Index: explore/beta/HSS_SQ.m
===================================================================
--- explore/beta/HSS_SQ.m	(revision e262dd68f6ba42ac365c68553db9621443f502ee)
+++ explore/beta/HSS_SQ.m	(revision e262dd68f6ba42ac365c68553db9621443f502ee)
@@ -0,0 +1,13 @@
+function Sq=HSS_SQ(volF,Q)
+%Sq=HSS_SQ(volF,Q), Q is a normalzied scattering wavevector by the diamter of the particle
+
+a1=-(1+2*volF)^2/(1-volF)^4;
+a2=6*volF*(1+0.5*volF)^2/(1-volF)^4;
+a3=volF*a1/2;
+%pi = 3.14159265358979;
+
+cq=4*pi*(a1./Q.^3 .* (sin(Q)-Q.*cos(Q)) + ...
+    a2./Q.^4 .* (2*Q.*sin(Q)- (Q.^2 - 2) .* cos(Q) - 2) + ...
+    a3./Q.^6 .* ((4*Q.^3 - 24 * Q) .* sin(Q) - (Q.^4 -12 * Q.^2 + 24) .* cos(Q) + 24) );
+
+Sq = 1 ./ (1 - cq * volF * 6 / pi);
Index: explore/beta/data_files/richard_test.txt
===================================================================
--- explore/beta/data_files/richard_test.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,1002 @@
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+
Index: explore/beta/data_files/richard_test2.txt
===================================================================
--- explore/beta/data_files/richard_test2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,1002 @@
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+
Index: explore/beta/data_files/richard_test3.txt
===================================================================
--- explore/beta/data_files/richard_test3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,1002 @@
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+1;287868;-1;0;
+
Index: explore/beta/data_files/richard_test4.txt
===================================================================
--- explore/beta/data_files/richard_test4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;100896;-1;0;
+
Index: explore/beta/data_files/richard_test5.txt
===================================================================
--- explore/beta/data_files/richard_test5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;102018;-1;0;
+
Index: explore/beta/data_files/richard_test6.txt
===================================================================
--- explore/beta/data_files/richard_test6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/richard_test6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.001;6.56235e+007;-1;0;
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+1;100906;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,102 @@
+0.01;6.3534e+008;-1;0;
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+1;100894;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD2.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;119279;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD3.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;6.85253e+008;-1;0;
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+1;102583;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD4.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD5.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;8.91223e+008;-1;0;
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+1;111639;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQD6.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQD6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQD6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;136591;-1;0;
+
Index: explore/beta/data_files/sasfit_ellipsoid_IQM.txt
===================================================================
--- explore/beta/data_files/sasfit_ellipsoid_IQM.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_ellipsoid_IQM.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;6.29133e+008;-1;0;
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+0.954993;170388;-1;0;
+0.977237;133341;-1;0;
+1;101365;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.0032;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq2.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00386;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq3.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00017;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq4.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.01111;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq5.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.01317;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq6.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00154;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq7.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq7.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq7.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.10903;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq8.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq8.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq8.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.12387;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq9.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq9.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sq9.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.03939;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+0.977237;1.00027;-1;0;
+1;1.00003;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff2.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff2.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00008;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff3.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff3.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+0.954993;1.00077;-1;0;
+0.977237;1.00031;-1;0;
+1;1.00001;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff4.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff4.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00009;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff5.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff5.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00027;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff6.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff6.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00005;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff7.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff7.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff7.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00092;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff8.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff8.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff8.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+1;1.00258;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff9.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff9.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_ellipsoid_sqeff9.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
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+0.954993;1.01939;-1;0;
+0.977237;1.00927;-1;0;
+1;1.00123;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_sphere_sq.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_sphere_sq.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_sphere_sq.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;0.0949455;-1;0;
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+0.977237;1.00226;-1;0;
+1;0.99318;-1;0;
+
Index: explore/beta/data_files/sasfit_polydisperse_sphere_sqeff.txt
===================================================================
--- explore/beta/data_files/sasfit_polydisperse_sphere_sqeff.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_polydisperse_sphere_sqeff.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;0.167948;-1;0;
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+0.0104713;0.168014;-1;0;
+0.0107152;0.16805;-1;0;
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+0.794328;1.00225;-1;0;
+0.812831;1.00059;-1;0;
+0.831764;0.999916;-1;0;
+0.851138;0.999999;-1;0;
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+0.891251;0.99972;-1;0;
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+0.954993;1.00044;-1;0;
+0.977237;1.00004;-1;0;
+1;0.999992;-1;0;
+
Index: explore/beta/data_files/sasfit_sphere_IQBD.txt
===================================================================
--- explore/beta/data_files/sasfit_sphere_IQBD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_sphere_IQBD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;1.94203e+009;-1;0;
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+0.954993;346314;-1;0;
+0.977237;315504;-1;0;
+1;287680;-1;0;
+
Index: explore/beta/data_files/sasfit_sphere_IQD.txt
===================================================================
--- explore/beta/data_files/sasfit_sphere_IQD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_sphere_IQD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;1.15633e+010;-1;0;
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+0.616595;2.10254e+006;-1;0;
+0.630957;1.8839e+006;-1;0;
+0.645654;1.67702e+006;-1;0;
+0.660693;1.49655e+006;-1;0;
+0.676083;1.34828e+006;-1;0;
+0.691831;1.22927e+006;-1;0;
+0.707946;1.13104e+006;-1;0;
+0.724436;1.04404e+006;-1;0;
+0.74131;961254;-1;0;
+0.758578;879886;-1;0;
+0.776247;800770;-1;0;
+0.794328;726456;-1;0;
+0.812831;659167;-1;0;
+0.831764;599626;-1;0;
+0.851138;547036;-1;0;
+0.870964;499857;-1;0;
+0.891251;456691;-1;0;
+0.912011;416771;-1;0;
+0.933254;379911;-1;0;
+0.954993;346162;-1;0;
+0.977237;315492;-1;0;
+1;287682;-1;0;
+
Index: explore/beta/data_files/sasfit_sphere_IQSD.txt
===================================================================
--- explore/beta/data_files/sasfit_sphere_IQSD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/sasfit_sphere_IQSD.txt	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,202 @@
+0.01;1.09788e+009;-1;0;
+0.0102329;1.09805e+009;-1;0;
+0.0104713;1.09822e+009;-1;0;
+0.0107152;1.09841e+009;-1;0;
+0.0109648;1.0986e+009;-1;0;
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+0.0114815;1.09901e+009;-1;0;
+0.011749;1.09924e+009;-1;0;
+0.0120226;1.09947e+009;-1;0;
+0.0123027;1.09971e+009;-1;0;
+0.0125893;1.09996e+009;-1;0;
+0.0128825;1.10023e+009;-1;0;
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+0.0134896;1.1008e+009;-1;0;
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+0.0162181;1.10371e+009;-1;0;
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+0.017378;1.10512e+009;-1;0;
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+0.0676083;1.28522e+009;-1;0;
+0.0691831;1.29582e+009;-1;0;
+0.0707946;1.30709e+009;-1;0;
+0.0724436;1.31907e+009;-1;0;
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+0.114815;1.80627e+009;-1;0;
+0.11749;1.84359e+009;-1;0;
+0.120226;1.87966e+009;-1;0;
+0.123027;1.91292e+009;-1;0;
+0.125893;1.94124e+009;-1;0;
+0.128825;1.96181e+009;-1;0;
+0.131826;1.97107e+009;-1;0;
+0.134896;1.96477e+009;-1;0;
+0.138038;1.93822e+009;-1;0;
+0.141254;1.88678e+009;-1;0;
+0.144544;1.80678e+009;-1;0;
+0.147911;1.69656e+009;-1;0;
+0.151356;1.55757e+009;-1;0;
+0.154882;1.39487e+009;-1;0;
+0.158489;1.21675e+009;-1;0;
+0.162181;1.03344e+009;-1;0;
+0.165959;8.55093e+008;-1;0;
+0.169824;6.90157e+008;-1;0;
+0.17378;5.44273e+008;-1;0;
+0.177828;4.20144e+008;-1;0;
+0.18197;3.18019e+008;-1;0;
+0.186209;2.36456e+008;-1;0;
+0.190546;1.73077e+008;-1;0;
+0.194984;1.25149e+008;-1;0;
+0.199526;8.99691e+007;-1;0;
+0.204174;6.50767e+007;-1;0;
