update from Atlas with major reorg

attic/classes/spherical-coordinates.txt

@@ -0,0 +1,48 @@
+#	Test data for spherical coordinates computed by Vector.angles()
+#
+#						π	π/2	π/3	π/4
+#						3.141592653590	1.570796326795	1.047197551197	0.785398163397
+#
+#							azimuth
+#	x	y					θ
+#	x1	x2				r	Φ1
+	1	1				1.414213562373	0.785398163397
+	1	0				1.000000000000	0.000000000000
+	0	1				1.000000000000	1.570796326795
+	0	0				0.000000000000	0.000000000000
+	1	-1				1.414213562373	5.497787143782
+	-1	1				1.414213562373	2.356194490192
+	0	-1				1.000000000000	4.712388980385
+	-1	-1				1.414213562373	3.926990816987
+#
+#	x	y	z				θ	Φ
+#	x1	x2	x3			r	Φ1	Φ2
+	1	1	1			1.732050807569	0.955316618125	0.785398163397
+	2	2	2			3.464101615138	0.955316618125	0.785398163397
+	0	0	0			0.000000000000	0.000000000000	0.000000000000
+	1	0	0			1.000000000000	0.000000000000	0.000000000000
+	0	1	0			1.000000000000	1.570796326795	0.000000000000
+	0	0	1			1.000000000000	1.570796326795	1.570796326795
+	1	1	0			1.414213562373	0.785398163397	0.000000000000
+	1	0	1			1.414213562373	0.785398163397	1.570796326795
+	0	1	1			1.414213562373	1.570796326795	0.785398163397
+	1	1	-1			1.732050807569	0.955316618125	5.497787143782
+#
+#	x	y	z	t			θ	Φ
+#	x1	x2	x3	x4		r	Φ1	Φ2	Φ3
+	1	1	1	0		1.732050807569	0.955316618125	0.785398163397	0.000000000000
+	2	2	2	0		3.464101615138	0.955316618125	0.785398163397	0.000000000000
+	1	1	1	1		2.000000000000	1.047197551197	0.955316618125	0.785398163397
+	2	2	2	2		4.000000000000	1.047197551197	0.955316618125	0.785398163397
+	1	0	0	0		1.000000000000	0.000000000000	0.000000000000	0.000000000000
+	0	1	0	0		1.000000000000	1.570796326795	0.000000000000	0.000000000000
+	0	0	1	0		1.000000000000	1.570796326795	1.570796326795	0.000000000000
+	0	0	0	1		1.000000000000	1.570796326795	1.570796326795	1.570796326795
+	1	1	0	0		1.414213562373	0.785398163397	0.000000000000	0.000000000000
+	0	1	1	0		1.414213562373	1.570796326795	0.785398163397	0.000000000000
+	0	0	1	1		1.414213562373	1.570796326795	1.570796326795	0.785398163397
+	1	0	0	1		1.414213562373	0.785398163397	1.570796326795	1.570796326795
+	1	0	1	0		1.414213562373	0.785398163397	1.570796326795	0.000000000000
+	0	1	0	1		1.414213562373	1.570796326795	0.785398163397	1.570796326795
+	1	1	1	-1		2.000000000000	1.047197551197	0.955316618125	5.497787143782
+	-1	-1	-1	-1		2.000000000000	2.094395102393	2.186276035465	3.926990816987

