tests.pipeline.NumericalExpressionTestCase.test_math_functions() - Code Metrics - Inspection of "Merge pull request #910 from quantopian/new-factor..." - quantopian/zipline - Measure and Improve Code Quality continuously with Scrutinizer

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created 2015-12-13 17:15 UTC

test_math_functions() B

↳ Parent: tests.pipeline.NumericalExpressionTestCase

Complexity

Conditions

Size

Total Lines

Duplication

Lines	0
Ratio	0 %

Metric	Value
cc	3
dl	0
loc	39
rs	8.8571

from operator import (
    add,
    and_,
    ge,
    gt,
    le,
    lt,
    methodcaller,
    mul,
    ne,
    or_,
)
from unittest import TestCase

import numpy
from numpy import (
    arange,
    eye,
    float64,
    full,
    isnan,
    zeros,
)
from pandas import (
    DataFrame,
    date_range,
    Int64Index,
)

from zipline.pipeline import Factor
from zipline.pipeline.expression import (
    NumericalExpression,
    NUMEXPR_MATH_FUNCS,
)

from zipline.utils.numpy_utils import datetime64ns_dtype, float64_dtype
from zipline.utils.test_utils import check_arrays


class F(Factor):
    dtype = float64_dtype
    inputs = ()
    window_length = 0


class G(Factor):
    dtype = float64_dtype
    inputs = ()
    window_length = 0


class H(Factor):
    dtype = float64_dtype
    inputs = ()
    window_length = 0


class DateFactor(Factor):
    dtype = datetime64ns_dtype
    inputs = ()
    window_length = 0


class NumericalExpressionTestCase(TestCase):

    def setUp(self):
        self.dates = date_range('2014-01-01', periods=5, freq='D')
        self.assets = Int64Index(range(5))
        self.f = F()
        self.g = G()
        self.h = H()
        self.d = DateFactor()
        self.fake_raw_data = {
            self.f: full((5, 5), 3),
            self.g: full((5, 5), 2),
            self.h: full((5, 5), 1),
            self.d: full((5, 5), 0, dtype='datetime64[ns]'),
        }
        self.mask = DataFrame(True, index=self.dates, columns=self.assets)

    def check_output(self, expr, expected):
        result = expr._compute(
            [self.fake_raw_data[input_] for input_ in expr.inputs],
            self.mask.index,
            self.mask.columns,
            self.mask.values,
        )
        check_arrays(result, expected)

    def check_constant_output(self, expr, expected):
        self.assertFalse(isnan(expected))
        return self.check_output(expr, full((5, 5), expected))

    def test_validate_good(self):
        f = self.f
        g = self.g

        NumericalExpression("x_0", (f,), dtype=float64_dtype)
        NumericalExpression("x_0 ", (f,), dtype=float64_dtype)
        NumericalExpression("x_0 + x_0", (f,), dtype=float64_dtype)
        NumericalExpression("x_0 + 2", (f,), dtype=float64_dtype)
        NumericalExpression("2 * x_0", (f,), dtype=float64_dtype)
        NumericalExpression("x_0 + x_1", (f, g), dtype=float64_dtype)
        NumericalExpression("x_0 + x_1 + x_0", (f, g), dtype=float64_dtype)
        NumericalExpression("x_0 + 1 + x_1", (f, g), dtype=float64_dtype)

    def test_validate_bad(self):
        f, g, h = self.f, self.g, self.h

        # Too few inputs.
        with self.assertRaises(ValueError):
            NumericalExpression("x_0", (), dtype=float64_dtype)
        with self.assertRaises(ValueError):
            NumericalExpression("x_0 + x_1", (f,), dtype=float64_dtype)

        # Too many inputs.
        with self.assertRaises(ValueError):
            NumericalExpression("x_0", (f, g), dtype=float64_dtype)
        with self.assertRaises(ValueError):
            NumericalExpression("x_0 + x_1", (f, g, h), dtype=float64_dtype)

        # Invalid variable name.
        with self.assertRaises(ValueError):
            NumericalExpression("x_0x_1", (f,), dtype=float64_dtype)
        with self.assertRaises(ValueError):
            NumericalExpression("x_0x_1", (f, g), dtype=float64_dtype)

        # Variable index must start at 0.
        with self.assertRaises(ValueError):
            NumericalExpression("x_1", (f,), dtype=float64_dtype)

        # Scalar operands must be numeric.
        with self.assertRaises(TypeError):
            "2" + f
        with self.assertRaises(TypeError):
            f + "2"
        with self.assertRaises(TypeError):
            f > "2"

