source: sasmodels/sasmodels/models/rpa.c @ bb73096

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since bb73096 was bb73096, checked in by butler, 7 years ago

Hide volume fraction parameter of component D since it is treated as the
matrix polymer and thus must always be 1-phia-phib-phid (and so
caculcate in c code). Relates to ticket #593.
  • Property mode set to 100644
File size: 17.9 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;
28  double Pdd,S0dd;
29  double Kaa,Kbb,Kcc;
30  double Kba,Kca,Kcb;
31  double Kda,Kdb,Kdc,Kdd;
32  double Zaa,Zab,Zac,Zba,Zbb,Zbc,Zca,Zcb,Zcc;
33  double DenT,T11,T12,T13,T21,T22,T23,T31,T32,T33;
34  double Y1,Y2,Y3,X11,X12,X13,X21,X22,X23,X31,X32,X33;
35  double ZZ,DenQ1,DenQ2,DenQ3,DenQ,Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33;
36  double N11,N12,N13,N21,N22,N23,N31,N32,N33;
37  double M11,M12,M13,M21,M22,M23,M31,M32,M33;
38  double S11,S12,S13,S14,S21,S22,S23,S24;
39  double S31,S32,S33,S34,S41,S42,S43,S44;
40  double Lad,Lbd,Lcd,Nav,Intg;
41 
42  // Set values for non existent parameters (eg. no A or B in case 0 and 1 etc)
43  //icase was shifted to N-1 from the original code
44  if (icase <= 1){
45    Phi[0] = Phi[1] = 0.0000001;
46    N[0] = N[1] = 1000.0;
47    L[0] = L[1] = 1.e-12;
48    v[0] = v[1] = 100.0;
49    b[0] = b[1] = 5.0;
50    Kab = Kac = Kad = Kbc = Kbd = -0.0004;
51  }
52  else if ((icase > 1) && (icase <= 4)){
53    Phi[0] = 0.0000001;
54    N[0] = 1000.0;
55    L[0] = 1.e-12;
56    v[0] = 100.0;
57    b[0] = 5.0;
58    Kab = Kac = Kad = -0.0004;
59  }
60 
61  // Set volume fraction of component D based on constraint that sum of vol frac =1
62  Phi[3]=1.0-Phi[0]-Phi[1]-Phi[2];
63
64  //set up values for cross terms in case of block copolymers (1,3,4,6,7,8,9)
65  Nab=sqrt(N[0]*N[1]);
66  Nac=sqrt(N[0]*N[2]);
67  Nad=sqrt(N[0]*N[3]);
68  Nbc=sqrt(N[1]*N[2]);
69  Nbd=sqrt(N[1]*N[3]);
70  Ncd=sqrt(N[2]*N[3]);
71
72  vab=sqrt(v[0]*v[1]);
73  vac=sqrt(v[0]*v[2]);
74  vad=sqrt(v[0]*v[3]);
75  vbc=sqrt(v[1]*v[2]);
76  vbd=sqrt(v[1]*v[3]);
77  vcd=sqrt(v[2]*v[3]);
78
79  Phiab=sqrt(Phi[0]*Phi[1]);
80  Phiac=sqrt(Phi[0]*Phi[2]);
81  Phiad=sqrt(Phi[0]*Phi[3]);
82  Phibc=sqrt(Phi[1]*Phi[2]);
83  Phibd=sqrt(Phi[1]*Phi[3]);
84  Phicd=sqrt(Phi[2]*Phi[3]);
85
86  // Calculate Q^2 * Rg^2 for each homopolymer assuming random walk
87  Xa=q*q*b[0]*b[0]*N[0]/6.0;
88  Xb=q*q*b[1]*b[1]*N[1]/6.0;
89  Xc=q*q*b[2]*b[2]*N[2]/6.0;
90  Xd=q*q*b[3]*b[3]*N[3]/6.0;
91
92  //calculate all partial structure factors Pij and normalize n^2
93  Paa=2.0*(exp(-Xa)-1.0+Xa)/(Xa*Xa); // free A chain form factor
94  S0aa=N[0]*Phi[0]*v[0]*Paa; // Phi * Vp * P(Q)= I(Q0)/delRho^2
95  Pab=((1.0-exp(-Xa))/Xa)*((1.0-exp(-Xb))/Xb); //AB diblock (anchored Paa * anchored Pbb) partial form factor
96  S0ab=(Phiab*vab*Nab)*Pab;
97  Pac=((1.0-exp(-Xa))/Xa)*exp(-Xb)*((1.0-exp(-Xc))/Xc); //ABC triblock AC partial form factor
98  S0ac=(Phiac*vac*Nac)*Pac;
99  Pad=((1.0-exp(-Xa))/Xa)*exp(-Xb-Xc)*((1.0-exp(-Xd))/Xd); //ABCD four block
100  S0ad=(Phiad*vad*Nad)*Pad;
101
102  S0ba=S0ab;
103  Pbb=2.0*(exp(-Xb)-1.0+Xb)/(Xb*Xb); // free B chain
104  S0bb=N[1]*Phi[1]*v[1]*Pbb;
105  Pbc=((1.0-exp(-Xb))/Xb)*((1.0-exp(-Xc))/Xc); // BC diblock
106  S0bc=(Phibc*vbc*Nbc)*Pbc;
107  Pbd=((1.0-exp(-Xb))/Xb)*exp(-Xc)*((1.0-exp(-Xd))/Xd); // BCD triblock
108  S0bd=(Phibd*vbd*Nbd)*Pbd;
