source: sasmodels/sasmodels/models/rpa.c @ 0c24a82

core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 0c24a82 was d680a2b, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

fix typo in rpa model definition (not: changes values produced)
  • Property mode set to 100644
File size: 16.8 KB
Line 
1double Iq(double q, double case_num,
2    double N[], double Phi[], double v[], double L[], double b[],
3    double Kab, double Kac, double Kad,
4    double Kbc, double Kbd, double Kcd
5    );
6
7double Iq(double q, double case_num,
8    double N[],    // DEGREE OF POLYMERIZATION
9    double Phi[],  // VOL FRACTION
10    double v[],    // SPECIFIC VOLUME
11    double L[],    // SCATT. LENGTH
12    double b[],    // SEGMENT LENGTH
13    double Kab, double Kac, double Kad,  // CHI PARAM
14    double Kbc, double Kbd, double Kcd
15    )
16{
17  int icase = (int)case_num;
18
19  double Nab,Nac,Nad,Nbc,Nbd,Ncd;
20  double Phiab,Phiac,Phiad,Phibc,Phibd,Phicd;
21  double vab,vac,vad,vbc,vbd,vcd;
22  double m;
23  double Xa,Xb,Xc,Xd;
24  double Paa,S0aa,Pab,S0ab,Pac,S0ac,Pad,S0ad;
25  double S0ba,Pbb,S0bb,Pbc,S0bc,Pbd,S0bd;
26  double S0ca,S0cb,Pcc,S0cc,Pcd,S0cd;
27  double S0da,S0db,S0dc,Pdd,S0dd;
28  double Kaa,Kbb,Kcc,Kdd;
29  double Kba,Kca,Kda,Kcb,Kdb,Kdc;
30  double Zaa,Zab,Zac,Zba,Zbb,Zbc,Zca,Zcb,Zcc;
31  double DenT,T11,T12,T13,T21,T22,T23,T31,T32,T33;
32  double Y1,Y2,Y3,X11,X12,X13,X21,X22,X23,X31,X32,X33;
33  double ZZ,DenQ1,DenQ2,DenQ3,DenQ,Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33;
34  double N11,N12,N13,N21,N22,N23,N31,N32,N33;
35  double M11,M12,M13,M21,M22,M23,M31,M32,M33;
36  double S11,S12,S13,S14,S21,S22,S23,S24;
37  double S31,S32,S33,S34,S41,S42,S43,S44;
38  double Lad,Lbd,Lcd,Nav,Intg;
39
40  //icase was shifted to N-1 from the original code
41  if (icase <= 1){
42    Phi[0] = Phi[1] = 0.0000001;
43    N[0] = N[1] = 1000.0;
44    L[0] = L[1] = 1.e-12;
45    v[0] = v[1] = 100.0;
46    b[0] = b[1] = 5.0;
47    Kab = Kac = Kad = Kbc = Kbd = -0.0004;
48  }
49  else if ((icase > 1) && (icase <= 4)){
50    Phi[0] = 0.0000001;
51    N[0] = 1000.0;
52    L[0] = 1.e-12;
53    v[0] = 100.0;
54    b[0] = 5.0;
55    Kab = Kac = Kad = -0.0004;
56  }
57
58  Nab=sqrt(N[0]*N[1]);
59  Nac=sqrt(N[0]*N[2]);
60  Nad=sqrt(N[0]*N[3]);
61  Nbc=sqrt(N[1]*N[2]);
62  Nbd=sqrt(N[1]*N[3]);
63  Ncd=sqrt(N[2]*N[3]);
64
65  vab=sqrt(v[0]*v[1]);
66  vac=sqrt(v[0]*v[2]);
67  vad=sqrt(v[0]*v[3]);
68  vbc=sqrt(v[1]*v[2]);
69  vbd=sqrt(v[1]*v[3]);
70  vcd=sqrt(v[2]*v[3]);
71
72  Phiab=sqrt(Phi[0]*Phi[1]);
73  Phiac=sqrt(Phi[0]*Phi[2]);
74  Phiad=sqrt(Phi[0]*Phi[3]);
75  Phibc=sqrt(Phi[1]*Phi[2]);
76  Phibd=sqrt(Phi[1]*Phi[3]);
77  Phicd=sqrt(Phi[2]*Phi[3]);
78
79  Xa=q*q*b[0]*b[0]*N[0]/6.0;
80  Xb=q*q*b[1]*b[1]*N[1]/6.0;
81  Xc=q*q*b[2]*b[2]*N[2]/6.0;
82  Xd=q*q*b[3]*b[3]*N[3]/6.0;
83
84  Paa=2.0*(exp(-Xa)-1.0+Xa)/(Xa*Xa);
85  S0aa=N[0]*Phi[0]*v[0]*Paa;
86  Pab=((1.0-exp(-Xa))/Xa)*((1.0-exp(-Xb))/Xb);
87  S0ab=(Phiab*vab*Nab)*Pab;
88  Pac=((1.0-exp(-Xa))/Xa)*exp(-Xb)*((1.0-exp(-Xc))/Xc);
89  S0ac=(Phiac*vac*Nac)*Pac;
90  Pad=((1.0-exp(-Xa))/Xa)*exp(-Xb-Xc)*((1.0-exp(-Xd))/Xd);
91  S0ad=(Phiad*vad*Nad)*Pad;
92
93  S0ba=S0ab;
94  Pbb=2.0*(exp(-Xb)-1.0+Xb)/(Xb*Xb);
95  S0bb=N[1]*Phi[1]*v[1]*Pbb;
96  Pbc=((1.0-exp(-Xb))/Xb)*((1.0-exp(-Xc))/Xc);
