[ae3ce4e] | 1 | /* |
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| 2 | libCylinderFit.h -- equates for CylinderFit XOP |
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| 3 | */ |
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[6515f36] | 4 | #if defined(_MSC_VER) |
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[6a2c931] | 5 | #include "winFuncs.h" |
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[6515f36] | 6 | #endif |
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[ae3ce4e] | 7 | |
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| 8 | /* Prototypes */ |
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| 9 | /* IGOR Fit Functions */ |
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| 10 | double CylinderForm(double dp[], double q); |
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| 11 | double EllipCyl76(double dp[], double q); |
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| 12 | double EllipCyl20(double dp[], double q); |
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| 13 | double TriaxialEllipsoid(double dp[], double q); |
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| 14 | double Parallelepiped(double dp[], double q); |
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| 15 | double HollowCylinder(double dp[], double q); |
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| 16 | double EllipsoidForm(double dp[], double q); |
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| 17 | double Cyl_PolyRadius(double dp[], double q); |
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| 18 | double Cyl_PolyLength(double dp[], double q); |
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| 19 | double CoreShellCylinder(double dp[], double q); |
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| 20 | double OblateForm(double dp[], double q); |
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| 21 | double ProlateForm(double dp[], double q); |
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| 22 | double FlexExclVolCyl(double dp[], double q); |
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| 23 | double FlexCyl_PolyLen(double dp[], double q); |
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| 24 | double FlexCyl_PolyRad(double dp[], double q); |
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| 25 | double FlexCyl_Ellip(double dp[], double q); |
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| 26 | double PolyCoShCylinder(double dp[], double q); |
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| 27 | double StackedDiscs(double dp[], double q); |
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| 28 | double LamellarFF(double dp[], double q); |
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| 29 | double LamellarFF_HG(double dp[], double q); |
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| 30 | double LamellarPS(double dp[], double q); |
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| 31 | double LamellarPS_HG(double dp[], double q); |
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[6e93a02] | 32 | double Lamellar_ParaCrystal(double dp[], double q); |
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| 33 | double Spherocylinder(double dp[], double q); |
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| 34 | double ConvexLens(double dp[], double q); |
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| 35 | double Dumbbell(double dp[], double q); |
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| 36 | double CappedCylinder(double dp[], double q); |
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| 37 | double Barbell(double dp[], double q); |
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| 38 | double PolyCoreBicelle(double dp[], double q); |
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| 39 | double CSParallelepiped(double dp[], double q); |
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[ae3ce4e] | 40 | |
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| 41 | /* internal functions */ |
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| 42 | double CylKernel(double qq, double rr,double h, double theta); |
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| 43 | double NR_BessJ1(double x); |
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| 44 | double EllipCylKernel(double qq, double ra,double nu, double theta); |
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| 45 | double TriaxialKernel(double q, double aa, double bb, double cc, double dx, double dy); |
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| 46 | double PPKernel(double aa, double mu, double uu); |
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| 47 | double HolCylKernel(double qq, double rcore, double rshell, double length, double dum); |
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| 48 | double EllipsoidKernel(double qq, double a, double va, double dum); |
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| 49 | double Cyl_PolyRadKernel(double q, double radius, double length, double zz, double delrho, double dumRad); |
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| 50 | double SchulzPoint_cpr(double dumRad, double radius, double zz); |
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| 51 | double Cyl_PolyLenKernel(double q, double radius, double len_avg, double zz, double delrho, double dumLen); |
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| 52 | double CoreShellCylKernel(double qq, double rcore, double thick, double rhoc, double rhos, double rhosolv, double length, double dum); |
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| 53 | double gfn4(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq); |
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| 54 | double gfn2(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq); |
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| 55 | double FlePolyLen_kernel(double q, double radius, double length, double lb, double zz, double delrho, double zi); |
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| 56 | double FlePolyRad_kernel(double q, double ravg, double Lc, double Lb, double zz, double delrho, double zi); |