109
110  S0ca=S0ac;
111  S0cb=S0bc;
112  Pcc=2.0*(exp(-Xc)-1.0+Xc)/(Xc*Xc); // Free C chain
113  S0cc=N[2]*Phi[2]*v[2]*Pcc;
114  Pcd=((1.0-exp(-Xc))/Xc)*((1.0-exp(-Xd))/Xd); // CD diblock
115  S0cd=(Phicd*vcd*Ncd)*Pcd;
116
117  S0da=S0ad;
118  S0db=S0bd;
119  S0dc=S0cd;
120  Pdd=2.0*(exp(-Xd)-1.0+Xd)/(Xd*Xd); // free D chain
121  S0dd=N[3]*Phi[3]*v[3]*Pdd;
122
123  // Reset all unused partial structure factors to 0 (depends on case)
124  //icase was shifted to N-1 from the original code
125  switch(icase){
126  case 0:
127    S0aa=0.000001;
128    S0ab=0.000002;
129    S0ac=0.000003;
130    S0ad=0.000004;
131    S0bb=0.000005;
132    S0bc=0.000006;
133    S0bd=0.000007;
134    S0cd=0.000008;
135    break;
136  case 1:
137    S0aa=0.000001;
138    S0ab=0.000002;
139    S0ac=0.000003;
140    S0ad=0.000004;
141    S0bb=0.000005;
142    S0bc=0.000006;
143    S0bd=0.000007;
144    break;
145  case 2:
146    S0aa=0.000001;
147    S0ab=0.000002;
148    S0ac=0.000003;
149    S0ad=0.000004;
150    S0bc=0.000005;
151    S0bd=0.000006;
152    S0cd=0.000007;
153    break;
154  case 3:
155    S0aa=0.000001;
156    S0ab=0.000002;
157    S0ac=0.000003;
158    S0ad=0.000004;
159    S0bc=0.000005;
160    S0bd=0.000006;
161    break;
162  case 4:
163    S0aa=0.000001;
164    S0ab=0.000002;
165    S0ac=0.000003;
166    S0ad=0.000004;
167    break;
168  case 5:
169    S0ab=0.000001;
170    S0ac=0.000002;
171    S0ad=0.000003;
172    S0bc=0.000004;
173    S0bd=0.000005;
174    S0cd=0.000006;
175    break;
176  case 6:
177    S0ab=0.000001;
178    S0ac=0.000002;
179    S0ad=0.000003;
180    S0bc=0.000004;
181    S0bd=0.000005;
182    break;
183  case 7:
184    S0ab=0.000001;
185    S0ac=0.000002;
186    S0ad=0.000003;
187    break;
188  case 8:
189    S0ac=0.000001;
190    S0ad=0.000002;
191    S0bc=0.000003;
192    S0bd=0.000004;
193    break;
194  default : //case 9:
195    break;
196  }
197  S0ba=S0ab;
198  S0ca=S0ac;
199  S0cb=S0bc;
200  S0da=S0ad;
201  S0db=S0bd;
202  S0dc=S0cd;
203
204  // self chi parameter is 0 ... of course
205  Kaa=0.0;
206  Kbb=0.0;
207  Kcc=0.0;
208  Kdd=0.0;
209
210  Kba=Kab;
211  Kca=Kac;
212  Kcb=Kbc;
213  Kda=Kad;
214  Kdb=Kbd;
215  Kdc=Kcd;
216
217  Zaa=Kaa-Kad-Kad;
218  Zab=Kab-Kad-Kbd;
219  Zac=Kac-Kad-Kcd;
220  Zba=Kba-Kbd-Kad;
221  Zbb=Kbb-Kbd-Kbd;
222  Zbc=Kbc-Kbd-Kcd;
223  Zca=Kca-Kcd-Kad;
224  Zcb=Kcb-Kcd-Kbd;
225  Zcc=Kcc-Kcd-Kcd;
226
227  DenT=(-(S0ac*S0bb*S0ca) + S0ab*S0bc*S0ca + S0ac*S0ba*S0cb - S0aa*S0bc*S0cb - S0ab*S0ba*S0cc + S0aa*S0bb*S0cc);
228
229  T11= (-(S0bc*S0cb) + S0bb*S0cc)/DenT;
230  T12= (S0ac*S0cb - S0ab*S0cc)/DenT;
231  T13= (-(S0ac*S0bb) + S0ab*S0bc)/DenT;
232  T21= (S0bc*S0ca - S0ba*S0cc)/DenT;
233  T22= (-(S0ac*S0ca) + S0aa*S0cc)/DenT;
234  T23= (S0ac*S0ba - S0aa*S0bc)/DenT;
235  T31= (-(S0bb*S0ca) + S0ba*S0cb)/DenT;
236  T32= (S0ab*S0ca - S0aa*S0cb)/DenT;
237  T33= (-(S0ab*S0ba) + S0aa*S0bb)/DenT;
238
239  Y1=T11*S0ad+T12*S0bd+T13*S0cd+1.0;
240  Y2=T21*S0ad+T22*S0bd+T23*S0cd+1.0;
241  Y3=T31*S0ad+T32*S0bd+T33*S0cd+1.0;
242
243  X11=Y1*Y1;
244  X12=Y1*Y2;
245  X13=Y1*Y3;
246  X21=Y2*Y1;
247  X22=Y2*Y2;
248  X23=Y2*Y3;
249  X31=Y3*Y1;
250  X32=Y3*Y2;
251  X33=Y3*Y3;
252
253  ZZ=S0ad*(T11*S0ad+T12*S0bd+T13*S0cd)+S0bd*(T21*S0ad+T22*S0bd+T23*S0cd)+S0cd*(T31*S0ad+T32*S0bd+T33*S0cd);
254
255  // D is considered the matrix or background component so enters here
