red;
1359 
1360  double sum00 = 0, sum10 = 0, sum20 = 0, sum30 = 0, sum40 = 0;
1361  for (std::size_t i = 0; i < N; ++i) {
1362  CoolPropDbl t = theta[i] * Tci_over_Tr;
1363  sum00 += n[i] * log(std::abs(sinh(t * tau)));
1364  sum10 += n[i] * t / tanh(t * tau);
1365  sum20 += -n[i] * POW2(t) / POW2(sinh(t * tau));
1366  sum30 += -2 * n[i] * POW3(t) * (1 / tanh(t * tau) - 1 / POW3(tanh(t * tau)));
1367  sum40 += -2 * n[i] * POW4(t) * (1 - 4 / POW2(tanh(t * tau)) + 3 / POW4(tanh(t * tau)));
1368  }
1369  derivs.alphar += sum00;
1370  derivs.dalphar_dtau += sum10;
1371  derivs.d2alphar_dtau2 += sum20;
1372  derivs.d3alphar_dtau3 += sum30;
1373  derivs.d4alphar_dtau4 += sum40;
1374 }
1375 
1376 #if ENABLE_CATCH
1377 mcx::MultiComplex<double> IdealHelmholtzGERG2004Sinh::one_mcx(const mcx::MultiComplex<double>& tau, const mcx::MultiComplex<double>& delta) const {
1378  // Check that the reducing temperature value is provided in the derivs structure
1379  CoolPropDbl T_red = _HUGE;
1380  if (ValidNumber(_Tr)) {
1381  T_red = _Tr; // Primarily useful for testing
1382  } else {
1383  throw ValueError("T_red needs to be stored somewhere for GERG2004Cosh");
1384  }
1385  auto Tci_over_Tr = Tc / T_red;
1386  auto diff_abs = [](const mcx::MultiComplex<double>& x) { return sqrt(x * x); }; // differentiable absolute value
1387 
1388  mcx::MultiComplex<double> sum00 = 0.0;
1389  for (std::size_t i = 0; i < N; ++i) {
1390  auto t = theta[i] * Tci_over_Tr;
1391  sum00 += n[i] * log(diff_abs(sinh(t * tau)));
1392  }
1393  return sum00;
1394 }
1395 #endif
1396 
1397 void IdealHelmholtzGERG2004Cosh::all(const CoolPropDbl& tau, const CoolPropDbl& delta, HelmholtzDerivatives& derivs) throw() {
1398  if (!enabled) {
1399  return;
1400  }
1401  // Check that the reducing temperature value is provided in the derivs structure
1402  CoolPropDbl T_red = _HUGE;
1403  if (ValidNumber(_Tr)) {
1404  T_red = _Tr; // Primarily useful for testing
1405  } else if (ValidNumber(derivs.T_red)) {
1406  T_red = derivs.T_red;
1407  } else {
1408  throw ValueError("T_red needs to be stored somewhere for GERG2004Cosh");
1409  }
1410  CoolPropDbl Tci_over_Tr = Tc / T_red;
1411 
1412  double sum00 = 0, sum10 = 0, sum20 = 0, sum30 = 0, sum40 = 0;
1413  for (std::size_t i = 0; i < N; ++i) {
1414  CoolPropDbl t = theta[i] * Tci_over_Tr;
1415  sum00 += -n[i] * log(std::abs(cosh(t * tau)));
1416  sum10 += -n[i] * t * tanh(t * tau);
1417  sum20 += -n[i] * POW2(t) / POW2(cosh(t * tau));
1418  sum30 += -2 * n[i] * POW3(t) * (POW3(tanh(t * tau)) - tanh(t * tau));
1419  sum40 += 2 * n[i] * POW4(t) * (3 * POW4(tanh(t * tau)) - 4 * POW2(tanh(t * tau)) + 1);
1420  }
1421  derivs.alphar += sum00;
1422  derivs.dalphar_dtau += sum10;
1423  derivs.d2alphar_dtau2 += sum20;
1424  derivs.d3alphar_dtau3 += sum30;
1425  derivs.d4alphar_dtau4 += sum40;
1426 }
1427 
1428 #if ENABLE_CATCH
1429 mcx::MultiComplex<double> IdealHelmholtzGERG2004Cosh::one_mcx(const mcx::MultiComplex<double>& tau, const mcx::MultiComplex<double>& delta) const {
1430  // Check that the reducing temperature value is provided in the derivs structure
1431  CoolPropDbl T_red = _HUGE;
1432  if (ValidNumber(_Tr)) {
1433  T_red = _Tr; // Primarily useful for testing
1434  } else {
1435  throw ValueError("T_red needs to be stored somewhere for GERG2004Cosh");
1436  }
