Changeset 0fa687d in sasmodels

Timestamp:

Nov 25, 2015 4:09:56 PM (8 years ago)

Author:

Paul Kienzle <pkienzle@…>

Branches:

master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests

Children:

4b41184

Parents:

319ab14

Message:

Use taylor series near q=0 for accurate single precision calculations

File:

• sasmodels/models/sphere.py (modified) (1 diff)

sasmodels/models/sphere.py

@@ -90 +90 @@
 Iq = """
     const double qr = q*radius;
+    const double qrsq = qr*qr;
     double sn, cn;
     SINCOS(qr, sn, cn);
-    const double bes = qr==0.0 ? 1.0 : 3.0*(sn-qr*cn)/(qr*qr*qr);
+    // Use taylor series for low Q to avoid cancellation error.  Tested against
+    // the following expression in quad precision:
+    //     3.0*(sn-qr*cn)/(qr*qr*qr);
+    // Note that the values differ from sasview ~ 5e-12 rather than 5e-14, but
+    // in this case it is likely cancellation errors in the original expression
+    // using double precision that are the source.  Single precision only
+    // requires the first 3 terms.  Double precision requires the 4th term.
+    // The fifth term is not needed, and is commented out below.
+    const double bes = (qr < 1e-1)
+        ? 1.0 + qrsq*(-3./30. + qrsq*(3./840. + qrsq*(-3./45360.)))// + qrsq*(3./3991680.))))
+        : 3.0*(sn/qr - cn)/qrsq;
     const double fq = bes * (sld - solvent_sld) * form_volume(radius);
     return 1.0e-4*fq*fq;
     """
-
 
 Iqxy = """