256  m=1.0/(S0dd-ZZ);
257
258  N11=m*X11+Zaa;
259  N12=m*X12+Zab;
260  N13=m*X13+Zac;
261  N21=m*X21+Zba;
262  N22=m*X22+Zbb;
263  N23=m*X23+Zbc;
264  N31=m*X31+Zca;
265  N32=m*X32+Zcb;
266  N33=m*X33+Zcc;
267
268  M11= N11*S0aa + N12*S0ab + N13*S0ac;
269  M12= N11*S0ab + N12*S0bb + N13*S0bc;
270  M13= N11*S0ac + N12*S0bc + N13*S0cc;
271  M21= N21*S0aa + N22*S0ab + N23*S0ac;
272  M22= N21*S0ab + N22*S0bb + N23*S0bc;
273  M23= N21*S0ac + N22*S0bc + N23*S0cc;
274  M31= N31*S0aa + N32*S0ab + N33*S0ac;
275  M32= N31*S0ab + N32*S0bb + N33*S0bc;
276  M33= N31*S0ac + N32*S0bc + N33*S0cc;
277
278  DenQ1=1.0+M11-M12*M21+M22+M11*M22-M13*M31-M13*M22*M31;
279  DenQ2=  M12*M23*M31+M13*M21*M32-M23*M32-M11*M23*M32+M33+M11*M33;
280  DenQ3=  -M12*M21*M33+M22*M33+M11*M22*M33;
281  DenQ=DenQ1+DenQ2+DenQ3;
282
283  Q11= (1.0 + M22-M23*M32 + M33 + M22*M33)/DenQ;
284  Q12= (-M12 + M13*M32 - M12*M33)/DenQ;
285  Q13= (-M13 - M13*M22 + M12*M23)/DenQ;
286  Q21= (-M21 + M23*M31 - M21*M33)/DenQ;
287  Q22= (1.0 + M11 - M13*M31 + M33 + M11*M33)/DenQ;
288  Q23= (M13*M21 - M23 - M11*M23)/DenQ;
289  Q31= (-M31 - M22*M31 + M21*M32)/DenQ;
290  Q32= (M12*M31 - M32 - M11*M32)/DenQ;
291  Q33= (1.0 + M11 - M12*M21 + M22 + M11*M22)/DenQ;
292
293  S11= Q11*S0aa + Q21*S0ab + Q31*S0ac;
294  S12= Q12*S0aa + Q22*S0ab + Q32*S0ac;
295  S13= Q13*S0aa + Q23*S0ab + Q33*S0ac;
296  S14=-S11-S12-S13;
297  S21= Q11*S0ba + Q21*S0bb + Q31*S0bc;
298  S22= Q12*S0ba + Q22*S0bb + Q32*S0bc;
299  S23= Q13*S0ba + Q23*S0bb + Q33*S0bc;
300  S24=-S21-S22-S23;
301  S31= Q11*S0ca + Q21*S0cb + Q31*S0cc;
302  S32= Q12*S0ca + Q22*S0cb + Q32*S0cc;
303  S33= Q13*S0ca + Q23*S0cb + Q33*S0cc;
304  S34=-S31-S32-S33;
305  S41=S14;
306  S42=S24;
307  S43=S34;
308  S44=S11+S22+S33+2.0*S12+2.0*S13+2.0*S23;
309
310  //calculate contrast where L[i] is the scattering length of i and D is the matrix
311  //need to verify why the sqrt of Nav rather than just Nav (assuming v is molar volume)
312  Nav=6.022045e+23;
313  Lad=(L[0]/v[0]-L[3]/v[3])*sqrt(Nav);
314  Lbd=(L[1]/v[1]-L[3]/v[3])*sqrt(Nav);
315  Lcd=(L[2]/v[2]-L[3]/v[3])*sqrt(Nav);
316
317  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;
318
319  return Intg;
320
321
322/*  Attempts at a new implementation --- supressed for now
323#if 1  // Sasview defaults
324  if (icase <= 1) {
325    N[0]=N[1]=1000.0;
326    Phi[0]=Phi[1]=0.0000001;
327    Kab=Kac=Kad=Kbc=Kbd=-0.0004;
328    L[0]=L[1]=1.0e-12;
329    v[0]=v[1]=100.0;
330    b[0]=b[1]=5.0;
331  } else if (icase <= 4) {
332    Phi[0]=0.0000001;
333    Kab=Kac=Kad=-0.0004;
334    L[0]=1.0e-12;
335    v[0]=100.0;
336    b[0]=5.0;
337  }
338#else
339  if (icase <= 1) {
340    N[0]=N[1]=0.0;
341    Phi[0]=Phi[1]=0.0;
342    Kab=Kac=Kad=Kbc=Kbd=0.0;
343    L[0]=L[1]=L[3];
344    v[0]=v[1]=v[3];
345    b[0]=b[1]=0.0;
346  } else if (icase <= 4) {
347    N[0] = 0.0;
348    Phi[0]=0.0;
349    Kab=Kac=Kad=0.0;
350    L[0]=L[3];
351    v[0]=v[3];
352    b[0]=0.0;
353  }
354#endif
355
356  const double Xa = q*q*b[0]*b[0]*N[0]/6.0;
357  const double Xb = q*q*b[1]*b[1]*N[1]/6.0;
358  const double Xc = q*q*b[2]*b[2]*N[2]/6.0;
359  const double Xd = q*q*b[3]*b[3]*N[3]/6.0;
360
361  // limit as Xa goes to 0 is 1
362  const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa;
363  const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb;