1437  auto Tci_over_Tr = Tc / T_red;
1438  auto diff_abs = [](const mcx::MultiComplex<double>& x) { return sqrt(x * x); }; // differentiable absolute value
1439 
1440  mcx::MultiComplex<double> sum00 = 0.0;
1441  for (std::size_t i = 0; i < N; ++i) {
1442  auto t = theta[i] * Tci_over_Tr;
1443  sum00 += -n[i] * log(diff_abs(cosh(t * tau)));
1444  }
1445  return sum00;
1446 }
1447 #endif
1448 
1449 
1450 //void IdealHelmholtzCP0AlyLee::to_json(rapidjson::Value &el, rapidjson::Document &doc){
1451 // el.AddMember("type","IdealGasHelmholtzCP0AlyLee",doc.GetAllocator());
1452 // rapidjson::Value _n(rapidjson::kArrayType);
1453 // for (std::size_t i=0; i<=4; ++i)
1454 // {
1455 // _n.PushBack(static_cast<double>(c[i]),doc.GetAllocator());
1456 // }
1457 // el.AddMember("c",_n,doc.GetAllocator());
1458 // el.AddMember("Tc",static_cast<double>(Tc),doc.GetAllocator());
1459 // el.AddMember("T0",static_cast<double>(T0),doc.GetAllocator());
1460 //}
1461 //CoolPropDbl IdealHelmholtzCP0AlyLee::base(const CoolPropDbl &tau, const CoolPropDbl &delta) throw()
1462 //{
1463 // if (!enabled){ return 0.0;}
1464 // return -tau*(anti_deriv_cp0_tau2(tau)-anti_deriv_cp0_tau2(tau0))+(anti_deriv_cp0_tau(tau)-anti_deriv_cp0_tau(tau0));
1465 //}
1466 //CoolPropDbl IdealHelmholtzCP0AlyLee::dTau(const CoolPropDbl &tau, const CoolPropDbl &delta) throw()
1467 //{
1468 // if (!enabled){ return 0.0;}
1469 // return -(anti_deriv_cp0_tau2(tau) - anti_deriv_cp0_tau2(tau0));
1470 //}
1471 //CoolPropDbl IdealHelmholtzCP0AlyLee::anti_deriv_cp0_tau2(const CoolPropDbl &tau)
1472 //{
1473 // return -c[0]/tau + 2*c[1]*c[2]/Tc/(exp(-2*c[2]*tau/Tc)-1) - 2*c[3]*c[4]/Tc*(exp(2*c[4]*tau/Tc)+1);
1474 //}
1475 //CoolPropDbl IdealHelmholtzCP0AlyLee::anti_deriv_cp0_tau(const CoolPropDbl &tau)
1476 //{
1477 // CoolPropDbl term1 = c[0]*log(tau);
1478 // CoolPropDbl term2 = 2*c[1]*c[2]*tau/(-Tc + Tc*exp(-2*c[2]*tau/Tc)) + c[1]*log(-1 + exp(-2*c[2]*tau/Tc)) + 2*c[1]*c[2]*tau/Tc;
1479 // CoolPropDbl term3 = -c[3]*(Tc*exp(2*c[4]*tau/Tc)*log(exp(2*c[4]*tau/Tc) + 1) + Tc*log(exp(2*c[4]*tau/Tc) + 1) - 2*c[4]*tau*exp(2*c[4]*tau/Tc))/(Tc*(exp(2*c[4]*tau/Tc) + 1));
1480 // return term1 + term2 + term3;
1481 //}
1482 //CoolPropDbl IdealHelmholtzCP0AlyLee::dTau2(const CoolPropDbl &tau, const CoolPropDbl &delta) throw()
1483 //{
1484 // if (!enabled){ return 0.0;}
1485 // return -c[0]/pow(tau,2) - c[1]*pow(c[2]/Tc/sinh(c[2]*tau/Tc),2) - c[3]*pow(c[4]/Tc/cosh(c[4]*tau/Tc),2);
1486 //}
1487 //CoolPropDbl IdealHelmholtzCP0AlyLee::dTau3(const CoolPropDbl &tau, const CoolPropDbl &delta) throw()
1488 //{
1489 // if (!enabled){ return 0.0;}
1490 // return 2*c[0]/pow(tau,3) + 2*c[1]*pow(c[2]/Tc,3)*cosh(c[2]*tau/Tc)/pow(sinh(c[2]*tau/Tc),3) + 2*c[3]*pow(c[4]/Tc,3)*sinh(c[4]*tau/Tc)/pow(cosh(c[4]*tau/Tc),3);
1491 //}
1492 
1493 }; /* namespace CoolProp */
1494 
1495 /*
1496 IdealHelmholtzEnthalpyEntropyOffset EnthalpyEntropyOffset;
1497 */
1498 
1499 #ifdef ENABLE_CATCH
1500 # include <math.h>
1501 # include <catch2/catch_all.hpp>
1502 # include "crossplatform_shared_ptr.h"
1503 
1504 class HelmholtzConsistencyFixture
1505 {
1506  public:
1507  CoolPropDbl numerical, analytic;
1508 
1509  shared_ptr<CoolProp::BaseHelmholtzTerm> PlanckEinstein, Lead, LogTau, IGPower, CP0Constant, CP0PolyT, SAFT, NonAnalytic, Soave, PR, XiangDeiters,
1510  GaoB, GERG2004Cosh, GERG2004Sinh;