97  S0bc=(Phibc*vbc*Nbc)*Pbc;
98  Pbd=((1.0-exp(-Xb))/Xb)*exp(-Xc)*((1.0-exp(-Xd))/Xd);
99  S0bd=(Phibd*vbd*Nbd)*Pbd;
100
101  S0ca=S0ac;
102  S0cb=S0bc;
103  Pcc=2.0*(exp(-Xc)-1.0+Xc)/(Xc*Xc);
104  S0cc=N[2]*Phi[2]*v[2]*Pcc;
105  Pcd=((1.0-exp(-Xc))/Xc)*((1.0-exp(-Xd))/Xd);
106  S0cd=(Phicd*vcd*Ncd)*Pcd;
107
108  S0da=S0ad;
109  S0db=S0bd;
110  S0dc=S0cd;
111  Pdd=2.0*(exp(-Xd)-1.0+Xd)/(Xd*Xd);
112  S0dd=N[3]*Phi[3]*v[3]*Pdd;
113  //icase was shifted to N-1 from the original code
114  switch(icase){
115  case 0:
116    S0aa=0.000001;
117    S0ab=0.000002;
118    S0ac=0.000003;
119    S0ad=0.000004;
120    S0bb=0.000005;
121    S0bc=0.000006;
122    S0bd=0.000007;
123    S0cd=0.000008;
124    break;
125  case 1:
126    S0aa=0.000001;
127    S0ab=0.000002;
128    S0ac=0.000003;
129    S0ad=0.000004;
130    S0bb=0.000005;
131    S0bc=0.000006;
132    S0bd=0.000007;
133    break;
134  case 2:
135    S0aa=0.000001;
136    S0ab=0.000002;
137    S0ac=0.000003;
138    S0ad=0.000004;
139    S0bc=0.000005;
140    S0bd=0.000006;
141    S0cd=0.000007;
142    break;
143  case 3:
144    S0aa=0.000001;
145    S0ab=0.000002;
146    S0ac=0.000003;
147    S0ad=0.000004;
148    S0bc=0.000005;
149    S0bd=0.000006;
150    break;
151  case 4:
152    S0aa=0.000001;
153    S0ab=0.000002;
154    S0ac=0.000003;
155    S0ad=0.000004;
156    break;
157  case 5:
158    S0ab=0.000001;
159    S0ac=0.000002;
160    S0ad=0.000003;
161    S0bc=0.000004;
162    S0bd=0.000005;
163    S0cd=0.000006;
164    break;
165  case 6:
166    S0ab=0.000001;
167    S0ac=0.000002;
168    S0ad=0.000003;
169    S0bc=0.000004;
170    S0bd=0.000005;
171    break;
172  case 7:
173    S0ab=0.000001;
174    S0ac=0.000002;
175    S0ad=0.000003;
176    break;
177  case 8:
178    S0ac=0.000001;
179    S0ad=0.000002;
180    S0bc=0.000003;
181    S0bd=0.000004;
182    break;
183  default : //case 9:
184    break;
185  }
186  S0ba=S0ab;
187  S0ca=S0ac;
188  S0cb=S0bc;
189  S0da=S0ad;
190  S0db=S0bd;
191  S0dc=S0cd;
192
193  Kaa=0.0;
194  Kbb=0.0;
195  Kcc=0.0;
196  Kdd=0.0;
197
198  Kba=Kab;
199  Kca=Kac;
200  Kcb=Kbc;
201  Kda=Kad;
202  Kdb=Kbd;
203  Kdc=Kcd;
204
205  Zaa=Kaa-Kad-Kad;
206  Zab=Kab-Kad-Kbd;
207  Zac=Kac-Kad-Kcd;
208  Zba=Kba-Kbd-Kad;
209  Zbb=Kbb-Kbd-Kbd;
210  Zbc=Kbc-Kbd-Kcd;
211  Zca=Kca-Kcd-Kad;
212  Zcb=Kcb-Kcd-Kbd;
213  Zcc=Kcc-Kcd-Kcd;
214
215  DenT=(-(S0ac*S0bb*S0ca) + S0ab*S0bc*S0ca + S0ac*S0ba*S0cb - S0aa*S0bc*S0cb - S0ab*S0ba*S0cc + S0aa*S0bb*S0cc);
216
217  T11= (-(S0bc*S0cb) + S0bb*S0cc)/DenT;
218  T12= (S0ac*S0cb - S0ab*S0cc)/DenT;
219  T13= (-(S0ac*S0bb) + S0ab*S0bc)/DenT;
220  T21= (S0bc*S0ca - S0ba*S0cc)/DenT;
221  T22= (-(S0ac*S0ca) + S0aa*S0cc)/DenT;
222  T23= (S0ac*S0ba - S0aa*S0bc)/DenT;
223  T31= (-(S0bb*S0ca) + S0ba*S0cb)/DenT;
224  T32= (S0ab*S0ca - S0aa*S0cb)/DenT;
225  T33= (-(S0ab*S0ba) + S0aa*S0bb)/DenT;
226
227  Y1=T11*S0ad+T12*S0bd+T13*S0cd+1.0;
228  Y2=T21*S0ad+T22*S0bd+T23*S0cd+1.0;
229  Y3=T31*S0ad+T32*S0bd+T33*S0cd+1.0;
230
231  X11=Y1*Y1;
232  X12=Y1*Y2;
233  X13=Y1*Y3;
234  X21=Y2*Y1;
235  X22=Y2*Y2;
236  X23=Y2*Y3;
237  X31=Y3*Y1;
238  X32=Y3*Y2;
239  X33=Y3*Y3;
240
241  ZZ=S0ad*(T11*S0ad+T12*S0bd+T13*S0cd)+S0bd*(T21*S0ad+T22*S0bd+T23*S0cd)+S0cd*(T31*S0ad+T32*S0bd+T33*S0cd);
242
243  m=1.0/(S0dd-ZZ);
244
245  N11=m*X11+Zaa;
246  N12=m*X12+Zab;
