1316 lines
2.8 MiB
Plaintext
1316 lines
2.8 MiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "cb977d1b-5910-4d86-bf69-a0e171cb2fd5",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/latex": [
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"$\\frac{9 x^{9}}{64} - \\frac{117 x^{8}}{74} + \\frac{576 x^{7}}{91} - \\frac{847 x^{6}}{93} - \\frac{23 x^{5}}{6} + \\frac{465 x^{4}}{23} - \\frac{216 x^{3}}{25} - \\frac{19 x^{2}}{2} + \\frac{91 x}{15}$"
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],
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"text/plain": [
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" 9 8 7 6 5 4 3 2 \n",
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"9⋅x 117⋅x 576⋅x 847⋅x 23⋅x 465⋅x 216⋅x 19⋅x 91⋅x\n",
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"──── - ────── + ────── - ────── - ───── + ────── - ────── - ───── + ────\n",
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" 64 74 91 93 6 23 25 2 15 "
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/latex": [
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"$\\frac{81 x^{8}}{64} - \\frac{468 x^{7}}{37} + \\frac{576 x^{6}}{13} - \\frac{1694 x^{5}}{31} - \\frac{115 x^{4}}{6} + \\frac{1860 x^{3}}{23} - \\frac{648 x^{2}}{25} - 19 x + \\frac{91}{15}$"
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],
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"text/plain": [
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" 8 7 6 5 4 3 2 \n",
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"81⋅x 468⋅x 576⋅x 1694⋅x 115⋅x 1860⋅x 648⋅x 91\n",
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"───── - ────── + ────── - ─────── - ────── + ─────── - ────── - 19⋅x + ──\n",
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" 64 37 13 31 6 23 25 15"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"0.0"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"using SymPy\n",
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"x = Sym(\"x\")\n",
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"f(x) = 91 * x^2/30 - 19 * x^3 / 6 - 54 * x^4 / 25 + 93 * x^5 / 23 - 23 * x^6 / 36 - 121 * x^7 / 93 + 72 * x^8 / 91 - 13 * x^9 / 74 + 9 * x^10 / 640\n",
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"\n",
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"Dx = Differential(x)\n",
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"\n",
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"Dx(f(x)) |> display\n",
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"Dx(Dx(f(x))) |> display\n",
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"\n",
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"f(0) |> display"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "23020315-a21b-40e9-b438-c2ea4c6906fa",
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"metadata": {},
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"outputs": [
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{
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"data": {
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|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 8,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"using Plots\n",
|
||
|
|
"using LaTeXStrings\n",
|
||
|
|
"\n",
|
||
|
|
"include(\"oneDTestFunctions.jl\")\n",
|
||
|
|
"\n",
|
||
|
|
"x = range(-1, 3, length=1000)\n",
|
||
|
|
"y1 = map(v -> v[1], oneDTestFunctions()[1].(x))\n",
|
||
|
|
"y2 = map(v -> v[2], oneDTestFunctions()[1].(x))\n",
|
||
|
|
"y3 = map(v -> v[3], oneDTestFunctions()[1].(x))\n",
|
||
|
|
"plot(x, y1, ylims=(-3,3), label=L\"$f(x)$\")\n",
|
||
|
|
"plot!(x, y2, label=L\"$\\frac{d}{dx}f(x)$\")\n",
|
||
|
|
"plot!(x, y3, label=L\"$\\frac{d^2}{dx^2}f(x)$\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
|
"id": "3926fcb9-62b8-45d3-ae64-8c626ac04901",
