Home License -- for personal use only. Not for government, academic, research, commercial, or other organizational use. 02-May-2026 21:53:12 optisection_test(): MATLAB/Octave version 9.11.0.2358333 (R2021b) Update 7 Test optisection(), to minimize unimodal functions. Number of test functions is 40 p00_optisection_test(): Minimize f(x) in [a,b] using the optisection method of Kodnyanko. The function f(x) is assumed to be unimodal. Success is determined if the interval is no more than 1e-05 Failure is determined if the number of iterations reaches 100 The proportionality coefficient C is 0.2 test 1 "f(x) = 1." [ A, B]: 1.900000000000e+00 3.100000000000e+00 [FA, FB]: 1.000000000000e+00 1.000000000000e+00 Function evaluations: 48 [ A, M, B]: 1.900000000000e+00 1.900016725559e+00 1.900020906949e+00 [FA,FM,FB]: 1.000000000000e+00 1.000000000000e+00 1.000000000000e+00 test 2 "f(x) = 20 + 16 / x." [ A, B]: 1.500000000000e+00 4.500000000000e+00 [FA, FB]: 3.066666666667e+01 2.355555555556e+01 Function evaluations: 49 [ A, M, B]: 4.499947732628e+00 4.499958186103e+00 4.500000000000e+00 [FA,FM,FB]: 2.355559685371e+01 2.355558859400e+01 2.355555555556e+01 test 3 "f(x) = 1.5 + exp(x)." [ A, B]: 5.000000000000e-01 4.000000000000e+00 [FA, FB]: 3.148721270700e+00 5.609815003314e+01 Function evaluations: 59 [ A, M, B]: 5.000000000000e-01 5.000041904175e-01 5.000052380219e-01 [FA,FM,FB]: 3.148721270700e+00 3.148728179545e+00 3.148729906761e+00 test 4 "f(x) = 3 + max ( 4 * cos ( x ), -3 )." [ A, B]: 1.000000000000e-01 4.900000000000e+00 [FA, FB]: 6.980016661112e+00 3.746049477690e+00 Function evaluations: 46 [ A, M, B]: 3.364000000000e+00 3.364032667107e+00 3.364040833884e+00 [FA,FM,FB]: 0.000000000000e+00 0.000000000000e+00 0.000000000000e+00 test 5 "f(x) = 1.2 + max ( 5 * exp ( x ) - 1, 1 )." [ A, B]: -1.600000000000e+00 1.100000000000e+00 [FA, FB]: 2.200000000000e+00 1.522083011973e+01 Function evaluations: 52 [ A, M, B]: -1.600000000000e+00 -1.599984585725e+00 -1.599980732156e+00 [FA,FM,FB]: 2.200000000000e+00 2.200000000000e+00 2.200000000000e+00 test 6 "f(x) = 1.5 + max ( cos ( 4 - x^2 ), 0.5 )." [ A, B]: 2.900000000000e+00 3.200000000000e+00 [FA, FB]: 2.000000000000e+00 2.499067659534e+00 Function evaluations: 41 [ A, M, B]: 2.900000000000e+00 2.900024923025e+00 2.900031153781e+00 [FA,FM,FB]: 2.000000000000e+00 2.000000000000e+00 2.000000000000e+00 test 7 "f(x) = 1.2 + max ( exp ( - x ), cos ( x ), x^4, x^2 )." [ A, B]: -6.000000000000e-01 1.100000000000e+00 [FA, FB]: 3.022118800391e+00 2.664100000000e+00 Function evaluations: 23 [ A, M, B]: 8.241229091799e-01 