247  N13=m*X13+Zac;
248  N21=m*X21+Zba;
249  N22=m*X22+Zbb;
250  N23=m*X23+Zbc;
251  N31=m*X31+Zca;
252  N32=m*X32+Zcb;
253  N33=m*X33+Zcc;
254
255  M11= N11*S0aa + N12*S0ab + N13*S0ac;
256  M12= N11*S0ab + N12*S0bb + N13*S0bc;
257  M13= N11*S0ac + N12*S0bc + N13*S0cc;
258  M21= N21*S0aa + N22*S0ab + N23*S0ac;
259  M22= N21*S0ab + N22*S0bb + N23*S0bc;
260  M23= N21*S0ac + N22*S0bc + N23*S0cc;
261  M31= N31*S0aa + N32*S0ab + N33*S0ac;
262  M32= N31*S0ab + N32*S0bb + N33*S0bc;
263  M33= N31*S0ac + N32*S0bc + N33*S0cc;
264
265  DenQ1=1.0+M11-M12*M21+M22+M11*M22-M13*M31-M13*M22*M31;
266  DenQ2=  M12*M23*M31+M13*M21*M32-M23*M32-M11*M23*M32+M33+M11*M33;
267  DenQ3=  -M12*M21*M33+M22*M33+M11*M22*M33;
268  DenQ=DenQ1+DenQ2+DenQ3;
269
270  Q11= (1.0 + M22-M23*M32 + M33 + M22*M33)/DenQ;
271  Q12= (-M12 + M13*M32 - M12*M33)/DenQ;
272  Q13= (-M13 - M13*M22 + M12*M23)/DenQ;
273  Q21= (-M21 + M23*M31 - M21*M33)/DenQ;
274  Q22= (1.0 + M11 - M13*M31 + M33 + M11*M33)/DenQ;
275  Q23= (M13*M21 - M23 - M11*M23)/DenQ;
276  Q31= (-M31 - M22*M31 + M21*M32)/DenQ;
277  Q32= (M12*M31 - M32 - M11*M32)/DenQ;
278  Q33= (1.0 + M11 - M12*M21 + M22 + M11*M22)/DenQ;
279
280  S11= Q11*S0aa + Q21*S0ab + Q31*S0ac;
281  S12= Q12*S0aa + Q22*S0ab + Q32*S0ac;
282  S13= Q13*S0aa + Q23*S0ab + Q33*S0ac;
283  S14=-S11-S12-S13;
284  S21= Q11*S0ba + Q21*S0bb + Q31*S0bc;
285  S22= Q12*S0ba + Q22*S0bb + Q32*S0bc;
286  S23= Q13*S0ba + Q23*S0bb + Q33*S0bc;
287  S24=-S21-S22-S23;
288  S31= Q11*S0ca + Q21*S0cb + Q31*S0cc;
289  S32= Q12*S0ca + Q22*S0cb + Q32*S0cc;
290  S33= Q13*S0ca + Q23*S0cb + Q33*S0cc;
291  S34=-S31-S32-S33;
292  S41=S14;
293  S42=S24;
294  S43=S34;
295  S44=S11+S22+S33+2.0*S12+2.0*S13+2.0*S23;
296
297  Nav=6.022045e+23;
298  Lad=(L[0]/v[0]-L[3]/v[3])*sqrt(Nav);
299  Lbd=(L[1]/v[1]-L[3]/v[3])*sqrt(Nav);
300  Lcd=(L[2]/v[2]-L[3]/v[3])*sqrt(Nav);
301
302  Intg=Lad*Lad*S11+Lbd*Lbd*S22+Lcd*Lcd*S33+2.0*Lad*Lbd*S12+2.0*Lbd*Lcd*S23+2.0*Lad*Lcd*S13;
303
304  return Intg;
305
306
307/*  Attempts at a new implementation --- supressed for now
308#if 1  // Sasview defaults
309  if (icase <= 1) {
310    N[0]=N[1]=1000.0;
311    Phi[0]=Phi[1]=0.0000001;
312    Kab=Kac=Kad=Kbc=Kbd=-0.0004;
313    L[0]=L[1]=1.0e-12;
314    v[0]=v[1]=100.0;
315    b[0]=b[1]=5.0;
316  } else if (icase <= 4) {
317    Phi[0]=0.0000001;
318    Kab=Kac=Kad=-0.0004;
319    L[0]=1.0e-12;
320    v[0]=100.0;
321    b[0]=5.0;
322  }
323#else
324  if (icase <= 1) {
325    N[0]=N[1]=0.0;
326    Phi[0]=Phi[1]=0.0;
327    Kab=Kac=Kad=Kbc=Kbd=0.0;
328    L[0]=L[1]=L[3];
329    v[0]=v[1]=v[3];
330    b[0]=b[1]=0.0;
331  } else if (icase <= 4) {
332    N[0] = 0.0;
333    Phi[0]=0.0;
334    Kab=Kac=Kad=0.0;
335    L[0]=L[3];
336    v[0]=v[3];
337    b[0]=0.0;
338  }
339#endif
340
341  const double Xa = q*q*b[0]*b[0]*N[0]/6.0;
342  const double Xb = q*q*b[1]*b[1]*N[1]/6.0;
343  const double Xc = q*q*b[2]*b[2]*N[2]/6.0;
344  const double Xd = q*q*b[3]*b[3]*N[3]/6.0;
345
346  // limit as Xa goes to 0 is 1
347  const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa;
348  const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb;
349  const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc;
350  const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd;
351
352  // limit as Xa goes to 0 is 1