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": true
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Golden ratio search\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\n",
|
||
|
|
" 2\t4.3255e-01\t-5.00000000e-01\t3.00000000e+00\n",
|
||
|
|
" 3\t4.3255e-01\t-5.00000000e-01\t1.66311896e+00\n",
|
||
|
|
" 4\t2.0218e-01\t-5.00000000e-01\t8.36881039e-01\n",
|
||
|
|
" 5\t3.3976e-04\t-5.00000000e-01\t3.26237921e-01\n",
|
||
|
|
" 6\t3.3976e-04\t-1.84405197e-01\t3.26237921e-01\n",
|
||
|
|
" 7\t3.3976e-04\t-1.84405197e-01\t1.31189606e-01\n",
|
||
|
|
" 8\t3.3976e-04\t-6.38587088e-02\t1.31189606e-01\n",
|
||
|
|
" 9\t3.3976e-04\t-6.38587088e-02\t5.66877794e-02\n",
|
||
|
|
" 10\t3.3976e-04\t-1.78140475e-02\t5.66877794e-02\n",
|
||
|
|
" 11\t3.3976e-04\t-1.78140475e-02\t2.82306137e-02\n",
|
||
|
|
" 12\t1.5573e-07\t-1.78140475e-02\t1.06431181e-02\n",
|
||
|
|
" 13\t1.5573e-07\t-6.94437747e-03\t1.06431181e-02\n",
|
||
|
|
" 14\t1.5573e-07\t-6.94437747e-03\t3.92529259e-03\n",
|
||
|
|
" 15\t1.5573e-07\t-2.79253295e-03\t3.92529259e-03\n",
|
||
|
|
" 16\t1.5573e-07\t-2.79253295e-03\t1.35931156e-03\n",
|
||
|
|
" 17\t1.5573e-07\t-1.20666946e-03\t1.35931156e-03\n",
|
||
|
|
" 18\t1.5573e-07\t-1.20666946e-03\t3.79194024e-04\n",
|
||
|
|
" 19\t1.5573e-07\t-6.00923513e-04\t3.79194024e-04\n",
|
||
|
|
" 20\t7.0543e-11\t-2.26551927e-04\t3.79194024e-04\n",
|
||
|
|
" 21\t7.0543e-11\t-2.26551927e-04\t1.47819659e-04\n",
|
||
|
|
" 22\t7.0543e-11\t-8.35547054e-05\t1.47819659e-04\n",
|
||
|
|
" 23\t7.0543e-11\t-8.35547054e-05\t5.94425162e-05\n",
|
||
|
|
" 24\t7.0543e-11\t-2.89346270e-05\t5.94425162e-05\n",
|
||
|
|
" 25\t7.0543e-11\t-2.89346270e-05\t2.56854513e-05\n",
|
||
|
|
" 26\t7.0543e-11\t-8.07161358e-06\t2.56854513e-05\n",
|
||
|
|
" 27\t7.0543e-11\t-8.07161358e-06\t1.27913999e-05\n",
|
||
|
|
" 28\t3.1963e-14\t-8.07161358e-06\t4.82243784e-06\n",
|
||
|
|
" 29\t3.1963e-14\t-3.14652419e-06\t4.82243784e-06\n",
|
||
|
|
" 30\t3.1963e-14\t-3.14652419e-06\t1.77856520e-06\n",
|
||
|
|
" 31\t3.1963e-14\t-1.26530744e-06\t1.77856520e-06\n",
|
||
|
|
" 32\t3.1963e-14\t-1.26530744e-06\t6.15909307e-07\n",
|
||
|
|
" 33\t3.1963e-14\t-5.46746585e-07\t6.15909307e-07\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
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||
|
|
"image/svg+xml": [
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||
|
|
"<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
|
||
|
|
"<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"400\" viewBox=\"0 0 2400 1600\">\n",
|
||
|
|
"<defs>\n",
|
||
|
|
" <clipPath id=\"clip140\">\n",
|
||
|
|
" <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
|
||
|
|
" </clipPath>\n",
|
||
|
|
"</defs>\n",
|
||
|
|
"<path clip-path=\"url(#clip140)\" d=\"M0 1600 L2400 1600 L2400 0 L0 0 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
|
||
|
|
"<defs>\n",
|
||
|
|
" <clipPath id=\"clip141\">\n",
|
||
|
|
" <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
|
||
|
|
" </clipPath>\n",
|
||
|
|
"</defs>\n",
|
||
|
|
"<path clip-path=\"url(#clip140)\" d=\"M332.011 1486.45 L2352.76 1486.45 L2352.76 47.2441 L332.011 47.2441 Z\" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
|
||
|
|
"<defs>\n",
|
||
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|
" <clipPath id=\"clip142\">\n",
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|
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" <rect x=\"332\" y=\"47\" width=\"2022\" height=\"1440\"/>\n",
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" </clipPath>\n",
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"(-1.0265155122631873e-7, \"optimal\")"
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]
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},
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||