1511  shared_ptr<CoolProp::ResidualHelmholtzGeneralizedExponential> Gaussian, Lemmon2005, Exponential, GERG2008, Power;
1512 
1513  HelmholtzConsistencyFixture() {
1514  shared_ptr<AbstractCubic> _SRK(new SRK(300, 4e6, 0.3, 8.314461));
1515  _SRK->set_Tr(300);
1516  _SRK->set_rhor(4000);
1517  Soave.reset(new CoolProp::ResidualHelmholtzGeneralizedCubic(_SRK));
1518 
1519  shared_ptr<AbstractCubic> _PR(new PengRobinson(300, 4e6, 0.3, 8.314461));
1520  _PR->set_Tr(300);
1521  _PR->set_rhor(4000);
1522  PR.reset(new CoolProp::ResidualHelmholtzGeneralizedCubic(_PR));
1523 
1524  {
1525  // Signs of eta are flipped relative to paper from Gao et al., implemented with opposite sign in CoolProp
1526  std::vector<CoolPropDbl> beta = {0.3696, 0.2962}, epsilon = {0.4478, 0.44689}, eta = {-2.8452, -2.8342}, gamma = {1.108, 1.313},
1527  n = {-1.6909858, 0.93739074}, t = {4.3315, 4.015}, d = {1, 1}, b = {1.244, 0.6826};
1528  GaoB.reset(new CoolProp::ResidualHelmholtzGaoB(n, t, d, eta, beta, gamma, epsilon, b));
1529  }
1530 
1531  XiangDeiters.reset(new CoolProp::ResidualHelmholtzXiangDeiters(300, 4e6, 4000, 0.3, 8.3144621));
1532 
1533  Lead.reset(new CoolProp::IdealHelmholtzLead(1, 3));
1534  LogTau.reset(new CoolProp::IdealHelmholtzLogTau(1.5));
1535  {
1536  std::vector<CoolPropDbl> n(4, 0), t(4, 1);
1537  n[0] = -0.1;
1538  n[2] = 0.1;
1539  t[1] = -1;
1540  t[2] = -2;
1541  t[3] = 2;
1542  IGPower.reset(new CoolProp::IdealHelmholtzPower(n, t));
1543  }
1544  {
1545  std::vector<CoolPropDbl> n(4, 0), t(4, 1), c(4, 1), d(4, -1);
1546  n[0] = 0.1;
1547  n[2] = 0.5;
1548  t[0] = -1.5;
1549  t[1] = -1;
1550  t[2] = -2;
1551  t[3] = -2;
1552  PlanckEinstein.reset(new CoolProp::IdealHelmholtzPlanckEinsteinGeneralized(n, t, c, d));
1553  }
1554  {
1555  std::vector<CoolPropDbl> c(3, 1), t(3, 0);
1556  t[1] = 1;
1557  t[2] = 2;
1558  c[1] = 2;
1559  c[2] = 3;
1560  CoolPropDbl T0 = 273.15, Tc = 345.857;
1561  CP0PolyT.reset(new CoolProp::IdealHelmholtzCP0PolyT(c, t, Tc, T0));
1562  }
1563  CP0Constant.reset(new CoolProp::IdealHelmholtzCP0Constant(4 / 8.314472, 300, 250));
1564  {
1565  // Nitrogen
1566  std::vector<CoolPropDbl> n(2, 0.0);
1567  n[0] = 0.137320000;
1568  n[1] = 0.900660000;
1569  std::vector<CoolPropDbl> theta(2, 0.0);
1570  theta[0] = 5.251822620;
1571  theta[1] = 13.788988208;
1572  CoolPropDbl rhomolar_crit = 11183.900000, T_crit = 126.192000000;
1573  GERG2004Cosh.reset(new CoolProp::IdealHelmholtzGERG2004Cosh(n, theta, T_crit));
1574  static_cast<CoolProp::IdealHelmholtzGERG2004Cosh*>(GERG2004Cosh.get())->set_Tred(T_crit * 1.3);
1575  }
1576  {
1577  // Nitrogen
1578  std::vector<CoolPropDbl> n(1, 0.0);
1579  n[0] = -0.146600000;
1580  std::vector<CoolPropDbl> theta(1, 0.0);
1581  theta[0] = -5.393067706;
1582  CoolPropDbl rhomolar_crit = 11183.900000, T_crit = 126.192000000;
1583  GERG2004Sinh.reset(new CoolProp::IdealHelmholtzGERG2004Sinh(n, theta, T_crit));
1584  static_cast<CoolProp::IdealHelmholtzGERG2004Sinh*>(GERG2004Sinh.get())->set_Tred(T_crit * 1.3);
1585  }
1586 
1587  {
1588  CoolPropDbl beta[] = {1.24, 0.821, 15.45, 2.21, 437, 0.743}, d[] = {1, 1, 2, 2, 3, 3},
1589  epsilon[] = {0.6734, 0.9239, 0.8636, 1.0507, 0.8482, 0.7522}, eta[] = {0.9667, 1.5154, 1.0591, 1.6642, 12.4856, 0.9662},
1590  gamma[] = {1.2827, 0.4317, 1.1217, 1.1871, 1.1243, 0.4203},