364  const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc;
365  const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd;
366
367  // limit as Xa goes to 0 is 1
368  const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa;
369  const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb;
370  const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc;
371  const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd;
372
373
374  // Note: S0ij only defined for copolymers; otherwise set to zero
375  // 0: C/D     binary mixture
376  // 1: C-D     diblock copolymer
377  // 2: B/C/D   ternery mixture
378  // 3: B/C-D   binary mixture,1 homopolymer, 1 diblock copolymer
379  // 4: B-C-D   triblock copolymer
380  // 5: A/B/C/D quaternary mixture
381  // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer
382  // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer
383  // 8: A-B/C-D binary mixture, 2 diblock copolymer
384  // 9: A-B-C-D tetra-block copolymer
385#if 0
386  const double S0aa = icase<5
387                      ? 1.0 : N[0]*Phi[0]*v[0]*Paa;
388  const double S0bb = icase<2
389                      ? 1.0 : N[1]*Phi[1]*v[1]*Pbb;
390  const double S0cc = N[2]*Phi[2]*v[2]*Pcc;
391  const double S0dd = N[3]*Phi[3]*v[3]*Pdd;
392  const double S0ab = icase<8
393                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
394  const double S0ac = icase<9
395                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
396  const double S0ad = icase<9
397                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
398  const double S0bc = (icase!=4 && icase!=7 && icase!= 9)
399                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
400  const double S0bd = (icase!=4 && icase!=7 && icase!= 9)
401                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
402  const double S0cd = (icase==0 || icase==2 || icase==5)
403                      ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
404#else  // sasview equivalent
405//printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc);
406  double S0aa = N[0]*Phi[0]*v[0]*Paa;
407  double S0bb = N[1]*Phi[1]*v[1]*Pbb;
408  double S0cc = N[2]*Phi[2]*v[2]*Pcc;
409  double S0dd = N[3]*Phi[3]*v[3]*Pdd;
410  double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
411  double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
412  double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
413  double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
414  double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
415  double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
416switch(icase){
417  case 0:
418    S0aa=0.000001;
419    S0ab=0.000002;
420    S0ac=0.000003;
421    S0ad=0.000004;
422    S0bb=0.000005;
423    S0bc=0.000006;
424    S0bd=0.000007;
425    S0cd=0.000008;
426    break;
427  case 1:
428    S0aa=0.000001;
429    S0ab=0.000002;
430    S0ac=0.000003;
431    S0ad=0.000004;
432    S0bb=0.000005;
433    S0bc=0.000006;
434    S0bd=0.000007;
435    break;
436  case 2:
437    S0aa=0.000001;
438    S0ab=0.000002;
439    S0ac=0.000003;
440    S0ad=0.000004;
441    S0bc=0.000005;
442    S0bd=0.000006;
443    S0cd=0.000007;
444    break;
445  case 3:
446    S0aa=0.000001;
447    S0ab=0.000002;
448    S0ac=0.000003;
449    S0ad=0.000004;
450    S0bc=0.000005;
451    S0bd=0.000006;
452    break;
