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@matthias-k
Created March 21, 2019 22:46
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{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import trlib"
]
},
{
"cell_type": "code",
"execution_count": 213,
"metadata": {},
"outputs": [],
"source": [
"# problem\n",
"\n",
"H = np.array([[1, 0], [0.0, 4]])\n",
"g = np.array([-0.5, -4.3])"
]
},
{
"cell_type": "code",
"execution_count": 214,
"metadata": {},
"outputs": [],
"source": [
"# compute loss function on grid for visualization\n",
"\n",
"d = 2\n",
"x_min = -2\n",
"x_max = 2\n",
"y_min = -2\n",
"y_max = 2\n",
"\n",
"xs = np.linspace(x_min, x_max, num=200)\n",
"ys = np.linspace(y_min, y_max, num=200)\n",
"\n",
"XX, YY = np.meshgrid(xs, ys)\n",
"flat_XX = XX.flatten()\n",
"flat_YY = YY.flatten()\n",
"\n",
"zs = np.vstack([XX.flatten(), YY.flatten()])\n",
"def loss(z):\n",
" return 0.5*z.dot(H.dot(z)) + g.dot(z)\n",
"\n",
"z = np.array([loss(z) for z in zs.T])\n",
"Z = z.reshape(XX.shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interior case"
]
},
{
"cell_type": "code",
"execution_count": 207,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1\n"
]
}
],
"source": [
"radius = 1.5\n",
"xstar, TR = trlib.trlib_solve(\n",
" hess=H,\n",
" grad=g,\n",
" radius=radius\n",
")\n",
"print(TR['ret'])"
]
},
{
"cell_type": "code",
"execution_count": 208,
"metadata": {},
"outputs": [],
"source": [
"global_min_x = flat_XX[np.argmin(z)]\n",
"global_min_y = flat_YY[np.argmin(z)]\n",
"\n",
"tr_inds = np.sqrt(flat_XX**2 + flat_YY**2) <= radius\n",
"min_ind = np.argmin(z[tr_inds])\n",
"tr_min_x = flat_XX[tr_inds][min_ind]\n",
"tr_min_y = flat_YY[tr_inds][min_ind]"
]
},
{
"cell_type": "code",
"execution_count": 209,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fbee2508d30>"
]
},
"execution_count": 209,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(7, 7))\n",
"plt.pcolormesh(XX, YY, Z)\n",
"#plt.colorbar()\n",
"plt.plot([0], [0], marker='o')\n",
"plt.plot([global_min_x], [global_min_y], marker='+', label='global minimum')\n",
"plt.contour(XX, YY, Z, levels=10, cmap='gray')\n",
"plt.gca().add_artist(plt.Circle([0, 0], radius=radius, fill=None, edgecolor='k'))\n",
"\n",
"plt.plot([xstar[0]], [xstar[1]], marker='x', label='trlib solution')\n",
"plt.plot([tr_min_x], [tr_min_y], marker='*', label='manual tr solution')\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## boundary case"
]
},
{
"cell_type": "code",
"execution_count": 210,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n"
]
}
],
"source": [
"radius = 1\n",
"xstar, TR = trlib.trlib_solve(\n",
" hess=H,\n",
" grad=g,\n",
" radius=radius\n",
")\n",
"print(TR['ret'])"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {},
"outputs": [],
"source": [
"global_min_x = flat_XX[np.argmin(z)]\n",
"global_min_y = flat_YY[np.argmin(z)]\n",
"\n",
"tr_inds = np.sqrt(flat_XX**2 + flat_YY**2) <= radius\n",
"min_ind = np.argmin(z[tr_inds])\n",
"tr_min_x = flat_XX[tr_inds][min_ind]\n",
"tr_min_y = flat_YY[tr_inds][min_ind]"
]
},
{
"cell_type": "code",
"execution_count": 212,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7fbee10877b8>"
]
},
"execution_count": 212,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x504 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(7, 7))\n",
"plt.pcolormesh(XX, YY, Z)\n",
"#plt.colorbar()\n",
"plt.plot([0], [0], marker='o')\n",
"plt.plot([global_min_x], [global_min_y], marker='+', label='global minimum')\n",
"plt.contour(XX, YY, Z, levels=10, cmap='gray')\n",
"plt.gca().add_artist(plt.Circle([0, 0], radius=radius, fill=None, edgecolor='k'))\n",
"\n",
"plt.plot([xstar[0]], [xstar[1]], marker='x', label='trlib solution')\n",
"plt.plot([tr_min_x], [tr_min_y], marker='*', label='manual tr solution')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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