1591  n[] = {1.2198, -0.4883, -0.0033293, -0.0035387, -0.51172, -0.16882}, t[] = {1, 2.124, 0.4, 3.5, 0.5, 2.7};
1592  Gaussian.reset(new CoolProp::ResidualHelmholtzGeneralizedExponential());
1593  Gaussian->add_Gaussian(
1594  std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(d, d + sizeof(d) / sizeof(d[0])),
1595  std::vector<CoolPropDbl>(t, t + sizeof(t) / sizeof(t[0])), std::vector<CoolPropDbl>(eta, eta + sizeof(eta) / sizeof(eta[0])),
1596  std::vector<CoolPropDbl>(epsilon, epsilon + sizeof(epsilon) / sizeof(epsilon[0])),
1597  std::vector<CoolPropDbl>(beta, beta + sizeof(beta) / sizeof(beta[0])),
1598  std::vector<CoolPropDbl>(gamma, gamma + sizeof(gamma) / sizeof(gamma[0])));
1599  }
1600  {
1601  CoolPropDbl d[] = {1, 1, 1, 2, 4, 1, 1, 2, 2, 3, 4, 5, 1, 5, 1, 2, 3, 5}, l[] = {0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3},
1602  m[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.7, 7, 6},
1603  n[] = {5.28076, -8.67658, 0.7501127, 0.7590023, 0.01451899, 4.777189, -3.330988, 3.775673, -2.290919,
1604  0.8888268, -0.6234864, -0.04127263, -0.08455389, -0.1308752, 0.008344962, -1.532005, -0.05883649, 0.02296658},
1605  t[] = {0.669, 1.05, 2.75, 0.956, 1, 2, 2.75, 2.38, 3.37, 3.47, 2.63, 3.45, 0.72, 4.23, 0.2, 4.5, 29, 24};
1606  Lemmon2005.reset(new CoolProp::ResidualHelmholtzGeneralizedExponential());
1607  Lemmon2005->add_Lemmon2005(
1608  std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(d, d + sizeof(d) / sizeof(d[0])),
1609  std::vector<CoolPropDbl>(t, t + sizeof(t) / sizeof(t[0])), std::vector<CoolPropDbl>(l, l + sizeof(l) / sizeof(l[0])),
1610  std::vector<CoolPropDbl>(m, m + sizeof(m) / sizeof(m[0])));
1611  }
1612  {
1613  CoolPropDbl d[] = {1, 1, 1, 3, 7, 1, 2, 5, 1, 1, 4, 2}, l[] = {0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3},
1614  n[] = {1.0038, -2.7662, 0.42921, 0.081363, 0.00024174, 0.48246, 0.75542, -0.00743, -0.4146, -0.016558, -0.10644, -0.021704},
1615  t[] = {0.25, 1.25, 1.5, 0.25, 0.875, 2.375, 2, 2.125, 3.5, 6.5, 4.75, 12.5};
1616  Power.reset(new CoolProp::ResidualHelmholtzGeneralizedExponential());
1617  Power->add_Power(std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(d, d + sizeof(d) / sizeof(d[0])),
1618  std::vector<CoolPropDbl>(t, t + sizeof(t) / sizeof(t[0])), std::vector<CoolPropDbl>(l, l + sizeof(l) / sizeof(l[0])));
1619  }
1620  {
1621 
1622  CoolPropDbl a = 1, epsilonbar = 12.2735737, kappabar = 1.09117041e-05, m = 1.01871348, vbarn = 0.0444215309;
1623  SAFT.reset(new CoolProp::ResidualHelmholtzSAFTAssociating(a, m, epsilonbar, vbarn, kappabar));
1624  }
1625  {
1626  CoolPropDbl n[] = {-0.666422765408, 0.726086323499, 0.0550686686128}, A[] = {0.7, 0.7, 0.7}, B[] = {0.3, 0.3, 1}, C[] = {10, 10, 12.5},
1627  D[] = {275, 275, 275}, a[] = {3.5, 3.5, 3}, b[] = {0.875, 0.925, 0.875}, beta[] = {0.3, 0.3, 0.3};
1628  NonAnalytic.reset(new CoolProp::ResidualHelmholtzNonAnalytic(
1629  std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(a, a + sizeof(a) / sizeof(a[0])),
1630  std::vector<CoolPropDbl>(b, b + sizeof(b) / sizeof(b[0])), std::vector<CoolPropDbl>(beta, beta + sizeof(beta) / sizeof(beta[0])),
1631  std::vector<CoolPropDbl>(A, A + sizeof(A) / sizeof(A[0])), std::vector<CoolPropDbl>(B, B + sizeof(B) / sizeof(B[0])),