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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||
|
|
}
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|
|
],
|
||
|
|
"source": [
|
||
|
|
"include(\"GRS.jl\")\n",
|
||
|
|
"GRS(oneDTestFunctions()[1], Plotg=2)"
|
||
|
|
]
|
||
|
|
},
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||
|
|
{
|
||
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"cell_type": "code",
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"execution_count": 4,
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||
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"id": "27d78090-9240-4313-8d9f-d1e7d88884a5",
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||
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"metadata": {
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|
"scrolled": true
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Dichotomic search\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t5.1784e-01\t-5.00000000e-01\t3.00000000e+00\t1.25000000e+00\t5.8857e-01\n",
|
||
|
|
" 4\t2.4399e-01\t-5.00000000e-01\t1.25000000e+00\t3.75000000e-01\t8.3549e-01\n",
|
||
|
|
" 5\t1.2585e-02\t-5.00000000e-01\t3.75000000e-01\t-6.25000000e-02\t-4.1386e-01\n",
|
||
|
|
" 6\t1.2585e-02\t-6.25000000e-02\t3.75000000e-01\t1.56250000e-01\t6.9460e-01\n",
|
||
|
|
" 7\t6.3294e-03\t-6.25000000e-02\t1.56250000e-01\t4.68750000e-02\t2.6271e-01\n",
|
||
|
|
" 8\t1.8664e-04\t-6.25000000e-02\t4.68750000e-02\t-7.81250000e-03\t-4.7971e-02\n",
|
||
|
|
" 9\t1.8664e-04\t-7.81250000e-03\t4.68750000e-02\t1.95312500e-02\t1.1480e-01\n",
|
||
|
|
" 10\t1.0350e-04\t-7.81250000e-03\t1.95312500e-02\t5.85937500e-03\t3.5219e-02\n",
|
||
|
|
" 11\t2.8958e-06\t-7.81250000e-03\t5.85937500e-03\t-9.76562500e-04\t-5.9335e-03\n",
|
||
|
|
" 12\t2.8958e-06\t-9.76562500e-04\t5.85937500e-03\t2.44140625e-03\t1.4754e-02\n",
|
||
|
|
" 13\t1.6260e-06\t-9.76562500e-04\t2.44140625e-03\t7.32421875e-04\t4.4383e-03\n",
|
||
|
|
" 14\t4.5206e-08\t-9.76562500e-04\t7.32421875e-04\t-1.22070312e-04\t-7.4070e-04\n",
|
||
|
|
" 15\t4.5206e-08\t-1.22070312e-04\t7.32421875e-04\t3.05175781e-04\t1.8505e-03\n",
|
||
|
|
" 16\t2.5423e-08\t-1.22070312e-04\t3.05175781e-04\t9.15527344e-05\t5.5534e-04\n",
|
||
|
|
" 17\t7.0626e-10\t-1.22070312e-04\t9.15527344e-05\t-1.52587891e-05\t-9.2572e-05\n",
|
||
|
|
" 18\t7.0626e-10\t-1.52587891e-05\t9.15527344e-05\t3.81469727e-05\t2.3141e-04\n",
|
||
|
|
" 19\t3.9726e-10\t-1.52587891e-05\t3.81469727e-05\t1.14440918e-05\t6.9426e-05\n",
|
||
|
|
" 20\t1.1035e-11\t-1.52587891e-05\t1.14440918e-05\t-1.90734863e-06\t-1.1571e-05\n",
|
||
|
|
" 21\t1.1035e-11\t-1.90734863e-06\t1.14440918e-05\t4.76837158e-06\t2.8928e-05\n",
|
||
|
|
" 22\t6.2073e-12\t-1.90734863e-06\t4.76837158e-06\t1.43051147e-06\t8.6784e-06\n",
|
||
|
|
" 23\t1.7243e-13\t-1.90734863e-06\t1.43051147e-06\t-2.38418579e-07\t-1.4464e-06\n",
|
||
|
|
" 24\t1.7243e-13\t-2.38418579e-07\t1.43051147e-06\t5.96046448e-07\t3.6160e-06\n",
|
||
|
|
" 25\t9.6989e-14\t-2.38418579e-07\t5.96046448e-07\t1.78813934e-07\t1.0848e-06\n",
|
||
|
|
" 26\t2.6941e-15\t-2.38418579e-07\t1.78813934e-07\t-2.98023224e-08\t-1.8080e-07\n"
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||
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|
]
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"</svg>\n"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
|
||
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|
"(-2.9802322387695312e-8, \"optimal\")"
|
||
|
|
]
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||
|
|
},
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"include(\"DIS.jl\")\n",
|
||
|
|
"DIS(oneDTestFunctions()[1], Plotg=2)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
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|
