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102 lines
3.6 KiB
Python
102 lines
3.6 KiB
Python
# -*- coding: utf-8 -*-
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"""
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偏导测试
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"""
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import logging
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from mbcp.mp_math.mp_math_typing import RealNumber
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from mbcp.mp_math.utils import Approx
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def three_var_func(x: RealNumber, y: RealNumber) -> RealNumber:
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return x ** 3 * y ** 2 - 3 * x * y ** 3 - x * y + 1
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class TestPartialDerivative:
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# 样例来源：同济大学《高等数学》第八版下册 第九章第二节 例6
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def test_2v_1o_1v(self):
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"""测试二元函数关于第一个变量(x)的一阶偏导 df/dx"""
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from mbcp.mp_math.utils import Approx
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from mbcp.mp_math.equation import get_partial_derivative_func
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partial_derivative_func = get_partial_derivative_func(three_var_func, 0)
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# assert partial_derivative_func(1, 2, 3) == 4.0
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def df_dx(x, y):
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"""原函数关于x的偏导"""
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return 3 * (x ** 2) * (y ** 2) - 3 * (y ** 3) - y
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logging.info(f"Expected: {df_dx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
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assert Approx(partial_derivative_func(1, 2)) == df_dx(1, 2)
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def test_2v_1o_2v(self):
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"""测试二元函数关于第二个变量(y)的一阶偏导 df/dy"""
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from mbcp.mp_math.utils import Approx
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from mbcp.mp_math.equation import get_partial_derivative_func
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partial_derivative_func = get_partial_derivative_func(three_var_func, 1)
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def df_dy(x, y):
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"""原函数关于y的偏导"""
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return 2 * (x ** 3) * y - 9 * x * (y ** 2) - x
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logging.info(f"Expected: {df_dy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
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assert Approx(partial_derivative_func(1, 2)) == df_dy(1, 2)
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def test_2v_2o_12v(self):
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"""高阶偏导d^2f/(dxdy)"""
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from mbcp.mp_math.utils import Approx
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from mbcp.mp_math.equation import get_partial_derivative_func
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partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 1))
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def df_dxdy(x, y):
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"""原函数关于y和x的偏导"""
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return 6 * x ** 2 * y - 9 * y ** 2 - 1
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logging.info(f"Expected: {df_dxdy(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
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assert Approx(partial_derivative_func(1, 2)) == df_dxdy(1, 2)
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def test_2v_2o_1v2(self):
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"""二阶偏导d^2f/(dx^2)"""
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from mbcp.mp_math.utils import Approx
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from mbcp.mp_math.equation import get_partial_derivative_func
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partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0))
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def df_dydx(x, y):
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"""原函数关于x和y的偏导"""
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return 6 * x * y ** 2
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logging.info(f"Expected: {df_dydx(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
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assert Approx(partial_derivative_func(1, 2)) == df_dydx(1, 2)
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def test_2v_3o_1v3(self):
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"""高阶偏导d^3f/(dx^3)"""
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from mbcp.mp_math.utils import Approx
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from mbcp.mp_math.equation import get_partial_derivative_func
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partial_derivative_func = get_partial_derivative_func(three_var_func, (0, 0, 0))
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def d3f_dx3(x, y):
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"""原函数关于x的三阶偏导"""
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return 6 * (y ** 2)
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logging.info(f"Expected: {d3f_dx3(1, 2)}, Actual: {partial_derivative_func(1, 2)}")
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assert Approx(partial_derivative_func(1, 2)) == d3f_dx3(1, 2)
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def test_possible_error(self):
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from mbcp.mp_math.equation import get_partial_derivative_func
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def two_vars_func(x: RealNumber, y: RealNumber) -> RealNumber:
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return x ** 2 * y ** 2
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partial_func = get_partial_derivative_func(two_vars_func, 0)
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partial_func_2 = get_partial_derivative_func(two_vars_func, (0, 0))
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assert Approx(partial_func_2(1, 2)) == 8
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