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| 57 | double EllipticalCross_fn(double qq, double a, double b); |
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| 58 | double CScyl(double qq, double rad, double radthick, double facthick, double rhoc, double rhos, double rhosolv, double length, double dum); |
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| 59 | double CSCylIntegration(double qq, double rad, double radthick, double facthick, double rhoc, double rhos, double rhosolv, double length); |
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| 60 | double Stackdisc_kern(double qq, double rcore, double rhoc, double rhol, double rhosolv, double length, double thick, double dum, double gsd, double d, double N); |
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[6e93a02] | 61 | double paraCryst_sn(double ww, double qval, double davg, long nl, double an); |
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| 62 | double paraCryst_an(double ww, double qval, double davg, long nl); |
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| 63 | double SphCyl_kernel(double w[], double x, double tt, double Theta); |
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| 64 | double ConvLens_kernel(double w[], double x, double tt, double theta); |
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| 65 | double Dumb_kernel(double w[], double x, double tt, double theta); |
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| 66 | double BicelleKernel(double qq, double rad, double radthick, double facthick, double rhoc, double rhoh, double rhor, double rhosolv, double length, double dum); |
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| 67 | double BicelleIntegration(double qq, double rad, double radthick, double facthick, double rhoc, double rhoh, double rhor, double rhosolv, double length); |
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| 68 | double CSPPKernel(double dp[], double mu, double uu); |
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[ae3ce4e] | 69 | |
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| 70 | /////////functions for WRC implementation of flexible cylinders |
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[34c2649] | 71 | static double |
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| 72 | gammaln(double xx) |
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| 73 | { |
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| 74 | double x,y,tmp,ser; |
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| 75 | static double cof[6]={76.18009172947146,-86.50532032941677, |
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| 76 | 24.01409824083091,-1.231739572450155, |
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| 77 | 0.1208650973866179e-2,-0.5395239384953e-5}; |
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| 78 | int j; |
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| 79 | |
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| 80 | y=x=xx; |
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| 81 | tmp=x+5.5; |
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| 82 | tmp -= (x+0.5)*log(tmp); |
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| 83 | ser=1.000000000190015; |
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| 84 | for (j=0;j<=5;j++) ser += cof[j]/++y; |
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| 85 | return -tmp+log(2.5066282746310005*ser/x); |
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| 86 | } |
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| 87 | |
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| 88 | // |
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| 89 | static double |
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| 90 | AlphaSquare(double x) |
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| 91 | { |
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| 92 | double yy; |
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| 93 | yy = pow( (1.0 + (x/3.12)*(x/3.12) + (x/8.67)*(x/8.67)*(x/8.67)),(0.176/3.0) ); |
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| 94 | |
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| 95 | return (yy); |
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| 96 | } |
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| 97 | |
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| 98 | // |
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| 99 | static double |
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| 100 | Rgsquarezero(double q, double L, double b) |
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| 101 | { |
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| 102 | double yy; |
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| 103 | yy = (L*b/6.0) * (1.0 - 1.5*(b/L) + 1.5*pow((b/L),2) - 0.75*pow((b/L),3)*(1.0 - exp(-2.0*(L/b)))); |
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| 104 | |
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| 105 | return (yy); |
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| 106 | } |
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| 107 | |
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| 108 | // |
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| 109 | static double |
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| 110 | Rgsquareshort(double q, double L, double b) |
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| 111 | { |
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| 112 | double yy; |
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| 113 | yy = AlphaSquare(L/b) * Rgsquarezero(q,L,b); |
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| 114 | |
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| 115 | return (yy); |
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| 116 | } |
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| 117 | |
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| 118 | // |
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| 119 | static double |
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| 120 | Rgsquare(double q, double L, double b) |
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| 121 | { |