353  const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa;
354  const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb;
355  const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc;
356  const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd;
357
358
359  // Note: S0ij only defined for copolymers; otherwise set to zero
360  // 0: C/D     binary mixture
361  // 1: C-D     diblock copolymer
362  // 2: B/C/D   ternery mixture
363  // 3: B/C-D   binary mixture,1 homopolymer, 1 diblock copolymer
364  // 4: B-C-D   triblock copolymer
365  // 5: A/B/C/D quaternary mixture
366  // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer
367  // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer
368  // 8: A-B/C-D binary mixture, 2 diblock copolymer
369  // 9: A-B-C-D tetra-block copolymer
370#if 0
371  const double S0aa = icase<5
372                      ? 1.0 : N[0]*Phi[0]*v[0]*Paa;
373  const double S0bb = icase<2
374                      ? 1.0 : N[1]*Phi[1]*v[1]*Pbb;
375  const double S0cc = N[2]*Phi[2]*v[2]*Pcc;
376  const double S0dd = N[3]*Phi[3]*v[3]*Pdd;
377  const double S0ab = icase<8
378                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
379  const double S0ac = icase<9
380                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
381  const double S0ad = icase<9
382                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
383  const double S0bc = (icase!=4 && icase!=7 && icase!= 9)
384                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
385  const double S0bd = (icase!=4 && icase!=7 && icase!= 9)
386                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
387  const double S0cd = (icase==0 || icase==2 || icase==5)
388                      ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
389#else  // sasview equivalent
390//printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc);
391  double S0aa = N[0]*Phi[0]*v[0]*Paa;
392  double S0bb = N[1]*Phi[1]*v[1]*Pbb;
393  double S0cc = N[2]*Phi[2]*v[2]*Pcc;
394  double S0dd = N[3]*Phi[3]*v[3]*Pdd;
395  double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
396  double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
397  double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
398  double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
399  double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
400  double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
401switch(icase){
402  case 0:
403    S0aa=0.000001;
404    S0ab=0.000002;
405    S0ac=0.000003;
406    S0ad=0.000004;
407    S0bb=0.000005;
408    S0bc=0.000006;
409    S0bd=0.000007;
410    S0cd=0.000008;
411    break;
412  case 1:
413    S0aa=0.000001;
414    S0ab=0.000002;
415    S0ac=0.000003;
416    S0ad=0.000004;
417    S0bb=0.000005;
418    S0bc=0.000006;
419    S0bd=0.000007;
420    break;
421  case 2:
422    S0aa=0.000001;
423    S0ab=0.000002;
424    S0ac=0.000003;
425    S0ad=0.000004;
426    S0bc=0.000005;
427    S0bd=0.000006;
428    S0cd=0.000007;
429    break;
430  case 3:
431    S0aa=0.000001;
432    S0ab=0.000002;
433    S0ac=0.000003;
434    S0ad=0.000004;
435    S0bc=0.000005;
436    S0bd=0.000006;
437    break;
438  case 4:
439    S0aa=0.000001;
440    S0ab=0.000002;
441    S0ac=0.000003;
442    S0ad=0.000004;