1632  std::vector<CoolPropDbl>(C, C + sizeof(C) / sizeof(C[0])), std::vector<CoolPropDbl>(D, D + sizeof(D) / sizeof(D[0]))));
1633  }
1634  {
1635  CoolPropDbl d[] = {2, 2, 2, 0, 0, 0}, g[] = {1.65533788, 1.65533788, 1.65533788, 1.65533788, 1.65533788, 1.65533788},
1636  l[] = {2, 2, 2, 2, 2, 2},
1637  n[] = {-3.821884669859, 8.30345065618981, -4.4832307260286, -1.02590136933231, 2.20786016506394, -1.07889905203761},
1638  t[] = {3, 4, 5, 3, 4, 5};
1639  Exponential.reset(new CoolProp::ResidualHelmholtzGeneralizedExponential());
1640  Exponential->add_Exponential(
1641  std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(d, d + sizeof(d) / sizeof(n[0])),
1642  std::vector<CoolPropDbl>(t, t + sizeof(t) / sizeof(d[0])), std::vector<CoolPropDbl>(g, g + sizeof(g) / sizeof(t[0])),
1643  std::vector<CoolPropDbl>(l, l + sizeof(l) / sizeof(l[0])));
1644  }
1645  {
1646  CoolPropDbl d[] = {1, 4, 1, 2, 2, 2, 2, 2, 3}, t[] = {0.0, 1.85, 7.85, 5.4, 0.0, 0.75, 2.8, 4.45, 4.25},
1647  n[] = {-0.0098038985517335, 0.00042487270143005, -0.034800214576142, -0.13333813013896, -0.011993694974627,
1648  0.069243379775168, -0.31022508148249, 0.24495491753226, 0.22369816716981},
1649  eta[] = {0.0, 0.0, 1.0, 1.0, 0.25, 0.0, 0.0, 0.0, 0.0}, epsilon[] = {0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5},
1650  beta[] = {0.0, 0.0, 1.0, 1.0, 2.5, 3.0, 3.0, 3.0, 3.0}, gamma[] = {0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5};
1651  GERG2008.reset(new CoolProp::ResidualHelmholtzGeneralizedExponential());
1652  GERG2008->add_GERG2008Gaussian(
1653  std::vector<CoolPropDbl>(n, n + sizeof(n) / sizeof(n[0])), std::vector<CoolPropDbl>(d, d + sizeof(d) / sizeof(n[0])),
1654  std::vector<CoolPropDbl>(t, t + sizeof(t) / sizeof(d[0])), std::vector<CoolPropDbl>(eta, eta + sizeof(eta) / sizeof(eta[0])),
1655  std::vector<CoolPropDbl>(epsilon, epsilon + sizeof(epsilon) / sizeof(epsilon[0])),
1656  std::vector<CoolPropDbl>(beta, beta + sizeof(beta) / sizeof(beta[0])),
1657  std::vector<CoolPropDbl>(gamma, gamma + sizeof(gamma) / sizeof(gamma[0])));
1658  }
1659  }
1660  void call(std::string d, shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1661  if (!d.compare("dTau")) {
1662  return dTau(term, tau, delta, ddelta);
1663  } else if (!d.compare("dTau2")) {
1664  return dTau2(term, tau, delta, ddelta);
1665  } else if (!d.compare("dTau3")) {
1666  return dTau3(term, tau, delta, ddelta);
1667  } else if (!d.compare("dTau4")) {
1668  return dTau4(term, tau, delta, ddelta);
1669  } else if (!d.compare("dDelta")) {
1670  return dDelta(term, tau, delta, ddelta);
1671  } else if (!d.compare("dDelta2")) {
1672  return dDelta2(term, tau, delta, ddelta);
1673  } else if (!d.compare("dDelta3")) {
1674  return dDelta3(term, tau, delta, ddelta);
1675  } else if (!d.compare("dDelta4")) {
1676  return dDelta4(term, tau, delta, ddelta);
1677  } else if (!d.compare("dDelta_dTau")) {
1678  return dDelta_dTau(term, tau, delta, ddelta);
1679  } else if (!d.compare("dDelta_dTau2")) {
1680  return dDelta_dTau2(term, tau, delta, ddelta);
1681  } else if (!d.compare("dDelta2_dTau")) {
1682  return dDelta2_dTau(term, tau, delta, ddelta);
1683  } else if (!d.compare("dDelta3_dTau")) {
1684  return dDelta3_dTau(term, tau, delta, ddelta);
1685  } else if (!d.compare("dDelta2_dTau2")) {
1686  return dDelta2_dTau2(term, tau, delta, ddelta);
1687  } else if (!d.compare("dDelta_dTau3")) {