+0.20893;4.83405e+007;-1;0;
+0.213796;3.79752e+007;-1;0;
+0.218776;3.25155e+007;-1;0;
+0.223872;3.07729e+007;-1;0;
+0.229087;3.17869e+007;-1;0;
+0.234423;3.47774e+007;-1;0;
+0.239883;3.91016e+007;-1;0;
+0.245471;4.4217e+007;-1;0;
+0.251189;4.96487e+007;-1;0;
+0.25704;5.49638e+007;-1;0;
+0.263027;5.97532e+007;-1;0;
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+0.275423;6.61993e+007;-1;0;
+0.281838;6.71538e+007;-1;0;
+0.288403;6.62456e+007;-1;0;
+0.295121;6.33794e+007;-1;0;
+0.301995;5.86609e+007;-1;0;
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+0.323594;3.76257e+007;-1;0;
+0.331131;3.03463e+007;-1;0;
+0.338844;2.38702e+007;-1;0;
+0.346737;1.85203e+007;-1;0;
+0.354813;1.4422e+007;-1;0;
+0.363078;1.15371e+007;-1;0;
+0.371535;9.71824e+006;-1;0;
+0.380189;8.75946e+006;-1;0;
+0.389045;8.43515e+006;-1;0;
+0.398107;8.52387e+006;-1;0;
+0.40738;8.8211e+006;-1;0;
+0.416869;9.14582e+006;-1;0;
+0.42658;9.34621e+006;-1;0;
+0.436516;9.30818e+006;-1;0;
+0.446684;8.96775e+006;-1;0;
+0.457088;8.32319e+006;-1;0;
+0.467735;7.43815e+006;-1;0;
+0.47863;6.42696e+006;-1;0;
+0.489779;5.422e+006;-1;0;
+0.501187;4.53582e+006;-1;0;
+0.512861;3.8351e+006;-1;0;
+0.524807;3.33533e+006;-1;0;
+0.537032;3.01191e+006;-1;0;
+0.549541;2.81758e+006;-1;0;
+0.562341;2.69803e+006;-1;0;
+0.57544;2.60286e+006;-1;0;
+0.588844;2.49273e+006;-1;0;
+0.60256;2.34441e+006;-1;0;
+0.616595;2.15378e+006;-1;0;
+0.630957;1.93454e+006;-1;0;
+0.645654;1.71112e+006;-1;0;
+0.660693;1.50765e+006;-1;0;
+0.676083;1.33891e+006;-1;0;
+0.691831;1.20764e+006;-1;0;
+0.707946;1.10743e+006;-1;0;
+0.724436;1.0275e+006;-1;0;
+0.74131;956824;-1;0;
+0.758578;886950;-1;0;
+0.776247;813770;-1;0;
+0.794328;738093;-1;0;
+0.812831;664273;-1;0;
+0.831764;597317;-1;0;
+0.851138;540247;-1;0;
+0.870964;493146;-1;0;
+0.891251;453695;-1;0;
+0.912011;418407;-1;0;
+0.933254;384175;-1;0;
+0.954993;349753;-1;0;
+0.977237;316205;-1;0;
+1;285720;-1;0;
+
Index: explore/beta/data_files/testPolydisperseGaussianSphere.dat
===================================================================
--- explore/beta/data_files/testPolydisperseGaussianSphere.dat	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
+++ explore/beta/data_files/testPolydisperseGaussianSphere.dat	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
@@ -0,0 +1,802 @@
+Filename:testPolydisperseGaussianSphere.dat**R0=20**PDI=0.1**contrast6e-06**volF=0.1
+File format : Q, <FQ>, <FQ^2>, PQ, betaQ, SQ, SQ_Eff
+1.000000e-03	2.070847e-01	4.666796e-02	1.352083e+01	9.189192e-01	4.556628e-01	4.997981e-01
+2.000000e-03	2.070582e-01	4.665534e-02	1.351717e+01	9.189320e-01	4.557763e-01	4.998954e-01
+3.000000e-03	2.070139e-01	4.663430e-02	1.351108e+01	9.189533e-01	4.559654e-01	5.000577e-01
+4.000000e-03	2.069519e-01	4.660487e-02	1.350255e+01	9.189830e-01	4.562303e-01	5.002849e-01
+5.000000e-03	2.068722e-01	4.656705e-02	1.349160e+01	9.190213e-01	4.565711e-01	5.005773e-01
+6.000000e-03	2.067749e-01	4.652087e-02	1.347822e+01	9.190680e-01	4.569877e-01	5.009348e-01
+7.000000e-03	2.066598e-01	4.646634e-02	1.346242e+01	9.191233e-01	4.574805e-01	5.013577e-01
+8.000000e-03	2.065272e-01	4.640349e-02	1.344421e+01	9.191870e-01	4.580495e-01	5.018461e-01
+9.000000e-03	2.063769e-01	4.633235e-02	1.342360e+01	9.192593e-01	4.586949e-01	5.024003e-01
+1.000000e-02	2.062091e-01	4.625296e-02	1.340060e+01	9.193401e-01	4.594170e-01	5.030203e-01
+1.100000e-02	2.060237e-01	4.616535e-02	1.337521e+01	9.194293e-01	4.602159e-01	5.037066e-01
+1.200000e-02	2.058208e-01	4.606957e-02	1.334746e+01	9.195271e-01	4.610919e-01	5.044594e-01
+1.300000e-02	2.056005e-01	4.596565e-02	1.331736e+01	9.196334e-01	4.620453e-01	5.052789e-01
+1.400000e-02	2.053627e-01	4.585366e-02	1.328491e+01	9.197481e-01	4.630764e-01	5.061655e-01
+1.500000e-02	2.051075e-01	4.573364e-02	1.325014e+01	9.198714e-01	4.641856e-01	5.071196e-01
+1.600000e-02	2.048349e-01	4.560565e-02	1.321306e+01	9.200032e-01	4.653731e-01	5.081415e-01
+1.700000e-02	2.045451e-01	4.546975e-02	1.317368e+01	9.201434e-01	4.666393e-01	5.092317e-01
+1.800000e-02	2.042380e-01	4.532601e-02	1.313204e+01	9.202922e-01	4.679847e-01	5.103905e-01
+1.900000e-02	2.039138e-01	4.517449e-02	1.308814e+01	9.204495e-01	4.694096e-01	5.116184e-01
+2.000000e-02	2.035724e-01	4.501527e-02	1.304201e+01	9.206152e-01	4.709145e-01	5.129159e-01
+2.100000e-02	2.032140e-01	4.484842e-02	1.299367e+01	9.207895e-01	4.724999e-01	5.142834e-01
+2.200000e-02	2.028387e-01	4.467401e-02	1.294314e+01	9.209722e-01	4.741661e-01	5.157216e-01
+2.300000e-02	2.024464e-01	4.449214e-02	1.289044e+01	9.211634e-01	4.759137e-01	5.172309e-01
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+7.960000e-01	6.238896e-04	2.879986e-06	8.344012e-04	1.351528e-01	1.002783e+00	1.000376e+00
+7.970000e-01	6.145055e-04	2.864674e-06	8.299650e-04	1.318185e-01	1.002721e+00	1.000359e+00
+7.980000e-01	6.049598e-04	2.849469e-06	8.255596e-04	1.284367e-01	1.002656e+00	1.000341e+00
+7.990000e-01	5.952585e-04	2.834371e-06	8.211854e-04	1.250128e-01	1.002586e+00	1.000323e+00
+8.000000e-01	5.854076e-04	2.819380e-06	8.168424e-04	1.215523e-01	1.002513e+00	1.000305e+00
Index: explore/beta/data_files/testPolydisperseGaussianSphere2.dat
===================================================================
--- explore/beta/data_files/testPolydisperseGaussianSphere2.dat	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
+++ explore/beta/data_files/testPolydisperseGaussianSphere2.dat	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
@@ -0,0 +1,802 @@
+Filename:testPolydisperseGaussianSphere2.dat**R0=20**PDI=0.15**contrast6e-06**volF=0.1
+File format : Q, <FQ>, <FQ^2>, IQ, betaQ, SQ, SQ_Eff
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Index: explore/beta/data_files/yun_ellipsoid.dat
===================================================================
--- explore/beta/data_files/yun_ellipsoid.dat	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
+++ explore/beta/data_files/yun_ellipsoid.dat	(revision 707cbdb658e48a4f556fe2eff07376dae9f5c679)
@@ -0,0 +1,802 @@
+Filename:testEllipsoid.dat**a=20**b=10**Reff=12.5992**volF=0.15
+File format : Q, <FQ>, <FQ>^2, <FQ^2>, betaQ, SQ, SQ_Eff
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+7.610000e-001	6.990000e-003	4.885646e-005	3.521731e-004	1.387285e-001	1.013874e+000	1.001925e+000
+7.620000e-001	7.098001e-003	5.037760e-005	3.527525e-004	1.428129e-001	1.013709e+000	1.001958e+000
+7.630000e-001	7.204703e-003	5.190336e-005	3.534065e-004	1.468659e-001	1.013537e+000	1.001988e+000
+7.640000e-001	7.310098e-003	5.343279e-005	3.541327e-004	1.508835e-001	1.013356e+000	1.002015e+000
+7.650000e-001	7.414178e-003	5.496494e-005	3.549287e-004	1.548619e-001	1.013168e+000	1.002039e+000
+7.660000e-001	7.516934e-003	5.649887e-005	3.557921e-004	1.587974e-001	1.012973e+000	1.002060e+000
+7.670000e-001	7.618358e-003	5.803366e-005	3.567205e-004	1.626867e-001	1.012770e+000	1.002077e+000
+7.680000e-001	7.718444e-003	5.956837e-005	3.577114e-004	1.665263e-001	1.012560e+000	1.002092e+000
+7.690000e-001	7.817183e-003	6.110208e-005	3.587624e-004	1.703135e-001	1.012343e+000	1.002102e+000
+7.700000e-001	7.914569e-003	6.263389e-005	3.598713e-004	1.740452e-001	1.012119e+000	1.002109e+000
+7.710000e-001	8.010593e-003	6.416288e-005	3.610356e-004	1.777190e-001	1.011888e+000	1.002113e+000
+7.720000e-001	8.105250e-003	6.568817e-005	3.622529e-004	1.813324e-001	1.011651e+000	1.002113e+000
+7.730000e-001	8.198532e-003	6.720886e-005	3.635209e-004	1.848831e-001	1.011408e+000	1.002109e+000
+7.740000e-001	8.290433e-003	6.872409e-005	3.648373e-004	1.883691e-001	1.011159e+000	1.002102e+000
+7.750000e-001	8.380946e-003	7.023297e-005	3.661997e-004	1.917887e-001	1.010904e+000	1.002091e+000
+7.760000e-001	8.470065e-003	7.173466e-005	3.676059e-004	1.951401e-001	1.010644e+000	1.002077e+000
+7.770000e-001	8.557784e-003	7.322830e-005	3.690535e-004	1.984219e-001	1.010377e+000	1.002059e+000
+7.780000e-001	8.644097e-003	7.471307e-005	3.705404e-004	2.016327e-001	1.010106e+000	1.002038e+000
+7.790000e-001	8.728999e-003	7.618812e-005	3.720641e-004	2.047715e-001	1.009830e+000	1.002013e+000
+7.800000e-001	8.812484e-003	7.765265e-005	3.736225e-004	2.078372e-001	1.009549e+000	1.001985e+000
+7.810000e-001	8.894546e-003	7.910585e-005	3.752135e-004	2.108289e-001	1.009263e+000	1.001953e+000
+7.820000e-001	8.975181e-003	8.054693e-005	3.768347e-004	2.137461e-001	1.008973e+000	1.001918e+000
+7.830000e-001	9.054384e-003	8.197512e-005	3.784840e-004	2.165881e-001	1.008679e+000	1.001880e+000
+7.840000e-001	9.132150e-003	8.338964e-005	3.801593e-004	2.193545e-001	1.008381e+000	1.001838e+000
+7.850000e-001	9.208474e-003	8.478975e-005	3.818584e-004	2.220450e-001	1.008079e+000	1.001794e+000
+7.860000e-001	9.283352e-003	8.617470e-005	3.835792e-004	2.246595e-001	1.007773e+000	1.001746e+000
+7.870000e-001	9.356781e-003	8.754377e-005	3.853197e-004	2.271977e-001	1.007465e+000	1.001696e+000
+7.880000e-001	9.428755e-003	8.889625e-005	3.870778e-004	2.296599e-001	1.007153e+000	1.001643e+000
+7.890000e-001	9.499272e-003	9.023143e-005	3.888515e-004	2.320460e-001	1.006838e+000	1.001587e+000
+7.900000e-001	9.568329e-003	9.154863e-005	3.906387e-004	2.343563e-001	1.006521e+000	1.001528e+000
+7.910000e-001	9.635921e-003	9.284719e-005	3.924375e-004	2.365911e-001	1.006201e+000	1.001467e+000
+7.920000e-001	9.702045e-003	9.412645e-005	3.942459e-004	2.387506e-001	1.005879e+000	1.001404e+000
+7.930000e-001	9.766700e-003	9.538577e-005	3.960620e-004	2.408355e-001	1.005555e+000	1.001338e+000
+7.940000e-001	9.829881e-003	9.662453e-005	3.978839e-004	2.428460e-001	1.005229e+000	1.001270e+000
+7.950000e-001	9.891588e-003	9.784212e-005	3.997098e-004	2.447829e-001	1.004902e+000	1.001200e+000
+7.960000e-001	9.951816e-003	9.903795e-005	4.015378e-004	2.466467e-001	1.004573e+000	1.001128e+000
+7.970000e-001	1.001057e-002	1.002114e-004	4.033660e-004	2.484380e-001	1.004243e+000	1.001054e+000
+7.980000e-001	1.006783e-002	1.013620e-004	4.051929e-004	2.501575e-001	1.003913e+000	1.000979e+000
+7.990000e-001	1.012362e-002	1.024892e-004	4.070164e-004	2.518061e-001	1.003581e+000	1.000902e+000
+8.000000e-001	1.017792e-002	1.035924e-004	4.088351e-004	2.533843e-001	1.003250e+000	1.000823e+000
Index: explore/beta/sasfit_compare.py
===================================================================
--- explore/beta/sasfit_compare.py	(revision 2a12351b8b7f57f6668c3974b81f6be423c68ba3)
+++ explore/beta/sasfit_compare.py	(revision 2a12351b8b7f57f6668c3974b81f6be423c68ba3)
@@ -0,0 +1,666 @@
+from __future__ import division, print_function
+# Make sasmodels available on the path
+import sys, os
+BETA_DIR = os.path.dirname(os.path.realpath(__file__))
+SASMODELS_DIR = os.path.dirname(os.path.dirname(BETA_DIR))
+sys.path.insert(0, SASMODELS_DIR)
+
+from collections import namedtuple
+
+from matplotlib import pyplot as plt
+import numpy as np
+from numpy import pi, sin, cos, sqrt, fabs
+from numpy.polynomial.legendre import leggauss
+from scipy.special import j1 as J1
+from numpy import inf
+from scipy.special import gammaln  # type: ignore
+
+Theory = namedtuple('Theory', 'Q F1 F2 P S I Seff Ibeta')
+Theory.__new__.__defaults__ = (None,) * len(Theory._fields)
+
+#Used to calculate F(q) for the cylinder, sphere, ellipsoid models
+def sas_sinx_x(x):
+    with np.errstate(all='ignore'):
+        retvalue = sin(x)/x
+    retvalue[x == 0.] = 1.
