'''Chemical Engineering Design Library (ChEDL). Utilities for process modeling. Copyright (C) 2018 Caleb Bell Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ''' from fluids.numerics import assert_close, assert_close1d from fluids.numerics.polynomial_roots import roots_cubic, roots_cubic_a1, roots_cubic_a2, roots_quadratic, roots_quartic def test_roots_quartic(): coeffs = [1.0, -3.274390673429134, 0.3619541556604501, 2.4841800045762747, -0.49619076425603237] expect_roots = ((-0.8246324500888049+1.1609047395516947e-17j), (0.2041867922778502-3.6197168963943884e-17j), (1.027869356838059+2.910620457054182e-17j), (2.86696697440203-4.51808300211488e-18j)) expect_mp_roots_real = [-0.824632450088805, 0.20418679227785, 1.0278693568380592, 2.86696697440203] roots_calc = roots_quartic(*coeffs) assert_close1d(expect_roots, roots_calc, rtol=1e-9) assert_close1d(expect_mp_roots_real, [i.real for i in roots_calc], rtol=1e-9) def test_roots_quadratic(): a, b, c = 1,2,3 v0, v1 = roots_quadratic(a, b, c) if v0.imag < v1.imag: v1, v0 = v0, v1 assert_close(v0, -1+1.4142135623730951j, rtol=1e-12) assert_close(v1, -1-1.4142135623730951j, rtol=1e-12) a, b, c = .1,2,3 v0, v1 = roots_quadratic(a, b, c) if v0.real < v1.real: v1, v0 = v0, v1 assert_close(v0, -1.6333997346592444, rtol=1e-12) assert_close(v1, -18.366600265340757, rtol=1e-12) a, b, c = 0,2,3 v0, v1 = roots_quadratic(a, b, c) assert_close(v0, -1.5, rtol=1e-12) assert_close(v1, -1.5, rtol=1e-12) assert v0 == v1 def test_roots_cubic_a1(): v0, v1, v2 = roots_cubic_a1(123.4,-23.34,1.234) assert_close(v0.real, 0.09446632563251711, rtol=1e-12) assert_close(v0.imag, -0.03257032605677779, rtol=1e-12) assert_close(v1.real, -123.588932651265, rtol=1e-12) assert_close(v1.imag, 1.5855372570428017e-15, atol=1e-12) assert_close(v2.real, 0.09446632563248869, rtol=1e-12) assert_close(v2.imag, +0.03257032605677779, rtol=1e-12) v0, v1, v2 = roots_cubic_a1(100.0, 1000.0, 10.0) assert_close(v0.real, -0.010010019045111562, rtol=1e-12) assert_close(v0.imag, -2.1316282072803006e-14, atol=1e-12) assert_close(v1.real, -88.73128838313305, rtol=1e-12) assert_close(v1.imag, 1.5855372570428017e-15, atol=1e-12) assert_close(v2.real, -11.258701597821826, rtol=1e-12) assert_close(v2.imag, 2.296510222925631e-14, atol=1e-12) def test_roots_cubic_a2(): v0, v1, v2 = roots_cubic_a2(1.0, 123.4,-23.34,1.234) assert_close(v0.real, 0.09446632563251711, rtol=1e-12) assert_close(v0.imag, -0.03257032605677779, rtol=1e-12) assert_close(v1.real, -123.588932651265, rtol=1e-12) assert_close(v1.imag, 1.5855372570428017e-15, atol=1e-12) assert_close(v2.real, 0.09446632563248869, rtol=1e-12) assert_close(v2.imag, +0.03257032605677779, rtol=1e-12) v0, v1, v2 = roots_cubic_a2(1.0, 100.0, 1000.0, 10.0) assert_close(v0.real, -0.010010019045111562, rtol=1e-12) assert_close(v0.imag, -2.1316282072803006e-14, atol=1e-12) assert_close(v1.real, -88.73128838313305, rtol=1e-12) assert_close(v1.imag, 1.5855372570428017e-15, atol=1e-12) assert_close(v2.real, -11.258701597821826, rtol=1e-12) assert_close(v2.imag, 2.296510222925631e-14, atol=1e-12) v0, v1, v2 = roots_cubic_a2(33.0, 100.0, 