1688  return dDelta_dTau3(term, tau, delta, ddelta);
1689  } else {
1690  throw CoolProp::ValueError("don't understand deriv type");
1691  }
1692  }
1693  shared_ptr<CoolProp::BaseHelmholtzTerm> get(std::string t) {
1694  if (!t.compare("Lead")) {
1695  return Lead;
1696  } else if (!t.compare("LogTau")) {
1697  return LogTau;
1698  } else if (!t.compare("IGPower")) {
1699  return IGPower;
1700  } else if (!t.compare("PlanckEinstein")) {
1701  return PlanckEinstein;
1702  } else if (!t.compare("CP0Constant")) {
1703  return CP0Constant;
1704  } else if (!t.compare("CP0PolyT")) {
1705  return CP0PolyT;
1706  } else if (!t.compare("GERG2004Cosh")) {
1707  return GERG2004Cosh;
1708  } else if (!t.compare("GERG2004Sinh")) {
1709  return GERG2004Sinh;
1710  } else if (!t.compare("SRK")) {
1711  return Soave;
1712  } else if (!t.compare("PengRobinson")) {
1713  return PR;
1714  } else if (!t.compare("XiangDeiters")) {
1715  return XiangDeiters;
1716  } else if (!t.compare("GaoB")) {
1717  return GaoB;
1718  }
1719 
1720  else if (!t.compare("Gaussian")) {
1721  return Gaussian;
1722  } else if (!t.compare("Lemmon2005")) {
1723  return Lemmon2005;
1724  } else if (!t.compare("Power")) {
1725  return Power;
1726  } else if (!t.compare("SAFT")) {
1727  return SAFT;
1728  } else if (!t.compare("NonAnalytic")) {
1729  return NonAnalytic;
1730  } else if (!t.compare("Exponential")) {
1731  return Exponential;
1732  } else if (!t.compare("GERG2008")) {
1733  return GERG2008;
1734  } else {
1735  throw CoolProp::ValueError(format("don't understand helmholtz type: %s", t.c_str()));
1736  }
1737  }
1738  void dTau(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl dtau) {
1739  CoolPropDbl term_plus = term->base(tau + dtau, delta);
1740  CoolPropDbl term_minus = term->base(tau - dtau, delta);
1741  numerical = (term_plus - term_minus) / (2 * dtau);
1742  analytic = term->dTau(tau, delta);
1743  };
1744  void dTau2(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl dtau) {
1745  CoolPropDbl term_plus = term->dTau(tau + dtau, delta);
1746  CoolPropDbl term_minus = term->dTau(tau - dtau, delta);
1747  numerical = (term_plus - term_minus) / (2 * dtau);
1748  analytic = term->dTau2(tau, delta);
1749  };
1750  void dTau3(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl dtau) {
1751  CoolPropDbl term_plus = term->dTau2(tau + dtau, delta);
1752  CoolPropDbl term_minus = term->dTau2(tau - dtau, delta);
1753  numerical = (term_plus - term_minus) / (2 * dtau);
1754  analytic = term->dTau3(tau, delta);
1755  };
1756  void dTau4(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl dtau) {
1757  CoolPropDbl term_plus = term->dTau3(tau + dtau, delta);
1758  CoolPropDbl term_minus = term->dTau3(tau - dtau, delta);
1759  numerical = (term_plus - term_minus) / (2 * dtau);
1760  analytic = term->dTau4(tau, delta);
1761  };
1762  void dDelta(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1763  CoolPropDbl term_plus = term->base(tau, delta + ddelta);
1764  CoolPropDbl term_minus = term->base(tau, delta - ddelta);
1765  numerical = (term_plus - term_minus) / (2 * ddelta);
1766  analytic = term->dDelta(tau, delta);
1767  };
1768  void dDelta2(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1769  CoolPropDbl term_plus = term->dDelta(tau, delta + ddelta);
