zero_at() method for RDF/CDF vectors

[rbeezer]

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 attachment: trac_11848-zero-at-vectors-v2.patch to the Sage library.

CC: @nexttime

Component: linear algebra

Author: Rob Beezer

Reviewer: Leif Leonhardy

Merged: sage-4.7.2.alpha3

Issue created by migration from https://trac.sagemath.org/ticket/11848

[rbeezer]

Attachment: trac_11848-zero-at-vectors.patch.gz

[rbeezer]

Author: Rob Beezer

[nexttime]

comment:2

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

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

[rbeezer]

comment:3

Attachment: trac_11848-zero-at-vectors-v2.patch.gz

Replying to @nexttime:

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

[nexttime]

comment:4

Replying to @rbeezer:

Replying to @nexttime:

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

Yep, immediately seen it. :)

[nexttime]

Description changed:

--- 
+++ 
@@ -1 +1,6 @@
 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 [attachment: trac_11848-zero-at-vectors-v2.patch](https://github.com/sagemath/sage-prod/files/10653733/trac_11848-zero-at-vectors-v2.patch.gz) to the Sage library.
+

[nexttime]

Reviewer: Leif Leonhardy

[nexttime]

comment:5

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

diff --git a/sage/misc/preparser.py b/sage/misc/preparser.py
--- a/sage/misc/preparser.py
+++ b/sage/misc/preparser.py
@@ -1383,11 +1383,15 @@
 
             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.