Beef-up tests for the itertool docs. (gh-116679)

Doc/library/itertools.rst

@@ -998,7 +998,7 @@ The following recipes have a more mathematical flavor:
 
    def sum_of_squares(it):
        "Add up the squares of the input values."
-       # sum_of_squares([10, 20, 30]) -> 1400
+       # sum_of_squares([10, 20, 30]) --> 1400
        return math.sumprod(*tee(it))
 
    def reshape(matrix, cols):
@@ -1019,17 +1019,16 @@ The following recipes have a more mathematical flavor:
 
    def convolve(signal, kernel):
        """Discrete linear convolution of two iterables.
+       Equivalent to polynomial multiplication.
 
-       The kernel is fully consumed before the calculations begin.
+       Convolutions are mathematically commutative; however, the inputs are
-       The signal is consumed lazily and can be infinite.
+       evaluated differently.  The signal is consumed lazily and can be
-
+       infinite. The kernel is fully consumed before the calculations begin.
-       Convolutions are mathematically commutative.
-       If the signal and kernel are swapped,
-       the output will be the same.
 
        Article:  https://betterexplained.com/articles/intuitive-convolution/
        Video:    https://www.youtube.com/watch?v=KuXjwB4LzSA
        """
+       # convolve([1, -1, -20], [1, -3]) --> 1 -4 -17 60
        # convolve(data, [0.25, 0.25, 0.25, 0.25]) --> Moving average (blur)
        # convolve(data, [1/2, 0, -1/2]) --> 1st derivative estimate
        # convolve(data, [1, -2, 1]) --> 2nd derivative estimate
@@ -1067,7 +1066,7 @@ The following recipes have a more mathematical flavor:
           f(x)  =  x³ -4x² -17x + 60
           f'(x) = 3x² -8x  -17
        """
-       # polynomial_derivative([1, -4, -17, 60]) -> [3, -8, -17]
+       # polynomial_derivative([1, -4, -17, 60]) --> [3, -8, -17]
        n = len(coefficients)
        powers = reversed(range(1, n))
        return list(map(operator.mul, coefficients, powers))
@@ -1169,6 +1168,12 @@ The following recipes have a more mathematical flavor:
 
     >>> take(10, count())
     [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+    >>> # Verify that the input is consumed lazily
+    >>> it = iter('abcdef')
+    >>> take(3, it)
+    ['a', 'b', 'c']
+    >>> list(it)
+    ['d', 'e', 'f']
 
     >>> list(prepend(1, [2, 3, 4]))
     [1, 2, 3, 4]
@@ -1181,25 +1186,45 @@ The following recipes have a more mathematical flavor:
 
     >>> list(tail(3, 'ABCDEFG'))
     ['E', 'F', 'G']
+    >>> # Verify the input is consumed greedily
+    >>> input_iterator = iter('ABCDEFG')
+    >>> output_iterator = tail(3, input_iterator)
+    >>> list(input_iterator)
+    []
 
     >>> it = iter(range(10))
     >>> consume(it, 3)
+    >>> # Verify the input is consumed lazily
     >>> next(it)
     3
+    >>> # Verify the input is consumed completely
     >>> consume(it)
     >>> next(it, 'Done')
     'Done'
 
     >>> nth('abcde', 3)
     'd'
-
     >>> nth('abcde', 9) is None
     True
+    >>> # Verify that the input is consumed lazily
+    >>> it = iter('abcde')
+    >>> nth(it, 2)
+    'c'
+    >>> list(it)
+    ['d', 'e']
 
     >>> [all_equal(s) for s in ('', 'A', 'AAAA', 'AAAB', 'AAABA')]
     [True, True, True, False, False]
     >>> [all_equal(s, key=str.casefold) for s in ('', 'A', 'AaAa', 'AAAB', 'AAABA')]
     [True, True, True, False, False]
+    >>> # Verify that the input is consumed lazily and that only
+    >>> # one element of a second equivalence class is used to disprove
+    >>> # the assertion that all elements are equal.
+    >>> it = iter('aaabbbccc')
+    >>> all_equal(it)
+    False
+    >>> ''.join(it)
+    'bbccc'
 
     >>> quantify(range(99), lambda x: x%2==0)
     50
@@ -1222,6 +1247,11 @@ The following recipes have a more mathematical flavor:
 
     >>> list(ncycles('abc', 3))
     ['a', 'b', 'c', 'a', 'b', 'c', 'a', 'b', 'c']
+    >>> # Verify greedy consumption of input iterator
+    >>> input_iterator = iter('abc')
+    >>> output_iterator = ncycles(input_iterator, 3)
+    >>> list(input_iterator)
+    []
 
     >>> sum_of_squares([10, 20, 30])
     1400
@@ -1248,12 +1278,22 @@ The following recipes have a more mathematical flavor:
 
     >>> list(transpose([(1, 2, 3), (11, 22, 33)]))
     [(1, 11), (2, 22), (3, 33)]
+    >>> # Verify that the inputs are consumed lazily
+    >>> input1 = iter([1, 2, 3])
+    >>> input2 = iter([11, 22, 33])
+    >>> output_iterator = transpose([input1, input2])
+    >>> next(output_iterator)
+    (1, 11)
+    >>> list(zip(input1, input2))
+    [(2, 22), (3, 33)]
 