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| 122 | double yy; |
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| 123 | yy = AlphaSquare(L/b)*L*b/6.0; |
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| 124 | |
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| 125 | return (yy); |
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| 126 | } |
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| 127 | |
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| 128 | // ?? funciton is not used - but should the log actually be log10??? |
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| 129 | static double |
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| 130 | miu(double x) |
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| 131 | { |
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| 132 | double yy; |
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| 133 | yy = (1.0/8.0)*(9.0*x - 2.0 + 2.0*log(1.0 + x)/x)*exp(1.0/2.565*(1.0/x + (1.0 - 1.0/(x*x))*log(1.0 + x))); |
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| 134 | |
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| 135 | return (yy); |
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| 136 | } |
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| 137 | |
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| 138 | //WR named this w (too generic) |
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| 139 | static double |
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| 140 | w_WR(double x) |
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| 141 | { |
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| 142 | double yy; |
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| 143 | yy = 0.5*(1 + tanh((x - 1.523)/0.1477)); |
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| 144 | |
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| 145 | return (yy); |
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| 146 | } |
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| 147 | |
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| 148 | // |
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| 149 | static double |
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| 150 | u1(double q, double L, double b) |
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| 151 | { |
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| 152 | double yy; |
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| 153 | |
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| 154 | yy = Rgsquareshort(q,L,b)*q*q; |
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| 155 | |
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| 156 | return (yy); |
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| 157 | } |
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| 158 | |
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| 159 | // was named u |
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| 160 | static double |
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| 161 | u_WR(double q, double L, double b) |
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| 162 | { |
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| 163 | double yy; |
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| 164 | yy = Rgsquare(q,L,b)*q*q; |
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| 165 | return (yy); |
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| 166 | } |
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| 167 | |
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| 168 | |
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| 169 | // |
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| 170 | static double |
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| 171 | Sdebye1(double q, double L, double b) |
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| 172 | { |
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| 173 | double yy; |
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| 174 | yy = 2.0*(exp(-u1(q,L,b)) + u1(q,L,b) -1.0)/( pow((u1(q,L,b)),2.0) ); |
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| 175 | |
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| 176 | return (yy); |
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| 177 | } |
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| 178 | |
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| 179 | |
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| 180 | // |
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| 181 | static double |
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| 182 | Sdebye(double q, double L, double b) |
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| 183 | { |
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| 184 | double yy; |
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| 185 | yy = 2.0*(exp(-u_WR(q,L,b)) + u_WR(q,L,b) -1.0)/(pow((u_WR(q,L,b)),2)); |
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| 186 | |
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| 187 | return (yy); |
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| 188 | } |
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| 189 | |
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| 190 | // |
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| 191 | static double |
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| 192 | Sexv(double q, double L, double b) |
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| 193 | { |
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| 194 | double yy,C1,C2,C3,miu,Rg2; |
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| 195 | C1=1.22; |
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| 196 | C2=0.4288; |
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| 197 | C3=-1.651; |
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| 198 | miu = 0.585; |
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| 199 | |
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| 200 | Rg2 = Rgsquare(q,L,b); |
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| 201 | |