        # Boolean binary operators must be between filters.
        with self.assertRaises(TypeError):
            f + (f > 2)
        with self.assertRaises(TypeError):
            (f > f) > f

    def test_combine_datetimes(self):
        with self.assertRaises(TypeError) as e:
            self.d + self.d
        message = e.exception.args[0]
        expected = (
            "Don't know how to compute datetime64[ns] + datetime64[ns].\n"
            "Arithmetic operators are only supported on Factors of dtype "
            "'float64'."
        )
        self.assertEqual(message, expected)

        # Confirm that * shows up in the error instead of +.
        with self.assertRaises(TypeError) as e:
            self.d * self.d
        message = e.exception.args[0]
        expected = (
            "Don't know how to compute datetime64[ns] * datetime64[ns].\n"
            "Arithmetic operators are only supported on Factors of dtype "
            "'float64'."
        )
        self.assertEqual(message, expected)

    def test_combine_datetime_with_float(self):
        # Test with both float-type factors and numeric values.
        for float_value in (self.f, float64(1.0), 1.0):
            for op, sym in ((add, '+'), (mul, '*')):
                with self.assertRaises(TypeError) as e:
                    op(self.f, self.d)
                message = e.exception.args[0]
                expected = (
                    "Don't know how to compute float64 {sym} datetime64[ns].\n"
                    "Arithmetic operators are only supported on Factors of "
                    "dtype 'float64'."
                ).format(sym=sym)
                self.assertEqual(message, expected)

                with self.assertRaises(TypeError) as e:
                    op(self.d, self.f)
                message = e.exception.args[0]
                expected = (
                    "Don't know how to compute datetime64[ns] {sym} float64.\n"
                    "Arithmetic operators are only supported on Factors of "
                    "dtype 'float64'."
                ).format(sym=sym)
                self.assertEqual(message, expected)

    def test_negate_datetime(self):
        with self.assertRaises(TypeError) as e:
            -self.d

        message = e.exception.args[0]
        expected = (
            "Can't apply unary operator '-' to instance of "
            "'DateFactor' with dtype 'datetime64[ns]'.\n"
            "'-' is only supported for Factors of dtype 'float64'."
        )
        self.assertEqual(message, expected)

    def test_negate(self):
        f, g = self.f, self.g

        self.check_constant_output(-f, -3.0)
        self.check_constant_output(--f, 3.0)
        self.check_constant_output(---f, -3.0)

        self.check_constant_output(-(f + f), -6.0)
        self.check_constant_output(-f + -f, -6.0)
        self.check_constant_output(-(-f + -f), 6.0)

        self.check_constant_output(f + -g, 1.0)
        self.check_constant_output(f - -g, 5.0)

        self.check_constant_output(-(f + g) + (f + g), 0.0)
        self.check_constant_output((f + g) + -(f + g), 0.0)
        self.check_constant_output(-(f + g) + -(f + g), -10.0)

    def test_add(self):
        f, g = self.f, self.g

        self.check_constant_output(f + g, 5.0)

        self.check_constant_output((1 + f) + g, 6.0)
        self.check_constant_output(1 + (f + g), 6.0)
        self.check_constant_output((f + 1) + g, 6.0)
        self.check_constant_output(f + (1 + g), 6.0)
        self.check_constant_output((f + g) + 1, 6.0)
        self.check_constant_output(f + (g + 1), 6.0)

        self.check_constant_output((f + f) + f, 9.0)
        self.check_constant_output(f + (f + f), 9.0)

        self.check_constant_output((f + g) + f, 8.0)
        self.check_constant_output(f + (g + f), 8.0)

        self.check_constant_output((f + g) + (f + g), 10.0)
        self.check_constant_output((f + g) + (g + f), 10.0)
        self.check_constant_output((g + f) + (f + g), 10.0)
        self.check_constant_output((g + f) + (g + f), 10.0)

    def test_subtract(self):
        f, g = self.f, self.g

        self.check_constant_output(f - g, 1.0)  # 3 - 2

        self.check_constant_output((1 - f) - g, -4.)   # (1 - 3) - 2
        self.check_constant_output(1 - (f - g), 0.0)   # 1 - (3 - 2)
        self.check_constant_output((f - 1) - g, 0.0)   # (3 - 1) - 2
        self.check_constant_output(f - (1 - g), 4.0)   # 3 - (1 - 2)
        self.check_constant_output((f - g) - 1, 0.0)   # (3 - 2) - 1
        self.check_constant_output(f - (g - 1), 2.0)   # 3 - (2 - 1)

