Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/optimize/tests/test_cython_optimize.py

@@ -0,0 +1,92 @@
+"""
+Test Cython optimize zeros API functions: ``bisect``, ``ridder``, ``brenth``,
+and ``brentq`` in `scipy.optimize.cython_optimize`, by finding the roots of a
+3rd order polynomial given a sequence of constant terms, ``a0``, and fixed 1st,
+2nd, and 3rd order terms in ``args``.
+
+.. math::
+
+    f(x, a0, args) =  ((args[2]*x + args[1])*x + args[0])*x + a0
+
+The 3rd order polynomial function is written in Cython and called in a Python
+wrapper named after the zero function. See the private ``_zeros`` Cython module
+in `scipy.optimize.cython_optimze` for more information.
+"""
+
+import numpy.testing as npt
+from scipy.optimize.cython_optimize import _zeros
+
+# CONSTANTS
+# Solve x**3 - A0 = 0  for A0 = [2.0, 2.1, ..., 2.9].
+# The ARGS have 3 elements just to show how this could be done for any cubic
+# polynomial.
+A0 = tuple(-2.0 - x/10.0 for x in range(10))  # constant term
+ARGS = (0.0, 0.0, 1.0)  # 1st, 2nd, and 3rd order terms
+XLO, XHI = 0.0, 2.0  # first and second bounds of zeros functions
+# absolute and relative tolerances and max iterations for zeros functions
+XTOL, RTOL, MITR = 0.001, 0.001, 10
+EXPECTED = [(-a0) ** (1.0/3.0) for a0 in A0]
+# = [1.2599210498948732,
+#    1.2805791649874942,
+#    1.300591446851387,
+#    1.3200061217959123,
+#    1.338865900164339,
+#    1.3572088082974532,
+#    1.375068867074141,
+#    1.3924766500838337,
+#    1.4094597464129783,
+#    1.4260431471424087]
+
+
+# test bisect
+def test_bisect():
+    npt.assert_allclose(
+        EXPECTED,
+        list(
+            _zeros.loop_example('bisect', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
+        ),
+        rtol=RTOL, atol=XTOL
+    )
+
+
+# test ridder
+def test_ridder():
+    npt.assert_allclose(
+        EXPECTED,
+        list(
+            _zeros.loop_example('ridder', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
+        ),
+        rtol=RTOL, atol=XTOL
+    )
+
+
+# test brenth
+def test_brenth():
+    npt.assert_allclose(
+        EXPECTED,
+        list(
+            _zeros.loop_example('brenth', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
+        ),
+        rtol=RTOL, atol=XTOL
+    )
+
+
+# test brentq
+def test_brentq():
+    npt.assert_allclose(
+        EXPECTED,
+        list(
+            _zeros.loop_example('brentq', A0, ARGS, XLO, XHI, XTOL, RTOL, MITR)
+        ),
+        rtol=RTOL, atol=XTOL
+    )
+
+
+# test brentq with full output
+def test_brentq_full_output():
+    output = _zeros.full_output_example(
+        (A0[0],) + ARGS, XLO, XHI, XTOL, RTOL, MITR)
+    npt.assert_allclose(EXPECTED[0], output['root'], rtol=RTOL, atol=XTOL)
+    npt.assert_equal(6, output['iterations'])
+    npt.assert_equal(7, output['funcalls'])
+    npt.assert_equal(0, output['error_num'])