453  case 4:
454    S0aa=0.000001;
455    S0ab=0.000002;
456    S0ac=0.000003;
457    S0ad=0.000004;
458    break;
459  case 5:
460    S0ab=0.000001;
461    S0ac=0.000002;
462    S0ad=0.000003;
463    S0bc=0.000004;
464    S0bd=0.000005;
465    S0cd=0.000006;
466    break;
467  case 6:
468    S0ab=0.000001;
469    S0ac=0.000002;
470    S0ad=0.000003;
471    S0bc=0.000004;
472    S0bd=0.000005;
473    break;
474  case 7:
475    S0ab=0.000001;
476    S0ac=0.000002;
477    S0ad=0.000003;
478    break;
479  case 8:
480    S0ac=0.000001;
481    S0ad=0.000002;
482    S0bc=0.000003;
483    S0bd=0.000004;
484    break;
485  default : //case 9:
486    break;
487  }
488#endif
489
490  // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F
491  const double Kaa = 0.0;
492  const double Kbb = 0.0;
493  const double Kcc = 0.0;
494  //const double Kdd = 0.0;
495  const double Zaa = Kaa - Kad - Kad;
496  const double Zab = Kab - Kad - Kbd;
497  const double Zac = Kac - Kad - Kcd;
498  const double Zbb = Kbb - Kbd - Kbd;
499  const double Zbc = Kbc - Kbd - Kcd;
500  const double Zcc = Kcc - Kcd - Kcd;
501//printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac);
502//printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc);
503//printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc);
504
505  // T = inv(S0)
506  const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc
507                       - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc);
508  const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT;
509  const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT;
510  const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT;
511  const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT;
512  const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT;
513  const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT;
514
515//printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13);
516//printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23);
517//printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33);
518
519  // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0)
520  const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd)
521                  + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd)
522                  + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd);
523
524  const double m=1.0/(S0dd-ZZ);
525
526  // eq 18d: Y = inv(S0)s0 + e
527  const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0;
528  const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0;
529  const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0;
530
531  // N = mYY^T + \kappa^F
532  const double N11 = m*Y1*Y1 + Zaa;
533  const double N12 = m*Y1*Y2 + Zab;
534  const double N13 = m*Y1*Y3 + Zac;
535  const double N22 = m*Y2*Y2 + Zbb;
536  const double N23 = m*Y2*Y3 + Zbc;
537  const double N33 = m*Y3*Y3 + Zcc;
538
539//printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13);
540//printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23);
541//printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33);
542//printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac);
543//printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc);
544//printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc);
545
546  // M = I + S0 N