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| 202 | yy = (1.0 - w_WR(q*sqrt(Rg2)))*Sdebye(q,L,b) + w_WR(q*sqrt(Rg2))*(C1*pow((q*sqrt(Rg2)),(-1.0/miu)) + C2*pow((q*sqrt(Rg2)),(-2.0/miu)) + C3*pow((q*sqrt(Rg2)),(-3.0/miu))); |
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| 203 | |
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| 204 | return (yy); |
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| 205 | } |
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| 206 | |
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| 207 | // this must be WR modified version |
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| 208 | static double |
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| 209 | Sexvnew(double q, double L, double b) |
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| 210 | { |
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| 211 | double yy,C1,C2,C3,miu; |
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| 212 | double del=1.05,C_star2,Rg2; |
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| 213 | |
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| 214 | C1=1.22; |
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| 215 | C2=0.4288; |
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| 216 | C3=-1.651; |
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| 217 | miu = 0.585; |
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| 218 | |
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| 219 | //calculating the derivative to decide on the corection (cutoff) term? |
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| 220 | // I have modified this from WRs original code |
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| 221 | |
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| 222 | if( (Sexv(q*del,L,b)-Sexv(q,L,b))/(q*del - q) >= 0.0 ) { |
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| 223 | C_star2 = 0.0; |
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| 224 | } else { |
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| 225 | C_star2 = 1.0; |
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| 226 | } |
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| 227 | |
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| 228 | Rg2 = Rgsquare(q,L,b); |
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| 229 | |
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| 230 | yy = (1.0 - w_WR(q*sqrt(Rg2)))*Sdebye(q,L,b) + C_star2*w_WR(q*sqrt(Rg2))*(C1*pow((q*sqrt(Rg2)),(-1.0/miu)) + C2*pow((q*sqrt(Rg2)),(-2.0/miu)) + C3*pow((q*sqrt(Rg2)),(-3.0/miu))); |
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| 231 | |
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| 232 | return (yy); |
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| 233 | } |
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| 234 | |
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| 235 | // these are the messy ones |
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| 236 | static double |
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| 237 | a2short(double q, double L, double b, double p1short, double p2short, double q0) |
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| 238 | { |
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| 239 | double yy,Rg2_sh; |
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| 240 | double t1,E,Rg2_sh2,Et1,Emt1,q02,q0p; |
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| 241 | double pi; |
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| 242 | |
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| 243 | E = 2.718281828459045091; |
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| 244 | pi = 4.0*atan(1.0); |
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| 245 | Rg2_sh = Rgsquareshort(q,L,b); |
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| 246 | Rg2_sh2 = Rg2_sh*Rg2_sh; |
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| 247 | t1 = ((q0*q0*Rg2_sh)/(b*b)); |
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| 248 | Et1 = pow(E,t1); |
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| 249 | Emt1 =pow(E,-t1); |
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| 250 | q02 = q0*q0; |
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| 251 | q0p = pow(q0,(-4.0 + p2short) ); |
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| 252 | |
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| 253 | //E is the number e |
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| 254 | yy = ((-(1.0/(L*((p1short - p2short))*Rg2_sh2)*((b*Emt1*q0p*((8.0*b*b*b*L - 8.0*b*b*b*Et1*L - 2.0*b*b*b*L*p1short + 2.0*b*b*b*Et1*L*p1short + 4.0*b*L*q02*Rg2_sh + 4.0*b*Et1*L*q02*Rg2_sh - 2.0*b*Et1*L*p1short*q02*Rg2_sh - Et1*pi*q02*q0*Rg2_sh2 + Et1*p1short*pi*q02*q0*Rg2_sh2))))))); |
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| 255 | |
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| 256 | return (yy); |
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| 257 | } |
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| 258 | |
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| 259 | // |
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| 260 | static double |
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| 261 | a1short(double q, double L, double b, double p1short, double p2short, double q0) |
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| 262 | { |
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| 263 | double yy,Rg2_sh; |
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| 264 | double t1,E,Rg2_sh2,Et1,Emt1,q02,q0p,b3; |
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| 265 | double pi; |
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| 266 | |
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| 267 | E = 2.718281828459045091; |
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| 268 | pi = 4.0*atan(1.0); |
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| 269 | Rg2_sh = Rgsquareshort(q,L,b); |
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| 270 | Rg2_sh2 = Rg2_sh*Rg2_sh; |
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| 271 | b3 = b*b*b; |
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| 272 | t1 = ((q0*q0*Rg2_sh)/(b*b)); |