+    return retvalue
+
+def sas_2J1x_x(x):
+    with np.errstate(all='ignore'):
+        retvalue = 2*J1(x)/x
+    retvalue[x == 0] = 1.
+    return retvalue
+
+def sas_3j1x_x(x):
+    """return 3*j1(x)/x"""
+    retvalue = np.empty_like(x)
+    with np.errstate(all='ignore'):
+        # GSL bessel_j1 taylor expansion
+        index = (x < 0.25)
+        y = x[index]**2
+        c1 = -1.0/10.0
+        c2 = +1.0/280.0
+        c3 = -1.0/15120.0
+        c4 = +1.0/1330560.0
+        c5 = -1.0/172972800.0
+        retvalue[index] = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*c5))))
+        index = ~index
+        y = x[index]
+        retvalue[index] = 3*(sin(y) - y*cos(y))/y**3
+    retvalue[x == 0.] = 1.
+    return retvalue
+
+#Used to cross check my models with sasview models
+def build_model(model_name, q, **pars):
+    from sasmodels.core import load_model_info, build_model as build_sasmodel
+    from sasmodels.data import empty_data1D
+    from sasmodels.direct_model import DirectModel
+    model_info = load_model_info(model_name)
+    model = build_sasmodel(model_info, dtype='double!')
+    data = empty_data1D(q)
+    calculator = DirectModel(data, model,cutoff=0)
+    calculator.pars = pars.copy()
+    calculator.pars.setdefault('background', 0)
+    return calculator
+
+#gives the hardsphere structure factor that sasview uses
+def _hardsphere_simple(q, radius_effective, volfraction):
+    CUTOFFHS = 0.05
+    if fabs(radius_effective) < 1.E-12:
+        HARDSPH = 1.0
+        return HARDSPH
+    X = 1.0/(1.0 -volfraction)
+    D = X*X
+    A = (1.+2.*volfraction)*D
+    A *= A
+    X = fabs(q*radius_effective*2.0)
+    if X < 5.E-06:
+        HARDSPH = 1./A
+        return HARDSPH
+    X2 = X*X
+    B = (1.0 +0.5*volfraction)*D
+    B *= B
+    B *= -6.*volfraction
+    G = 0.5*volfraction*A
+    if X < CUTOFFHS:
+        FF = 8.0*A +6.0*B + 4.0*G + ( -0.8*A -B/1.5 -0.5*G +(A/35. +0.0125*B +0.02*G)*X2)*X2
+        HARDSPH = 1./(1. + volfraction*FF )
+        return HARDSPH
+    X4 = X2*X2
+    S, C = sin(X), cos(X)
+    FF =  ((G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )/X2 + B*(2.*X*S -(X2-2.)*C -2.) )/X + A*(S-X*C))/X
+    HARDSPH = 1./(1. + 24.*volfraction*FF/X2)
+    return HARDSPH
+
+def hardsphere_simple(q, radius_effective, volfraction):
+    SQ = [_hardsphere_simple(qk, radius_effective, volfraction) for qk in q]
+    return np.array(SQ)
+
+#Used in gaussian quadrature for polydispersity
+#returns values and the probability of those values based on gaussian distribution
+N_GAUSS = 35
+NSIGMA_GAUSS = 3
+def gaussian_distribution(center, sigma, lb, ub):
+    #3 standard deviations covers approx. 99.7%
+    if sigma != 0:
+        nsigmas = NSIGMA_GAUSS
+        x = np.linspace(center-sigma*nsigmas, center+sigma*nsigmas, num=N_GAUSS)
+        x = x[(x >= lb) & (x <= ub)]
+        px = np.exp((x-center)**2 / (-2.0 * sigma * sigma))
+        return x, px
+    else:
+        return np.array([center]), np.array([1])
+
+N_SCHULZ = 80
+NSIGMA_SCHULZ = 8
+def schulz_distribution(center, sigma, lb, ub):
+    if sigma != 0:
+        nsigmas = NSIGMA_SCHULZ
+        x = np.linspace(center-sigma*nsigmas, center+sigma*nsigmas, num=N_SCHULZ)
+        x = x[(x >= lb) & (x <= ub)]
+        R = x/center
+        z = (center/sigma)**2
+        arg = z*np.log(z) + (z-1)*np.log(R) - R*z - np.log(center) - gammaln(z)
+        px = np.exp(arg)
+        return x, px
+    else:
+        return np.array([center]), np.array([1])
+
+#returns the effective radius used in sasview
+def ER_ellipsoid(radius_polar, radius_equatorial):
+    ee = np.empty_like(radius_polar)
+    if radius_polar > radius_equatorial:
+        ee = (radius_polar**2 - radius_equatorial**2)/radius_polar**2
+    elif radius_polar < radius_equatorial:
+        ee = (radius_equatorial**2 - radius_polar**2) / radius_equatorial**2
+    else:
+        ee = 2*radius_polar
+    if radius_polar * radius_equatorial != 0:
+        bd = 1.0 - ee
+        e1 = np.sqrt(ee)
+        b1 = 1.0 + np.arcsin(e1) / (e1*np.sqrt(bd))
+        bL = (1.0 + e1) / (1.0 - e1)
+        b2 = 1.0 + bd / 2 / e1 * np.log(bL)
+        delta = 0.75 * b1 * b2
+    ddd = np.zeros_like(radius_polar)
+    ddd = 2.0*(delta + 1.0)*radius_polar*radius_equatorial**2
+    return 0.5*ddd**(1.0 / 3.0)
+
+def ellipsoid_volume(radius_polar, radius_equatorial):
+    volume = (4./3.)*pi*radius_polar*radius_equatorial**2
+    return volume
+
+# F1 is F(q)
+# F2 is F(g)^2
+#IQM is I(q) with monodispersity
+#IQSM is I(q) with structure factor S(q) and monodispersity
+#IQBM is I(q) with Beta Approximation and monodispersity
+#SQ is monodisperse approach for structure factor
+#SQ_EFF is the effective structure factor from beta approx
+def ellipsoid_theta(q, radius_polar, radius_equatorial, sld, sld_solvent,
+                    volfraction=0, radius_effective=None):
+    #creates values z and corresponding probabilities w from legendre-gauss quadrature
+    volume = ellipsoid_volume(radius_polar, radius_equatorial)
+    z, w = leggauss(76)
+    F1 = np.zeros_like(q)
+    F2 = np.zeros_like(q)
+    #use a u subsition(u=cos) and then u=(z+1)/2 to change integration from
+    #0->2pi with respect to alpha to -1->1 with respect to z, allowing us to use
+    #legendre-gauss quadrature
+    for k, qk in enumerate(q):
+        r = sqrt(radius_equatorial**2*(1-((z+1)/2)**2)+radius_polar**2*((z+1)/2)**2)
+        form = (sld-sld_solvent)*volume*sas_3j1x_x(qk*r)
+        F2[k] = np.sum(w*form**2)
+        F1[k] = np.sum(w*form)
+    #the 1/2 comes from the change of variables mentioned above
+    F2 = F2/2.0
+    F1 = F1/2.0
+    if radius_effective is None:
+        radius_effective = ER_ellipsoid(radius_polar,radius_equatorial)
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    SQ_EFF = 1 + F1**2/F2*(SQ - 1)
+    IQM = 1e-4*F2/volume
+    IQSM = volfraction*IQM*SQ
+    IQBM = volfraction*IQM*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQM, S=SQ, I=IQSM, Seff=SQ_EFF, Ibeta=IQBM)
+
+#IQD is I(q) polydispursed, IQSD is I(q)S(q) polydispursed, etc.
+#IQBD HAS NOT BEEN CROSS CHECKED AT ALL
+def ellipsoid_pe(q, radius_polar, radius_equatorial, sld, sld_solvent,
+                 radius_polar_pd=0.1, radius_equatorial_pd=0.1,
+                 radius_polar_pd_type='gaussian',
+                 radius_equatorial_pd_type='gaussian',
+                 volfraction=0, radius_effective=None,
+                 background=0, scale=1,
+                 norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_polar_pd_type == 'gaussian':
+        Rp_val, Rp_prob = gaussian_distribution(radius_polar, radius_polar_pd*radius_polar, 0, inf)
+    elif radius_polar_pd_type == 'schulz':
+        Rp_val, Rp_prob = schulz_distribution(radius_polar, radius_polar_pd*radius_polar, 0, inf)
+    if radius_equatorial_pd_type == 'gaussian':
+        Re_val, Re_prob = gaussian_distribution(radius_equatorial, radius_equatorial_pd*radius_equatorial, 0, inf)
+    elif radius_equatorial_pd_type == 'schulz':
+        Re_val, Re_prob = schulz_distribution(radius_equatorial, radius_equatorial_pd*radius_equatorial, 0, inf)
+    total_weight = total_volume = 0
+    radius_eff = 0
+    F1, F2 = np.zeros_like(q), np.zeros_like(q)
+    for k, Rpk in enumerate(Rp_val):
+        print("ellipsoid cycle", k, "of", len(Rp_val))
+        for i, Rei in enumerate(Re_val):
+            theory = ellipsoid_theta(q, Rpk, Rei, sld, sld_solvent)
+            volume = ellipsoid_volume(Rpk, Rei)
+            weight = Rp_prob[k]*Re_prob[i]
+            total_weight += weight
+            total_volume += weight*volume
+            F1 += theory.F1*weight
+            F2 += theory.F2*weight
+            radius_eff += weight*ER_ellipsoid(Rpk, Rei)
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+    if radius_effective is None:
+        radius_effective = radius_eff/total_weight
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        # Note: internally, sasview uses F2/total_volume because:
+        #   average_volume = total_volume/total_weight
+        #   F2/total_weight / average_volume
+        #     = F2/total_weight / total_volume/total_weight
+        #     = F2/total_volume
+        IQD = F2/average_volume*1e-4*volfraction
+        F1 *= 1e-2  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-4
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+
+#polydispersity for sphere
+def sphere_r(q,radius,sld,sld_solvent,
+             radius_pd=0.1, radius_pd_type='gaussian',
+             volfraction=0, radius_effective=None,
+             background=0, scale=1,
+             norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_pd_type == 'gaussian':
+        radius_val, radius_prob = gaussian_distribution(radius, radius_pd*radius, 0, inf)
+    elif radius_pd_type == 'schulz':
+        radius_val, radius_prob = schulz_distribution(radius, radius_pd*radius, 0, inf)
+    total_weight = total_volume = 0
+    F1 = np.zeros_like(q)
+    F2 = np.zeros_like(q)
+    for k, rk in enumerate(radius_val):
+        volume = 4./3.*pi*rk**3
+        total_weight += radius_prob[k]
+        total_volume += radius_prob[k]*volume
+        form = (sld-sld_solvent)*volume*sas_3j1x_x(q*rk)
+        F2 += radius_prob[k]*form**2
+        F1 += radius_prob[k]*form
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+
+    if radius_effective is None:
+        radius_effective = radius
+    average_volume = total_volume/total_weight
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        IQD = F2/average_volume*1e-4*volfraction
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+
+###############################################################################
+###############################################################################
+###############################################################################
+##################                                           ##################
+##################                   TESTS                   ##################
+##################                                           ##################
+###############################################################################
+###############################################################################
+###############################################################################
+
+def popn(d, keys):
+    """
+    Splits a dict into two, with any key of *d* which is in *keys* removed
+    from *d* and added to *b*. Returns *b*.
