source: sasmodels/sasmodels/models/rpa.c @ 4329539

core_shell_microgelscostrafo411magnetic_modelticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change on this file since 4329539 was 4329539, checked in by butler, 7 years ago

add comments to rpa c code to help code readability. Addresses ticket
#593
  • Property mode set to 100644
File size: 17.8 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;
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 up values for cross terms in case of block copolymers (1,3,4,6,7,8,9)
62  Nab=sqrt(N[0]*N[1]);
63  Nac=sqrt(N[0]*N[2]);
64  Nad=sqrt(N[0]*N[3]);
65  Nbc=sqrt(N[1]*N[2]);
66  Nbd=sqrt(N[1]*N[3]);
67  Ncd=sqrt(N[2]*N[3]);
68
69  vab=sqrt(v[0]*v[1]);
70  vac=sqrt(v[0]*v[2]);
71  vad=sqrt(v[0]*v[3]);
72  vbc=sqrt(v[1]*v[2]);
73  vbd=sqrt(v[1]*v[3]);
74  vcd=sqrt(v[2]*v[3]);
75
76  Phiab=sqrt(Phi[0]*Phi[1]);
77  Phiac=sqrt(Phi[0]*Phi[2]);
78  Phiad=sqrt(Phi[0]*Phi[3]);
79  Phibc=sqrt(Phi[1]*Phi[2]);
80  Phibd=sqrt(Phi[1]*Phi[3]);
81  Phicd=sqrt(Phi[2]*Phi[3]);
82
83  // Calculate Q^2 * Rg^2 for each homopolymer assuming random walk
84  Xa=q*q*b[0]*b[0]*N[0]/6.0;
85  Xb=q*q*b[1]*b[1]*N[1]/6.0;
86  Xc=q*q*b[2]*b[2]*N[2]/6.0;
87  Xd=q*q*b[3]*b[3]*N[3]/6.0;
88
89  //calculate all partial structure factors Pij and normalize n^2
90  Paa=2.0*(exp(-Xa)-1.0+Xa)/(Xa*Xa); // free A chain form factor
91  S0aa=N[0]*Phi[0]*v[0]*Paa; // Phi * Vp * P(Q)= I(Q0)/delRho^2
92  Pab=((1.0-exp(-Xa))/Xa)*((1.0-exp(-Xb))/Xb); //AB diblock (anchored Paa * anchored Pbb) partial form factor
93  S0ab=(Phiab*vab*Nab)*Pab;
94  Pac=((1.0-exp(-Xa))/Xa)*exp(-Xb)*((1.0-exp(-Xc))/Xc); //ABC triblock AC partial form factor
95  S0ac=(Phiac*vac*Nac)*Pac;
96  Pad=((1.0-exp(-Xa))/Xa)*exp(-Xb-Xc)*((1.0-exp(-Xd))/Xd); //ABCD four block
97  S0ad=(Phiad*vad*Nad)*Pad;
98
99  S0ba=S0ab;
100  Pbb=2.0*(exp(-Xb)-1.0+Xb)/(Xb*Xb); // free B chain
101  S0bb=N[1]*Phi[1]*v[1]*Pbb;
102  Pbc=((1.0-exp(-Xb))/Xb)*((1.0-exp(-Xc))/Xc); // BC diblock
103  S0bc=(Phibc*vbc*Nbc)*Pbc;
104  Pbd=((1.0-exp(-Xb))/Xb)*exp(-Xc)*((1.0-exp(-Xd))/Xd); // BCD triblock
105  S0bd=(Phibd*vbd*Nbd)*Pbd;
106
107  S0ca=S0ac;
108  S0cb=S0bc;
109  Pcc=2.0*(exp(-Xc)-1.0+Xc)/(Xc*Xc); // Free C chain
110  S0cc=N[2]*Phi[2]*v[2]*Pcc;
111  Pcd=((1.0-exp(-Xc))/Xc)*((1.0-exp(-Xd))/Xd); // CD diblock
112  S0cd=(Phicd*vcd*Ncd)*Pcd;
113
114  S0da=S0ad;
115  S0db=S0bd;
116  S0dc=S0cd;
117  Pdd=2.0*(exp(-Xd)-1.0+Xd)/(Xd*Xd); // free D chain
118  S0dd=N[3]*Phi[3]*v[3]*Pdd;
119
120  // Reset all unused partial structure factors to 0 (depends on case)
121  //icase was shifted to N-1 from the original code
122  switch(icase){
123  case 0:
124    S0aa=0.000001;
125    S0ab=0.000002;
126    S0ac=0.000003;
127    S0ad=0.000004;
128    S0bb=0.000005;
129    S0bc=0.000006;
130    S0bd=0.000007;
131    S0cd=0.000008;
132    break;
133  case 1:
134    S0aa=0.000001;
135    S0ab=0.000002;
136    S0ac=0.000003;
137    S0ad=0.000004;
138    S0bb=0.000005;
139    S0bc=0.000006;
140    S0bd=0.000007;
141    break;
142  case 2:
143    S0aa=0.000001;
144    S0ab=0.000002;
145    S0ac=0.000003;
146    S0ad=0.000004;
147    S0bc=0.000005;
148    S0bd=0.000006;
149    S0cd=0.000007;
150    break;
151  case 3:
152    S0aa=0.000001;
153    S0ab=0.000002;
154    S0ac=0.000003;
155    S0ad=0.000004;
156    S0bc=0.000005;
157    S0bd=0.000006;
158    break;
159  case 4:
160    S0aa=0.000001;
161    S0ab=0.000002;
162    S0ac=0.000003;
163    S0ad=0.000004;
164    break;
165  case 5:
166    S0ab=0.000001;
167    S0ac=0.000002;
168    S0ad=0.000003;
169    S0bc=0.000004;
170    S0bd=0.000005;
171    S0cd=0.000006;
172    break;
173  case 6:
174    S0ab=0.000001;
175    S0ac=0.000002;
176    S0ad=0.000003;
177    S0bc=0.000004;
178    S0bd=0.000005;
179    break;
180  case 7:
