Changeset 01c8d9e in sasmodels for sasmodels/models/ellipsoid.c

Timestamp:

Aug 7, 2018 12:32:18 PM (6 years ago)

Author:

Suczewski <ges3@…>

Branches:

master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

c11d09f

Parents:

707cbdb

Message:

beta approximation, first pass

File:

• sasmodels/models/ellipsoid.c (modified) (2 diffs)

sasmodels/models/ellipsoid.c

@@ -20 +20 @@
     //     i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du
     const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0;
-
+  
     // translate a point in [-1,1] to a point in [0, 1]
     // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2;
@@ -36 +36 @@
     const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial);
     return 1.0e-4 * s * s * form;
+} 
+
+static void
+Fq(double q,
+    double *F1,
+    double *F2,
+    double sld,
+    double sld_solvent,
+    double radius_polar,
+    double radius_equatorial)
+{
+    // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955)
+    //     i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT
+    //          = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT
+    //          = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT
+    // u-substitution of
+    //     u = sin, du = cos dT
+    //     i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du
+    const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0;
+    // translate a point in [-1,1] to a point in [0, 1]
+    // const double u = GAUSS_Z[i]*(upper-lower)/2 + (upper+lower)/2;
+    const double zm = 0.5;
+    const double zb = 0.5;
+    double total_F2 = 0.0;
+    double total_F1 = 0.0;
+    for (int i=0;i<GAUSS_N;i++) {
+        const double u = GAUSS_Z[i]*zm + zb;
+        const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one);
+        const double f = sas_3j1x_x(q*r);
+        total_F2 += GAUSS_W[i] * f * f;
+        total_F1 += GAUSS_W[i] * f;
+    }
+    // translate dx in [-1,1] to dx in [lower,upper]
+    const double form_squared_avg = total_F2*zm;
+    const double form_avg = total_F1*zm;
+    const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial);
+    *F2 = 1e-4 * s * s * form_squared_avg;
+    *F1 = 1e-2 * s * form_avg;
 }
+
+
+
+
+
 
 static double