+    """
+    b = {}
+    for k in keys:
+        try:
+            b[k] = d.pop(k)
+        except KeyError:
+            pass
+    return b
+
+def sasmodels_theory(q, Pname, **pars):
+    """
+    Call sasmodels to compute the model with and without a hard sphere
+    structure factor.
+    """
+    #mono_pars = {k: (0 if k.endswith('_pd') else v) for k, v in pars.items()}
+    Ppars = pars.copy()
+    Spars = popn(Ppars, ['radius_effective', 'volfraction'])
+    Ipars = pars.copy()
+
+    # Autofill npts and nsigmas for the given pd type
+    for k, v in pars.items():
+        if k.endswith("_pd_type"):
+            if v == "gaussian":
+                n, nsigmas = N_GAUSS, NSIGMA_GAUSS
+            elif v == "schulz":
+                n, nsigmas = N_SCHULZ, NSIGMA_SCHULZ
+            Ppars.setdefault(k.replace("_pd_type", "_pd_n"), n)
+            Ppars.setdefault(k.replace("_pd_type", "_pd_nsigma"), nsigmas)
+            Ipars.setdefault(k.replace("_pd_type", "_pd_n"), n)
+            Ipars.setdefault(k.replace("_pd_type", "_pd_nsigma"), nsigmas)
+
+    #Ppars['scale'] = Spars.get('volfraction', 1)
+    P = build_model(Pname, q)
+    S = build_model("hardsphere", q)
+    I = build_model(Pname+"@hardsphere", q)
+    Pq = P(**Ppars)*pars.get('volfraction', 1)
+    Sq = S(**Spars)
+    Iq = I(**Ipars)
+    #Iq = Pq*Sq*pars.get('volfraction', 1)
+    #Sq = Iq/Pq
+    #Iq = None#= Sq = None
+    r = dict(I._kernel.results())
+    return Theory(Q=q, F1=None, F2=None, P=Pq, S=None, I=None, Seff=r["S_eff(Q)"], Ibeta=Iq)
+
+def compare(title, target, actual, fields='F1 F2 P S I Seff Ibeta'):
+    """
+    Plot fields in common between target and actual, along with relative error.
+    """
+    available = [s for s in fields.split()
+                 if getattr(target, s) is not None and getattr(actual, s) is not None]
+    rows = len(available)
+    for row, field in enumerate(available):
+        Q = target.Q
+        I1, I2 = getattr(target, field), getattr(actual, field)
+        plt.subplot(rows, 2, 2*row+1)
+        plt.loglog(Q, abs(I1), label="target "+field)
+        plt.loglog(Q, abs(I2), label="value "+field)
+        #plt.legend(loc="upper left", bbox_to_anchor=(1,1))
+        plt.legend(loc='lower left')
+        plt.subplot(rows, 2, 2*row+2)
+        plt.semilogx(Q, I2/I1 - 1, label="relative error")
+        #plt.semilogx(Q, I1/I2 - 1, label="relative error")
+    plt.tight_layout()
+    plt.suptitle(title)
+    plt.show()
+
+def data_file(name):
+    return os.path.join(BETA_DIR, 'data_files', name)
+
+def load_sasfit(path):
+    data = np.loadtxt(path, dtype=str, delimiter=';').T
+    data = np.vstack((map(float, v) for v in data[0:2]))
+    return data
+
+COMPARISON = {}  # Type: Dict[(str,str,str)] -> Callable[(), None]
+
+def compare_sasview_sphere(pd_type='schulz'):
+    q = np.logspace(-5, 0, 250)
+    model = 'sphere'
+    pars = dict(
+        radius=20, sld=4, sld_solvent=1,
+        background=0,
+        radius_pd=.1, radius_pd_type=pd_type,
+        volfraction=0.15,
+        #radius_effective=12.59921049894873,  # equivalent average sphere radius
+        )
+    target = sasmodels_theory(q, model, **pars)
+    actual = sphere_r(q, norm='sasview', **pars)
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'sphere', 'gaussian')] = lambda: compare_sasview_sphere(pd_type='gaussian')
+COMPARISON[('sasview', 'sphere', 'schulz')] = lambda: compare_sasview_sphere(pd_type='schulz')
+
+def compare_sasview_ellipsoid(pd_type='gaussian'):
+    q = np.logspace(-5, 0, 50)
+    model = 'ellipsoid'
+    pars = dict(
+        radius_polar=20, radius_equatorial=400, sld=4, sld_solvent=1,
+        background=0,
+        radius_polar_pd=0.1, radius_polar_pd_type=pd_type,
+        radius_equatorial_pd=0.1, radius_equatorial_pd_type=pd_type,
+        volfraction=0.15,
+        radius_effective=270.7543927018,
+        #radius_effective=12.59921049894873,
+        )
+    target = sasmodels_theory(q, model, effective_radius_mode=0, structure_factor_mode=1, **pars)
+    actual = ellipsoid_pe(q, norm='sasview', **pars)
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'ellipsoid', 'gaussian')] = lambda: compare_sasview_ellipsoid(pd_type='gaussian')
+COMPARISON[('sasview', 'ellipsoid', 'schulz')] = lambda: compare_sasview_ellipsoid(pd_type='schulz')
+
+def compare_yun_ellipsoid_mono():
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0, 'radius_polar_pd_type': 'gaussian',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0, 'radius_equatorial_pd_type': 'gaussian',
+        'sld': 2, 'sld_solvent': 1,
+        'volfraction': 0.15,
+        # Yun uses radius for same volume sphere for effective radius
+        # whereas sasview uses the average curvature.
+        'radius_effective': 12.59921049894873,
+    }
+
+    data = np.loadtxt(data_file('yun_ellipsoid.dat'),skiprows=2).T
+    Q = data[0]
+    F1 = data[1]
+    P = data[3]*pars['volfraction']
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = ellipsoid_pe(Q, norm='yun', **pars)
+    title = " ".join(("yun", "ellipsoid", "no pd"))
+    #compare(title, target, actual, fields="P S I Seff Ibeta")
+    compare(title, target, actual)
+COMPARISON[('yun', 'ellipsoid', 'gaussian')] = compare_yun_ellipsoid_mono
+COMPARISON[('yun', 'ellipsoid', 'schulz')] = compare_yun_ellipsoid_mono
+
+def compare_yun_sphere_gauss():
+    # Note: yun uses gauss limits from R0/10 to R0 + 5 sigma steps sigma/100
+    # With pd = 0.1, that's 14 sigma and 1400 points.
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'gaussian',
+        'sld': 6, 'sld_solvent': 0,
+        'volfraction': 0.1,
+    }
+
+    data = np.loadtxt(data_file('testPolydisperseGaussianSphere.dat'), skiprows=2).T
+    Q = data[0]
+    F1 = data[1]
+    F2 = data[2]
+    P = data[3]
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = sphere_r(Q, norm='yun', **pars)
+    title = " ".join(("yun", "sphere", "10% dispersion 10% Vf"))
+    compare(title, target, actual)
+    data = np.loadtxt(data_file('testPolydisperseGaussianSphere2.dat'), skiprows=2).T
+    pars.update(radius_pd=0.15)
+    Q = data[0]
+    F1 = data[1]
+    F2 = data[2]
+    P = data[3]
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = sphere_r(Q, norm='yun', **pars)
+    title = " ".join(("yun", "sphere", "15% dispersion 10% Vf"))
+    compare(title, target, actual)
+COMPARISON[('yun', 'sphere', 'gaussian')] = compare_yun_sphere_gauss
+
+
+def compare_sasfit_sphere_gauss():
+    #N=1,s=2,X0=20,distr radius R=20,eta_core=4,eta_solv=1,.3
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'gaussian',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3,
+    }
+
+    Q, IQ = load_sasfit(data_file('sasfit_sphere_IQD.txt'))
+    Q, IQSD = load_sasfit(data_file('sasfit_sphere_IQSD.txt'))
+    Q, IQBD = load_sasfit(data_file('sasfit_sphere_IQBD.txt'))
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_sphere_sq.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_sphere_sqeff.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+    actual = sphere_r(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "sphere", "pd=10% gaussian"))
+    compare(title, target, actual)
+    #compare(title, target, actual, fields="P")
+COMPARISON[('sasfit', 'sphere', 'gaussian')] = compare_sasfit_sphere_gauss
+
+def compare_sasfit_sphere_schulz():
+    #radius=20,sld=4,sld_solvent=1,volfraction=0.3,radius_pd=0.1
+    #We have scaled the output from sasfit by 1e-4*volume*volfraction
+    #0.10050378152592121
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'schulz',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3,
+    }
+
+    Q, IQ = load_sasfit(data_file('richard_test.txt'))
+    Q, IQSD = load_sasfit(data_file('richard_test2.txt'))
+    Q, IQBD = load_sasfit(data_file('richard_test3.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=None, I=IQSD, Seff=None, Ibeta=IQBD)
+    actual = sphere_r(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "sphere", "pd=10% schulz"))
+    compare(title, target, actual)
+COMPARISON[('sasfit', 'sphere', 'schulz')] = compare_sasfit_sphere_schulz
+
+def compare_sasfit_ellipsoid_schulz():
+    #polarradius=20, equatorialradius=10, sld=4,sld_solvent=1,volfraction=0.3,radius_polar_pd=0.1
+    #Effective radius =13.1353356684
+    #We have scaled the output from sasfit by 1e-4*volume*volfraction
+    #0.10050378152592121
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0.1, 'radius_polar_pd_type': 'schulz',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0., 'radius_equatorial_pd_type': 'schulz',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3, 'radius_effective': 13.1353356684,
+    }
+
+    Q, IQ = load_sasfit(data_file('richard_test4.txt'))
+    Q, IQSD = load_sasfit(data_file('richard_test5.txt'))
+    Q, IQBD = load_sasfit(data_file('richard_test6.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=None, I=IQSD, Seff=None, Ibeta=IQBD)
+    actual = ellipsoid_pe(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "ellipsoid", "pd=10% schulz"))
+    compare(title, target, actual)
+COMPARISON[('sasfit', 'ellipsoid', 'schulz')] = compare_sasfit_ellipsoid_schulz
+
+
+def compare_sasfit_ellipsoid_gaussian():
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0, 'radius_polar_pd_type': 'gaussian',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0, 'radius_equatorial_pd_type': 'gaussian',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0, 'radius_effective': None,
+    }
+
+    #Rp=20,Re=10,eta_core=4,eta_solv=1
+    Q, PQ0 = load_sasfit(data_file('sasfit_ellipsoid_IQM.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ0)
+    compare("sasfit ellipsoid no poly", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr 10% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp10 = load_sasfit(data_file('sasfit_ellipsoid_IQD.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.1, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp10)
+    compare("sasfit ellipsoid P(Q) 10% Rp", target, actual); plt.show()
+    #N=1,s=1,X0=10,distr 10% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re10 = load_sasfit(data_file('sasfit_ellipsoid_IQD2.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.1, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re10)
+    compare("sasfit ellipsoid P(Q) 10% Re", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr 30% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp30 = load_sasfit(data_file('sasfit_ellipsoid_IQD3.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.3, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp30)
+    compare("sasfit ellipsoid P(Q) 30% Rp", target, actual); plt.show()
+    #N=1,s=3,X0=10,distr 30% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re30 = load_sasfit(data_file('sasfit_ellipsoid_IQD4.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.3, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re30)
+    compare("sasfit ellipsoid P(Q) 30% Re", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr 60% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp60 = load_sasfit(data_file('sasfit_ellipsoid_IQD5.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.6, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp60)
+    compare("sasfit ellipsoid P(Q) 60% Rp", target, actual); plt.show()
+    #N=1,s=6,X0=10,distr 60% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re60 = load_sasfit(data_file('sasfit_ellipsoid_IQD6.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.6, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re60)
+    compare("sasfit ellipsoid P(Q) 60% Re", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 15% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq2.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff2.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 15% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq3.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff3.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 15% Vf", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq4.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff4.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 30% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq5.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff5.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 30% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq6.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff6.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 30% Vf", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq7.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff7.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 60% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq8.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff8.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 60% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq9.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff9.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 60% Vf", target, actual); plt.show()
+COMPARISON[('sasfit', 'ellipsoid', 'gaussian')] = compare_sasfit_ellipsoid_gaussian
+
+def main():
+    key = tuple(sys.argv[1:])
+    if key not in COMPARISON:
+        print("usage: sasfit_compare.py [sasview|sasfit|yun] [sphere|ellipsoid] [gaussian|schulz]")
+        return
+    comparison = COMPARISON[key]
+    comparison()
+
+if __name__ == "__main__":
+    main()
Index: explore/beta/sasfit_compare_new.py
===================================================================
--- explore/beta/sasfit_compare_new.py	(revision 2586ab720d3b2b10de9655ce116d09447ec16125)
+++ explore/beta/sasfit_compare_new.py	(revision 2586ab720d3b2b10de9655ce116d09447ec16125)
@@ -0,0 +1,914 @@
+from __future__ import division, print_function
+# Make sasmodels available on the path
+import sys, os
+BETA_DIR = os.path.dirname(os.path.realpath(__file__))
+SASMODELS_DIR = os.path.dirname(os.path.dirname(BETA_DIR))
+sys.path.insert(0, SASMODELS_DIR)
+
+from collections import namedtuple
+
+from matplotlib import pyplot as plt
+import numpy as np
+from numpy import pi, sin, cos, sqrt, fabs
+from numpy.polynomial.legendre import leggauss
+from scipy.special import j1 as J1
+from numpy import inf
+from scipy.special import gammaln  # type: ignore
+
+Theory = namedtuple('Theory', 'Q F1 F2 P S I Seff Ibeta')
+Theory.__new__.__defaults__ = (None,) * len(Theory._fields)
+
+#Used to calculate F(q) for the cylinder, sphere, ellipsoid models
+# RKH adding vesicle and hollow_cylinder to test sasview special cases of ER and VR
+# BEWARE there are issues here if you run this from python3 (i.e. qt5 version of sasview), so do "source activate sasview"
+def sas_sinx_x(x):
+    with np.errstate(all='ignore'):
+        retvalue = sin(x)/x
+    retvalue[x == 0.] = 1.