"execution_count": 5,
|
||
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|
"id": "c58460c5-c7bf-441c-a29c-3b43477bae62",
|
||
|
|
"metadata": {
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||
|
|
"scrolled": true
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Dichotomic search with safeguarded interpolation (0.3000)\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t4.6647e-01\t-5.00000000e-01\t3.00000000e+00\t1.13641217e+00\t3.2205e-01\n",
|
||
|
|
" 4\t4.0396e-01\t-5.00000000e-01\t1.13641217e+00\t6.45488518e-01\t3.0611e-01\n",
|
||
|
|
" 5\t1.8075e-01\t-5.00000000e-01\t6.45488518e-01\t3.01841963e-01\t8.8071e-01\n",
|
||
|
|
" 6\t1.0638e-02\t-5.00000000e-01\t3.01841963e-01\t6.12893739e-02\t3.3443e-01\n",
|
||
|
|
" 7\t1.0638e-02\t-5.00000000e-01\t6.12893739e-02\t-1.07097438e-01\t-7.4538e-01\n",
|
||
|
|
" 8\t2.5086e-04\t-1.07097438e-01\t6.12893739e-02\t9.13789778e-03\t5.4637e-02\n",
|
||
|
|
" 9\t2.5086e-04\t-1.07097438e-01\t9.13789778e-03\t-2.57327030e-02\t-1.6225e-01\n",
|
||
|
|
" 10\t5.3189e-06\t-2.57327030e-02\t9.13789778e-03\t-1.32328247e-03\t-8.0445e-03\n",
|
||
|
|
" 11\t5.3189e-06\t-1.32328247e-03\t9.13789778e-03\t1.81507161e-03\t1.0980e-02\n",
|
||
|
|
" 12\t4.3014e-11\t-1.32328247e-03\t1.81507161e-03\t3.76571780e-06\t2.2845e-05\n",
|
||
|
|
" 13\t4.3014e-11\t-1.32328247e-03\t3.76571780e-06\t-3.94348738e-04\t-2.3939e-03\n",
|
||
|
|
" 14\t4.3014e-11\t-3.94348738e-04\t3.76571780e-06\t-1.15668619e-04\t-7.0185e-04\n",
|
||
|
|
" 15\t4.3014e-11\t-1.15668619e-04\t3.76571780e-06\t-3.20645832e-05\t-1.9453e-04\n",
|
||
|
|
" 16\t4.3014e-11\t-3.20645832e-05\t3.76571780e-06\t-6.98337251e-06\t-4.2366e-05\n",
|
||
|
|
" 17\t5.1438e-21\t-6.98337251e-06\t3.76571780e-06\t4.11796824e-11\t2.4982e-10\n"
|
||
|
|
]
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||
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|
},
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||
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{
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||
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|
"data": {
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"(4.1179682402735445e-11, \"optimal\")"
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"DIS(oneDTestFunctions()[1]; sfgrd=0.30, Plotg=2)"
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]
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},
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{
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"cell_type": "code",
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"id": "c7856508-6940-4e1e-b9d0-0f6ae39e47b8",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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||
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"Univariate Newton's Method\n",
|
||
|
|
"feval\trel gap\t\tx\t\tf(x)\t\tf'(x)\t\tf''(x)\n",
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||
|
|
" 1\t2.6990e-02\t1.00000000e-01\t2.6990e-02\t5.0500e-01\t3.9859e+00\n",
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||
|
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" 2\t2.2210e-03\t-2.66964885e-02\t2.2210e-03\t-1.6855e-01\t6.5539e+00\n",
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||
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" 3\t2.9054e-06\t-9.78183164e-04\t2.9054e-06\t-5.9434e-03\t6.0852e+00\n",
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||
|
|
" 4\t6.7444e-12\t-1.49111486e-06\t6.7444e-12\t-9.0461e-06\t6.0667e+00\n",
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||
|
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" 5\t3.6771e-23\t-3.48170895e-12\t3.6771e-23\t-2.1122e-11\t6.0667e+00\n"
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]
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},