1770  CoolPropDbl term_minus = term->dDelta(tau, delta - ddelta);
1771  numerical = (term_plus - term_minus) / (2 * ddelta);
1772  analytic = term->dDelta2(tau, delta);
1773  };
1774  void dDelta3(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1775  CoolPropDbl term_plus = term->dDelta2(tau, delta + ddelta);
1776  CoolPropDbl term_minus = term->dDelta2(tau, delta - ddelta);
1777  numerical = (term_plus - term_minus) / (2 * ddelta);
1778  analytic = term->dDelta3(tau, delta);
1779  };
1780  void dDelta4(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1781  CoolPropDbl term_plus = term->dDelta3(tau, delta + ddelta);
1782  CoolPropDbl term_minus = term->dDelta3(tau, delta - ddelta);
1783  numerical = (term_plus - term_minus) / (2 * ddelta);
1784  analytic = term->dDelta4(tau, delta);
1785  };
1786  void dDelta_dTau(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1787  CoolPropDbl term_plus = term->dTau(tau, delta + ddelta);
1788  CoolPropDbl term_minus = term->dTau(tau, delta - ddelta);
1789  numerical = (term_plus - term_minus) / (2 * ddelta);
1790  analytic = term->dDelta_dTau(tau, delta);
1791  };
1792  void dDelta_dTau2(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1793  CoolPropDbl term_plus = term->dTau2(tau, delta + ddelta);
1794  CoolPropDbl term_minus = term->dTau2(tau, delta - ddelta);
1795  numerical = (term_plus - term_minus) / (2 * ddelta);
1796  analytic = term->dDelta_dTau2(tau, delta);
1797  };
1798  void dDelta2_dTau(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1799  CoolPropDbl term_plus = term->dDelta_dTau(tau, delta + ddelta);
1800  CoolPropDbl term_minus = term->dDelta_dTau(tau, delta - ddelta);
1801  numerical = (term_plus - term_minus) / (2 * ddelta);
1802  analytic = term->dDelta2_dTau(tau, delta);
1803  };
1804  void dDelta3_dTau(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1805  CoolPropDbl term_plus = term->dDelta2_dTau(tau, delta + ddelta);
1806  CoolPropDbl term_minus = term->dDelta2_dTau(tau, delta - ddelta);
1807  numerical = (term_plus - term_minus) / (2 * ddelta);
1808  analytic = term->dDelta3_dTau(tau, delta);
1809  };
1810  void dDelta2_dTau2(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1811  CoolPropDbl term_plus = term->dDelta_dTau2(tau, delta + ddelta);
1812  CoolPropDbl term_minus = term->dDelta_dTau2(tau, delta - ddelta);
1813  numerical = (term_plus - term_minus) / (2 * ddelta);
1814  analytic = term->dDelta2_dTau2(tau, delta);
1815  };
1816  void dDelta_dTau3(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, CoolPropDbl ddelta) {
1817  CoolPropDbl term_plus = term->dTau3(tau, delta + ddelta);
1818  CoolPropDbl term_minus = term->dTau3(tau, delta - ddelta);
1819  numerical = (term_plus - term_minus) / (2 * ddelta);
1820  analytic = term->dDelta_dTau3(tau, delta);
1821  };
1822  double get_analytic_mcx(shared_ptr<CoolProp::BaseHelmholtzTerm> term, CoolPropDbl tau, CoolPropDbl delta, int ntau, int ndelta) {
1823  try {
1824  using fcn_t = std::function<mcx::MultiComplex<double>(const std::vector<mcx::MultiComplex<double>>&)>;
1825  fcn_t f = [&term](const std::vector<mcx::MultiComplex<double>>& x) { return term->one_mcx(x[0], x[1]); };
1826  return mcx::diff_mcxN(f, std::vector<double>{tau, delta}, std::vector<int>{ntau, ndelta});
1827  } catch (CoolProp::NotImplementedError e) {
1828  return _HUGE;
1829  }