+    return retvalue
+
+def sas_2J1x_x(x):
+    with np.errstate(all='ignore'):
+        retvalue = 2*J1(x)/x
+    retvalue[x == 0] = 1.
+    return retvalue
+
+def sas_3j1x_x(x):
+    """return 3*j1(x)/x"""
+    retvalue = np.empty_like(x)
+    with np.errstate(all='ignore'):
+        # GSL bessel_j1 taylor expansion
+        index = (x < 0.25)
+        y = x[index]**2
+        c1 = -1.0/10.0
+        c2 = +1.0/280.0
+        c3 = -1.0/15120.0
+        c4 = +1.0/1330560.0
+        c5 = -1.0/172972800.0
+        retvalue[index] = 1.0 + y*(c1 + y*(c2 + y*(c3 + y*(c4 + y*c5))))
+        index = ~index
+        y = x[index]
+        retvalue[index] = 3*(sin(y) - y*cos(y))/y**3
+    retvalue[x == 0.] = 1.
+    return retvalue
+
+#Used to cross check my models with sasview models
+def build_model(model_name, q, **pars):
+    from sasmodels.core import load_model_info, build_model as build_sasmodel
+    from sasmodels.data import empty_data1D
+    from sasmodels.direct_model import DirectModel
+    model_info = load_model_info(model_name)
+    model = build_sasmodel(model_info, dtype='double!')
+    data = empty_data1D(q)
+    calculator = DirectModel(data, model,cutoff=0)
+    calculator.pars = pars.copy()
+    calculator.pars.setdefault('background', 0)
+    return calculator
+
+#gives the hardsphere structure factor that sasview uses
+def _hardsphere_simple(q, radius_effective, volfraction):
+    CUTOFFHS = 0.05
+    if fabs(radius_effective) < 1.E-12:
+        HARDSPH = 1.0
+        return HARDSPH
+    X = 1.0/(1.0 -volfraction)
+    D = X*X
+    A = (1.+2.*volfraction)*D
+    A *= A
+    X = fabs(q*radius_effective*2.0)
+    if X < 5.E-06:
+        HARDSPH = 1./A
+        return HARDSPH
+    X2 = X*X
+    B = (1.0 +0.5*volfraction)*D
+    B *= B
+    B *= -6.*volfraction
+    G = 0.5*volfraction*A
+    if X < CUTOFFHS:
+        FF = 8.0*A +6.0*B + 4.0*G + ( -0.8*A -B/1.5 -0.5*G +(A/35. +0.0125*B +0.02*G)*X2)*X2
+        HARDSPH = 1./(1. + volfraction*FF )
+        return HARDSPH
+    X4 = X2*X2
+    S, C = sin(X), cos(X)
+    FF =  ((G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )/X2 + B*(2.*X*S -(X2-2.)*C -2.) )/X + A*(S-X*C))/X
+    HARDSPH = 1./(1. + 24.*volfraction*FF/X2)
+    return HARDSPH
+
+def hardsphere_simple(q, radius_effective, volfraction):
+    SQ = [_hardsphere_simple(qk, radius_effective, volfraction) for qk in q]
+    return np.array(SQ)
+
+#Used in gaussian quadrature for polydispersity
+#returns values and the probability of those values based on gaussian distribution
+N_GAUSS = 35
+NSIGMA_GAUSS = 3
+def gaussian_distribution(center, sigma, lb, ub):
+    #3 standard deviations covers approx. 99.7%
+    if sigma != 0:
+        nsigmas = NSIGMA_GAUSS
+        x = np.linspace(center-sigma*nsigmas, center+sigma*nsigmas, num=N_GAUSS)
+        x = x[(x >= lb) & (x <= ub)]
+        px = np.exp((x-center)**2 / (-2.0 * sigma * sigma))
+        return x, px
+    else:
+        return np.array([center]), np.array([1])
+
+N_SCHULZ = 80
+NSIGMA_SCHULZ = 8
+def schulz_distribution(center, sigma, lb, ub):
+    if sigma != 0:
+        nsigmas = NSIGMA_SCHULZ
+        x = np.linspace(center-sigma*nsigmas, center+sigma*nsigmas, num=N_SCHULZ)
+        x = x[(x >= lb) & (x <= ub)]
+        R = x/center
+        z = (center/sigma)**2
+        arg = z*np.log(z) + (z-1)*np.log(R) - R*z - np.log(center) - gammaln(z)
+        px = np.exp(arg)
+        return x, px
+    else:
+        return np.array([center]), np.array([1])
+
+#returns the effective radius used in sasview
+def ER_ellipsoid(radius_polar, radius_equatorial):
+    ee = np.empty_like(radius_polar)
+    if radius_polar > radius_equatorial:
+        ee = (radius_polar**2 - radius_equatorial**2)/radius_polar**2
+    elif radius_polar < radius_equatorial:
+        ee = (radius_equatorial**2 - radius_polar**2) / radius_equatorial**2
+    else:
+        ee = 2*radius_polar
+    if radius_polar * radius_equatorial != 0:
+        bd = 1.0 - ee
+        e1 = np.sqrt(ee)
+        b1 = 1.0 + np.arcsin(e1) / (e1*np.sqrt(bd))
+        bL = (1.0 + e1) / (1.0 - e1)
+        b2 = 1.0 + bd / 2 / e1 * np.log(bL)
+        delta = 0.75 * b1 * b2
+    ddd = np.zeros_like(radius_polar)
+    ddd = 2.0*(delta + 1.0)*radius_polar*radius_equatorial**2
+    return 0.5*ddd**(1.0 / 3.0)
+
+def ellipsoid_volume(radius_polar, radius_equatorial):
+    volume = (4./3.)*pi*radius_polar*radius_equatorial**2
+    return volume
+
+# F1 is F(q)
+# F2 is F(g)^2
+#IQM is I(q) with monodispersity
+#IQSM is I(q) with structure factor S(q) and monodispersity
+#IQBM is I(q) with Beta Approximation and monodispersity
+#SQ is monodisperse approach for structure factor
+#SQ_EFF is the effective structure factor from beta approx
+def ellipsoid_theta(q, radius_polar, radius_equatorial, sld, sld_solvent,
+                    volfraction=0, radius_effective=None):
+    #creates values z and corresponding probabilities w from legendre-gauss quadrature
+    volume = ellipsoid_volume(radius_polar, radius_equatorial)
+    z, w = leggauss(76)
+    F1 = np.zeros_like(q)
+    F2 = np.zeros_like(q)
+    #use a u subsition(u=cos) and then u=(z+1)/2 to change integration from
+    #0->2pi with respect to alpha to -1->1 with respect to z, allowing us to use
+    #legendre-gauss quadrature
+    for k, qk in enumerate(q):
+        r = sqrt(radius_equatorial**2*(1-((z+1)/2)**2)+radius_polar**2*((z+1)/2)**2)
+        form = (sld-sld_solvent)*volume*sas_3j1x_x(qk*r)
+        F2[k] = np.sum(w*form**2)
+        F1[k] = np.sum(w*form)
+    #the 1/2 comes from the change of variables mentioned above
+    F2 = F2/2.0
+    F1 = F1/2.0
+    if radius_effective is None:
+        radius_effective = ER_ellipsoid(radius_polar,radius_equatorial)
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    SQ_EFF = 1 + F1**2/F2*(SQ - 1)
+    IQM = 1e-4*F2/volume
+    IQSM = volfraction*IQM*SQ
+    IQBM = volfraction*IQM*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQM, S=SQ, I=IQSM, Seff=SQ_EFF, Ibeta=IQBM)
+
+#IQD is I(q) polydispursed, IQSD is I(q)S(q) polydispursed, etc.
