[Numpy-svn] r5665 - trunk/numpy/lib
numpy-svn@scip...
numpy-svn@scip...
Wed Aug 20 10:48:29 CDT 2008
Author: cdavid
Date: 2008-08-20 10:48:17 -0500 (Wed, 20 Aug 2008)
New Revision: 5665
Modified:
trunk/numpy/lib/scimath.py
Log:
Add a note on scimath.sqrt for the definition of square root as the principal square root.
Modified: trunk/numpy/lib/scimath.py
===================================================================
--- trunk/numpy/lib/scimath.py 2008-08-19 06:33:09 UTC (rev 5664)
+++ trunk/numpy/lib/scimath.py 2008-08-20 15:48:17 UTC (rev 5665)
@@ -192,6 +192,22 @@
>>> np.lib.scimath.sqrt([-1,4])
array([ 0.+1.j, 2.+0.j])
+
+ Notes
+ -----
+
+ As the numpy.sqrt, this returns the principal square root of x, which is
+ what most people mean when they use square root; the principal square root
+ of x is not any number z such as z^2 = x.
+
+ For positive numbers, the principal square root is defined as the positive
+ number z such as z^2 = x.
+
+ The principal square root of -1 is i, the principal square root of any
+ negative number -x is defined a i * sqrt(x). For any non zero complex
+ number, it is defined by using the following branch cut: x = r e^(i t) with
+ r > 0 and -pi < t <= pi. The principal square root is then
+ sqrt(r) e^(i t/2).
"""
x = _fix_real_lt_zero(x)
return nx.sqrt(x)
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