zero_at() method for RDF/CDF vectors

[Rob Beezer]

This patch adds a method to replace small entries of a floating-point vector with zeros, according to a provided tolerance. It mirrors the matrix method of the same name.

---

Apply only trac_11848-zero-at-vectors-v2.patch​ to the Sage library.

[Leif Leonhardy]

if
    s/complex matrices/complex vectors/
    s/imaginaryparts/imaginary parts/
then
    ok

(Not yet tested, will do shortly...)

[Rob Beezer]

Replying to leif:

Thanks for the editorial work. ;-) v2 patch includes indicated changes.

[Leif Leonhardy]

Replying to rbeezer:

Replying to leif:

Thanks for the editorial work. ;-) v2 patch includes indicated changes.

Yep, immediately seen it. :)

[Leif Leonhardy]

This function is (e.g.) required by a doctest fix for #7852:

sage/misc/preparser.py

@@ -1383 +1383 @@
 
             sage: A = matrix(RDF, 5, 5, 2)
             sage: b = vector(RDF, 5, range(5))
-            sage: A \ b
+            sage: # On at least one platform, we get a "negative zero":
+            sage: v = A \ b
+            sage: v.zero_at(1e-19)
             (0.0, 0.5, 1.0, 1.5, 2.0)
-            sage: A._backslash_(b)
+            sage: v = A._backslash_(b)
+            sage: v.zero_at(1e-19)
             (0.0, 0.5, 1.0, 1.5, 2.0)
-            sage: A * BackslashOperator() * b
+            sage: v = A * BackslashOperator() * b
+            sage: v.zero_at(1e-19)
             (0.0, 0.5, 1.0, 1.5, 2.0)
         """
         return self.left._backslash_(right)

With both patches applied, the tests now pass on the Skynet machine "cleo" (Linux IA64 / Itanium 2), where they previously failed, so positive review.

[Leif Leonhardy]

Now also used in sage/matrix/matrix_double_dense.pyx, to fix another doctest error introduced by #7852 (noisy zero in a vector result).