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"data": {
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"</svg>\n"
|
||
|
|
]
|
||
|
|
},
|
||
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|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"(-3.481708945640477e-12, \"optimal\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 6,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"include(\"UNM.jl\")\n",
|
||
|
|
"UNM(oneDTestFunctions()[1]; x=0.1, Plotg=3)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 30,
|
||
|
|
"id": "044fd698-e21d-4b00-a141-4a9ea7a6f486",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Golden ratio search\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\n",
|
||
|
|
" 2\t4.3255e-01\t-5.00000000e-01\t3.00000000e+00\n",
|
||
|
|
" 3\t4.3255e-01\t-5.00000000e-01\t1.66311896e+00\n",
|
||
|
|
" 4\t2.0218e-01\t-5.00000000e-01\t8.36881039e-01\n",
|
||
|
|
" 5\t3.3976e-04\t-5.00000000e-01\t3.26237921e-01\n",
|
||
|
|
" 6\t3.3976e-04\t-1.84405197e-01\t3.26237921e-01\n",
|
||
|
|
" 7\t3.3976e-04\t-1.84405197e-01\t1.31189606e-01\n",
|
||
|
|
" 8\t3.3976e-04\t-6.38587088e-02\t1.31189606e-01\n",
|
||
|
|
" 9\t3.3976e-04\t-6.38587088e-02\t5.66877794e-02\n",
|
||
|
|
" 10\t3.3976e-04\t-1.78140475e-02\t5.66877794e-02\n",
|
||
|
|
" 11\t3.3976e-04\t-1.78140475e-02\t2.82306137e-02\n",
|
||
|
|
" 12\t1.5573e-07\t-1.78140475e-02\t1.06431181e-02\n",
|
||
|
|
" 13\t1.5573e-07\t-6.94437747e-03\t1.06431181e-02\n",
|
||
|
|
" 14\t1.5573e-07\t-6.94437747e-03\t3.92529259e-03\n",
|
||
|
|
" 15\t1.5573e-07\t-2.79253295e-03\t3.92529259e-03\n",
|
||
|
|
" 16\t1.5573e-07\t-2.79253295e-03\t1.35931156e-03\n",
|
||
|
|
" 17\t1.5573e-07\t-1.20666946e-03\t1.35931156e-03\n",
|
||
|
|
" 18\t1.5573e-07\t-1.20666946e-03\t3.79194024e-04\n",
|
||
|
|
" 19\t1.5573e-07\t-6.00923513e-04\t3.79194024e-04\n",
|
||
|
|
" 20\t7.0543e-11\t-2.26551927e-04\t3.79194024e-04\n",
|
||
|
|
" 21\t7.0543e-11\t-2.26551927e-04\t1.47819659e-04\n",
|
||
|
|
" 22\t7.0543e-11\t-8.35547054e-05\t1.47819659e-04\n",
|
||
|
|
" 23\t7.0543e-11\t-8.35547054e-05\t5.94425162e-05\n",
|
||
|
|
" 24\t7.0543e-11\t-2.89346270e-05\t5.94425162e-05\n",
|
||
|
|
" 25\t7.0543e-11\t-2.89346270e-05\t2.56854513e-05\n",
|
||
|
|
" 26\t7.0543e-11\t-8.07161358e-06\t2.56854513e-05\n",
|
||
|
|
" 27\t7.0543e-11\t-8.07161358e-06\t1.27913999e-05\n",
|
||
|
|
" 28\t3.1963e-14\t-8.07161358e-06\t4.82243784e-06\n",
|
||
|
|
" 29\t3.1963e-14\t-3.14652419e-06\t4.82243784e-06\n",
|
||
|
|
" 30\t3.1963e-14\t-3.14652419e-06\t1.77856520e-06\n",
|
||
|
|
" 31\t3.1963e-14\t-1.26530744e-06\t1.77856520e-06\n",
|
||
|
|
" 32\t3.1963e-14\t-1.26530744e-06\t6.15909307e-07\n",
|
||
|
|
" 33\t3.1963e-14\t-5.46746585e-07\t6.15909307e-07\n",
|
||
|
|
"Dichotomic search\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t5.1784e-01\t-5.00000000e-01\t3.00000000e+00\t1.25000000e+00\t5.8857e-01\n",
|
||
|
|
" 4\t2.4399e-01\t-5.00000000e-01\t1.25000000e+00\t3.75000000e-01\t8.3549e-01\n",
|
||
|
|
" 5\t1.2585e-02\t-5.00000000e-01\t3.75000000e-01\t-6.25000000e-02\t-4.1386e-01\n",
|
||
|
|
" 6\t1.2585e-02\t-6.25000000e-02\t3.75000000e-01\t1.56250000e-01\t6.9460e-01\n",
|
||
|
|
" 7\t6.3294e-03\t-6.25000000e-02\t1.56250000e-01\t4.68750000e-02\t2.6271e-01\n",
|
||
|
|
" 8\t1.8664e-04\t-6.25000000e-02\t4.68750000e-02\t-7.81250000e-03\t-4.7971e-02\n",
|
||
|
|
" 9\t1.8664e-04\t-7.81250000e-03\t4.68750000e-02\t1.95312500e-02\t1.1480e-01\n",
|
||
|
|
" 10\t1.0350e-04\t-7.81250000e-03\t1.95312500e-02\t5.85937500e-03\t3.5219e-02\n",
|
||
|
|
" 11\t2.8958e-06\t-7.81250000e-03\t5.85937500e-03\t-9.76562500e-04\t-5.9335e-03\n",
|
||
|
|
" 12\t2.8958e-06\t-9.76562500e-04\t5.85937500e-03\t2.44140625e-03\t1.4754e-02\n",
|
||
|
|
" 13\t1.6260e-06\t-9.76562500e-04\t2.44140625e-03\t7.32421875e-04\t4.4383e-03\n",