181    S0ab=0.000001;
182    S0ac=0.000002;
183    S0ad=0.000003;
184    break;
185  case 8:
186    S0ac=0.000001;
187    S0ad=0.000002;
188    S0bc=0.000003;
189    S0bd=0.000004;
190    break;
191  default : //case 9:
192    break;
193  }
194  S0ba=S0ab;
195  S0ca=S0ac;
196  S0cb=S0bc;
197  S0da=S0ad;
198  S0db=S0bd;
199  S0dc=S0cd;
200
201  // self chi parameter is 0 ... of course
202  Kaa=0.0;
203  Kbb=0.0;
204  Kcc=0.0;
205  Kdd=0.0;
206
207  Kba=Kab;
208  Kca=Kac;
209  Kcb=Kbc;
210  Kda=Kad;
211  Kdb=Kbd;
212  Kdc=Kcd;
213
214  Zaa=Kaa-Kad-Kad;
215  Zab=Kab-Kad-Kbd;
216  Zac=Kac-Kad-Kcd;
217  Zba=Kba-Kbd-Kad;
218  Zbb=Kbb-Kbd-Kbd;
219  Zbc=Kbc-Kbd-Kcd;
220  Zca=Kca-Kcd-Kad;
221  Zcb=Kcb-Kcd-Kbd;
222  Zcc=Kcc-Kcd-Kcd;
223
224  DenT=(-(S0ac*S0bb*S0ca) + S0ab*S0bc*S0ca + S0ac*S0ba*S0cb - S0aa*S0bc*S0cb - S0ab*S0ba*S0cc + S0aa*S0bb*S0cc);
225
226  T11= (-(S0bc*S0cb) + S0bb*S0cc)/DenT;
227  T12= (S0ac*S0cb - S0ab*S0cc)/DenT;
228  T13= (-(S0ac*S0bb) + S0ab*S0bc)/DenT;
229  T21= (S0bc*S0ca - S0ba*S0cc)/DenT;
230  T22= (-(S0ac*S0ca) + S0aa*S0cc)/DenT;
231  T23= (S0ac*S0ba - S0aa*S0bc)/DenT;
232  T31= (-(S0bb*S0ca) + S0ba*S0cb)/DenT;
233  T32= (S0ab*S0ca - S0aa*S0cb)/DenT;
234  T33= (-(S0ab*S0ba) + S0aa*S0bb)/DenT;
235
236  Y1=T11*S0ad+T12*S0bd+T13*S0cd+1.0;
237  Y2=T21*S0ad+T22*S0bd+T23*S0cd+1.0;
238  Y3=T31*S0ad+T32*S0bd+T33*S0cd+1.0;
239
240  X11=Y1*Y1;
241  X12=Y1*Y2;
242  X13=Y1*Y3;
243  X21=Y2*Y1;
244  X22=Y2*Y2;
245  X23=Y2*Y3;
246  X31=Y3*Y1;
247  X32=Y3*Y2;
248  X33=Y3*Y3;
249
250  ZZ=S0ad*(T11*S0ad+T12*S0bd+T13*S0cd)+S0bd*(T21*S0ad+T22*S0bd+T23*S0cd)+S0cd*(T31*S0ad+T32*S0bd+T33*S0cd);
251
252  // D is considered the matrix or background component so enters here
253  m=1.0/(S0dd-ZZ);
254
255  N11=m*X11+Zaa;
256  N12=m*X12+Zab;
257  N13=m*X13+Zac;
258  N21=m*X21+Zba;
259  N22=m*X22+Zbb;
260  N23=m*X23+Zbc;
261  N31=m*X31+Zca;
262  N32=m*X32+Zcb;
263  N33=m*X33+Zcc;
264
265  M11= N11*S0aa + N12*S0ab + N13*S0ac;
266  M12= N11*S0ab + N12*S0bb + N13*S0bc;
267  M13= N11*S0ac + N12*S0bc + N13*S0cc;
268  M21= N21*S0aa + N22*S0ab + N23*S0ac;
269  M22= N21*S0ab + N22*S0bb + N23*S0bc;
270  M23= N21*S0ac + N22*S0bc + N23*S0cc;
271  M31= N31*S0aa + N32*S0ab + N33*S0ac;
272  M32= N31*S0ab + N32*S0bb + N33*S0bc;
273  M33= N31*S0ac + N32*S0bc + N33*S0cc;
274
275  DenQ1=1.0+M11-M12*M21+M22+M11*M22-M13*M31-M13*M22*M31;
276  DenQ2=  M12*M23*M31+M13*M21*M32-M23*M32-M11*M23*M32+M33+M11*M33;
277  DenQ3=  -M12*M21*M33+M22*M33+M11*M22*M33;
278  DenQ=DenQ1+DenQ2+DenQ3;
279
280  Q11= (1.0 + M22-M23*M32 + M33 + M22*M33)/DenQ;
281  Q12= (-M12 + M13*M32 - M12*M33)/DenQ;
282  Q13= (-M13 - M13*M22 + M12*M23)/DenQ;
283  Q21= (-M21 + M23*M31 - M21*M33)/DenQ;
284  Q22= (1.0 + M11 - M13*M31 + M33 + M11*M33)/DenQ;
285  Q23= (M13*M21 - M23 - M11*M23)/DenQ;
286  Q31= (-M31 - M22*M31 + M21*M32)/DenQ;
287  Q32= (M12*M31 - M32 - M11*M32)/DenQ;
288  Q33= (1.0 + M11 - M12*M21 + M22 + M11*M22)/DenQ;
289
290  S11= Q11*S0aa + Q21*S0ab + Q31*S0ac;
291  S12= Q12*S0aa + Q22*S0ab + Q32*S0ac;
292  S13= Q13*S0aa + Q23*S0ab + Q33*S0ac;
293  S14=-S11-S12-S13;
294  S21= Q11*S0ba + Q21*S0bb + Q31*S0bc;
295  S22= Q12*S0ba + Q22*S0bb + Q32*S0bc;
296  S23= Q13*S0ba + Q23*S0bb + Q33*S0bc;
297  S24=-S21-S22-S23;
298  S31= Q11*S0ca + Q21*S0cb + Q31*S0cc;
299  S32= Q12*S0ca + Q22*S0cb + Q32*S0cc;
300  S33= Q13*S0ca + Q23*S0cb + Q33*S0cc;
301  S34=-S31-S32-S33;
302  S41=S14;
303  S42=S24;
304  S43=S34;
305  S44=S11+S22+S33+2.0*S12+2.0*S13+2.0*S23;
306
307  //calculate contrast where L[i] is the scattering length of i and D is the matrix
308  //need to verify why the sqrt of Nav rather than just Nav (assuming v is molar volume)
309  Nav=6.022045e+23;
310  Lad=(L[0]/v[0]-L[3]/v[3])*sqrt(Nav);
311  Lbd=(L[1]/v[1]-L[3]/v[3])*sqrt(Nav);
312  Lcd=(L[2]/v[2]-L[3]/v[3])*sqrt(Nav);
313