+#IQBD HAS NOT BEEN CROSS CHECKED AT ALL
+def ellipsoid_pe(q, radius_polar, radius_equatorial, sld, sld_solvent,
+                 radius_polar_pd=0.1, radius_equatorial_pd=0.1,
+                 radius_polar_pd_type='gaussian',
+                 radius_equatorial_pd_type='gaussian',
+                 volfraction=0, radius_effective=None,
+                 background=0, scale=1,
+                 norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_polar_pd_type == 'gaussian':
+        Rp_val, Rp_prob = gaussian_distribution(radius_polar, radius_polar_pd*radius_polar, 0, inf)
+    elif radius_polar_pd_type == 'schulz':
+        Rp_val, Rp_prob = schulz_distribution(radius_polar, radius_polar_pd*radius_polar, 0, inf)
+    if radius_equatorial_pd_type == 'gaussian':
+        Re_val, Re_prob = gaussian_distribution(radius_equatorial, radius_equatorial_pd*radius_equatorial, 0, inf)
+    elif radius_equatorial_pd_type == 'schulz':
+        Re_val, Re_prob = schulz_distribution(radius_equatorial, radius_equatorial_pd*radius_equatorial, 0, inf)
+    total_weight = total_volume = 0
+    radius_eff = 0
+    F1, F2 = np.zeros_like(q), np.zeros_like(q)
+    for k, Rpk in enumerate(Rp_val):
+        print("ellipsoid cycle", k, "of", len(Rp_val))
+        for i, Rei in enumerate(Re_val):
+            theory = ellipsoid_theta(q, Rpk, Rei, sld, sld_solvent)
+            volume = ellipsoid_volume(Rpk, Rei)
+            weight = Rp_prob[k]*Re_prob[i]
+            total_weight += weight
+            total_volume += weight*volume
+            F1 += theory.F1*weight
+            F2 += theory.F2*weight
+            radius_eff += weight*ER_ellipsoid(Rpk, Rei)
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+    if radius_effective is None:
+        radius_effective = radius_eff/total_weight
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        # Note: internally, sasview uses F2/total_volume because:
+        #   average_volume = total_volume/total_weight
+        #   F2/total_weight / average_volume
+        #     = F2/total_weight / total_volume/total_weight
+        #     = F2/total_volume
+        IQD = F2/average_volume*1e-4*volfraction
+        F1 *= 1e-2  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-4
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+
+#polydispersity for sphere
+def sphere_r(q,radius,sld,sld_solvent,
+             radius_pd=0.1, radius_pd_type='gaussian',
+             volfraction=0, radius_effective=None,
+             background=0, scale=1,
+             norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_pd_type == 'gaussian':
+        radius_val, radius_prob = gaussian_distribution(radius, radius_pd*radius, 0, inf)
+    elif radius_pd_type == 'schulz':
+        radius_val, radius_prob = schulz_distribution(radius, radius_pd*radius, 0, inf)
+    total_weight = total_volume = 0
+    F1 = np.zeros_like(q)
+    F2 = np.zeros_like(q)
+    for k, rk in enumerate(radius_val):
+        volume = 4./3.*pi*rk**3
+        total_weight += radius_prob[k]
+        total_volume += radius_prob[k]*volume
+        form = (sld-sld_solvent)*volume*sas_3j1x_x(q*rk)
+        F2 += radius_prob[k]*form**2
+        F1 += radius_prob[k]*form
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+
+    if radius_effective is None:
+        radius_effective = radius
+        print("radius_effective  ",radius_effective)
+        average_volume = total_volume/total_weight
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        IQD = F2/average_volume*1e-4*volfraction
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+
+#polydispersity for vesicle
+def vesicle_pe(q,radius=20, thickness=10, sld=4, sld_solvent=1, volfraction=0.03,
+        radius_pd=0.1, thickness_pd=0.2, radius_pd_type="gaussian", thickness_pd_type="gaussian",
+        radius_effective=None, background=0, scale=1,
+                 norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_pd_type == 'gaussian':
+        R_val, R_prob = gaussian_distribution(radius, radius_pd*radius, 0, inf)
+    elif radius_pd_type == 'schulz':
+        R_val, R_prob = schulz_distribution(radius, radius_pd*radius, 0, inf)
+    if thickness_pd_type == 'gaussian':
+        T_val, T_prob = gaussian_distribution(thickness, thickness_pd*thickness, 0, inf)
+    elif thickness_pd_type == 'schulz':
+        T_val, T_prob = schulz_distribution(thickness, thickness_pd*thickness, 0, inf)
+    total_weight = total_volume = total_shell = 0
+    radius_eff = 0
+    F1, F2 = np.zeros_like(q), np.zeros_like(q)
+    for k, Rk in enumerate(R_val):
+        print("vesicle cycle", k, "of", len(R_val)," Rk ",Rk)
+        volume_in = 4./3.*pi*Rk**3
+        form_in = (sld-sld_solvent)*volume_in*sas_3j1x_x(q*Rk)
+        for i, Ti in enumerate(T_val):
+            Rout = Rk + Ti
+            volume_out = 4./3.*pi*Rout**3
+            form_out = (sld-sld_solvent)*volume_out*sas_3j1x_x(q*Rout)
+            form = form_out - form_in
+            volume = volume_out - volume_in
+            weight = R_prob[k]*T_prob[i]
+            total_weight += weight
+            total_shell += weight*volume
+            total_volume += weight*volume_out
+            F1 += form*weight
+            F2 += form**2*weight
+            radius_eff += weight*Rout
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+    if radius_effective is None:
+        radius_effective = radius_eff/total_weight
+        print("radius_effective  ",radius_effective)
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        # Note: internally, sasview uses F2/total_volume because:
+        #   average_volume = total_volume/total_weight
+        #   F2/total_weight / average_volume
+        #     = F2/total_weight / total_volume/total_weight
+        #     = F2/total_volume
+        IQD = F2/average_volume*1e-4*volfraction
+        F1 *= 1e-2  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-4
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+    # RKH SORT THIS OUT WHEN HAVE NEW MODEL
+    vfff=volfraction*(30./20.)**3
+    print("radius_effective, fudged volfaction for S(Q) ",radius_effective,vfff)
+    SQ = hardsphere_simple(q, radius_effective, vfff)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+#
+#polydispersity for hollow_cylinder
+def hollow_cylinder_pe(q,radius=20, thickness=10, sld=4, sld_solvent=1, volfraction=0.15,
+        radius_pd=0.1, thickness_pd=0.2, length_pd=0.05, radius_pd_type="gaussian", thickness_pd_type="gaussian",
+        radius_effective=None, background=0, scale=1,
+                 norm='sasview'):
+    if norm not in ['sasview', 'sasfit', 'yun']:
+        raise TypeError("unknown norm "+norm)
+    if radius_pd_type == 'gaussian':
+        R_val, R_prob = gaussian_distribution(radius, radius_pd*radius, 0, inf)
+    elif radius_pd_type == 'schulz':
+        R_val, R_prob = schulz_distribution(radius, radius_pd*radius, 0, inf)
+    if thickness_pd_type == 'gaussian':
+        T_val, T_prob = gaussian_distribution(thickness, thickness_pd*thickness, 0, inf)
+    elif thickness_pd_type == 'schulz':
+        T_val, T_prob = schulz_distribution(thickness, thickness_pd*thickness, 0, inf)
+    if length_pd_type == 'gaussian':
+        T_val, T_prob = gaussian_distribution(length, length_pd*length, 0, inf)
+    elif length_pd_type == 'schulz':
+        L_val, L_prob = schulz_distribution(length, length_pd*length, 0, inf)
+    total_weight = total_volume = total_shell = 0
+    radius_eff = 0
+    F1, F2 = np.zeros_like(q), np.zeros_like(q)
+    for k, Rk in enumerate(R_val):
+        print("hollow_cylinder cycle", k, "of", len(R_val)," Rk ",Rk)
+        for i, Ti in enumerate(T_val):
+            for j, Lj in enumerate(L_val):
+                Rout = Rk + Ti
+                volume_out = pi*Rout**2*Lj
+                volume_in = pi*Rk**2*Lj
+                volume = volume_out - volume_in
+                theory = hollow_cylinder_theta(q, Rk, Ti, Lj, sld, sld_solvent,
+                    volfraction=0, radius_effective=None)
+                weight = R_prob[k]*T_prob[i]*L_prob[j]
+                total_weight += weight
+                total_shell += weight*volume
+                total_volume += weight*volume_out
+                F1 += theory.F1*weight
+                F2 += theory.F2*weight
+                radius_eff += weight*ER_hollow_cylinder(radius, thickness, length)
+    F1 /= total_weight
+    F2 /= total_weight
+    average_volume = total_volume/total_weight
+    if radius_effective is None:
+        radius_effective = radius_eff/total_weight
+        print("radius_effective  ",radius_effective)
+    if norm == 'sasfit':
+        IQD = F2
+    elif norm == 'sasview':
+        # Note: internally, sasview uses F2/total_volume because:
+        #   average_volume = total_volume/total_weight
+        #   F2/total_weight / average_volume
+        #     = F2/total_weight / total_volume/total_weight
+        #     = F2/total_volume
+        IQD = F2/average_volume*1e-4*volfraction
+        F1 *= 1e-2  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-4
+    elif norm == 'yun':
+        F1 *= 1e-6  # Yun is using sld in 1/A^2, not 1e-6/A^2
+        F2 *= 1e-12
+        IQD = F2/average_volume*1e8*volfraction
+# RKH SORT THIS OUT WHEN HAVE NEW MODEL
+    vfff=volfraction
+    print("radius_effective, volfaction for S(Q) ",radius_effective,vfff)
+    SQ = hardsphere_simple(q, radius_effective, vfff)
+    beta = F1**2/F2
+    SQ_EFF = 1 + beta*(SQ - 1)
+    IQSD = IQD*SQ
+    IQBD = IQD*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQD, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+
+# RKH copying Paul K's ellipsoid here, this computes everything for monodisperse case
+# and supplies partial results for polydisperse case.
+def hollow_cylinder_theta(q, radius, thickness, length, sld, sld_solvent,
+                    volfraction=0, radius_effective=None):
+    #creates values z and corresponding probabilities w from legendre-gauss quadrature
+    z, w = leggauss(76)
+    F1 = np.zeros_like(q)
+    F2 = np.zeros_like(q)
+    #use a u subsition(u=cos) and then u=(z+1)/2 to change integration from
+    #0->2pi with respect to alpha to -1->1 with respect to z, allowing us to use
+    #legendre-gauss quadrature
+    lower = 0.0
+    upper = 1.0
+    gamma_sq = (radius/(radius+thickness))**2
+    for k, qk in enumerate(q):
+        for i, zt in enumerate(z):
+            # quadrature loop
+            cos_theta = 0.5*( zt* (upper-lower) + lower + upper  )
+            sin_theta = sqrt(1.0 - cos_theta*cos_theta)
+            aaa=(radius+thickness)*qk*sin_theta
+            ## sas_J1 expects an array, so try direct use of J1
+            lam1 = J1(aaa)/aaa
+            aaa=radius*qk*sin_theta
+            lam2 = J1(aaa)/aaa
+            psi = (lam1 - gamma_sq*lam2)/(1.0 - gamma_sq)
+            #Note: lim_{thickness -> 0} psi = sas_J0(radius*qab)
+            #Note: lim_{radius -> 0} psi = sas_2J1x_x(thickness*qab)
+            aaa=0.5*length*qk*cos_theta
+            t2 = sin(aaa)/aaa
+#            t2 = sas_sinx_x(0.5*length*qk*cos_theta)
+            form = psi*t2
+            F1[i] += w[i] * form
+            F2[i] += w[i] * form * form
+    volume = pi*((radius + thickness)**2 - radius**2)*length
+    s = (sld - sld_solvent) * volume
+    F2 = F2*s*(upper - lower)/2.0
+    F1 = F1*s*s*(upper - lower)/2.0
+    if radius_effective is None:
+        radius_effective = ER_hollow_cylinder(radius, thickness, length)
+    SQ = hardsphere_simple(q, radius_effective, volfraction)
+    SQ_EFF = 1 + F1**2/F2*(SQ - 1)
+    IQM = 1e-4*F2/volume
+    IQSM = volfraction*IQM*SQ
+    IQBM = volfraction*IQM*SQ_EFF
+    return Theory(Q=q, F1=F1, F2=F2, P=IQM, S=SQ, I=IQSM, Seff=SQ_EFF, Ibeta=IQBM)
+#
+def ER_hollow_cylinder(radius, thickness, length):
+    """
+    :param radius:      Cylinder core radius
+    :param thickness:   Cylinder wall thickness
+    :param length:      Cylinder length
+    :return:            Effective radius
+    """
+    router = radius + thickness
+    if router == 0 or length == 0:
+        return 0.0
+    len1 = router
+    len2 = length/2.0
+    term1 = len1*len1*2.0*len2/2.0
+    term2 = 1.0 + (len2/len1)*(1.0 + 1/len2/2.0)*(1.0 + pi*len1/len2/2.0)
+    ddd = 3.0*term1*term2
+    diam = pow(ddd, (1.0/3.0))
+    return diam
+
+###############################################################################
+###############################################################################
+###############################################################################
+##################                                           ##################
+##################                   TESTS                   ##################
+##################                                           ##################
+###############################################################################
+###############################################################################
+###############################################################################
+
+def popn(d, keys):
+    """
+    Splits a dict into two, with any key of *d* which is in *keys* removed
+    from *d* and added to *b*. Returns *b*.
