Merge branch 'fix-sg-posvars'

* fix null-space normalization w/r to round-offs
* fix signedRatStr for near-integer numbers
* fix position formula for Wyckoff site e in SG 209  F432

Resolve #43.

Author: pavoljuhas

src/diffpy/structure/symmetryutilities.py

@@ -362,7 +362,7 @@ def signedRatStr(self, x):
 
         Return string.
         """
-        s = str(x)
+        s = "{:.8g}".format(x)
         if len(s) < 6:  return "%+g" % x
         den = numpy.array([3.0, 6.0, 7.0, 9.0])
         nom = x * den
@@ -387,11 +387,19 @@ def _findNullSpace(self):
         self.null_space = self.null_space[order[::-1]]
         # rationalize by the smallest element larger than cutoff
         cutoff = 1.0/32
-        for i in range(len(self.null_space)):
-            row = self.null_space[i]
-            small = numpy.fabs(row[numpy.fabs(row) > cutoff]).min()
-            signedsmall = row[numpy.fabs(row) == small][0]
-            self.null_space[i] = self.null_space[i] / signedsmall
+        for row in self.null_space:
+            abrow = numpy.abs(row)
+            sgrow = numpy.sign(row)
+            # equalize items with round-off-equal absolute value
+            ii = abrow.argsort()
+            delta = 1e-8 * abrow[ii[-1]]
+            for k in ii[1:]:
+                if abrow[k] - abrow[k - 1] < delta:
+                    abrow[k] = abrow[k - 1]
+            # find the smallest nonzero absolute element
+            jnz = numpy.flatnonzero(abrow > cutoff)
+            idx = jnz[abrow[jnz].argmin()]
+            row[:] = (sgrow * abrow) / sgrow[idx] / abrow[idx]
         return
 
 

src/diffpy/structure/tests/testsymmetryutilities.py

@@ -210,6 +210,15 @@ def test___init__(self):
         self.assertEqual(16, self.g227oc.multiplicity)
         return
 
+
+    def test_signedRatStr(self):
+        "check GeneratorSite.signedRatStr()"
+        g = self.g117c
+        self.assertEqual('-1', g.signedRatStr(-1.00000000000002))
+        self.assertEqual('+1', g.signedRatStr(1.00000000000002))
+        return
+
+
     def test_positionFormula(self):
         """check GeneratorSite.positionFormula()
         """
@@ -236,6 +245,20 @@ def test_positionFormula(self):
         self.assertEqual([], self.g227oc.pparameters)
         return
 
+
+    def test_positionFormula_sg209(self):
+        """check positionFormula at [x, 1-x, -x] site or F432 space group.
+        """
+        sg209 = GetSpaceGroup('F 4 3 2')
+        xyz = [0.05198,  0.94802,  -0.05198]
+        g209e = GeneratorSite(sg209, xyz)
+        pfm = g209e.positionFormula(xyz)
+        self.assertEqual('x', pfm['x'])
+        self.assertEqual('-x+1', pfm['y'].replace(' ', ''))
+        self.assertEqual('-x+1', pfm['z'].replace(' ', ''))
+        return
+
+
     def test_UFormula(self):
         """check GeneratorSite.UFormula()
         """