        self.check_constant_output((f - f) - f, -3.)   # (3 - 3) - 3
        self.check_constant_output(f - (f - f), 3.0)   # 3 - (3 - 3)

        self.check_constant_output((f - g) - f, -2.)   # (3 - 2) - 3
        self.check_constant_output(f - (g - f), 4.0)   # 3 - (2 - 3)

        self.check_constant_output((f - g) - (f - g), 0.0)  # (3 - 2) - (3 - 2)
        self.check_constant_output((f - g) - (g - f), 2.0)  # (3 - 2) - (2 - 3)
        self.check_constant_output((g - f) - (f - g), -2.)  # (2 - 3) - (3 - 2)
        self.check_constant_output((g - f) - (g - f), 0.0)  # (2 - 3) - (2 - 3)

    def test_multiply(self):
        f, g = self.f, self.g

        self.check_constant_output(f * g, 6.0)

        self.check_constant_output((2 * f) * g, 12.0)
        self.check_constant_output(2 * (f * g), 12.0)
        self.check_constant_output((f * 2) * g, 12.0)
        self.check_constant_output(f * (2 * g), 12.0)
        self.check_constant_output((f * g) * 2, 12.0)
        self.check_constant_output(f * (g * 2), 12.0)

        self.check_constant_output((f * f) * f, 27.0)
        self.check_constant_output(f * (f * f), 27.0)

        self.check_constant_output((f * g) * f, 18.0)
        self.check_constant_output(f * (g * f), 18.0)

        self.check_constant_output((f * g) * (f * g), 36.0)
        self.check_constant_output((f * g) * (g * f), 36.0)
        self.check_constant_output((g * f) * (f * g), 36.0)
        self.check_constant_output((g * f) * (g * f), 36.0)

        self.check_constant_output(f * f * f * 0 * f * f, 0.0)

    def test_divide(self):
        f, g = self.f, self.g

        self.check_constant_output(f / g, 3.0 / 2.0)

        self.check_constant_output(
            (2 / f) / g,
            (2 / 3.0) / 2.0
        )
        self.check_constant_output(
            2 / (f / g),
            2 / (3.0 / 2.0),
        )
        self.check_constant_output(
            (f / 2) / g,
            (3.0 / 2) / 2.0,
        )
        self.check_constant_output(
            f / (2 / g),
            3.0 / (2 / 2.0),
        )
        self.check_constant_output(
            (f / g) / 2,
            (3.0 / 2.0) / 2,
        )
        self.check_constant_output(
            f / (g / 2),
            3.0 / (2.0 / 2),
        )
        self.check_constant_output(
            (f / f) / f,
            (3.0 / 3.0) / 3.0
        )
        self.check_constant_output(
            f / (f / f),
            3.0 / (3.0 / 3.0),
        )
        self.check_constant_output(
            (f / g) / f,
            (3.0 / 2.0) / 3.0,
        )
        self.check_constant_output(
            f / (g / f),
            3.0 / (2.0 / 3.0),
        )

        self.check_constant_output(
            (f / g) / (f / g),
            (3.0 / 2.0) / (3.0 / 2.0),
        )
        self.check_constant_output(
            (f / g) / (g / f),
            (3.0 / 2.0) / (2.0 / 3.0),
        )
        self.check_constant_output(
            (g / f) / (f / g),
            (2.0 / 3.0) / (3.0 / 2.0),
        )
        self.check_constant_output(
            (g / f) / (g / f),
            (2.0 / 3.0) / (2.0 / 3.0),
        )

    def test_pow(self):
        f, g = self.f, self.g

        self.check_constant_output(f ** g, 3.0 ** 2)
        self.check_constant_output(2 ** f, 2.0 ** 3)
        self.check_constant_output(f ** 2, 3.0 ** 2)

        self.check_constant_output((f + g) ** 2, (3.0 + 2.0) ** 2)
        self.check_constant_output(2 ** (f + g), 2 ** (3.0 + 2.0))

        self.check_constant_output(f ** (f ** g), 3.0 ** (3.0 ** 2.0))
        self.check_constant_output((f ** f) ** g, (3.0 ** 3.0) ** 2.0)

        self.check_constant_output((f ** g) ** (f ** g), 9.0 ** 9.0)
        self.check_constant_output((f ** g) ** (g ** f), 9.0 ** 8.0)
        self.check_constant_output((g ** f) ** (f ** g), 8.0 ** 9.0)
        self.check_constant_output((g ** f) ** (g ** f), 8.0 ** 8.0)