|
||
|
|
" 14\t4.5206e-08\t-9.76562500e-04\t7.32421875e-04\t-1.22070312e-04\t-7.4070e-04\n",
|
||
|
|
" 15\t4.5206e-08\t-1.22070312e-04\t7.32421875e-04\t3.05175781e-04\t1.8505e-03\n",
|
||
|
|
" 16\t2.5423e-08\t-1.22070312e-04\t3.05175781e-04\t9.15527344e-05\t5.5534e-04\n",
|
||
|
|
" 17\t7.0626e-10\t-1.22070312e-04\t9.15527344e-05\t-1.52587891e-05\t-9.2572e-05\n",
|
||
|
|
" 18\t7.0626e-10\t-1.52587891e-05\t9.15527344e-05\t3.81469727e-05\t2.3141e-04\n",
|
||
|
|
" 19\t3.9726e-10\t-1.52587891e-05\t3.81469727e-05\t1.14440918e-05\t6.9426e-05\n",
|
||
|
|
" 20\t1.1035e-11\t-1.52587891e-05\t1.14440918e-05\t-1.90734863e-06\t-1.1571e-05\n",
|
||
|
|
" 21\t1.1035e-11\t-1.90734863e-06\t1.14440918e-05\t4.76837158e-06\t2.8928e-05\n",
|
||
|
|
" 22\t6.2073e-12\t-1.90734863e-06\t4.76837158e-06\t1.43051147e-06\t8.6784e-06\n",
|
||
|
|
" 23\t1.7243e-13\t-1.90734863e-06\t1.43051147e-06\t-2.38418579e-07\t-1.4464e-06\n",
|
||
|
|
" 24\t1.7243e-13\t-2.38418579e-07\t1.43051147e-06\t5.96046448e-07\t3.6160e-06\n",
|
||
|
|
" 25\t9.6989e-14\t-2.38418579e-07\t5.96046448e-07\t1.78813934e-07\t1.0848e-06\n",
|
||
|
|
" 26\t2.6941e-15\t-2.38418579e-07\t1.78813934e-07\t-2.98023224e-08\t-1.8080e-07\n",
|
||
|
|
"Dichotomic search with safeguarded interpolation (0.5000)\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t5.1782e-01\t-5.00000000e-01\t3.00000000e+00\t1.24996500e+00\t5.8848e-01\n",
|
||
|
|
" 4\t2.4399e-01\t-5.00000000e-01\t1.24996500e+00\t3.75000000e-01\t8.3549e-01\n",
|
||
|
|
" 5\t1.2582e-02\t-5.00000000e-01\t3.75000000e-01\t-6.24912502e-02\t-4.1379e-01\n",
|
||
|
|
" 6\t1.2582e-02\t-6.24912502e-02\t3.75000000e-01\t1.56250000e-01\t6.9460e-01\n",
|
||
|
|
" 7\t6.3299e-03\t-6.24912502e-02\t1.56250000e-01\t4.68771874e-02\t2.6272e-01\n",
|
||
|
|
" 8\t1.8633e-04\t-6.24912502e-02\t4.68771874e-02\t-7.80593770e-03\t-4.7931e-02\n",
|
||
|
|
" 9\t1.8633e-04\t-7.80593770e-03\t4.68771874e-02\t1.95350780e-02\t1.1483e-01\n",
|
||
|
|
" 10\t1.0368e-04\t-7.80593770e-03\t1.95350780e-02\t5.86429675e-03\t3.5248e-02\n",
|
||
|
|
" 11\t2.8610e-06\t-7.80593770e-03\t5.86429675e-03\t-9.70683769e-04\t-5.8978e-03\n",
|
||
|
|
" 12\t2.8610e-06\t-9.70683769e-04\t5.86429675e-03\t2.44673814e-03\t1.4787e-02\n",
|
||
|
|
" 13\t1.6508e-06\t-9.70683769e-04\t2.44673814e-03\t7.37993013e-04\t4.4720e-03\n",
|
||
|
|
" 14\t4.1053e-08\t-9.70683769e-04\t7.37993013e-04\t-1.16328291e-04\t-7.0585e-04\n",
|
||
|
|
" 15\t4.1053e-08\t-1.16328291e-04\t7.37993013e-04\t3.10823818e-04\t1.8847e-03\n",
|
||
|
|
" 16\t2.8681e-08\t-1.16328291e-04\t3.10823818e-04\t9.72434918e-05\t5.8985e-04\n",
|
||
|
|
" 17\t2.7609e-10\t-1.16328291e-04\t9.72434918e-05\t-9.54026395e-06\t-5.7878e-05\n",
|
||
|
|
" 18\t2.7609e-10\t-9.54026395e-06\t9.72434918e-05\t4.38505461e-05\t2.6601e-04\n",
|
||
|
|
" 19\t2.7609e-10\t-9.54026395e-06\t4.38505461e-05\t1.71546072e-05\t1.0407e-04\n",
|
||
|
|
" 20\t4.3960e-11\t-9.54026395e-06\t1.71546072e-05\t3.80690466e-06\t2.3095e-05\n",
|
||
|
|
" 21\t2.4925e-11\t-9.54026395e-06\t3.80690466e-06\t-2.86654617e-06\t-1.7390e-05\n",
|
||
|
|
" 22\t6.7038e-13\t-2.86654617e-06\t3.80690466e-06\t4.70112506e-07\t2.8520e-06\n",
|
||
|
|
" 23\t6.7038e-13\t-2.86654617e-06\t4.70112506e-07\t-1.19818347e-06\t-7.2690e-06\n",
|
||
|
|
" 24\t4.0195e-13\t-1.19818347e-06\t4.70112506e-07\t-3.64018798e-07\t-2.2084e-06\n",
|
||
|
|
" 25\t8.5330e-15\t-3.64018798e-07\t4.70112506e-07\t5.30385125e-08\t3.2177e-07\n",
|
||
|
|
"Dichotomic search with safeguarded interpolation (0.3000)\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t4.6647e-01\t-5.00000000e-01\t3.00000000e+00\t1.13641217e+00\t3.2205e-01\n",
|
||
|
|
" 4\t4.0396e-01\t-5.00000000e-01\t1.13641217e+00\t6.45488518e-01\t3.0611e-01\n",
|
||
|
|
" 5\t1.8075e-01\t-5.00000000e-01\t6.45488518e-01\t3.01841963e-01\t8.8071e-01\n",
|
||
|
|
