C 代码 实现测试问题 标量变量的标量函数的最小化.rar

28 February 2022 09:21:27 AM TEST_MIN_TEST C version Test the TEST_MIN library. p00_title_test p00_title prints the title of any problem. Problem Title 1 Simple quadratic, (x-2)^2+1. 2 Quadratic plus exponential, x^2 + e^(-x). 3 Quartic, x^4 + 2x^2 + x + 3. 4 Steep valley, e^x + 1/(100x). 5 Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2). 6 line, 2 - x. 7 The dying snake, ( x + sin(x) ) * e^(-x^2). 8 The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4 9 The oscillatory parabola 10 The cosine combo 11 1 + |3x-1| 12 The fuzzy parabola 13 The lazy W 14 Humps TEST02 For each problem, evaluate the function at the starting point and the solution. Problem 1 Simple quadratic, (x-2)^2+1. F(X_START) = 2.30323 F(X_SOL) = 1 Problem 2 Quadratic plus exponential, x^2 + e^(-x). F(X_START) = 1.08933 F(X_SOL) = 0.827184 Problem 3 Quartic, x^4 + 2x^2 + x + 3. F(X_START) = 14.0625 F(X_SOL) = 2.87849 Problem 4 Steep valley, e^x + 1/(100x). F(X_START) = 2.59624 F(X_SOL) = 1.20492 Problem 5 Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2). F(X_START) = 1.48836 F(X_SOL) = 0.628026 Problem 6 line, 2 - x. F(X_START) = -5.2 F(X_SOL) = -7 Problem 7 The dying snake, ( x + sin(x) ) * e^(-x^2). F(X_START) = -5.61222e-11 F(X_SOL) = -0.824239 Problem 8 The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4 F(X_START) = 29.7647 F(X_SOL) = -10000 Problem 9 The oscillatory parabola F(X_START) = 9.36573 F(X_SOL) = -9.97791 Problem 10 The cosine combo F(X_START) = -1.33593 F(X_SOL) = -13.0797 Problem 11 1 + |3x-1| F(X_START) = 2.25 F(X_SOL) = 1 Problem 12 The fuzzy parabola F(X_START) = 1.39593 F(X_SOL) = -0.9921 Problem 13 The lazy W F(X_START) = 4.6302 F(X_SOL) = -5.24307 Problem 14 Humps F(X_START) = 47.4483 F(X_SOL) = 11.2528 TEST03 For each problem, compare the exact and approximate gradients at the starting point. Problem 1 Simple quadratic, (x-2)^2+1. X 3.14159 F'(X) (exact) 2.28319 F'(X) (difference) 2.28319 Problem 2 Quadratic plus exponential, x^2 + e^(-x). X 0.8 F'(X) (exact) 1.15067 F'(X) (difference) 1.15067 Problem 3 Quartic, x^4 + 2x^2 + x + 3. X 1.5 F'(X) (exact) 20.5 F'(X) (difference) 20.5 Problem 4 Steep valley, e^x + 1/(100x). X 0.95 F'(X) (exact) 2.57463 F'(X) (difference) 2.57463 Problem 5 Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2). X 1.5 F'(X) (exact) 2.47725 F'(X) (difference) 2.47725 Problem 6 line, 2 - x. X 7.2 F'(X) (exact) -1 F'(X) (difference) -1 Problem 7 The dying snake, ( x + sin(x) ) * e^(-x^2). X -5 F'(X) (exact) -5.43395e-10 F'(X) (difference) -5.43395e-10 Problem 8 The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4 X 3.1 F'(X) (exact) 18.1064 F'(X) (difference) 18.1064 Problem 9 The oscillatory parabola X -2 F'(X) (exact) 55.0698 F'(X) (difference) 55.0698 Problem 10 The cosine combo X 0.5 F'(X) (exact) 41.2254 F'(X) (difference) 41.2254 Problem 11 1 + |3x-1| X 0.75 F'(X) (exact) 3 F'(X) (difference) 3 Problem 12 The fuzzy parabola X 1 F'(X) (exact) -46.669 F'(X) (difference) -46.669 Problem 13 The lazy W X -0.1 F'(X) (exact) 4.392 F'(X) (difference) 4.392 Problem 14 Humps X 0.4 