93 lines
2.6 KiB
Python
93 lines
2.6 KiB
Python
"""
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Test Cython optimize zeros API functions: ``bisect``, ``ridder``, ``brenth``,
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and ``brentq`` in `scipy.optimize.cython_optimize`, by finding the roots of a
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3rd order polynomial given a sequence of constant terms, ``a0``, and fixed 1st,
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2nd, and 3rd order terms in ``args``.
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.. math::
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f(x, a0, args) = ((args[2]*x + args[1])*x + args[0])*x + a0
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The 3rd order polynomial function is written in Cython and called in a Python
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wrapper named after the zero function. See the private ``_zeros`` Cython module
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in `scipy.optimize.cython_optimze` for more information.
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"""
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import numpy.testing as npt
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from scipy.optimize.cython_optimize import _zeros
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# CONSTANTS
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# Solve x**3 - A0 = 0 for A0 = [2.0, 2.1, ..., 2.9].
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# The ARGS have 3 elements just to show how this could be done for any cubic
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# polynomial.
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A0 = tuple(-2.0 - x/10.0 for x in range(10)) # constant term
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ARGS = (0.0, 0.0, 1.0) # 1st, 2nd, and 3rd order terms
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XLO, XHI = 0.0, 2.0 # first and second bounds of zeros functions
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# absolute and relative tolerances and max iterations for zeros functions
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XTOL, RTOL, MITR = 0.001, 0.001, 10
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EXPECTED = [(-a0) ** (1.0/3.0) for a0 in A0]
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# = [1.2599210498948732,
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# 1.2805791649874942,
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# 1.300591446851387,
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# 1.3200061217959123,
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# 1.338865900164339,
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# 1.3572088082974532,
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# 1.375068867074141,
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# 1.3924766500838337,
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# 1.4094597464129783,
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# 1.4260431471424087]
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# test bisect
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def test_bisect():
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npt.assert_allclose(
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EXPECTED,
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list(
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_zeros.loop_example('bisect', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
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),
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rtol=RTOL, atol=XTOL
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)
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# test ridder
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def test_ridder():
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npt.assert_allclose(
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EXPECTED,
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list(
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_zeros.loop_example('ridder', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
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),
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rtol=RTOL, atol=XTOL
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)
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# test brenth
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def test_brenth():
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npt.assert_allclose(
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EXPECTED,
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list(
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_zeros.loop_example('brenth', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
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),
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rtol=RTOL, atol=XTOL
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)
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# test brentq
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def test_brentq():
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npt.assert_allclose(
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EXPECTED,
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list(
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_zeros.loop_example('brentq', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
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),
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rtol=RTOL, atol=XTOL
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)
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# test brentq with full output
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def test_brentq_full_output():
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output = _zeros.full_output_example(
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(A0[0],) + ARGS, XLO, XHI, XTOL, RTOL, MITR)
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npt.assert_allclose(EXPECTED[0], output['root'], rtol=RTOL, atol=XTOL)
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npt.assert_equal(6, output['iterations'])
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npt.assert_equal(7, output['funcalls'])
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npt.assert_equal(0, output['error_num'])
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