314  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;
315
316  return Intg;
317
318
319/*  Attempts at a new implementation --- supressed for now
320#if 1  // Sasview defaults
321  if (icase <= 1) {
322    N[0]=N[1]=1000.0;
323    Phi[0]=Phi[1]=0.0000001;
324    Kab=Kac=Kad=Kbc=Kbd=-0.0004;
325    L[0]=L[1]=1.0e-12;
326    v[0]=v[1]=100.0;
327    b[0]=b[1]=5.0;
328  } else if (icase <= 4) {
329    Phi[0]=0.0000001;
330    Kab=Kac=Kad=-0.0004;
331    L[0]=1.0e-12;
332    v[0]=100.0;
333    b[0]=5.0;
334  }
335#else
336  if (icase <= 1) {
337    N[0]=N[1]=0.0;
338    Phi[0]=Phi[1]=0.0;
339    Kab=Kac=Kad=Kbc=Kbd=0.0;
340    L[0]=L[1]=L[3];
341    v[0]=v[1]=v[3];
342    b[0]=b[1]=0.0;
343  } else if (icase <= 4) {
344    N[0] = 0.0;
345    Phi[0]=0.0;
346    Kab=Kac=Kad=0.0;
347    L[0]=L[3];
348    v[0]=v[3];
349    b[0]=0.0;
350  }
351#endif
352
353  const double Xa = q*q*b[0]*b[0]*N[0]/6.0;
354  const double Xb = q*q*b[1]*b[1]*N[1]/6.0;
355  const double Xc = q*q*b[2]*b[2]*N[2]/6.0;
356  const double Xd = q*q*b[3]*b[3]*N[3]/6.0;
357
358  // limit as Xa goes to 0 is 1
359  const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa;
360  const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb;
361  const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc;
362  const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd;
363
364  // limit as Xa goes to 0 is 1
365  const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa;
366  const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb;
367  const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc;
368  const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd;
369
370
371  // Note: S0ij only defined for copolymers; otherwise set to zero
372  // 0: C/D     binary mixture
373  // 1: C-D     diblock copolymer
374  // 2: B/C/D   ternery mixture
375  // 3: B/C-D   binary mixture,1 homopolymer, 1 diblock copolymer
376  // 4: B-C-D   triblock copolymer
377  // 5: A/B/C/D quaternary mixture
378  // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer
379  // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer
380  // 8: A-B/C-D binary mixture, 2 diblock copolymer
381  // 9: A-B-C-D tetra-block copolymer
382#if 0
383  const double S0aa = icase<5
384                      ? 1.0 : N[0]*Phi[0]*v[0]*Paa;
385  const double S0bb = icase<2
386                      ? 1.0 : N[1]*Phi[1]*v[1]*Pbb;
387  const double S0cc = N[2]*Phi[2]*v[2]*Pcc;
388  const double S0dd = N[3]*Phi[3]*v[3]*Pdd;
389  const double S0ab = icase<8
390                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
391  const double S0ac = icase<9
392                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
393  const double S0ad = icase<9
394                      ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
395  const double S0bc = (icase!=4 && icase!=7 && icase!= 9)
396                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
397  const double S0bd = (icase!=4 && icase!=7 && icase!= 9)
398                      ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
399  const double S0cd = (icase==0 || icase==2 || icase==5)
400                      ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
401#else  // sasview equivalent
402//printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc);
403  double S0aa = N[0]*Phi[0]*v[0]*Paa;
404  double S0bb = N[1]*Phi[1]*v[1]*Pbb;
405  double S0cc = N[2]*Phi[2]*v[2]*Pcc;
406  double S0dd = N[3]*Phi[3]*v[3]*Pdd;
407  double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb;
408  double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb);
409  double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc);
410  double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc;