1830  }
1831  double err(double v1, double v2) {
1832  if (std::abs(v2) > 1e-15) {
1833  return std::abs((v1 - v2) / v2);
1834  } else {
1835  return std::abs(v1 - v2);
1836  }
1837  }
1838 };
1839 
1840 std::string terms[] = {"Lead", "LogTau", "IGPower", "PlanckEinstein", "CP0Constant", "CP0PolyT", "Gaussian",
1841  "Lemmon2005", "Power", "SAFT", "NonAnalytic", "Exponential", "GERG2008", "SRK",
1842  "PengRobinson", "XiangDeiters", "GaoB", "GERG2004Cosh", "GERG2004Sinh"};
1843 std::string derivs[] = {"dTau", "dTau2", "dTau3", "dDelta", "dDelta2", "dDelta3", "dDelta_dTau",
1844  "dDelta_dTau2", "dDelta2_dTau", "dTau4", "dDelta_dTau3", "dDelta2_dTau2", "dDelta3_dTau", "dDelta4"};
1845 std::map<std::string, std::tuple<int, int>> counts = {
1846  {"dTau", {1, 0}},
1847  {"dTau2", {2, 0}},
1848  {"dTau3", {3, 0}},
1849  {"dTau4", {4, 0}},
1850  {"dDelta", {0, 1}},
1851  {"dDelta2", {0, 2}},
1852  {"dDelta3", {0, 3}},
1853  {"dDelta4", {0, 4}},
1854  {"dDelta_dTau", {1, 1}},
1855  {"dDelta_dTau2", {2, 1}},
1856  {"dDelta2_dTau", {1, 2}},
1857  {"dDelta_dTau3", {3, 1}},
1858  {"dDelta2_dTau2", {2, 2}},
1859  {"dDelta3_dTau", {1, 3}},
1860 };
1861 
1862 TEST_CASE_METHOD(HelmholtzConsistencyFixture, "Helmholtz energy derivatives", "[helmholtz]") {
1863  shared_ptr<CoolProp::BaseHelmholtzTerm> term;
1864  std::size_t n = sizeof(terms) / sizeof(terms[0]);
1865  for (std::size_t i = 0; i < n; ++i) {
1866  term = get(terms[i]);
1867  for (std::size_t j = 0; j < sizeof(derivs) / sizeof(derivs[0]); ++j) {
1868  if (terms[i] == "SAFT"
1869  && (derivs[j] == "dTau4" || derivs[j] == "dDelta_dTau3" || derivs[j] == "dDelta2_dTau2" || derivs[j] == "dDelta3_dTau"
1870  || derivs[j] == "dDelta4")) {
1871  continue;
1872  }
1873  double tau = 1.3, delta = 0.9;
1874  call(derivs[j], term, tau, delta, 1e-5);
1875  double alphar = term->base(tau, delta);
1876 
1877  // Do calculations with multicomplex, if the one_mcx function has been implemented
1878  auto [ntau, ndelta] = counts.at(derivs[j]);
1879  double numerical_mcx = _HUGE;
1880  double alphar_mcx = _HUGE;
1881  try {
1882  numerical_mcx = get_analytic_mcx(term, tau, delta, ntau, ndelta);
1883  alphar_mcx = term->one_mcx(tau, delta).real();
1884  } catch (std::exception& /* e */) {
1885  //std::cout << e.what() << std::endl;
1886  }
1887  CAPTURE(alphar_mcx);
1888  CAPTURE(numerical_mcx);
1889 
1890  CAPTURE(derivs[j]);
1891  CAPTURE(alphar);
1892  double numerical_finitediff = numerical;
1893  CAPTURE(numerical_finitediff);
1894  CAPTURE(analytic);
1895  CAPTURE(terms[i]);
1896  double deriv_tolerance = 1e-9;
1897  if (terms[i] == "GERG2004Cosh" || terms[i] == "GERG2004Sinh" || terms[i] == "CP0PolyT") {
1898  deriv_tolerance = 1e-7; // due to, I think, a loss in precision in the log function of multicomplex
1899  }
1900  double val_tolerance = 1e-15;
1901  if (terms[i] == "CP0PolyT") {
1902  val_tolerance = 1e-10; // due to, I think, a loss in precision in the log function of multicomplex
1903  }
1904 
1905  if (std::isfinite(numerical_mcx)) {
1906  CHECK(err(analytic, numerical_mcx) < deriv_tolerance);
1907  CHECK(err(alphar, alphar_mcx) < val_tolerance);
1908  } else {
1909  CHECK(err(analytic, numerical_finitediff) < deriv_tolerance);
1910  }
1911  }
1912  }
1913 }
1914 
1915 #endif
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