+    """
+    b = {}
+    for k in keys:
+        try:
+            b[k] = d.pop(k)
+        except KeyError:
+            pass
+    return b
+
+def sasmodels_theory(q, Pname, **pars):
+    """
+    Call sasmodels to compute the model with and without a hard sphere
+    structure factor.
+    """
+    #mono_pars = {k: (0 if k.endswith('_pd') else v) for k, v in pars.items()}
+    Ppars = pars.copy()
+    Spars = popn(Ppars, ['radius_effective', 'volfraction'])
+    Ipars = pars.copy()
+
+    # Autofill npts and nsigmas for the given pd type
+    for k, v in pars.items():
+        if k.endswith("_pd_type"):
+            if v == "gaussian":
+                n, nsigmas = N_GAUSS, NSIGMA_GAUSS
+            elif v == "schulz":
+                n, nsigmas = N_SCHULZ, NSIGMA_SCHULZ
+            Ppars.setdefault(k.replace("_pd_type", "_pd_n"), n)
+            Ppars.setdefault(k.replace("_pd_type", "_pd_nsigma"), nsigmas)
+            Ipars.setdefault(k.replace("_pd_type", "_pd_n"), n)
+            Ipars.setdefault(k.replace("_pd_type", "_pd_nsigma"), nsigmas)
+
+    #Ppars['scale'] = Spars.get('volfraction', 1)
+    P = build_model(Pname, q)
+    S = build_model("hardsphere", q)
+    I = build_model(Pname+"@hardsphere", q)
+    Pq = P(**Ppars)*pars.get('volfraction', 1)
+    Sq = S(**Spars)
+    Iq = I(**Ipars)
+    #Iq = Pq*Sq*pars.get('volfraction', 1)
+    #Sq = Iq/Pq
+    #Iq = None#= Sq = None
+    r = dict(I._kernel.results())
+    #print(r)
+    return Theory(Q=q, F1=None, F2=None, P=Pq, S=None, I=None, Seff=r["S_eff(Q)"], Ibeta=Iq)
+
+def compare(title, target, actual, fields='F1 F2 P S I Seff Ibeta'):
+    """
+    Plot fields in common between target and actual, along with relative error.
+    """
+    available = [s for s in fields.split()
+                 if getattr(target, s) is not None and getattr(actual, s) is not None]
+    rows = len(available)
+    for row, field in enumerate(available):
+        Q = target.Q
+        I1, I2 = getattr(target, field), getattr(actual, field)
+        plt.subplot(rows, 2, 2*row+1)
+        plt.loglog(Q, abs(I1), label="target "+field)
+        plt.loglog(Q, abs(I2), label="value "+field)
+        #plt.legend(loc="upper left", bbox_to_anchor=(1,1))
+        plt.legend(loc='lower left')
+        plt.subplot(rows, 2, 2*row+2)
+        plt.semilogx(Q, I2/I1 - 1, label="relative error")
+        #plt.semilogx(Q, I1/I2 - 1, label="relative error")
+    plt.tight_layout()
+    plt.suptitle(title)
+    plt.show()
+
+def data_file(name):
+    return os.path.join(BETA_DIR, 'data_files', name)
+
+def load_sasfit(path):
+    data = np.loadtxt(path, dtype=str, delimiter=';').T
+    data = np.vstack((list(map(float, v)) for v in data[0:2]))
+    return data
+
+COMPARISON = {}  # Type: Dict[(str,str,str)] -> Callable[(), None]
+
+def compare_sasview_sphere(pd_type='schulz'):
+    q = np.logspace(-5, 0, 250)
+    model = 'sphere'
+    pars = dict(
+        radius=20, sld=4, sld_solvent=1,
+        background=0,
+        radius_pd=.1, radius_pd_type=pd_type,
+        volfraction=0.15,
+        radius_effective=12.59921049894873,  # equivalent average sphere radius
+        )
+    target = sasmodels_theory(q, model, effective_radius_mode=0, structure_factor_mode=1, **pars)
+    actual = sphere_r(q, norm='sasview', **pars)
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'sphere', 'gaussian')] = lambda: compare_sasview_sphere(pd_type='gaussian')
+COMPARISON[('sasview', 'sphere', 'schulz')] = lambda: compare_sasview_sphere(pd_type='schulz')
+
+
+def compare_sasview_vesicle(pd_type='gaussian'):
+    q = np.logspace(-5, 0, 250)
+    model = 'vesicle'
+    print("F2 seems OK, but big issues with S(Q), wo work in progress")
+# NOTE parameers for vesicle model are soon to be changed to remove "volfraction"
+    pars = dict(
+        radius=20, thickness=10, sld=4, sld_solvent=1, volfraction=0.03,
+        background=0,
+        radius_pd=0.1, thickness_pd=0.0, radius_pd_type=pd_type, thickness_pd_type=pd_type
+        #,radius_effective=12.59921049894873,  # equivalent average sphere radius
+        )
+    target = sasmodels_theory(q, model, effective_radius_mode=0, structure_factor_mode=1, **pars)
+    actual = vesicle_pe(q, norm='sasview', **pars)
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'vesicle', 'gaussian')] = lambda: compare_sasview_vesicle(pd_type='gaussian')
+COMPARISON[('sasview', 'vesicle', 'schulz')] = lambda: compare_sasview_vesicle(pd_type='schulz')
+
+def compare_sasview_hollow_cylinder(pd_type='gaussian'):
+    q = np.logspace(-5, 0, 250)
+    model = 'hollow_cylinder'
+    print(model)
+    print("just about works for monodisperse, polydisperse needs work")
+# NOTE parameters for hollow_cylinder model are soon to be changed to remove "volfraction"
+# setting all three pd to zero is OK
+    pars = dict(
+        radius=20, thickness=10, length=80, sld=4, sld_solvent=1,
+        background=0,
+        radius_pd=0.1, thickness_pd=0.0, length_pd=0.0, radius_pd_type=pd_type, thickness_pd_type=pd_type, length_pd_type=pd_type
+        #,radius_effective=12.59921049894873,  # equivalent average sphere radius
+        )
+    target = sasmodels_theory(q, model, effective_radius_mode=0, structure_factor_mode=1, **pars)
+    actual = hollow_cylinder_pe(q, norm='sasview', **pars)
+# RKH monodisp was OK,    actual = hollow_cylinder_theta(q,radius=20, thickness=10, length=80, sld=4, sld_solvent=1 )
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'hollow_cylinder', 'gaussian')] = lambda: compare_sasview_hollow_cylinder(pd_type='gaussian')
+COMPARISON[('sasview', 'hollow_cylinder', 'schulz')] = lambda: compare_sasview_hollow_cylinder(pd_type='schulz')
+
+
+def compare_sasview_ellipsoid(pd_type='gaussian'):
+    q = np.logspace(-5, 0, 50)
+    model = 'ellipsoid'
+    pars = dict(
+        radius_polar=20, radius_equatorial=400, sld=4, sld_solvent=1,
+        background=0,
+        radius_polar_pd=0.1, radius_polar_pd_type=pd_type,
+        radius_equatorial_pd=0.1, radius_equatorial_pd_type=pd_type,
+        volfraction=0.15,
+        radius_effective=270.7543927018,
+        #radius_effective=12.59921049894873,
+        )
+    target = sasmodels_theory(q, model, effective_radius_mode=0, structure_factor_mode=1, **pars)
+    actual = ellipsoid_pe(q, norm='sasview', **pars)
+# RKH test       actual = ellipsoid_theta(q, radius_polar=20, radius_equatorial=400, sld=4, sld_solvent=1, volfraction=0.15, radius_effective=270.)
+    title = " ".join(("sasmodels", model, pd_type))
+    compare(title, target, actual)
+COMPARISON[('sasview', 'ellipsoid', 'gaussian')] = lambda: compare_sasview_ellipsoid(pd_type='gaussian')
+COMPARISON[('sasview', 'ellipsoid', 'schulz')] = lambda: compare_sasview_ellipsoid(pd_type='schulz')
+
+def compare_yun_ellipsoid_mono():
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0, 'radius_polar_pd_type': 'gaussian',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0, 'radius_equatorial_pd_type': 'gaussian',
+        'sld': 2, 'sld_solvent': 1,
+        'volfraction': 0.15,
+        # Yun uses radius for same volume sphere for effective radius
+        # whereas sasview uses the average curvature.
+        'radius_effective': 12.59921049894873,
+    }
+
+    data = np.loadtxt(data_file('yun_ellipsoid.dat'),skiprows=2).T
+    Q = data[0]
+    F1 = data[1]
+    P = data[3]*pars['volfraction']
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = ellipsoid_pe(Q, norm='yun', **pars)
+    title = " ".join(("yun", "ellipsoid", "no pd"))
+    #compare(title, target, actual, fields="P S I Seff Ibeta")
+    compare(title, target, actual)
+COMPARISON[('yun', 'ellipsoid', 'gaussian')] = compare_yun_ellipsoid_mono
+COMPARISON[('yun', 'ellipsoid', 'schulz')] = compare_yun_ellipsoid_mono
+
+def compare_yun_sphere_gauss():
+    # Note: yun uses gauss limits from R0/10 to R0 + 5 sigma steps sigma/100
+    # With pd = 0.1, that's 14 sigma and 1400 points.