" 6\t1.0638e-02\t-5.00000000e-01\t3.01841963e-01\t6.12893739e-02\t3.3443e-01\n",
|
||
|
|
" 7\t1.0638e-02\t-5.00000000e-01\t6.12893739e-02\t-1.07097438e-01\t-7.4538e-01\n",
|
||
|
|
" 8\t2.5086e-04\t-1.07097438e-01\t6.12893739e-02\t9.13789778e-03\t5.4637e-02\n",
|
||
|
|
" 9\t2.5086e-04\t-1.07097438e-01\t9.13789778e-03\t-2.57327030e-02\t-1.6225e-01\n",
|
||
|
|
" 10\t5.3189e-06\t-2.57327030e-02\t9.13789778e-03\t-1.32328247e-03\t-8.0445e-03\n",
|
||
|
|
" 11\t5.3189e-06\t-1.32328247e-03\t9.13789778e-03\t1.81507161e-03\t1.0980e-02\n",
|
||
|
|
" 12\t4.3014e-11\t-1.32328247e-03\t1.81507161e-03\t3.76571780e-06\t2.2845e-05\n",
|
||
|
|
" 13\t4.3014e-11\t-1.32328247e-03\t3.76571780e-06\t-3.94348738e-04\t-2.3939e-03\n",
|
||
|
|
" 14\t4.3014e-11\t-3.94348738e-04\t3.76571780e-06\t-1.15668619e-04\t-7.0185e-04\n",
|
||
|
|
" 15\t4.3014e-11\t-1.15668619e-04\t3.76571780e-06\t-3.20645832e-05\t-1.9453e-04\n",
|
||
|
|
" 16\t4.3014e-11\t-3.20645832e-05\t3.76571780e-06\t-6.98337251e-06\t-4.2366e-05\n",
|
||
|
|
" 17\t5.1438e-21\t-6.98337251e-06\t3.76571780e-06\t4.11796824e-11\t2.4982e-10\n",
|
||
|
|
"Dichotomic search with safeguarded interpolation (0.0500)\n",
|
||
|
|
"feval\trel gap\t\tx_-\t\tx_+\t\tx\t\tf'(x)\n",
|
||
|
|
" 3\t4.6647e-01\t-5.00000000e-01\t3.00000000e+00\t1.13641217e+00\t3.2205e-01\n",
|
||
|
|
" 4\t4.3846e-01\t-5.00000000e-01\t1.13641217e+00\t9.84326389e-01\t7.5871e-02\n",
|
||
|
|
" 5\t4.3486e-01\t-5.00000000e-01\t9.84326389e-01\t9.10110069e-01\t3.0546e-02\n",
|
||
|
|
" 6\t4.3266e-01\t-5.00000000e-01\t9.10110069e-01\t8.39604566e-01\t4.0287e-02\n",
|
||
|
|
" 7\t4.2833e-01\t-5.00000000e-01\t8.39604566e-01\t7.72624338e-01\t9.6308e-02\n",
|
||
|
|
" 8\t4.1949e-01\t-5.00000000e-01\t7.72624338e-01\t7.08993121e-01\t1.8704e-01\n",
|
||
|
|
" 9\t4.0260e-01\t-5.00000000e-01\t7.08993121e-01\t6.41091591e-01\t3.1515e-01\n",
|
||
|
|
" 10\t3.5812e-01\t-5.00000000e-01\t6.41091591e-01\t5.37106669e-01\t5.4285e-01\n",
|
||
|
|
" 11\t2.5177e-01\t-5.00000000e-01\t5.37106669e-01\t3.84368359e-01\t8.2455e-01\n",
|
||
|
|
" 12\t9.4246e-02\t-5.00000000e-01\t3.84368359e-01\t2.00583037e-01\t7.9589e-01\n",
|
||
|
|
" 13\t9.8947e-03\t-5.00000000e-01\t2.00583037e-01\t5.90289844e-02\t3.2347e-01\n",
|
||
|
|
" 14\t1.4196e-04\t-5.00000000e-01\t5.90289844e-02\t6.86585262e-03\t4.1202e-02\n",
|
||
|
|
" 15\t1.4196e-04\t-5.00000000e-01\t6.86585262e-03\t-1.84774400e-02\t-1.1528e-01\n",
|
||
|
|
" 16\t1.1298e-07\t-1.84774400e-02\t6.86585262e-03\t1.93016015e-04\t1.1706e-03\n",
|
||
|
|
" 17\t1.1298e-07\t-1.84774400e-02\t1.93016015e-04\t-7.40506786e-04\t-4.4976e-03\n",
|
||
|
|
" 18\t1.5154e-13\t-7.40506786e-04\t1.93016015e-04\t2.23515295e-07\t1.3560e-06\n",
|
||
|
|
" 19\t1.5154e-13\t-7.40506786e-04\t2.23515295e-07\t-3.68129998e-05\t-2.2335e-04\n",
|
||
|
|
" 20\t1.5154e-13\t-3.68129998e-05\t2.23515295e-07\t-1.62831046e-06\t-9.8784e-06\n",
|
||
|
|
" 21\t9.8526e-25\t-1.62831046e-06\t2.23515295e-07\t5.69923312e-13\t3.4575e-12\n",
|
||
|
|
"Univariate Newton's Method\n",
|
||
|
|
"feval\trel gap\t\tx\t\tf(x)\t\tf'(x)\t\tf''(x)\n",
|
||
|
|
" 1\t8.9644e-01\t-5.00000000e-01\t8.9644e-01\t-3.1432e+00\t2.8378e-01\n",
|
||
|
|
" 2\t8.9644e-01\t1.05758636e+01\t5.9574e+07\t6.5971e+07\t6.5518e+07\n",
|
||
|
|
" 3\t8.9644e-01\t9.56895366e+00\t1.8219e+07\t2.2809e+07\t2.5586e+07\n",
|
||
|
|
" 4\t8.9644e-01\t8.67749933e+00\t5.5618e+06\t7.8820e+06\t9.9974e+06\n",
|
||
|
|
" 5\t8.9644e-01\t7.88908699e+00\t1.6941e+06\t2.7220e+06\t3.9088e+06\n",
|
||
|
|
" 6\t8.9644e-01\t7.19272084e+00\t5.1457e+05\t9.3922e+05\t1.5295e+06\n",
|
||
|
|
" 7\t8.9644e-01\t6.57866301e+00\t1.5577e+05\t3.2375e+05\t5.9911e+05\n",
|
||
|
|
" 8\t8.9644e-01\t6.03828653e+00\t4.6968e+04\t1.1145e+05\t2.3496e+05\n",
|
||
|
|
" 9\t8.9644e-01\t5.56393556e+00\t1.4098e+04\t3.8312e+04\t9.2284e+04\n",
|
||
|
|
" 10\t8.9644e-01\t5.14878422e+00\t4.2138e+03\t1.3146e+04\t3.6305e+04\n",
