Changeset 86aa992 in sasmodels for sasmodels/models/rectangular_prism.c

Timestamp:

Aug 14, 2018 12:09:49 PM (6 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

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

Children:

6d90684

Parents:

71b751d (diff), d089a00 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.

Message:

Merge branch 'master' into beta_approx

File:

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

sasmodels/models/rectangular_prism.c

@@ -68 +68 @@
 }
 
+static void
+Fq(double q,
+    double *F1,
+    double *F2,
+    double sld,
+    double solvent_sld,
+    double length_a,
+    double b2a_ratio,
+    double c2a_ratio)
+{
+    const double length_b = length_a * b2a_ratio;
+    const double length_c = length_a * c2a_ratio;
+    const double a_half = 0.5 * length_a;
+    const double b_half = 0.5 * length_b;
+    const double c_half = 0.5 * length_c;
+
+   //Integration limits to use in Gaussian quadrature
+    const double v1a = 0.0;
+    const double v1b = M_PI_2;  //theta integration limits
+    const double v2a = 0.0;
+    const double v2b = M_PI_2;  //phi integration limits
+
+    double outer_sum_F1 = 0.0;
+    double outer_sum_F2 = 0.0;
+    for(int i=0; i<GAUSS_N; i++) {
+        const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b );
+        double sin_theta, cos_theta;
+        SINCOS(theta, sin_theta, cos_theta);
+
+        const double termC = sas_sinx_x(q * c_half * cos_theta);
+
+        double inner_sum_F1 = 0.0;
+        double inner_sum_F2 = 0.0;
+        for(int j=0; j<GAUSS_N; j++) {
+            double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b );
+            double sin_phi, cos_phi;
+            SINCOS(phi, sin_phi, cos_phi);
+
+            // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0
+            const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi);
+            const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi);
+            const double AP = termA * termB * termC;
+            inner_sum_F1 += GAUSS_W[j] * AP;
+            inner_sum_F2 += GAUSS_W[j] * AP * AP;
+        }
+        inner_sum_F1 = 0.5 * (v2b-v2a) * inner_sum_F1;
+        inner_sum_F2 = 0.5 * (v2b-v2a) * inner_sum_F2;
+        outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta;
+        outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta;
+    }
+
+    outer_sum_F1 *= 0.5*(v1b-v1a);
+    outer_sum_F2 *= 0.5*(v1b-v1a);
+
+    // Normalize by Pi (Eqn. 16).
+    // The term (ABC)^2 does not appear because it was introduced before on
+    // the definitions of termA, termB, termC.
+    // The factor 2 appears because the theta integral has been defined between
+    // 0 and pi/2, instead of 0 to pi.
+    outer_sum_F1 /= M_PI_2;
+    outer_sum_F2 /= M_PI_2;
+
+    // Multiply by contrast and volume
+    const double s = (sld-solvent_sld) * (length_a * length_b * length_c);
+
+    // Convert from [1e-12 A-1] to [cm-1]
+    *F1 = 1e-2 * s * outer_sum_F1;
+    *F2 = 1e-4 * s * s * outer_sum_F2;
+}
+
 
 static double
@@ -82 +152 @@
     const double b_half = 0.5 * length_b;
     const double c_half = 0.5 * length_c;
-    const double volume = length_a * length_b * length_c;
 
     // Amplitude AP from eqn. (13)
-
     const double termA = sas_sinx_x(qa * a_half);
     const double termB = sas_sinx_x(qb * b_half);
     const double termC = sas_sinx_x(qc * c_half);
-
     const double AP = termA * termB * termC;
 
-    // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization.
-    const double delrho = sld - solvent_sld;
+    // Multiply by contrast and volume
+    const double s = (sld-solvent_sld) * (length_a * length_b * length_c);
 
     // Convert from [1e-12 A-1] to [cm-1]
-    return 1.0e-4 * square(volume * delrho * AP);
+    return 1.0e-4 * square(s * AP);
 }