    def test_mod(self):
        f, g = self.f, self.g

        self.check_constant_output(f % g, 3.0 % 2.0)
        self.check_constant_output(f % 2.0, 3.0 % 2.0)
        self.check_constant_output(g % f, 2.0 % 3.0)

        self.check_constant_output((f + g) % 2, (3.0 + 2.0) % 2)
        self.check_constant_output(2 % (f + g), 2 % (3.0 + 2.0))

        self.check_constant_output(f % (f % g), 3.0 % (3.0 % 2.0))
        self.check_constant_output((f % f) % g, (3.0 % 3.0) % 2.0)

        self.check_constant_output((f + g) % (f * g), 5.0 % 6.0)

    def test_math_functions(self):
        f, g = self.f, self.g

        fake_raw_data = self.fake_raw_data
        alt_fake_raw_data = {
            self.f: full((5, 5), .5),
            self.g: full((5, 5), -.5),
        }

        for funcname in NUMEXPR_MATH_FUNCS:
            method = methodcaller(funcname)
            func = getattr(numpy, funcname)

            # These methods have domains in [0, 1], so we need alternate inputs
            # that are in the domain.
            if funcname in ('arcsin', 'arccos', 'arctanh'):
                self.fake_raw_data = alt_fake_raw_data
            else:
                self.fake_raw_data = fake_raw_data

            f_val = self.fake_raw_data[f][0, 0]
            g_val = self.fake_raw_data[g][0, 0]

            self.check_constant_output(method(f), func(f_val))
            self.check_constant_output(method(g), func(g_val))

            self.check_constant_output(method(f) + 1, func(f_val) + 1)
            self.check_constant_output(1 + method(f), 1 + func(f_val))

            self.check_constant_output(method(f + .25), func(f_val + .25))
            self.check_constant_output(method(.25 + f), func(.25 + f_val))

            self.check_constant_output(
                method(f) + method(g),
                func(f_val) + func(g_val),
            )
            self.check_constant_output(
                method(f + g),
                func(f_val + g_val),
            )

    def test_comparisons(self):
        f, g, h = self.f, self.g, self.h
        self.fake_raw_data = {
            f: arange(25).reshape(5, 5),
            g: arange(25).reshape(5, 5) - eye(5),
            h: full((5, 5), 5),
        }
        f_data = self.fake_raw_data[f]
        g_data = self.fake_raw_data[g]

        cases = [
            # Sanity Check with hand-computed values.
            (f, g, eye(5), zeros((5, 5))),
            (f, 10, f_data, 10),
            (10, f, 10, f_data),
            (f, f, f_data, f_data),
            (f + 1, f, f_data + 1, f_data),
            (1 + f, f, 1 + f_data, f_data),
            (f, g, f_data, g_data),
            (f + 1, g, f_data + 1, g_data),
            (f, g + 1, f_data, g_data + 1),
            (f + 1, g + 1, f_data + 1, g_data + 1),
            ((f + g) / 2, f ** 2, (f_data + g_data) / 2, f_data ** 2),
        ]
        for op in (gt, ge, lt, le, ne):
            for expr_lhs, expr_rhs, expected_lhs, expected_rhs in cases:
                self.check_output(
                    op(expr_lhs, expr_rhs),
                    op(expected_lhs, expected_rhs),
                )

    def test_boolean_binops(self):
        f, g, h = self.f, self.g, self.h
        self.fake_raw_data = {
            f: arange(25).reshape(5, 5),
            g: arange(25).reshape(5, 5) - eye(5),
            h: full((5, 5), 5),
        }

        # Should be True on the diagonal.
        eye_filter = f > g
        # Should be True in the first row only.
        first_row_filter = f < h

        eye_mask = eye(5, dtype=bool)
        first_row_mask = zeros((5, 5), dtype=bool)
        first_row_mask[0] = 1

        self.check_output(eye_filter, eye_mask)
        self.check_output(first_row_filter, first_row_mask)

        for op in (and_, or_):  # NumExpr doesn't support xor.
            self.check_output(
                op(eye_filter, first_row_filter),
                op(eye_mask, first_row_mask),
            )