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| 273 | Et1 = pow(E,t1); |
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| 274 | Emt1 =pow(E,-t1); |
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| 275 | q02 = q0*q0; |
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| 276 | q0p = pow(q0,(-4.0 + p1short) ); |
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| 277 | |
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| 278 | yy = ((1.0/(L*((p1short - p2short))*Rg2_sh2)*((b*Emt1*q0p*((8.0*b3*L - 8.0*b3*Et1*L - 2.0*b3*L*p2short + 2.0*b3*Et1*L*p2short + 4.0*b*L*q02*Rg2_sh + 4.0*b*Et1*L*q02*Rg2_sh - 2.0*b*Et1*L*p2short*q02*Rg2_sh - Et1*pi*q02*q0*Rg2_sh2 + Et1*p2short*pi*q02*q0*Rg2_sh2)))))); |
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| 279 | |
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| 280 | return(yy); |
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| 281 | } |
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| 282 | |
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| 283 | |
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| 284 | //need to define this on my own |
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| 285 | static double |
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| 286 | sech_WR(double x) |
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| 287 | { |
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| 288 | return(1/cosh(x)); |
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| 289 | } |
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| 290 | |
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| 291 | // this one will be lots of trouble |
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| 292 | static double |
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| 293 | a2long(double q, double L, double b, double p1, double p2, double q0) |
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| 294 | { |
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| 295 | double yy,C1,C2,C3,C4,C5,miu,C,Rg2; |
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| 296 | double t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,pi; |
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| 297 | double E,b2,b3,b4,q02,q03,q04,q05,Rg22; |
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| 298 | |
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| 299 | pi = 4.0*atan(1.0); |
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| 300 | E = 2.718281828459045091; |
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| 301 | if( L/b > 10.0) { |
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| 302 | C = 3.06/pow((L/b),0.44); |
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| 303 | } else { |
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| 304 | C = 1.0; |
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| 305 | } |
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| 306 | |
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| 307 | C1 = 1.22; |
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| 308 | C2 = 0.4288; |
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| 309 | C3 = -1.651; |
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| 310 | C4 = 1.523; |
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| 311 | C5 = 0.1477; |
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| 312 | miu = 0.585; |
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| 313 | |
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| 314 | Rg2 = Rgsquare(q,L,b); |
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| 315 | Rg22 = Rg2*Rg2; |
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| 316 | b2 = b*b; |
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| 317 | b3 = b*b*b; |
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| 318 | b4 = b3*b; |
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| 319 | q02 = q0*q0; |
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| 320 | q03 = q0*q0*q0; |
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| 321 | q04 = q03*q0; |
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| 322 | q05 = q04*q0; |
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| 323 | |
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| 324 | t1 = (1.0/(b* p1*pow(q0,((-1.0) - p1 - p2)) - b*p2*pow(q0,((-1.0) - p1 - p2)) )); |
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| 325 | |
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| 326 | t2 = (b*C*(((-1.0*((14.0*b3)/(15.0*q03*Rg2))) + (14.0*b3*pow(E,(-((q02*Rg2)/b2))))/(15.0*q03*Rg2) + (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*((11.0/15.0 + (7*b2)/(15.0*q02*Rg2)))*Rg2)/b)))/L; |
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| 327 | |
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| 328 | t3 = (sqrt(Rg2)*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2.0))/(2.0*C5); |
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| 329 | |
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| 330 | t4 = (b4*sqrt(Rg2)*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2))/(C5*q04*Rg22); |
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| 331 | |
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| 332 | t5 = (2.0*b4*(((2.0*q0*Rg2)/b - (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*Rg2)/b))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q04*Rg22); |
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| 333 | |
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| 334 | t6 = (8.0*b4*b*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q05*Rg22); |
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| 335 | |
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| 336 | t7 = (((-((3.0*C3*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 3.0/miu)))/miu)) - (2.0*C2*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 2.0/miu)))/miu - (C1*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 1.0/miu)))/miu)); |
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| 337 | |
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| 338 | t8 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))); |
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| 339 | |
