Merge pull request #687 from SasView/adding_trOh_model_pythonC

Adding truncated octahedron model (python and c)

Author: sara-mokhtari

sasmodels/models/img/octa-truncated.png

@@ -0,0 +1,249 @@
+#include <math.h>
+#include <stdio.h> 
+
+//truncated octahedron volume 
+// NOTE: needs to be called form_volume() for a shape category
+static double
+form_volume(double length_a, double b2a_ratio, double c2a_ratio, double t)
+{
+// length_a is the half height along the a axis of the octahedron without truncature
+// length_b is the half height along the b axis of the octahedron without truncature
+// length_c is the half height along the c axis of the octahedron without truncature
+// b2a_ratio is length_b divided by Length_a
+// c2a_ratio is Length_c divided by Length_a
+// t varies from 0.5 (cuboctahedron) to 1 (octahedron)
+    return (4./3.) * cube(length_a) * b2a_ratio * c2a_ratio *(1.-3*cube(1.-t));
+}
+
+// remark: Iq() is generally not used because have_Fq is set to True in the Python file
+static double
+Iq(double q,
+    double sld,
+    double solvent_sld,
+    double length_a,
+    double b2a_ratio,
+    double c2a_ratio,
+    double t)
+{
+    const double length_b = length_a * b2a_ratio;
+    const double length_c = length_a * c2a_ratio;
+
+
+   //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 = 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);
+
+        double inner_sum = 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);
+
+            //HERE: Octahedron formula
+            // q is the modulus of the scattering vector in [A-1]
+            // NOTE: capital QX QY QZ are the three components in [A-1] of the scattering vector
+            // NOTE: qx qy qz are rescaled components (no unit) for computing AA, BB and CC terms
+            const double Qx = q * sin_theta * cos_phi;
+    	    const double Qy = q * sin_theta * sin_phi;
+    	    const double Qz = q * cos_theta;
+    	    const double qx = Qx * length_a;
+    	    const double qy = Qy * length_b;
+    	    const double qz = Qz * length_c;
+
+            const double AA = 1./((qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qx)*sin(qy*(1.-t)-qx*t)+(qy+qx)*sin(qy*(1.-t)+qx*t))+
+                                1./((qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qx)*sin(qz*(1.-t)-qx*t)+(qz+qx)*sin(qz*(1.-t)+qx*t));
+
+            const double BB = 1./((qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qy)*sin(qz*(1.-t)-qy*t)+(qz+qy)*sin(qz*(1.-t)+qy*t))+
+                                1./((qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qy)*sin(qx*(1.-t)-qy*t)+(qx+qy)*sin(qx*(1.-t)+qy*t));
+
+            const double CC = 1./((qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qz)*sin(qx*(1.-t)-qz*t)+(qx+qz)*sin(qx*(1.-t)+qz*t))+
+                                1./((qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qz)*sin(qy*(1.-t)-qz*t)+(qy+qz)*sin(qy*(1.-t)+qz*t));
+
+
+	    // normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
+            const double AP = 6./(1.-3*(1.-t)*(1.-t)*(1.-t))*(AA+BB+CC);
+
+            inner_sum += GAUSS_W[j] * AP * AP;
+
+
+        }
+        inner_sum = 0.5 * (v2b-v2a) * inner_sum;
+        outer_sum += GAUSS_W[i] * inner_sum * sin_theta;
+    }
+
+    double answer = 0.5*(v1b-v1a)*outer_sum;
+
+    // The factor 2 appears because the theta integral has been defined between
+    // 0 and pi/2, instead of 0 to pi.
+    answer /= M_PI_2; //Form factor P(q)
+
+    // Multiply by contrast^2 and volume^2
+    // contrast
+    const double s = (sld-solvent_sld);
+    // volume
+    // s *= form_volume(length_a, b2a_ratio,c2a_ratio, t);
+    answer *= square(s*form_volume(length_a, b2a_ratio,c2a_ratio, t));
+
+    // Convert from [1e-12 A-1] to [cm-1]
+    answer *= 1.0e-4;
+
+	if (isnan(answer) || isinf(answer)) {
+        return 0.0;
+    }
+
+    return answer;
+}
+
+// Fq() is called because option "have_Fq = True" is set to True in the Python file
+static void
+Fq(double q,
+    double *F1,
+    double *F2,
+    double sld,
+    double solvent_sld,
+    double length_a,
+    double b2a_ratio,
+    double c2a_ratio,
+    double t)
+{
+    const double length_b = length_a * b2a_ratio;
+    const double length_c = length_a * c2a_ratio;
+
+