8.241302106243e-01 8.241360517798e-01 [FA,FM,FB]: 1.879200969655e+00 1.879195610725e+00 1.879200231843e+00 test 8 "f(x) = 0.2 + max ( 3 * ( x - 2 )^2, 20 * ( x - 1 ) )." [ A, B]: -6.000000000000e+00 1.150000000000e+01 [FA, FB]: 1.922000000000e+02 2.709500000000e+02 Function evaluations: 21 [ A, M, B]: 1.116956851200e+00 1.116959144960e+00 1.116968320000e+00 [FA,FM,FB]: 2.539295607928e+00 2.539283455009e+00 2.539366400000e+00 test 9 "f(x) = 1.2 + abs ( x - 1 )." [ A, B]: -2.000000000000e-01 4.000000000000e+00 [FA, FB]: 2.400000000000e+00 4.200000000000e+00 Function evaluations: 22 [ A, M, B]: 9.999956185907e-01 1.000001255735e+00 1.000005765451e+00 [FA,FM,FB]: 1.200004381409e+00 1.200001255735e+00 1.200005765451e+00 test 10 "f(x) = 12 + 1000 * abs ( x - 2.8 )^8.4." [ A, B]: -4.000000000000e-01 5.100000000000e+00 [FA, FB]: 1.750895052498e+07 1.092744405677e+06 Function evaluations: 32 [ A, M, B]: 2.804791040000e+00 2.804817013016e+00 2.804823506270e+00 [FA,FM,FB]: 1.200000000000e+01 1.200000000000e+01 1.200000000000e+01 test 11 "f(x) = 0.3 + cos ( x^2 + 2 * x - 3.0 )" [ A, B]: -9.000000000000e-01 5.000000000000e-01 [FA, FB]: -3.611788377749e-01 1.217539443505e-01 Function evaluations: 22 [ A, M, B]: -7.349770240000e-02 -7.349696839680e-02 -7.349638119424e-02 [FA,FM,FB]: -6.999999999996e-01 -6.999999999999e-01 -6.999999999987e-01 test 12 "f(x) = 0.2 + ( x - 1.5 )^2" [ A, B]: 1.000000000000e+00 3.000000000000e+00 [FA, FB]: 4.500000000000e-01 2.450000000000e+00 Function evaluations: 22 [ A, M, B]: 1.499991674094e+00 1.500000264028e+00 1.500007135976e+00 [FA,FM,FB]: 2.000000000693e-01 2.000000000001e-01 2.000000000509e-01 test 13 "f(x) = 100 + ( 1 - exp ( x ) * sin ( x ) )^2." [ A, B]: 1.000000000000e-01 1.000000000000e+00 [FA, FB]: 1.007915073909e+02 1.016572836354e+02 Function evaluations: 20 [ A, M, B]: 5.885307722138e-01 5.885322821632e-01 5.885341696000e-01 [FA,FM,FB]: 1.000000000000e+02 1.000000000000e+02 1.000000000000e+02 test 14 "f(x) = 1.2 - cos ( x^2 )" [ A, B]: -1.200000000000e+00 1.500000000000e+00 [FA, FB]: 1.069576291262e+00 1.828173622723e+00 Function evaluations: 66 [ A, M, B]: 6.157824000002e-05 6.157887136873e-05 6.157902921090e-05 [FA,FM,FB]: 2.000000000000e-01 2.000000000000e-01 2.000000000000e-01 test 15 "f(x) = 1.2 + exp ( - x^2 ) + x" [ A, B]: 2.000000000000e-01 5.700000000000e+00 [FA, FB]: 6.203947195762e+00 6.900000000000e+00 Function evaluations: 22 [ A, M, B]: 1.679620332749e+00 1.679627714724e+00 1.679633620304e+00 [FA,FM,FB]: 3.177315111497e+00 3.177315111363e+00 3.177315111364e+00 test 16 "f(x) = 1.2 + exp ( - x ) + 3.5 * sin ( x )." [ A, B]: 2.000000000000e+00 6.200000000000e+00 [FA, FB]: 4.517876277126e+00 9.112165207751e-01 Function evaluations: 18 [ A, M, B]: 4.714897667686e+00 4.714932899840e+00 4.714976940032e+00 [FA,FM,FB]: -2.291028203362e+00 -2.291028207540e+00 -2.291028206637e+00 test 17 "f(x) = 2.3 + 3 * exp ( x ) - x^2 + 5 * x" [ A, B]: -3.900000000000e+00 2.500000000000e+00 [FA, FB]: -3.234927426566e+01 4.509748188211e+01 Function evaluations: 52 [ A, M, B]: -3.900000000000e+00 -3.899963462459e+00 -3.899954328074e+00 [FA,FM,FB]: -3.234927426566e+01 -3.234880436766e+01 -3.234868689357e+01 test 18 "f(x) = 1.2 + 3 * cosh ( x - 2 ) - 2 * sinh ( x - 3 )" [ A, B]: 1.000000000000e+00 4.900000000000e+00 [FA, FB]: 1.308296272014e+01 2.200742706119e+01 Function evaluations: 20 [ A, M, B]: 2.657649310720e+00 2.657675483177e+00 2.657682026291e+00 [FA,FM,FB]: 5.570630884688e+00 5.570630884081e+00 5.570630884397e+00 test 19 "f(x) = 2.3 + ( exp ( 3 - x ) + 4 * ( x - 2 ) )^2" [ A, B]: 1.000000000000e+00 2.900000000000e+00 [FA, FB]: 1.378570124170e+01 2.443863336830e+01 Function evaluations: 18 [ A, M, B]: 1.613701074944e+00 1.613706055680e+00 1.613712281600e+00 [FA,FM,FB]: 8.326153779296e+00 8.326153779094e+00 8.326153779525e+00 test 20 "f(x) = x^3 - 3 * x^2 - 5 * x - 8" [ A, B]: 1.000000000000e+00 5.000000000000e+00 [FA, FB]: 1.000000000000e+00 3.300000000000e+01 Function evaluations: 21 [ A, M, B]: 2.632985102746e+00 2.632991813632e+00 2.632997182341e+00 [FA,FM,FB]: -7.709296862911e+00 -7.709296863220e+00 -7.709296863150e+00 test 21 "f(x) = 1.2 + cos ( x ) + 0.1 * x" [ A, B]: 9.000000000000e-01 6.200000000000e+00 [FA, FB]: 1.911609968271e+00 2.816542097023e+00 Function evaluations: 17 [ A, M, B]: 3.041405148160e+00 3.041422515200e+00 3.041444224000e+00 [FA,FM,FB]: 5.091550863369e-01 5.091550861399e-01 5.091550863156e-01 test 22 "f(x) = 10.2 + abs ( ( x - 5 )^3 )" [ A, B]: 3.000000000000e+00 7.800000000000e+00 [FA, FB]: 1.820000000000e+01 3.215200000000e+01 Function evaluations: 15 [ A, M, B]: 4.999970304000e+00 4.999994880000e+00 5.000025600000e+00 [FA,FM,FB]: 1.020000000000e+01 1.020000000000e+01 1.020000000000e+01 test 23 "f(x) = 1.2 + log ( x ) * cos ( 2 * ( 4 - x ) )" [ A, B]: 2.700000000000e+00 3.100000000000e+00 [FA, FB]: 3.488937264437e-01 9.429430703290e-01 Function evaluations: 41 [ A, M, B]: 2.700000000000e+00 2.700026584560e+00 2.700033230700e+00 [FA,FM,FB]: 3.488937264437e-01 3.489125147110e-01 3.489172122510e-01 test 24 "f(x) = 1.2 + ( x - 7.4 )^2" [ A, B]: 1.000000000000e+00 1.700000000000e+01 [FA, FB]: 4.216000000000e+01 9.336000000000e+01 Function evaluations: 17 [ A, M, B]: 