1			from operator import (
2			add,
3			and_,
4			ge,
5			gt,
6			le,
7			lt,
8			methodcaller,
9			mul,
10			ne,
11			or_,
12			)
13			from unittest import TestCase
14
15			import numpy
16			from numpy import (
17			arange,
18			eye,
19			float64,
20			full,
21			isnan,
22			zeros,
23			)
24			from pandas import (
25			DataFrame,
26			date_range,
27			Int64Index,
28			)
29
30			from zipline.pipeline import Factor
31			from zipline.pipeline.expression import (
32			NumericalExpression,
33			NUMEXPR_MATH_FUNCS,
34			)
35
36			from zipline.utils.numpy_utils import datetime64ns_dtype, float64_dtype
37			from zipline.utils.test_utils import check_arrays
38
39
40			class F(Factor):
41			dtype = float64_dtype
42			inputs = ()
43			window_length = 0
44
45
46			class G(Factor):
47			dtype = float64_dtype
48			inputs = ()
49			window_length = 0
50
51
52			class H(Factor):
53			dtype = float64_dtype
54			inputs = ()
55			window_length = 0
56
57
58			class DateFactor(Factor):
59			dtype = datetime64ns_dtype
60			inputs = ()
61			window_length = 0
62
63
64			class NumericalExpressionTestCase(TestCase):
65
66			def setUp(self):
67			self.dates = date_range('2014-01-01', periods=5, freq='D')
68			self.assets = Int64Index(range(5))
69			self.f = F()
70			self.g = G()
71			self.h = H()
72			self.d = DateFactor()
73			self.fake_raw_data = {
74			self.f: full((5, 5), 3),
75			self.g: full((5, 5), 2),
76			self.h: full((5, 5), 1),
77			self.d: full((5, 5), 0, dtype='datetime64[ns]'),
78			}
79			self.mask = DataFrame(True, index=self.dates, columns=self.assets)
80
81			def check_output(self, expr, expected):
82			result = expr._compute(
83			[self.fake_raw_data[input_] for input_ in expr.inputs],
84			self.mask.index,
85			self.mask.columns,
86			self.mask.values,
87			)
88			check_arrays(result, expected)
89
90			def check_constant_output(self, expr, expected):
91			self.assertFalse(isnan(expected))
92			return self.check_output(expr, full((5, 5), expected))
93
94			def test_validate_good(self):
95			f = self.f
96			g = self.g
97
98			NumericalExpression("x_0", (f,), dtype=float64_dtype)
99			NumericalExpression("x_0 ", (f,), dtype=float64_dtype)
100			NumericalExpression("x_0 + x_0", (f,), dtype=float64_dtype)
101			NumericalExpression("x_0 + 2", (f,), dtype=float64_dtype)
102			NumericalExpression("2 * x_0", (f,), dtype=float64_dtype)
103			NumericalExpression("x_0 + x_1", (f, g), dtype=float64_dtype)
104			NumericalExpression("x_0 + x_1 + x_0", (f, g), dtype=float64_dtype)
105			NumericalExpression("x_0 + 1 + x_1", (f, g), dtype=float64_dtype)
106
107			def test_validate_bad(self):
108			f, g, h = self.f, self.g, self.h
109
110			# Too few inputs.
111			with self.assertRaises(ValueError):
112			NumericalExpression("x_0", (), dtype=float64_dtype)
113			with self.assertRaises(ValueError):
114			NumericalExpression("x_0 + x_1", (f,), dtype=float64_dtype)
115
116			# Too many inputs.
117			with self.assertRaises(ValueError):
118			NumericalExpression("x_0", (f, g), dtype=float64_dtype)
119			with self.assertRaises(ValueError):
120			NumericalExpression("x_0 + x_1", (f, g, h), dtype=float64_dtype)
121
122			# Invalid variable name.
123			with self.assertRaises(ValueError):
124			NumericalExpression("x_0x_1", (f,), dtype=float64_dtype)
125			with self.assertRaises(ValueError):
126			NumericalExpression("x_0x_1", (f, g), dtype=float64_dtype)
127
128			# Variable index must start at 0.
129			with self.assertRaises(ValueError):
130			NumericalExpression("x_1", (f,), dtype=float64_dtype)
131
132			# Scalar operands must be numeric.
133			with self.assertRaises(TypeError):
134			"2" + f
135			with self.assertRaises(TypeError):
136			f + "2"
137			with self.assertRaises(TypeError):
138			f > "2"
139
140			# Boolean binary operators must be between filters.