1000.0, 10.0) assert_close(v0.real, -0.010009986884777167, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -1.5101465217091263, rtol=1e-12) assert_close(v1.imag, 5.2907707087197915, atol=1e-12) assert_close(v2.real, -1.5101465217091263, rtol=1e-12) assert_close(v2.imag, -5.2907707087197915, atol=1e-12) def test_roots_cubic(): v0, v1, v2 = roots_cubic(1.0, 123.4,-23.34,1.234) assert_close(v0.real, -123.588932651265, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, 0.0944663256325029, rtol=1e-12) assert_close(v1.imag, 0.03257032605695922, atol=1e-12) assert_close(v2.real, 0.0944663256325029, rtol=1e-12) assert_close(v2.imag, -0.03257032605695922, rtol=1e-12) v0, v1, v2 = roots_cubic(1.0, 100.0, 1000.0, 10.0) assert_close(v0.real, -0.010010019045111562, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -88.73128838313305, rtol=1e-12) assert_close(v1.imag, 0, atol=0) assert_close(v2.real, -11.258701597821826, rtol=1e-12) assert_close(v2.imag, 0, atol=0) v0, v1, v2 = roots_cubic(33.0, 100.0, 1000.0, 10.0) assert_close(v0.real, -0.010009986884774058, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -1.5101465217091279, rtol=1e-12) assert_close(v1.imag, 5.290770708719792, atol=1e-12) assert_close(v2.real, -1.5101465217091279, rtol=1e-12) assert_close(v2.imag, -5.290770708719792, atol=1e-12) # a=0 case # arbitrary choice on which root to repeat v0, v1, v2 = roots_cubic(0.0, 1.0, 2.0, 3.0) assert_close(v0.real, -1.0, rtol=1e-12) assert_close(v0.imag, 1.4142135623730951, rtol=1e-12) assert_close(v1.real, -1.0, rtol=1e-12) assert_close(v1.imag, 1.4142135623730951, rtol=1e-12) assert_close(v2.real, -1.0, rtol=1e-12) assert_close(v2.imag, -1.4142135623730951, rtol=1e-12) # case with different branch v0, v1, v2 = roots_cubic(0.0, .1, 2.0, 3.0) assert_close(v0.real, -1.6333997346592444, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -1.6333997346592444, rtol=1e-12) assert_close(v1.imag, 0, atol=0) assert_close(v2.real, -18.366600265340757, rtol=1e-12) assert_close(v2.imag, 0, atol=0) # case with repeating quadratic root v0, v1, v2 = roots_cubic(0.0, 0.0, 2.0, 3.0) assert_close(v0.real, -1.5, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -1.5, rtol=1e-12) assert_close(v1.imag, 0, atol=0) assert_close(v2.real, -1.5, rtol=1e-12) assert_close(v2.imag, 0, atol=0) # Nasty case T >= 0.0 v0, v1, v2 = roots_cubic(1.0, -0.9317082987361708, -0.061964336199539824, -0.001069098250830773) assert_close(v0.real, 0.9950599982590833, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -0.031675849761456265, rtol=1e-12) assert_close(v1.imag, 0.008428900244340058, rtol=1e-12) assert_close(v2.real, -0.031675849761456265, rtol=1e-12) assert_close(v2.imag, -0.008428900244340058, rtol=1e-12) # sincos case v0, v1, v2 = roots_cubic(1.0, -0.9999998288102078, -1.5499734058215601e-07, -2.77199246547356e-15) assert_close(v0.real, 0.9999999838075536, rtol=1e-12) assert_close(v0.imag, 0, atol=0) assert_close(v1.real, -1.341318024428162e-07, rtol=1e-12) assert_close(v1.imag, 0.0, atol=1e-12) assert_close(v2.real, -2.0865543459702707e-08, rtol=1e-12) assert_close(v2.imag, -0.0, atol=1e-12)