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| 340 | t9 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15*q02*Rg2))) + (7.0*b2)/(15.0*q02*Rg2))))/L; |
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| 341 | |
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| 342 | t10 = (2.0*b4*(((-1) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))/(q04*Rg22); |
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| 343 | |
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| 344 | |
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| 345 | yy = ((-1.0*(t1* ((-pow(q0,-p1)*(((b2*pi)/(L*q02) + t2 + t3 - t4 + t5 - t6 + 1.0/2.0*t7*t8)) - b*p1*pow(q0,((-1.0) - p1))*(((-((b*pi)/(L*q0))) + t9 + t10 + 1.0/2.0*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))))))); |
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| 346 | |
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| 347 | return (yy); |
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| 348 | } |
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| 349 | // |
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| 350 | static double |
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| 351 | a1long(double q, double L, double b, double p1, double p2, double q0) |
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| 352 | { |
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| 353 | double yy,C,C1,C2,C3,C4,C5,miu,Rg2; |
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| 354 | double t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15; |
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| 355 | double E,pi; |
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| 356 | double b2,b3,b4,q02,q03,q04,q05,Rg22; |
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| 357 | |
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| 358 | pi = 4.0*atan(1.0); |
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| 359 | E = 2.718281828459045091; |
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| 360 | |
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| 361 | if( L/b > 10.0) { |
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| 362 | C = 3.06/pow((L/b),0.44); |
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| 363 | } else { |
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| 364 | C = 1.0; |
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| 365 | } |
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| 366 | |
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| 367 | C1 = 1.22; |
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| 368 | C2 = 0.4288; |
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| 369 | C3 = -1.651; |
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| 370 | C4 = 1.523; |
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| 371 | C5 = 0.1477; |
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| 372 | miu = 0.585; |
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| 373 | |
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| 374 | Rg2 = Rgsquare(q,L,b); |
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| 375 | Rg22 = Rg2*Rg2; |
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| 376 | b2 = b*b; |
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| 377 | b3 = b*b*b; |
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| 378 | b4 = b3*b; |
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| 379 | q02 = q0*q0; |
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| 380 | q03 = q0*q0*q0; |
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| 381 | q04 = q03*q0; |
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| 382 | q05 = q04*q0; |
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| 383 | |
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| 384 | t1 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15.0*q02*Rg2))) + (7.0*b2)/(15.0*q02*Rg2)))); |
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| 385 | |
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| 386 | t2 = (2.0*b4*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))); |
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| 387 | |
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| 388 | t3 = ((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu)))); |
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| 389 | |
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| 390 | t4 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))); |
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| 391 | |
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| 392 | t5 = (1.0/(b*p1*pow(q0,((-1.0) - p1 - p2)) - b*p2*pow(q0,((-1.0) - p1 - p2)))); |
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| 393 | |
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| 394 | t6 = (b*C*(((-((14.0*b3)/(15.0*q03*Rg2))) + (14.0*b3*pow(E,(-((q02*Rg2)/b2))))/(15.0*q03*Rg2) + (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*((11.0/15.0 + (7.0*b2)/(15.0*q02*Rg2)))*Rg2)/b))); |
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| 395 | |
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| 396 | t7 = (sqrt(Rg2)*((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu))))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2)); |
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| 397 | |
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| 398 | t8 = (b4*sqrt(Rg2)*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*pow(sech_WR(((-C4) + (sqrt(Rg2)*q0)/b)/C5),2)); |
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| 399 | |
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| 400 | t9 = (2.0*b4*(((2.0*q0*Rg2)/b - (2.0*pow(E,(-((q02*Rg2)/b2)))*q0*Rg2)/b))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))); |
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| 401 | |
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| 402 | t10 = (8.0*b4*b*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))); |
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| 403 | |
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| 404 | t11 = (((-((3.0*C3*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 3.0/miu)))/miu)) - (2.0*C2*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 2.0/miu)))/miu - (C1*sqrt(Rg2)*pow((((sqrt(Rg2)*q0)/b)),((-1.0) - 1.0/miu)))/miu)); |