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'gaussian',
+        'sld': 6, 'sld_solvent': 0,
+        'volfraction': 0.1,
+    }
+
+    data = np.loadtxt(data_file('testPolydisperseGaussianSphere.dat'), skiprows=2).T
+    Q = data[0]
+    F1 = data[1]
+    F2 = data[2]
+    P = data[3]
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = sphere_r(Q, norm='yun', **pars)
+    title = " ".join(("yun", "sphere", "10% dispersion 10% Vf"))
+    compare(title, target, actual)
+    data = np.loadtxt(data_file('testPolydisperseGaussianSphere2.dat'), skiprows=2).T
+    pars.update(radius_pd=0.15)
+    Q = data[0]
+    F1 = data[1]
+    F2 = data[2]
+    P = data[3]
+    S = data[5]
+    Seff = data[6]
+    target = Theory(Q=Q, F1=F1, P=P, S=S, Seff=Seff)
+    actual = sphere_r(Q, norm='yun', **pars)
+    title = " ".join(("yun", "sphere", "15% dispersion 10% Vf"))
+    compare(title, target, actual)
+COMPARISON[('yun', 'sphere', 'gaussian')] = compare_yun_sphere_gauss
+
+
+def compare_sasfit_sphere_gauss():
+    #N=1,s=2,X0=20,distr radius R=20,eta_core=4,eta_solv=1,.3
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'gaussian',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3,
+    }
+
+    Q, IQ = load_sasfit(data_file('sasfit_sphere_IQD.txt'))
+    Q, IQSD = load_sasfit(data_file('sasfit_sphere_IQSD.txt'))
+    Q, IQBD = load_sasfit(data_file('sasfit_sphere_IQBD.txt'))
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_sphere_sq.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_sphere_sqeff.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=SQ, I=IQSD, Seff=SQ_EFF, Ibeta=IQBD)
+    actual = sphere_r(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "sphere", "pd=10% gaussian"))
+    compare(title, target, actual)
+    #compare(title, target, actual, fields="P")
+COMPARISON[('sasfit', 'sphere', 'gaussian')] = compare_sasfit_sphere_gauss
+
+def compare_sasfit_sphere_schulz():
+    #radius=20,sld=4,sld_solvent=1,volfraction=0.3,radius_pd=0.1
+    #We have scaled the output from sasfit by 1e-4*volume*volfraction
+    #0.10050378152592121
+    pars = {
+        'radius': 20, 'radius_pd': 0.1, 'radius_pd_type': 'schulz',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3,
+    }
+
+    Q, IQ = load_sasfit(data_file('richard_test.txt'))
+    Q, IQSD = load_sasfit(data_file('richard_test2.txt'))
+    Q, IQBD = load_sasfit(data_file('richard_test3.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=None, I=IQSD, Seff=None, Ibeta=IQBD)
+    actual = sphere_r(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "sphere", "pd=10% schulz"))
+    compare(title, target, actual)
+COMPARISON[('sasfit', 'sphere', 'schulz')] = compare_sasfit_sphere_schulz
+
+def compare_sasfit_ellipsoid_schulz():
+    #polarradius=20, equatorialradius=10, sld=4,sld_solvent=1,volfraction=0.3,radius_polar_pd=0.1
+    #Effective radius =13.1353356684
+    #We have scaled the output from sasfit by 1e-4*volume*volfraction
+    #0.10050378152592121
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0.1, 'radius_polar_pd_type': 'schulz',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0., 'radius_equatorial_pd_type': 'schulz',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0.3, 'radius_effective': 13.1353356684,
+    }
+
+    Q, IQ = load_sasfit(data_file('richard_test4.txt'))
+    Q, IQSD = load_sasfit(data_file('richard_test5.txt'))
+    Q, IQBD = load_sasfit(data_file('richard_test6.txt'))
+    target = Theory(Q=Q, F1=None, F2=None, P=IQ, S=None, I=IQSD, Seff=None, Ibeta=IQBD)
+    actual = ellipsoid_pe(Q, norm="sasfit", **pars)
+    title = " ".join(("sasfit", "ellipsoid", "pd=10% schulz"))
+    compare(title, target, actual)
+COMPARISON[('sasfit', 'ellipsoid', 'schulz')] = compare_sasfit_ellipsoid_schulz
+
+
+def compare_sasfit_ellipsoid_gaussian():
+    pars = {
+        'radius_polar': 20, 'radius_polar_pd': 0, 'radius_polar_pd_type': 'gaussian',
+        'radius_equatorial': 10, 'radius_equatorial_pd': 0, 'radius_equatorial_pd_type': 'gaussian',
+        'sld': 4, 'sld_solvent': 1,
+        'volfraction': 0, 'radius_effective': None,
+    }
+
+    #Rp=20,Re=10,eta_core=4,eta_solv=1
+    Q, PQ0 = load_sasfit(data_file('sasfit_ellipsoid_IQM.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ0)
+    compare("sasfit ellipsoid no poly", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr 10% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp10 = load_sasfit(data_file('sasfit_ellipsoid_IQD.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.1, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp10)
+    compare("sasfit ellipsoid P(Q) 10% Rp", target, actual); plt.show()
+    #N=1,s=1,X0=10,distr 10% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re10 = load_sasfit(data_file('sasfit_ellipsoid_IQD2.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.1, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re10)
+    compare("sasfit ellipsoid P(Q) 10% Re", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr 30% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp30 = load_sasfit(data_file('sasfit_ellipsoid_IQD3.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.3, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp30)
+    compare("sasfit ellipsoid P(Q) 30% Rp", target, actual); plt.show()
+    #N=1,s=3,X0=10,distr 30% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re30 = load_sasfit(data_file('sasfit_ellipsoid_IQD4.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.3, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re30)
+    compare("sasfit ellipsoid P(Q) 30% Re", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr 60% polar Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Rp60 = load_sasfit(data_file('sasfit_ellipsoid_IQD5.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.6, radius_equatorial_pd=0.0, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Rp60)
+    compare("sasfit ellipsoid P(Q) 60% Rp", target, actual); plt.show()
+    #N=1,s=6,X0=10,distr 60% equatorial Rp=20,Re=10,eta_core=4,eta_solv=1, no structure poly
+    Q, PQ_Re60 = load_sasfit(data_file('sasfit_ellipsoid_IQD6.txt'))
+    pars.update(volfraction=0, radius_polar_pd=0.0, radius_equatorial_pd=0.6, radius_effective=None)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, P=PQ_Re60)
+    compare("sasfit ellipsoid P(Q) 60% Re", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 15% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq2.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff2.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 15% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.15
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq3.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff3.txt'))
+    pars.update(volfraction=0.15, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 15% Vf", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq4.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff4.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 30% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq5.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff5.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 30% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.3
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq6.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff6.txt'))
+    pars.update(volfraction=0.3, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 30% Vf", target, actual); plt.show()
+
+    #N=1,s=2,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.1354236254,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq7.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff7.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.1, radius_equatorial_pd=0, radius_effective=13.1354236254)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 10% Rp 60% Vf", target, actual); plt.show()
+    #N=1,s=6,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.0901197149,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq8.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff8.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.3, radius_equatorial_pd=0, radius_effective=13.0901197149)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 30% Rp 60% Vf", target, actual); plt.show()
+    #N=1,s=12,X0=20,distr polar Rp=20,Re=10,eta_core=4,eta_solv=1, hardsphere ,13.336060917,.6
+    Q, SQ = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sq9.txt'))
+    Q, SQ_EFF = load_sasfit(data_file('sasfit_polydisperse_ellipsoid_sqeff9.txt'))
+    pars.update(volfraction=0.6, radius_polar_pd=0.6, radius_equatorial_pd=0, radius_effective=13.336060917)
+    actual = ellipsoid_pe(Q, norm='sasfit', **pars)
+    target = Theory(Q=Q, S=SQ, Seff=SQ_EFF)
+    compare("sasfit ellipsoid P(Q) 60% Rp 60% Vf", target, actual); plt.show()
+COMPARISON[('sasfit', 'ellipsoid', 'gaussian')] = compare_sasfit_ellipsoid_gaussian
+
+def main():
+    key = tuple(sys.argv[1:])
+    if key not in COMPARISON:
+        print("Usage: python sasfit_compare.py [sasview|sasfit|yun] [sphere|ellipsoid|vesicle|hollow_cylinder] [gaussian|schulz]")
+        print("But not for [yun sphere schulz], and vesicle & hollow_cylinder only with sasview.")
+        print("Note this compares chosen source against internal python code here, with adjustment for known scale etc issues.")
+        return
+    comparison = COMPARISON[key]
+    comparison()
+
+if __name__ == "__main__":
+    main()
Index: explore/beta/sphereFormFactor.m
===================================================================
--- explore/beta/sphereFormFactor.m	(revision e262dd68f6ba42ac365c68553db9621443f502ee)
+++ explore/beta/sphereFormFactor.m	(revision e262dd68f6ba42ac365c68553db9621443f502ee)
@@ -0,0 +1,5 @@
+function data=sphereFormFactor(Q,radius)
+
+data= ( 3 * (sin(Q*radius) - Q*radius.*cos(Q*radius)) ./ (Q*radius).^3).^2 ;
+
+return;
Index: explore/beta/testPolyDiseperseSphricalBeta.m
===================================================================
--- explore/beta/testPolyDiseperseSphricalBeta.m	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
+++ explore/beta/testPolyDiseperseSphricalBeta.m	(revision cdd676ee81b9f92bb2f3239a7585f3d382f933f7)
@@ -0,0 +1,88 @@
+close all
+clear all
+
+R0=20;       %mean radius. unit: Angstroms
+PDI=0.1;       %unit: relative polydispersity
+volF=0.1;
+contrast=6e-6;    %contrast,angstrom^-1, scattering length density difference
+
+Filename='testPolydisperseGaussianSphere.dat';
+
+Q=[0.001:0.001:0.8];
+
+N=10;
+
+deltaR=R0*PDI;
+SplitN=100;
+R=[R0/N:deltaR/SplitN:R0+5*deltaR];
+
+FGaussian=1/sqrt(2*pi*deltaR^2)*exp(-(R-R0).^2/2/deltaR^2);
+
+Ni=FGaussian*deltaR/SplitN;
+%trapz(R,FGaussian)
+%sum(FGaussian*deltaR/SplitN)
+sum(Ni)
+
+
+Vi=4*pi*R.^3/3;
+AverageVolume=sum(Ni.*Vi);
+
+
+IQN=zeros(size(Q));
+%IQ=sphereFormFactor(Q,R0);
+
+for i=1:length(R)
+    IQN=IQN+Ni(i)*Vi(i)^2*contrast^2*sphereFormFactor(Q,R(i));
+    %IQ=1*AverageVolume^2*contrast^2*sphereFormFactor(Q,R0);
+    %IQ=sphereFormFactor(Q,R(500));
+end
+
+IQ=volF/AverageVolume*IQN;
+
+IQ=IQ*1e8;  %convert from A^-1 to cm^-1
+loglog(Q,IQ,'b.-')
+
+FQ=zeros(size(Q));
+
+for i=1:length(R)
+    FQ=FQ+Ni(i)*Vi(i)*contrast*3*(sin(Q*R(i)) - Q*R(i).*cos(Q*R(i))) ./ (Q*R(i)).^3;
+end
+
+beta=FQ.^2./IQN;
+figure
+semilogx(Q,beta,'g*-');
+
+%stop
+
+NormIQN=IQN/IQN(1);
+
+FQ2=beta.*IQ;
+
+normQ=Q*R0*2;
+Sq=HSS_SQ(volF,normQ);
+
+figure
+loglog(Q,IQ,'bo-');
+figure
+plot(Q,beta,'g*-');
+figure
+plot(Q,Sq,'b.-');
+figure
+Sq_eff=1+beta.*(Sq-1);
+plot(Q,Sq_eff,'gd-');
+
+fileID=fopen(Filename,'w');
+
+FileString=strcat('Filename:',Filename, '**R0=', num2str(R0),'**PDI=', num2str(PDI),...
+    '**contrast',num2str(contrast), '**volF=',num2str(volF));
+Outputformat='File format : Q, <FQ>, <FQ^2>, PQ, betaQ, SQ, SQ_Eff';
+fprintf(fileID,'%s\n', FileString);
+fprintf(fileID,'%s\n', Outputformat);
+for i=1:length(Q)
+    %file format : Q, <FQ>, <FQ^2>, PQ, betaQ, SQ, SQ_Eff
+    fprintf(fileID,'%e\t%e\t%e\t%e\t%e\t%e\t%e\n',...
+        Q(i),FQ(i),IQN(i),IQ(i),beta(i),Sq(i),Sq_eff(i));
+end
+
+fclose(fileID)
+
Index: explore/precision.py
===================================================================
--- explore/precision.py	(revision fba9ca0239129ed28284a0b435ba2a9524913f36)
+++ explore/precision.py	(revision fba9ca0239129ed28284a0b435ba2a9524913f36)
@@ -403,10 +403,12 @@
 )
 add_function(
-    name="debye",
+    name="gauss_coil",
     mp_function=lambda x: 2*(mp.exp(-x**2) + x**2 - 1)/x**4,
     np_function=lambda x: 2*(np.expm1(-x**2) + x**2)/x**4,
     ocl_function=make_ocl("""
     const double qsq = q*q;
-    if (qsq < 1.0) { // Pade approximation
+    // For double: use O(5) Pade with 0.5 cutoff (10 mad + 1 divide)
+    // For single: use O(7) Taylor with 0.8 cutoff (7 mad)
+    if (qsq < 0.0) {
         const double x = qsq;
         if (0) { // 0.36 single
@@ -418,5 +420,5 @@
             const double B1=3./8., B2=3./56., B3=1./336.;
             return (((A3*x + A2)*x + A1)*x + 1.)/(((B3*x + B2)*x + B1)*x + 1.);
-        } else if (1) { // 1.0 for single, 0.25 for double
+        } else if (0) { // 1.0 for single, 0.25 for double
             // PadeApproximant[2*Exp[-x^2] + x^2-1)/x^4, {x, 0, 8}]
             const double A1=1./15., A2=1./60, A3=0., A4=1./75600.;
@@ -431,5 +433,5 @@
                   /(((((B5*x + B4)*x + B3)*x + B2)*x + B1)*x + 1.);
         }
-    } else if (qsq < 1.) { // Taylor series; 0.9 for single, 0.25 for double
+    } else if (qsq < 0.8) {
         const double x = qsq;
         const double C0 = +1.;