attic/classes/sum-nth-element.rst

@@ -0,0 +1,85 @@
+======================================
+Pythonic way to sum n-th list element?
+======================================
+
+Examples inspired by Guy Middleton's question on Python-list, Fri Apr 18 22:21:08 CEST 2003. Message: https://mail.python.org/pipermail/python-list/2003-April/218568.html
+
+Guy Middleton::
+
+    >>> my_list = [[1, 2, 3], [40, 50, 60], [9, 8, 7]]
+    >>> import functools as ft
+    >>> ft.reduce(lambda a, b: a+b, [sub[1] for sub in my_list])
+    60
+
+LR::
+
+    >>> ft.reduce(lambda a, b: a + b[1], my_list, 0)
+    60
+
+Fernando Perez::
+
+    >>> import numpy as np
+    >>> my_array = np.array(my_list)
+    >>> np.sum(my_array[:, 1])
+    60
+
+Skip Montanaro::
+
+    >>> import operator
+    >>> ft.reduce(operator.add, [sub[1] for sub in my_list], 0)
+    60
+    >>> ft.reduce(operator.add, [sub[1] for sub in []])
+    Traceback (most recent call last):
+      ...
+    TypeError: reduce() of empty sequence with no initial value
+    >>> ft.reduce(operator.add, [sub[1] for sub in []], 0)
+    0
+
+
+Evan Simpson::
+
+    >>> total = 0
+    >>> for sub in my_list:
+    ...     total += sub[1]
+    >>> total
+    60
+
+Alex Martelli (``sum`` was added in Python 2.3, released July 9, 2003)::
+
+    >>> sum([sub[1] for sub in my_list])
+    60
+
+After generator expressions (added in Python 2.4, November 30, 2004)::
+
+    >>> sum(sub[1] for sub in my_list)
+    60
+
+If you want the sum of a list of items, you should write it in a way 
+that looks like "the sum of a list of items", not in a way that looks 
+like "loop over these items, maintain another variable t, perform a 
+sequence of additions".  Why do we have high level languages if not to 
+express our intentions at a higher level and let the language worry 
+about what low-level operations are needed to implement it?
+
+David Eppstein
+
+Alex Martelli
+
+https://mail.python.org/pipermail/python-list/2003-April/186311.html
+
+"The sum" is so frequently needed that I wouldn't mind at all if
+Python singled it out as a built-in.  But "reduce(operator.add, ..."
+just isn't a great way to express it, in my opinion (and yet as an
+old APL'er, and FP-liker, I _should_ like it -- but I don't).
+
+https://mail.python.org/pipermail/python-list/2003-April/225323.html
+
+Four years later, having coded a lot of Python, taught it widely,
+written a lot about it, and so on, I've changed my mind: I now
+think that reduce is more trouble than it's worth and Python
+would be better off without it, if it was being designed from
+scratch today -- it would not substantially reduce (:-) Python's 
+power and WOULD substantially ease the teaching/&c task.  That's
+not a strong-enough argument to REMOVE a builtin, of course, and
+thus that's definitely NOT what I'm arguing for.  But I do suggest
+avoiding reduce in most cases -- that's all.

attic/classes/test_vector_spherical.py

@@ -0,0 +1,37 @@
+"""
+Test spherical coordinates in ``Vector`` class
+"""
+
+import sys
+from vector_v5 import Vector
+
+FIXTURE = 'spherical-coordinates.txt'
+EPSILON = 10**-8
+
+def parse_float_cells(cells):
+    floats = []
+    for cell in cells:
+        try:
+            floats.append(float(cell))
+        except ValueError:
+            continue
+    return floats
+
+def load_fixture(verbose=False):
+    with open(FIXTURE, encoding='utf8') as text:
+        for line in text:
+            if line.startswith('#'):  # comment line
+                continue
+            cells = line.split('\t')
+            cartesian = parse_float_cells(cells[:5])
+            spherical = parse_float_cells(cells[5:])
+            v = Vector(cartesian)
+            if verbose:
+                print(repr(v), '\t->', spherical)
+            diff = abs(abs(v) - spherical[0])
+            assert diff < EPSILON, 'expected {}, got {}'.format(spherical[0], abs(v))
+            assert all(abs(av - af) < EPSILON for av, af in zip(v.angles(), spherical[1:])), (
+                'expected {}, got {}'.format(spherical[1:], list(v.angles())))
+
+if __name__=='__main__':
+    load_fixture('-v' in sys.argv)