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| 405 | |
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| 406 | t12 = ((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))); |
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| 407 | |
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| 408 | t13 = (b*C*((4.0/15.0 - pow(E,(-((q02*Rg2)/b2)))*((11.0/15.0 + (7.0*b2)/(15.0*q02* Rg2))) + (7.0*b2)/(15.0*q02*Rg2)))); |
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| 409 | |
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| 410 | t14 = (2.0*b4*(((-1.0) + pow(E,(-((q02*Rg2)/b2))) + (q02*Rg2)/b2))*((1.0 + 1.0/2.0*(((-1.0) - tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5)))))); |
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| 411 | |
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| 412 | t15 = ((C3*pow((((sqrt(Rg2)*q0)/b)),((-3.0)/miu)) + C2*pow((((sqrt(Rg2)*q0)/b)),((-2.0)/miu)) + C1*pow((((sqrt(Rg2)*q0)/b)),((-1.0)/miu)))); |
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| 413 | |
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| 414 | |
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| 415 | yy = (pow(q0,p1)*(((-((b*pi)/(L*q0))) +t1/L +t2/(q04*Rg22) + 1.0/2.0*t3*t4)) + (t5*((pow(q0,(p1 - p2))*(((-pow(q0,(-p1)))*(((b2*pi)/(L*q02) +t6/L +t7/(2.0*C5) -t8/(C5*q04*Rg22) +t9/(q04*Rg22) -t10/(q05*Rg22) + 1.0/2.0*t11*t12)) - b*p1*pow(q0,((-1.0) - p1))*(((-((b*pi)/(L*q0))) +t13/L +t14/(q04*Rg22) + 1.0/2.0*t15*((1.0 + tanh(((-C4) + (sqrt(Rg2)*q0)/b)/C5))))))))))); |
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| 416 | |
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| 417 | return (yy); |
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| 418 | } |
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| 419 | |
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| 420 | |
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| 421 | static double |
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| 422 | Sk_WR(double q, double L, double b) |
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| 423 | { |
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| 424 | // |
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| 425 | double p1,p2,p1short,p2short,q0; |
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| 426 | double C,ans,q0short,Sexvmodify,pi; |
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| 427 | |
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| 428 | pi = 4.0*atan(1.0); |
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| 429 | |
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| 430 | p1 = 4.12; |
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| 431 | p2 = 4.42; |
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| 432 | p1short = 5.36; |
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| 433 | p2short = 5.62; |
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| 434 | q0 = 3.1; |
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| 435 | // |
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| 436 | q0short = fmax(1.9/sqrt(Rgsquareshort(q,L,b)),3.0); |
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| 437 | |
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| 438 | // |
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| 439 | if(L/b > 10.0) { |
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| 440 | C = 3.06/pow((L/b),0.44); |
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| 441 | } else { |
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| 442 | C = 1.0; |
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| 443 | } |
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| 444 | // |
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| 445 | |
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| 446 | if( L > 4*b ) { // Longer Chains |
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| 447 | if (q*b <= 3.1) { //Modified by Yun on Oct. 15, |
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| 448 | Sexvmodify = Sexvnew(q, L, b); |
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| 449 | ans = Sexvmodify + C * (4.0/15.0 + 7.0/(15.0*u_WR(q,L,b)) - (11.0/15.0 + 7.0/(15.0*u_WR(q,L,b)))*exp(-u_WR(q,L,b)))*(b/L); |
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| 450 | } else { //q(i)*b > 3.1 |
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| 451 | ans = a1long(q, L, b, p1, p2, q0)/(pow((q*b),p1)) + a2long(q, L, b, p1, p2, q0)/(pow((q*b),p2)) + pi/(q*L); |
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| 452 | } |
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| 453 | } else { //L <= 4*b Shorter Chains |
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| 454 | if (q*b <= fmax(1.9/sqrt(Rgsquareshort(q,L,b)),3.0) ) { |
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| 455 | if (q*b<=0.01) { |
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| 456 | ans = 1.0 - Rgsquareshort(q,L,b)*(q*q)/3.0; |
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| 457 | } else { |
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| 458 | ans = Sdebye1(q,L,b); |
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| 459 | } |
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| 460 | } else { //q*b > max(1.9/sqrt(Rgsquareshort(q(i),L,b)),3) |
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| 461 | ans = a1short(q,L,b,p1short,p2short,q0short)/(pow((q*b),p1short)) + a2short(q,L,b,p1short,p2short,q0short)/(pow((q*b),p2short)) + pi/(q*L); |
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| 462 | } |
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| 463 | } |
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| 464 | |
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| 465 | return(ans); |
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| 466 | //return(a2long(q, L, b, p1, p2, q0)); |
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| 467 | } |
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| 468 | |
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