     >>> list(matmul([(7, 5), (3, 5)], [[2, 5], [7, 9]]))
     [(49, 80), (41, 60)]
     >>> list(matmul([[2, 5], [7, 9], [3, 4]], [[7, 11, 5, 4, 9], [3, 5, 2, 6, 3]]))
     [(29, 47, 20, 38, 33), (76, 122, 53, 82, 90), (33, 53, 23, 36, 39)]
 
+    >>> list(convolve([1, -1, -20], [1, -3])) == [1, -4, -17, 60]
+    True
     >>> data = [20, 40, 24, 32, 20, 28, 16]
     >>> list(convolve(data, [0.25, 0.25, 0.25, 0.25]))
     [5.0, 15.0, 21.0, 29.0, 29.0, 26.0, 24.0, 16.0, 11.0, 4.0]
@@ -1261,6 +1301,18 @@ The following recipes have a more mathematical flavor:
     [20, 20, -16, 8, -12, 8, -12, -16]
     >>> list(convolve(data, [1, -2, 1]))
     [20, 0, -36, 24, -20, 20, -20, -4, 16]
+    >>> # Verify signal is consumed lazily and the kernel greedily
+    >>> signal_iterator = iter([10, 20, 30, 40, 50])
+    >>> kernel_iterator = iter([1, 2, 3])
+    >>> output_iterator = convolve(signal_iterator, kernel_iterator)
+    >>> list(kernel_iterator)
+    []
+    >>> next(output_iterator)
+    10
+    >>> next(output_iterator)
+    40
+    >>> list(signal_iterator)
+    [30, 40, 50]
 
     >>> from fractions import Fraction
     >>> from decimal import Decimal
@@ -1348,6 +1400,17 @@ The following recipes have a more mathematical flavor:
     >>> # Test list input. Lists do not support None for the stop argument
     >>> list(iter_index(list('AABCADEAF'), 'A'))
     [0, 1, 4, 7]
+    >>> # Verify that input is consumed lazily
+    >>> input_iterator = iter('AABCADEAF')
+    >>> output_iterator = iter_index(input_iterator, 'A')
+    >>> next(output_iterator)
+    0
+    >>> next(output_iterator)
+    1
+    >>> next(output_iterator)
+    4
+    >>> ''.join(input_iterator)
+    'DEAF'
 
     >>> list(sieve(30))
     [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
@@ -1499,6 +1562,17 @@ The following recipes have a more mathematical flavor:
     [0, 2, 4, 6, 8]
     >>> list(odds)
     [1, 3, 5, 7, 9]
+    >>> # Verify that the input is consumed lazily
+    >>> input_iterator = iter(range(10))
+    >>> evens, odds = partition(is_odd, input_iterator)
+    >>> next(odds)
+    1
+    >>> next(odds)
+    3
+    >>> next(evens)
+    0
+    >>> list(input_iterator)
+    [4, 5, 6, 7, 8, 9]
 
     >>> list(subslices('ABCD'))
     ['A', 'AB', 'ABC', 'ABCD', 'B', 'BC', 'BCD', 'C', 'CD', 'D']
@@ -1518,6 +1592,13 @@ The following recipes have a more mathematical flavor:
     ['A', 'B', 'C', 'D']
     >>> list(unique_everseen('ABBcCAD', str.casefold))
     ['A', 'B', 'c', 'D']
+    >>> # Verify that the input is consumed lazily
+    >>> input_iterator = iter('AAAABBBCCDAABBB')
+    >>> output_iterator = unique_everseen(input_iterator)
+    >>> next(output_iterator)
+    'A'
+    >>> ''.join(input_iterator)
+    'AAABBBCCDAABBB'
 
     >>> list(unique_justseen('AAAABBBCCDAABBB'))
     ['A', 'B', 'C', 'D', 'A', 'B']
@@ -1525,6 +1606,13 @@ The following recipes have a more mathematical flavor:
     ['A', 'B', 'C', 'A', 'D']
     >>> list(unique_justseen('ABBcCAD', str.casefold))
     ['A', 'B', 'c', 'A', 'D']
+    >>> # Verify that the input is consumed lazily
+    >>> input_iterator = iter('AAAABBBCCDAABBB')
+    >>> output_iterator = unique_justseen(input_iterator)
+    >>> next(output_iterator)
+    'A'
+    >>> ''.join(input_iterator)
+    'AAABBBCCDAABBB'
 
     >>> d = dict(a=1, b=2, c=3)
     >>> it = iter_except(d.popitem, KeyError)
@@ -1545,6 +1633,12 @@ The following recipes have a more mathematical flavor:
 
     >>> first_true('ABC0DEF1', '9', str.isdigit)
     '0'
+    >>> # Verify that inputs are consumed lazily
+    >>> it = iter('ABC0DEF1')
+    >>> first_true(it, predicate=str.isdigit)
+    '0'
+    >>> ''.join(it)
+    'DEF1'
 
 
 .. testcode::