443    break;
444  case 5:
445    S0ab=0.000001;
446    S0ac=0.000002;
447    S0ad=0.000003;
448    S0bc=0.000004;
449    S0bd=0.000005;
450    S0cd=0.000006;
451    break;
452  case 6:
453    S0ab=0.000001;
454    S0ac=0.000002;
455    S0ad=0.000003;
456    S0bc=0.000004;
457    S0bd=0.000005;
458    break;
459  case 7:
460    S0ab=0.000001;
461    S0ac=0.000002;
462    S0ad=0.000003;
463    break;
464  case 8:
465    S0ac=0.000001;
466    S0ad=0.000002;
467    S0bc=0.000003;
468    S0bd=0.000004;
469    break;
470  default : //case 9:
471    break;
472  }
473#endif
474
475  // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F
476  const double Kaa = 0.0;
477  const double Kbb = 0.0;
478  const double Kcc = 0.0;
479  //const double Kdd = 0.0;
480  const double Zaa = Kaa - Kad - Kad;
481  const double Zab = Kab - Kad - Kbd;
482  const double Zac = Kac - Kad - Kcd;
483  const double Zbb = Kbb - Kbd - Kbd;
484  const double Zbc = Kbc - Kbd - Kcd;
485  const double Zcc = Kcc - Kcd - Kcd;
486//printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac);
487//printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc);
488//printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc);
489
490  // T = inv(S0)
491  const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc
492                       - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc);
493  const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT;
494  const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT;
495  const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT;
496  const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT;
497  const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT;
498  const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT;
499
500//printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13);
501//printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23);
502//printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33);
503
504  // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0)
505  const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd)
506                  + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd)
507                  + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd);
508
509  const double m=1.0/(S0dd-ZZ);
510
511  // eq 18d: Y = inv(S0)s0 + e
512  const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0;
513  const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0;
514  const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0;
515
516  // N = mYY^T + \kappa^F
517  const double N11 = m*Y1*Y1 + Zaa;
518  const double N12 = m*Y1*Y2 + Zab;
519  const double N13 = m*Y1*Y3 + Zac;
520  const double N22 = m*Y2*Y2 + Zbb;
521  const double N23 = m*Y2*Y3 + Zbc;
522  const double N33 = m*Y3*Y3 + Zcc;
523
524//printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13);
525//printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23);
526//printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33);
527//printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac);
528//printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc);
529//printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc);
530
531  // M = I + S0 N
532  const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0;