F'(X) (exact) -488.109 F'(X) (difference) -488.109 TEST04 For each problem, compare the exact and approximate second derivatives at the starting point. Problem 1 Simple quadratic, (x-2)^2+1. X: 3.14159 F"(X) (exact): 2 F"(X) (difference): 2 Problem 2 Quadratic plus exponential, x^2 + e^(-x). X: 0.8 F"(X) (exact): 2.44933 F"(X) (difference): 2.44933 Problem 3 Quartic, x^4 + 2x^2 + x + 3. X: 1.5 F"(X) (exact): 31 F"(X) (difference): 31 Problem 4 Steep valley, e^x + 1/(100x). X: 0.95 F"(X) (exact): 2.60904 F"(X) (difference): 2.60904 Problem 5 Steep valley, e^x - 2x + 1/(100x) - 1/(1000000x^2). X: 1.5 F"(X) (exact): 4.48761 F"(X) (difference): 4.48762 Problem 6 line, 2 - x. X: 7.2 F"(X) (exact): 0 F"(X) (difference): 0 Problem 7 The dying snake, ( x + sin(x) ) * e^(-x^2). X: -5 F"(X) (exact): 8.39789e-09 F"(X) (difference): -5.15675e-09 Problem 8 The "Thin Pole", x^2+1+log((pi-x)^2)/pi^4 X: 3.1 F"(X) (exact): -5.86854 F"(X) (difference): -5.86855 Problem 9 The oscillatory parabola X: -2 F"(X) (exact): -277.798 F"(X) (difference): -277.798 Problem 10 The cosine combo X: 0.5 F"(X) (exact): 177.651 F"(X) (difference): 177.651 Problem 11 1 + |3x-1| X: 0.75 F"(X) (exact): 0 F"(X) (difference): 0 Problem 12 The fuzzy parabola X: 1 F"(X) (exact): -1110.15 F"(X) (difference): -1110.15 Problem 13 The lazy W X: -0.1 F"(X) (exact): -13.76 F"(X) (difference): -13.76 Problem 14 Humps X: 0.4 F"(X) (exact): 5058.22 F"(X) (difference): 5058.22 TEST05 For each problem, take a few steps of the bisection method. Problem 1 Simple quadratic, (x-2)^2+1. 0 X: 0 1.5708 3.14159 F: 5 1.18422 2.30323 1 X: 1.5708 2.35619 3.14159 F: 1.18422 1.12687 2.30323 2 X: 1.5708 1.9635 2.35619 F: 1.18422 1.00133 1.12687 3 X: 1.76715 1.9635 2.15984 F: 1.05422 1.00133 1.02555 4 X: 1.86532 1.9635 2.06167 F: 1.01814 1.00133 1.0038 5 X: 1.9635 2.01258 2.06167 F: 1.00133 1.00016 1.0038 6 X: 1.9635 1.98804 2.01258 F: 1.00133 1.00014 1.00016 7 X: 1.98804 2.00031 2.01258 F: 1.00014 1 1.00016 8 X: 1.99418 2.00031 2.00645 F: 1.00003 1 1.00004 9 X: 1.99724 2.00031 2.00338 F: 1.00001 1 1.00001 10 X: 1.99878 2.00031 2.00184 F: 1 1 1 Problem 2 Quadratic plus exponential, x^2 + e^(-x). 0 X: 0 0.5 1 F: 1 0.856531 1.36788 1 X: 0 0.25 0.5 F: 1 0.841301 0.856531 2 X: 0.25 0.375 0.5 F: 0.841301 0.827914 0.856531 3 X: 0.3125 0.375 0.4375 F: 0.829272 0.827914 0.837055 4 X: 0.3125 0.34375 0.375 F: 0.829272 0.82727 0.827914 5 X: 0.34375 0.359375 0.375 F: 0.82727 0.827263 0.827914 6 X: 0.34375 0.351562 0.359375 F: 0.82727 0.827184 0.827263 7 X: 0.347656 0.351562 0.355469 F: 0.827207 0.827184 0.827203 8 X: 0.349609 0.351562 0.353516 F: 0.82719 0.827184 0.827188 9 X: 0.350586 0.351562 0.352539 F: 0.827186 0.827184 0.827185 10 X: 0.351074 0.351562 0.352051 F: 0.827185 0.827184 0.827184 Problem 3 Quartic, x^4 + 2x^2 + x + 3. 0 X: -2 0 2 F: 25 3 29 1 X: -1 0 1 F: 5 3 7 2 X: -0.5 0 0.5 F: 3.0625 3 4.0625 3 X: -0.5 -0.25 0 F: 3.0625 2.87891 3 4 X: -0.375 -0.25 -0.125 F: 2.92603 2.87891 2.90649 5 X: -0.3125 -0.25 -0.1875 F: 2.89235 2.87891 2.88405 6 X: -0.28125 -0.25 -0.21875 F: 2.88321 2.87891 2.87924 7 X: -0.25 -0.234375 -0.218