141			with self.assertRaises(TypeError):
142			f + (f > 2)
143			with self.assertRaises(TypeError):
144			(f > f) > f
145
146			def test_combine_datetimes(self):
147			with self.assertRaises(TypeError) as e:
148			self.d + self.d
149			message = e.exception.args[0]
150			expected = (
151			"Don't know how to compute datetime64[ns] + datetime64[ns].\n"
152			"Arithmetic operators are only supported on Factors of dtype "
153			"'float64'."
154			)
155			self.assertEqual(message, expected)
156
157			# Confirm that * shows up in the error instead of +.
158			with self.assertRaises(TypeError) as e:
159			self.d * self.d
160			message = e.exception.args[0]
161			expected = (
162			"Don't know how to compute datetime64[ns] * datetime64[ns].\n"
163			"Arithmetic operators are only supported on Factors of dtype "
164			"'float64'."
165			)
166			self.assertEqual(message, expected)
167
168			def test_combine_datetime_with_float(self):
169			# Test with both float-type factors and numeric values.
170			for float_value in (self.f, float64(1.0), 1.0):
171			for op, sym in ((add, '+'), (mul, '*')):
172			with self.assertRaises(TypeError) as e:
173			op(self.f, self.d)
174			message = e.exception.args[0]
175			expected = (
176			"Don't know how to compute float64 {sym} datetime64[ns].\n"
177			"Arithmetic operators are only supported on Factors of "
178			"dtype 'float64'."
179			).format(sym=sym)
180			self.assertEqual(message, expected)
181
182			with self.assertRaises(TypeError) as e:
183			op(self.d, self.f)
184			message = e.exception.args[0]
185			expected = (
186			"Don't know how to compute datetime64[ns] {sym} float64.\n"
187			"Arithmetic operators are only supported on Factors of "
188			"dtype 'float64'."
189			).format(sym=sym)
190			self.assertEqual(message, expected)
191
192			def test_negate_datetime(self):
193			with self.assertRaises(TypeError) as e:
194			-self.d
195
196			message = e.exception.args[0]
197			expected = (
198			"Can't apply unary operator '-' to instance of "
199			"'DateFactor' with dtype 'datetime64[ns]'.\n"
200			"'-' is only supported for Factors of dtype 'float64'."
201			)
202			self.assertEqual(message, expected)
203
204			def test_negate(self):
205			f, g = self.f, self.g
206
207			self.check_constant_output(-f, -3.0)
208			self.check_constant_output(--f, 3.0)
209			self.check_constant_output(---f, -3.0)
210
211			self.check_constant_output(-(f + f), -6.0)
212			self.check_constant_output(-f + -f, -6.0)
213			self.check_constant_output(-(-f + -f), 6.0)
214
215			self.check_constant_output(f + -g, 1.0)
216			self.check_constant_output(f - -g, 5.0)
217
218			self.check_constant_output(-(f + g) + (f + g), 0.0)
219			self.check_constant_output((f + g) + -(f + g), 0.0)
220			self.check_constant_output(-(f + g) + -(f + g), -10.0)
221
222			def test_add(self):
223			f, g = self.f, self.g
224
225			self.check_constant_output(f + g, 5.0)
226
227			self.check_constant_output((1 + f) + g, 6.0)
228			self.check_constant_output(1 + (f + g), 6.0)
229			self.check_constant_output((f + 1) + g, 6.0)
230			self.check_constant_output(f + (1 + g), 6.0)
231			self.check_constant_output((f + g) + 1, 6.0)
232			self.check_constant_output(f + (g + 1), 6.0)
233
234			self.check_constant_output((f + f) + f, 9.0)
235			self.check_constant_output(f + (f + f), 9.0)
236
237			self.check_constant_output((f + g) + f, 8.0)
238			self.check_constant_output(f + (g + f), 8.0)
239
240			self.check_constant_output((f + g) + (f + g), 10.0)
241			self.check_constant_output((f + g) + (g + f), 10.0)
242			self.check_constant_output((g + f) + (f + g), 10.0)
243			self.check_constant_output((g + f) + (g + f), 10.0)
244
245			def test_subtract(self):
246			f, g = self.f, self.g
247
248			self.check_constant_output(f - g, 1.0) # 3 - 2