533  const double Mab = N11*S0ab + N12*S0bb + N13*S0bc;
534  const double Mac = N11*S0ac + N12*S0bc + N13*S0cc;
535  const double Mba = N12*S0aa + N22*S0ab + N23*S0ac;
536  const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0;
537  const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc;
538  const double Mca = N13*S0aa + N23*S0ab + N33*S0ac;
539  const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc;
540  const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0;
541//printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac);
542//printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc);
543//printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc);
544
545  // Q = inv(M) = inv(I + S0 N)
546  const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc
547                       + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca);
548
549  const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ;
550  const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ;
551  const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ;
552  //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ;
553  const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ;
554  const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ;
555  //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ;
556  //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ;
557  const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ;
558
559//printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13);
560//printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23);
561//printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33);
562  // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F
563  // eq A1 in the appendix
564  // To solve for S, use:
565  //      S = inv(inv(S^0) + N) inv(S^0) S^0
566  //        = inv(S^0 inv(S^0) + N) S^0
567  //        = inv(I + S^0 N) S^0
568  //        = Q S^0
569  const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac;
570  const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac;
571  const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac;
572  const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc;
573  const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc;
574  const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc;
575  // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below
576  //const double S14=-S11-S12-S13;
577  //const double S24=-S12-S22-S23;
578  //const double S34=-S13-S23-S33;
579  //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23);
580
581  // eq 12 of Akcasu, 1990: I(q) = L^T S L
582  // Note: eliminate cases without A and B polymers by setting Lij to 0
583  // Note: 1e-13 to convert from fm to cm for scattering length
584  const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13;
585  const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav;
586  const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav;
587  const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav;
588
589  const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33
590                    + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13);
591
592  return result;
593*/
594}
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