547  const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0;
548  const double Mab = N11*S0ab + N12*S0bb + N13*S0bc;
549  const double Mac = N11*S0ac + N12*S0bc + N13*S0cc;
550  const double Mba = N12*S0aa + N22*S0ab + N23*S0ac;
551  const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0;
552  const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc;
553  const double Mca = N13*S0aa + N23*S0ab + N33*S0ac;
554  const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc;
555  const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0;
556//printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac);
557//printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc);
558//printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc);
559
560  // Q = inv(M) = inv(I + S0 N)
561  const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc
562                       + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca);
563
564  const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ;
565  const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ;
566  const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ;
567  //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ;
568  const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ;
569  const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ;
570  //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ;
571  //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ;
572  const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ;
573
574//printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13);
575//printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23);
576//printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33);
577  // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F
578  // eq A1 in the appendix
579  // To solve for S, use:
580  //      S = inv(inv(S^0) + N) inv(S^0) S^0
581  //        = inv(S^0 inv(S^0) + N) S^0
582  //        = inv(I + S^0 N) S^0
583  //        = Q S^0
584  const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac;
585  const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac;
586  const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac;
587  const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc;
588  const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc;
589  const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc;
590  // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below
591  //const double S14=-S11-S12-S13;
592  //const double S24=-S12-S22-S23;
593  //const double S34=-S13-S23-S33;
594  //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23);
595
596  // eq 12 of Akcasu, 1990: I(q) = L^T S L
597  // Note: eliminate cases without A and B polymers by setting Lij to 0
598  // Note: 1e-13 to convert from fm to cm for scattering length
599  const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13;
600  const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav;
601  const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav;
602  const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav;
603
604  const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33
605                    + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13);
606
607  return result;
608*/
609}
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