249
250			self.check_constant_output((1 - f) - g, -4.) # (1 - 3) - 2
251			self.check_constant_output(1 - (f - g), 0.0) # 1 - (3 - 2)
252			self.check_constant_output((f - 1) - g, 0.0) # (3 - 1) - 2
253			self.check_constant_output(f - (1 - g), 4.0) # 3 - (1 - 2)
254			self.check_constant_output((f - g) - 1, 0.0) # (3 - 2) - 1
255			self.check_constant_output(f - (g - 1), 2.0) # 3 - (2 - 1)
256
257			self.check_constant_output((f - f) - f, -3.) # (3 - 3) - 3
258			self.check_constant_output(f - (f - f), 3.0) # 3 - (3 - 3)
259
260			self.check_constant_output((f - g) - f, -2.) # (3 - 2) - 3
261			self.check_constant_output(f - (g - f), 4.0) # 3 - (2 - 3)
262
263			self.check_constant_output((f - g) - (f - g), 0.0) # (3 - 2) - (3 - 2)
264			self.check_constant_output((f - g) - (g - f), 2.0) # (3 - 2) - (2 - 3)
265			self.check_constant_output((g - f) - (f - g), -2.) # (2 - 3) - (3 - 2)
266			self.check_constant_output((g - f) - (g - f), 0.0) # (2 - 3) - (2 - 3)
267
268			def test_multiply(self):
269			f, g = self.f, self.g
270
271			self.check_constant_output(f * g, 6.0)
272
273			self.check_constant_output((2 * f) * g, 12.0)
274			self.check_constant_output(2 * (f * g), 12.0)
275			self.check_constant_output((f * 2) * g, 12.0)
276			self.check_constant_output(f * (2 * g), 12.0)
277			self.check_constant_output((f * g) * 2, 12.0)
278			self.check_constant_output(f * (g * 2), 12.0)
279
280			self.check_constant_output((f * f) * f, 27.0)
281			self.check_constant_output(f * (f * f), 27.0)
282
283			self.check_constant_output((f * g) * f, 18.0)
284			self.check_constant_output(f * (g * f), 18.0)
285
286			self.check_constant_output((f * g) * (f * g), 36.0)
287			self.check_constant_output((f * g) * (g * f), 36.0)
288			self.check_constant_output((g * f) * (f * g), 36.0)
289			self.check_constant_output((g * f) * (g * f), 36.0)
290
291			self.check_constant_output(f * f * f * 0 * f * f, 0.0)
292
293			def test_divide(self):
294			f, g = self.f, self.g
295
296			self.check_constant_output(f / g, 3.0 / 2.0)
297
298			self.check_constant_output(
299			(2 / f) / g,
300			(2 / 3.0) / 2.0
301			)
302			self.check_constant_output(
303			2 / (f / g),
304			2 / (3.0 / 2.0),
305			)
306			self.check_constant_output(
307			(f / 2) / g,
308			(3.0 / 2) / 2.0,
309			)
310			self.check_constant_output(
311			f / (2 / g),
312			3.0 / (2 / 2.0),
313			)
314			self.check_constant_output(
315			(f / g) / 2,
316			(3.0 / 2.0) / 2,
317			)
318			self.check_constant_output(
319			f / (g / 2),
320			3.0 / (2.0 / 2),
321			)
322			self.check_constant_output(
323			(f / f) / f,
324			(3.0 / 3.0) / 3.0
325			)
326			self.check_constant_output(
327			f / (f / f),
328			3.0 / (3.0 / 3.0),
329			)
330			self.check_constant_output(
331			(f / g) / f,
332			(3.0 / 2.0) / 3.0,
333			)
334			self.check_constant_output(
335			f / (g / f),
336			3.0 / (2.0 / 3.0),
337			)
338
339			self.check_constant_output(
340			(f / g) / (f / g),
341			(3.0 / 2.0) / (3.0 / 2.0),
342			)
343			self.check_constant_output(
344			(f / g) / (g / f),
345			(3.0 / 2.0) / (2.0 / 3.0),
346			)
347			self.check_constant_output(
348			(g / f) / (f / g),
349			(2.0 / 3.0) / (3.0 / 2.0),
350			)
351			self.check_constant_output(
352			(g / f) / (g / f),
353			(2.0 / 3.0) / (2.0 / 3.0),
354			)
355
356			def test_pow(self):
357			f, g = self.f, self.g
358
359			self.check_constant_output(f g, 3.0 2)
360			self.check_constant_output(2 f, 2.0 3)
361			self.check_constant_output(f 2, 3.0 2)
362
363			self.check_constant_output((f + g) 2, (3.0 + 2.0) 2)
364			self.check_constant_output(2 (f + g), 2 (3.0 + 2.0))
365
366			self.check_constant_output(f (f g), 3.0 (3.0 2.0))
367			self.check_constant_output((f f) g, (3.0 3.0) 2.0)
368
369			self.check_constant_output((f g) (f g), 9.0 9.0)