411  double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc);
412  double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd;
413switch(icase){
414  case 0:
415    S0aa=0.000001;
416    S0ab=0.000002;
417    S0ac=0.000003;
418    S0ad=0.000004;
419    S0bb=0.000005;
420    S0bc=0.000006;
421    S0bd=0.000007;
422    S0cd=0.000008;
423    break;
424  case 1:
425    S0aa=0.000001;
426    S0ab=0.000002;
427    S0ac=0.000003;
428    S0ad=0.000004;
429    S0bb=0.000005;
430    S0bc=0.000006;
431    S0bd=0.000007;
432    break;
433  case 2:
434    S0aa=0.000001;
435    S0ab=0.000002;
436    S0ac=0.000003;
437    S0ad=0.000004;
438    S0bc=0.000005;
439    S0bd=0.000006;
440    S0cd=0.000007;
441    break;
442  case 3:
443    S0aa=0.000001;
444    S0ab=0.000002;
445    S0ac=0.000003;
446    S0ad=0.000004;
447    S0bc=0.000005;
448    S0bd=0.000006;
449    break;
450  case 4:
451    S0aa=0.000001;
452    S0ab=0.000002;
453    S0ac=0.000003;
454    S0ad=0.000004;
455    break;
456  case 5:
457    S0ab=0.000001;
458    S0ac=0.000002;
459    S0ad=0.000003;
460    S0bc=0.000004;
461    S0bd=0.000005;
462    S0cd=0.000006;
463    break;
464  case 6:
465    S0ab=0.000001;
466    S0ac=0.000002;
467    S0ad=0.000003;
468    S0bc=0.000004;
469    S0bd=0.000005;
470    break;
471  case 7:
472    S0ab=0.000001;
473    S0ac=0.000002;
474    S0ad=0.000003;
475    break;
476  case 8:
477    S0ac=0.000001;
478    S0ad=0.000002;
479    S0bc=0.000003;
480    S0bd=0.000004;
481    break;
482  default : //case 9:
483    break;
484  }
485#endif
486
487  // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F
488  const double Kaa = 0.0;
489  const double Kbb = 0.0;
490  const double Kcc = 0.0;
491  //const double Kdd = 0.0;
492  const double Zaa = Kaa - Kad - Kad;
493  const double Zab = Kab - Kad - Kbd;
494  const double Zac = Kac - Kad - Kcd;
495  const double Zbb = Kbb - Kbd - Kbd;
496  const double Zbc = Kbc - Kbd - Kcd;
497  const double Zcc = Kcc - Kcd - Kcd;
498//printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac);
499//printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc);
500//printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc);
501
502  // T = inv(S0)
503  const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc
504                       - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc);
505  const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT;
506  const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT;
507  const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT;
508  const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT;
509  const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT;
510  const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT;
511
512//printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13);
513//printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23);
514//printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33);
515
516  // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0)
517  const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd)
518                  + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd)
519                  + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd);
520
521  const double m=1.0/(S0dd-ZZ);
522
523  // eq 18d: Y = inv(S0)s0 + e
524  const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0;
525  const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0;
526  const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0;
527
528  // N = mYY^T + \kappa^F
529  const double N11 = m*Y1*Y1 + Zaa;
530  const double N12 = m*Y1*Y2 + Zab;
531  const double N13 = m*Y1*Y3 + Zac;
532  const double N22 = m*Y2*Y2 + Zbb;
533  const double N23 = m*Y2*Y3 + Zbc;
534  const double N33 = m*Y3*Y3 + Zcc;
535