+   //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);
+
+        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);
+
+            //HERE: Octahedron formula
+            // q is the modulus of the scattering vector in [A-1]
+            // NOTE: capital QX QY QZ are the three components in [A-1] of the scattering vector
+            // NOTE: qx qy qz are rescaled components (no unit) for computing AA, BB and CC terms
+            const double Qx = q * sin_theta * cos_phi;
+    	    const double Qy = q * sin_theta * sin_phi;
+    	    const double Qz = q * cos_theta;
+    	    const double qx = Qx * length_a;
+    	    const double qy = Qy * length_b;
+    	    const double qz = Qz * length_c;
+            const double AA = 1./(2*(qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qx)*sin(qy*(1.-t)-qx*t)+(qy+qx)*sin(qy*(1.-t)+qx*t))+
+                                1./(2*(qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qx)*sin(qz*(1.-t)-qx*t)+(qz+qx)*sin(qz*(1.-t)+qx*t));
+
+            const double BB = 1./(2*(qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qy)*sin(qz*(1.-t)-qy*t)+(qz+qy)*sin(qz*(1.-t)+qy*t))+
+                                1./(2*(qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qy)*sin(qx*(1.-t)-qy*t)+(qx+qy)*sin(qx*(1.-t)+qy*t));
+
+            const double CC = 1./(2*(qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qz)*sin(qx*(1.-t)-qz*t)+(qx+qz)*sin(qx*(1.-t)+qz*t))+
+                                1./(2*(qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qz)*sin(qy*(1.-t)-qz*t)+(qy+qz)*sin(qy*(1.-t)+qz*t));
+
+	    // normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
+            const double AP = 6./(1.-3*(1.-t)*(1.-t)*(1.-t))*(AA+BB+CC);
+
+
+            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);
+
+    // 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
+    // contrast
+    const double s = (sld-solvent_sld);
+    // volume
+    // s *= form_volume(length_a, b2a_ratio,c2a_ratio, t);
+	
+    // Convert from [1e-12 A-1] to [cm-1]
+    *F1 = 1e-2 * s * form_volume(length_a, b2a_ratio,c2a_ratio, t) * outer_sum_F1;
+    *F2 = 1e-4 * square(s * form_volume(length_a, b2a_ratio,c2a_ratio, t)) * outer_sum_F2;
+
+    if (isnan(*F1) || isinf(*F1)) {
+        *F1 = 0.0;
+    }
+    if (isnan(*F2) || isinf(*F2)) {
+        *F2 = 0.0;
+    }
+}
+
+
+static double
+Iqabc(double qa, double qb, double qc,
+    double sld,
+    double solvent_sld,
+    double length_a,
+    double b2a_ratio,
+    double c2a_ratio,
+    double t)
+{
+    const double length_b = length_a * b2a_ratio;
+    const double length_c = length_a * c2a_ratio;
+
+
+    //HERE: Octahedron formula
+    // NOTE: qa qb qc are the three components in [A-1] of the scattering vector
+    // NOTE: qx qy qz are rescaled components (no unit) for computing AA, BB and CC terms
+    const double qx = qa * length_a;
+    const double qy = qb * length_b;
+    const double qz = qc * length_c;
+    const double AA = 1./(2*(qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qx)*sin(qy*(1.-t)-qx*t)+(qy+qx)*sin(qy*(1.-t)+qx*t))+
+                                1./(2*(qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qx)*sin(qz*(1.-t)-qx*t)+(qz+qx)*sin(qz*(1.-t)+qx*t));
+
+    const double BB = 1./(2*(qz*qz-qx*qx)*(qz*qz-qy*qy))*((qz-qy)*sin(qz*(1.-t)-qy*t)+(qz+qy)*sin(qz*(1.-t)+qy*t))+
+                                1./(2*(qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qy)*sin(qx*(1.-t)-qy*t)+(qx+qy)*sin(qx*(1.-t)+qy*t));
+
+    const double CC = 1./(2*(qx*qx-qy*qy)*(qx*qx-qz*qz))*((qx-qz)*sin(qx*(1.-t)-qz*t)+(qx+qz)*sin(qx*(1.-t)+qz*t))+
+                                1./(2*(qy*qy-qz*qz)*(qy*qy-qx*qx))*((qy-qz)*sin(qy*(1.-t)-qz*t)+(qy+qz)*sin(qy*(1.-t)+qz*t));
+
+	    // normalisation to 1. of AP at q = 0. Division by a Factor 4/3.
+    const double AP = 6./(1.-3*(1.-t)*(1.-t)*(1.-t))*(AA+BB+CC);
+
+    // Multiply by contrast and volume
+    // contrast
+    const double s = (sld-solvent_sld);
+    // volume
+    // s *= form_volume(length_a, b2a_ratio,c2a_ratio, t);
+
+    // Convert from [1e-12 A-1] to [cm-1]
+    double answer = 1.0e-4 * square(s * form_volume(length_a, b2a_ratio,c2a_ratio, t) * AP);
+    if (isnan(answer) || isinf(answer)) {
+        return 0.0;
+    }
+
+    return answer;
+}
+
+
+