370			self.check_constant_output((f g) (g f), 9.0 8.0)
371			self.check_constant_output((g f) (f g), 8.0 9.0)
372			self.check_constant_output((g f) (g f), 8.0 8.0)
373
374			def test_mod(self):
375			f, g = self.f, self.g
376
377			self.check_constant_output(f % g, 3.0 % 2.0)
378			self.check_constant_output(f % 2.0, 3.0 % 2.0)
379			self.check_constant_output(g % f, 2.0 % 3.0)
380
381			self.check_constant_output((f + g) % 2, (3.0 + 2.0) % 2)
382			self.check_constant_output(2 % (f + g), 2 % (3.0 + 2.0))
383
384			self.check_constant_output(f % (f % g), 3.0 % (3.0 % 2.0))
385			self.check_constant_output((f % f) % g, (3.0 % 3.0) % 2.0)
386
387			self.check_constant_output((f + g) % (f * g), 5.0 % 6.0)
388
389			def test_math_functions(self):
390			f, g = self.f, self.g
391
392			fake_raw_data = self.fake_raw_data
393			alt_fake_raw_data = {
394			self.f: full((5, 5), .5),
395			self.g: full((5, 5), -.5),
396			}
397
398			for funcname in NUMEXPR_MATH_FUNCS:
399			method = methodcaller(funcname)
400			func = getattr(numpy, funcname)
401
402			# These methods have domains in [0, 1], so we need alternate inputs
403			# that are in the domain.
404			if funcname in ('arcsin', 'arccos', 'arctanh'):
405			self.fake_raw_data = alt_fake_raw_data
406			else:
407			self.fake_raw_data = fake_raw_data
408
409			f_val = self.fake_raw_data[f][0, 0]
410			g_val = self.fake_raw_data[g][0, 0]
411
412			self.check_constant_output(method(f), func(f_val))
413			self.check_constant_output(method(g), func(g_val))
414
415			self.check_constant_output(method(f) + 1, func(f_val) + 1)
416			self.check_constant_output(1 + method(f), 1 + func(f_val))
417
418			self.check_constant_output(method(f + .25), func(f_val + .25))
419			self.check_constant_output(method(.25 + f), func(.25 + f_val))
420
421			self.check_constant_output(
422			method(f) + method(g),
423			func(f_val) + func(g_val),
424			)
425			self.check_constant_output(
426			method(f + g),
427			func(f_val + g_val),
428			)
429
430			def test_comparisons(self):
431			f, g, h = self.f, self.g, self.h
432			self.fake_raw_data = {
433			f: arange(25).reshape(5, 5),
434			g: arange(25).reshape(5, 5) - eye(5),
435			h: full((5, 5), 5),
436			}
437			f_data = self.fake_raw_data[f]
438			g_data = self.fake_raw_data[g]
439
440			cases = [
441			# Sanity Check with hand-computed values.
442			(f, g, eye(5), zeros((5, 5))),
443			(f, 10, f_data, 10),
444			(10, f, 10, f_data),
445			(f, f, f_data, f_data),
446			(f + 1, f, f_data + 1, f_data),
447			(1 + f, f, 1 + f_data, f_data),
448			(f, g, f_data, g_data),
449			(f + 1, g, f_data + 1, g_data),
450			(f, g + 1, f_data, g_data + 1),
451			(f + 1, g + 1, f_data + 1, g_data + 1),
452			((f + g) / 2, f 2, (f_data + g_data) / 2, f_data 2),
453			]
454			for op in (gt, ge, lt, le, ne):
455			for expr_lhs, expr_rhs, expected_lhs, expected_rhs in cases:
456			self.check_output(
457			op(expr_lhs, expr_rhs),
458			op(expected_lhs, expected_rhs),
459			)
460
461			def test_boolean_binops(self):
462			f, g, h = self.f, self.g, self.h
463			self.fake_raw_data = {
464			f: arange(25).reshape(5, 5),
465			g: arange(25).reshape(5, 5) - eye(5),
466			h: full((5, 5), 5),
467			}
468
469			# Should be True on the diagonal.
470			eye_filter = f > g
471			# Should be True in the first row only.
472			first_row_filter = f < h
473
474			eye_mask = eye(5, dtype=bool)
475			first_row_mask = zeros((5, 5), dtype=bool)
476			first_row_mask[0] = 1
477
478			self.check_output(eye_filter, eye_mask)
479			self.check_output(first_row_filter, first_row_mask)
480
481			for op in (and_, or_): # NumExpr doesn't support xor.
482			self.check_output(
483			op(eye_filter, first_row_filter),
484			op(eye_mask, first_row_mask),
485			)
486

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