Utils: PEP8 changes.

pykrylov/tools/utils.py

@@ -1,22 +1,26 @@
-# Various utilities.
+"""Utilities related to linear operators."""
 
 import numpy as np
 from math import copysign, sqrt
 
 
 def machine_epsilon():
+    """Return the machine epsilon in double precision."""
     return np.finfo(np.double).eps
 
 
 def roots_quadratic(q2, q1, q0, tol=1.0e-8, nitref=1):
-    """
+    """Find the real roots of a quadratic.
+
     Find the real roots of the quadratic q(x) = q2 * x^2 + q1 * x + q0.
     The numbers a0, a1 and a0 must be real.
 
     This function is written after the GALAHAD function of the same name.
     See http://galahad.rl.ac.uk.
     """
-    a2 = float(q2) ; a1 = float(q1) ; a0 = float(q0)
+    a2 = float(q2)
+    a1 = float(q1)
+    a0 = float(q0)
 
     # Case of a linear function.
     if a2 == 0.0:
@@ -26,25 +30,25 @@ def roots_quadratic(q2, q1, q0, tol=1.0e-8, nitref=1):
             else:
                 return []
         else:
-            roots = [-a0/a1]
+            roots = [-a0 / a1]
     else:
         # Case of a quadratic.
         rhs = tol * a1 * a1
-        if abs(a0*a2) > rhs:
+        if abs(a0 * a2) > rhs:
             rho = a1 * a1 - 4.0 * a2 * a0
             if rho < 0.0:
                 return []
             # There are two real roots.
             d = -0.5 * (a1 + copysign(sqrt(rho), a1))
-            roots = [d/a2, a0/d]
+            roots = [d / a2, a0 / d]
         else:
             # Ill-conditioned quadratic.
-            roots = [-a1/a2, 0.0]
+            roots = [-a1 / a2, 0.0]
 
     # Perform a few Newton iterations to improve accuracy.
     new_roots = []
     for root in roots:
-        for it in range(nitref):
+        for _ in range(nitref):
             val = (a2 * root + a1) * root + a0
             der = 2.0 * a2 * root + a1
             if der == 0.0:
@@ -57,7 +61,8 @@ def roots_quadratic(q2, q1, q0, tol=1.0e-8, nitref=1):
 
 
 def check_symmetric(op, repeats=10):
-    """
+    """Cheap symmetry check.
+
     Cheap check that a linear operator is symmetric. Supply `op`, a callable
     linear operator. A set of `repeats` random vectors will be generated.
     This function returns `True` or `False`.
@@ -67,7 +72,7 @@ def check_symmetric(op, repeats=10):
         return False
     eps = machine_epsilon()
     np.random.seed(1)
-    for k in xrange(repeats):
+    for _ in xrange(repeats):
         x = np.random.random(n)
         w = op * x
         r = op * w
@@ -80,6 +85,6 @@ def check_symmetric(op, repeats=10):
     return True
 
 
-if __name__ == '__main__':
-    roots = roots_quadratic(2.0e+20, .1, -4)
-    print 'Received: ', roots
+# if __name__ == '__main__':
+#     roots = roots_quadratic(2.0e+20, .1, -4)
+#     print 'Received: ', roots