|
||
|
|
" 11\t8.9644e-01\t4.78667921e+00\t1.2567e+03\t4.5027e+03\t1.4306e+04\n",
|
||
|
|
" 12\t8.9644e-01\t4.47193861e+00\t3.7665e+02\t1.5400e+03\t5.6432e+03\n",
|
||
|
|
" 13\t8.9644e-01\t4.19905074e+00\t1.1571e+02\t5.2675e+02\t2.2235e+03\n",
|
||
|
|
" 14\t8.9644e-01\t3.96214954e+00\t3.8146e+01\t1.8107e+02\t8.6974e+02\n",
|
||
|
|
" 15\t8.9644e-01\t3.75395648e+00\t1.4626e+01\t6.3360e+01\t3.3222e+02\n",
|
||
|
|
" 16\t8.9644e-01\t3.56323926e+00\t7.0040e+00\t2.3292e+01\t1.1868e+02\n",
|
||
|
|
" 17\t8.9644e-01\t3.36697475e+00\t4.0363e+00\t9.6173e+00\t3.5828e+01\n",
|
||
|
|
" 18\t8.9644e-01\t3.09854269e+00\t2.2767e+00\t4.5568e+00\t1.0606e+01\n",
|
||
|
|
" 19\t8.9644e-01\t2.66890891e+00\t1.1804e+00\t7.6520e-01\t6.7669e+00\n",
|
||
|
|
" 20\t8.9644e-01\t2.55582999e+00\t1.1328e+00\t1.1808e-01\t4.5954e+00\n",
|
||
|
|
" 21\t8.9644e-01\t2.53013577e+00\t1.1312e+00\t7.0288e-03\t4.0462e+00\n",
|
||
|
|
" 22\t8.9644e-01\t2.52839863e+00\t1.1312e+00\t3.2604e-05\t4.0087e+00\n",
|
||
|
|
" 23\t8.9644e-01\t2.52839050e+00\t1.1312e+00\t7.1395e-10\t4.0085e+00\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
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"<path clip-path=\"url(#clip640)\" d=\"M2217.38 425.945 Q2215.58 430.575 2213.86 431.987 Q2212.15 433.399 2209.28 433.399 L2205.88 433.399 L2205.88 429.834 L2208.38 429.834 Q2210.14 429.834 2211.11 429 Q2212.08 428.167 2213.26 425.065 L2214.03 423.121 L2203.54 397.612 L2208.05 397.612 L2216.16 417.889 L2224.26 397.612 L2228.77 397.612 L2217.38 425.945 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /><path clip-path=\"url(#clip640)\" d=\"M2245.83 404.394 Q2242.68 404.394 2240.83 406.547 Q2239 408.7 2239 412.45 Q2239 416.176 2240.83 418.352 Q2242.68 420.505 2245.83 420.505 Q2248.98 420.505 2250.81 418.352 Q2252.66 416.176 2252.66 412.45 Q2252.66 408.7 2250.81 406.547 Q2248.98 404.394 2245.83 404.394 M2255.11 389.741 L2255.11 394.001 Q2253.35 393.167 2251.55 392.728 Q2249.77 392.288 2248.01 392.288 Q2243.38 392.288 2240.92 395.413 Q2238.49 398.538 2238.15 404.857 Q2239.51 402.843 2241.57 401.778 Q2243.63 400.69 2246.11 400.69 Q2251.32 400.69 2254.33 403.862 Q2257.36 407.01 2257.36 412.45 Q2257.36 417.774 2254.21 420.991 Q2251.06 424.209 2245.83 424.209 Q2239.84 424.209 2236.66 419.626 Q2233.49 415.019 2233.49 406.292 Q2233.49 398.098 2237.38 393.237 Q2241.27 388.353 2247.82 388.353 Q2249.58 388.353 2251.36 388.7 Q2253.17 389.047 2255.11 389.741 Z\" fill=\"#000000\" fill-rule=\"nonzero\" fill-opacity=\"1\" /></svg>\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"include(\"oneDTestFunctions.jl\")\n",
|
||
|
|
"include(\"GRS.jl\")\n",
|
||
|
|
"include(\"DIS.jl\")\n",
|
||
|
|
"include(\"UNM.jl\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt = plot(yscale = :log,\n",
|
||
|
|
" xlims=(0, 35),\n",
|
||
|
|
" ylims=(1e-15, Inf),\n",
|
||
|
|
" guidefontsize=16)\n",
|
||
|
|
"\n",
|
||
|
|
"GRS(oneDTestFunctions()[1], plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"DIS(oneDTestFunctions()[1], plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"DIS(oneDTestFunctions()[1]; sfgrd=0.49999, plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"DIS(oneDTestFunctions()[1]; sfgrd=0.30, plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"DIS(oneDTestFunctions()[1]; sfgrd=0.05, plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"UNM(oneDTestFunctions()[1]; plt=plt, plotatend=false, Plotg=1)\n",
|
||
|
|
"display(plt)"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Julia 1.9.3",
|
||
|
|
"language": "julia",
|
||
|
|
"name": "julia-1.9"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"file_extension": ".jl",
|
||
|
|
"mimetype": "application/julia",
|
||
|
|
"name": "julia",
|
||
|
|
"version": "1.9.3"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|