7.399983616000e+00 7.400000000000e+00 7.400020480000e+00 [FA,FM,FB]: 1.200000000268e+00 1.200000000000e+00 1.200000000419e+00 test 25 "f(x) = 1.2 + exp ( 3 - x ) + 4 * ( x - 2 )" [ A, B]: 1.000000000000e+00 4.000000000000e+00 [FA, FB]: 6.589056098931e+00 5.567879441171e+00 Function evaluations: 19 [ A, M, B]: 2.306845517824e+00 2.306851809280e+00 2.306859673600e+00 [FA,FM,FB]: 3.813705638933e+00 3.813705638881e+00 3.813705638927e+00 test 26 "f(x) = 1.5 + exp ( - 2 * ( x + 6 ) ) + 13 * sin ( x )" [ A, B]: 2.000000000000e+00 6.500000000000e+00 [FA, FB]: 1.332086666127e+01 4.296559845155e+00 Function evaluations: 19 [ A, M, B]: 4.712379115520e+00 4.712390912000e+00 4.712405657600e+00 [FA,FM,FB]: -1.149999999887e+01 -1.149999999948e+01 -1.149999999770e+01 test 27 "f(x) = 1.2 + sinh ( x ) - 2 * x" [ A, B]: 6.000000000000e-01 2.700000000000e+00 [FA, FB]: 6.366535821482e-01 3.206263106067e+00 Function evaluations: 21 [ A, M, B]: 1.316955832320e+00 1.316958650892e+00 1.316969925181e+00 [FA,FM,FB]: 2.981350137229e-01 2.981350137197e-01 2.981350138445e-01 test 28 "f(x) = 12.2 + 10 * sin ( 19 * x - 2 )" [ A, B]: 1.900000000000e+00 2.100000000000e+00 [FA, FB]: 1.661723806669e+01 1.419539705239e+01 Function evaluations: 15 [ A, M, B]: 2.006740428800e+00 2.006753536000e+00 2.006769920000e+00 [FA,FM,FB]: 2.200000305957e+00 2.200000000014e+00 2.200000489731e+00 test 29 "f(x) = 2.2 + abs ( x - 8 )" [ A, B]: -1.230000000000e+01 5.500000000000e+00 [FA, FB]: 2.250000000000e+01 4.700000000000e+00 Function evaluations: 56 [ A, M, B]: 5.499934963177e+00 5.499947970542e+00 5.500000000000e+00 [FA,FM,FB]: 4.700065036823e+00 4.700052029458e+00 4.700000000000e+00 test 30 "f(x) = 1.2 + x - 5 * sin ( 2 * x )" [ A, B]: -5.000000000000e-01 2.200000000000e+00 [FA, FB]: 4.907354924039e+00 8.158010369448e+00 Function evaluations: 25 [ A, M, B]: 7.353122415220e-01 7.353140969479e-01 7.353164162302e-01 [FA,FM,FB]: -3.039622732668e+00 -3.039622732715e+00 -3.039622732678e+00 test 31 "f(x) = 1.2 + sin ( 2.5 * sqrt ( abs ( x ) + x ) )" [ A, B]: 1.400000000000e+00 3.000000000000e+00 [FA, FB]: 3.367326698402e-01 1.041213981155e+00 Function evaluations: 23 [ A, M, B]: 1.776523317278e+00 1.776527715324e+00 1.776533212883e+00 [FA,FM,FB]: 2.000000000264e-01 2.000000000010e-01 2.000000000172e-01 test 32 "f(x) = 1.2 + max ( 20 * log ( x^2 + 3 ), exp ( x - 2.5 ) + x - 1 )" [ A, B]: -1.000000000000e+00 1.000000000000e+00 [FA, FB]: 2.892588722240e+01 2.892588722240e+01 Function evaluations: 42 [ A, M, B]: -1.220668415046e-08 -1.218362572037e-08 -1.209139200000e-08 [FA,FM,FB]: 2.317224577336e+01 2.317224577336e+01 