536//printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13);
537//printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23);
538//printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33);
539//printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac);
540//printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc);
541//printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc);
542
543  // M = I + S0 N
544  const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0;
545  const double Mab = N11*S0ab + N12*S0bb + N13*S0bc;
546  const double Mac = N11*S0ac + N12*S0bc + N13*S0cc;
547  const double Mba = N12*S0aa + N22*S0ab + N23*S0ac;
548  const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0;
549  const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc;
550  const double Mca = N13*S0aa + N23*S0ab + N33*S0ac;
551  const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc;
552  const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0;
553//printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac);
554//printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc);
555//printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc);
556
557  // Q = inv(M) = inv(I + S0 N)
558  const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc
559                       + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca);
560
561  const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ;
562  const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ;
563  const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ;
564  //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ;
565  const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ;
566  const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ;
567  //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ;
568  //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ;
569  const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ;
570
571//printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13);
572//printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23);
573//printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33);
574  // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F
575  // eq A1 in the appendix
576  // To solve for S, use:
577  //      S = inv(inv(S^0) + N) inv(S^0) S^0
578  //        = inv(S^0 inv(S^0) + N) S^0
579  //        = inv(I + S^0 N) S^0
580  //        = Q S^0
581  const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac;
582  const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac;
583  const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac;
584  const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc;
585  const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc;
586  const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc;
587  // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below
588  //const double S14=-S11-S12-S13;
589  //const double S24=-S12-S22-S23;
590  //const double S34=-S13-S23-S33;
591  //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23);
592
593  // eq 12 of Akcasu, 1990: I(q) = L^T S L
594  // Note: eliminate cases without A and B polymers by setting Lij to 0
595  // Note: 1e-13 to convert from fm to cm for scattering length
596  const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13;
597  const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav;
598  const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav;
599  const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav;
600
601  const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33
602                    + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13);
603
604  return result;
605*/
606}
Note: See TracBrowser for help on using the repository browser.