2.317224577336e+01 test 33 "f(x) = 1.2 + 5 * x * ( x - 1 ) * exp ( x - 0.5 )" [ A, B]: -1.200000000000e+00 1.200000000000e+00 [FA, FB]: 3.611422517496e+00 3.616503248965e+00 Function evaluations: 26 [ A, M, B]: 6.180330650755e-01 6.180343844894e-01 6.180360337569e-01 [FA,FM,FB]: -1.282156514372e-01 -1.282156514416e-01 -1.282156514163e-01 test 34 "f(x) = 1.2 - 4 * x * sin ( x )" [ A, B]: 3.000000000000e-01 4.500000000000e+00 [FA, FB]: 8.453757520064e-01 1.879554211797e+01 Function evaluations: 21 [ A, M, B]: 2.028753043046e+00 2.028760089477e+00 2.028765726622e+00 [FA,FM,FB]: -6.078822964514e+00 -6.078822964611e+00 -6.078822964302e+00 test 35 "f(x) = 1.2 + 3 * x^4 + ( x - 1 )^2" [ A, B]: -1.350000000000e+01 1.500000000000e+01 [FA, FB]: 7.582000000000e+02 8.722000000000e+02 Function evaluations: 25 [ A, M, B]: 2.499984170189e-01 2.500003296215e-01 2.500018597036e-01 [FA,FM,FB]: 1.950000000010e+00 1.950000000000e+00 1.950000000014e+00 test 36 "f(x) = 1.2 + 3 * cos ( exp ( - 2 * x ) )." [ A, B]: -8.000000000000e-01 2.100000000000e+00 [FA, FB]: 1.914982736338e+00 4.199662705334e+00 Function evaluations: 26 [ A, M, B]: -5.723680046223e-01 -5.723629028884e-01 -5.723588215012e-01 [FA,FM,FB]: -1.799999999445e+00 -1.799999999754e+00 -1.799999997781e+00 test 37 "f(x) = 3.2 + 3 * cos ( x^3 + 2.4 )" [ A, B]: 2.200000000000e+00 2.500000000000e+00 [FA, FB]: 5.858723987943e+00 5.236649286663e+00 Function evaluations: 17 [ A, M, B]: 2.369741851648e+00 2.369754434560e+00 2.369770163200e+00 [FA,FM,FB]: 2.000001012243e-01 2.000000034257e-01 2.000000707616e-01 test 38 "f(x) = exp ( - x^2 ) + 2 * ( x^2 - x + 1 )^2" [ A, B]: -1.000000000000e+00 4.000000000000e+00 [FA, FB]: 1.836787944117e+01 3.380000001125e+02 Function evaluations: 22 [ A, M, B]: 6.380472868864e-01 6.380489646080e-01 6.380510617600e-01 [FA,FM,FB]: 1.848472243228e+00 1.848472243226e+00 1.848472243248e+00 test 39 "f(x) = 25 * ( x - 1 ) + max ( - 2 * ( x - 1 ), 8 * ( x - 1 ) )" [ A, B]: 0.000000000000e+00 2.500000000000e+00 [FA, FB]: -2.300000000000e+01 4.950000000000e+01 Function evaluations: 100 [ A, M, B]: 0.000000000000e+00 3.182868713023e-10 3.978585891278e-10 [FA,FM,FB]: -2.300000000000e+01 -2.299999999268e+01 -2.299999999085e+01 test 40 "f(x) = max ( 2 - x^2, 5 - ( x - 4 )^2 )" [ A, B]: 1.000000000000e+00 3.800000000000e+00 [FA, FB]: 1.000000000000e+00 4.960000000000e+00 Function evaluations: 21 [ A, M, B]: 1.624994109358e+00 1.624997867454e+00 1.625012899840e+00 [FA,FM,FB]: -6.406058554485e-01 -6.406180692316e-01 -6.405637259264e-01 optisection_test(): Normal end of execution. 02-May-2026 21:53:12