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Compare scipy current implementation of BFGS with a more efficient one.
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:05.689392", | |
"start_time": "2017-03-12T17:11:04.905123" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"from scipy.linalg import get_blas_funcs, eigh\n", | |
"import matplotlib.pyplot as plt\n", | |
"import time\n", | |
"import cProfile\n", | |
"%matplotlib inline\n", | |
"\n", | |
"sym_rank1update=get_blas_funcs('syr', dtype='d')\n", | |
"sym_rank2update=get_blas_funcs('syr2', dtype='d')\n", | |
"sym_matrixvectorproduct=get_blas_funcs('symv', dtype='d')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:05.703566", | |
"start_time": "2017-03-12T17:11:05.692494" | |
}, | |
"collapsed": true, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [], | |
"source": [ | |
"def BFGS_ineficient(Hk, sk, yk, gfk, I):\n", | |
" \n", | |
" rhok = 1.0 / (np.dot(yk, sk))\n", | |
" \n", | |
" A1 = I - sk[:, np.newaxis] * yk[np.newaxis, :] * rhok\n", | |
" A2 = I - yk[:, np.newaxis] * sk[np.newaxis, :] * rhok\n", | |
" Hk = np.dot(A1, np.dot(Hk, A2)) + (rhok * sk[:, np.newaxis] * sk[np.newaxis, :])\n", | |
" \n", | |
" pk = -np.dot(Hk, gfk)\n", | |
" \n", | |
" return Hk, pk" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:05.721120", | |
"start_time": "2017-03-12T17:11:05.706224" | |
}, | |
"collapsed": true, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [], | |
"source": [ | |
"def BFGS(Hk, sk, yk, gfk):\n", | |
" ykdotsk = np.dot(yk, sk)\n", | |
" rhok = 1.0 / ykdotsk\n", | |
" Hkyk = sym_matrixvectorproduct(1, Hk, yk)\n", | |
" const = rhok**2*(ykdotsk+Hkyk.dot(yk))\n", | |
" Hk = sym_rank2update(-rhok, sk, Hkyk, a=Hk)\n", | |
" Hk = sym_rank1update(const, sk, a=Hk)\n", | |
" \n", | |
" pk = sym_matrixvectorproduct(-1, Hk, gfk)\n", | |
" \n", | |
" return Hk, pk" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:10.615885", | |
"start_time": "2017-03-12T17:11:05.723480" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [], | |
"source": [ | |
"delta_n = 200\n", | |
"max_n = 2000\n", | |
"range_n = range(delta_n, max_n+delta_n, delta_n)\n", | |
"avgtime_bfgs = []\n", | |
"avgtime_bfgs_ineficient = []\n", | |
"for n in range_n:\n", | |
"\n", | |
" I = np.eye(n, dtype=int)\n", | |
" C = np.random.uniform(size=(n, n))\n", | |
" H = np.dot(C.T, C)\n", | |
" s = np.random.uniform(size=n)\n", | |
" y = np.random.uniform(size=n)\n", | |
" g = np.random.uniform(size=n)\n", | |
" aux = np.triu(H)\n", | |
"\n", | |
" start_time = time.time()\n", | |
" H1, p = BFGS(aux, s, y, g)\n", | |
" execution_time = time.time()-start_time\n", | |
" avgtime_bfgs += [execution_time]\n", | |
"\n", | |
" start_time = time.time()\n", | |
" H1_ineficient, p_ineficient = BFGS_ineficient(H, s, y, g, I)\n", | |
" execution_time = time.time()-start_time\n", | |
" avgtime_bfgs_ineficient += [execution_time]\n", | |
"\n", | |
"avgtime_bfgs = np.asarray(avgtime_bfgs)\n", | |
"avgtime_bfgs_ineficient = np.asarray(avgtime_bfgs_ineficient)\n", | |
"mean = np.mean(avgtime_bfgs_ineficient/avgtime_bfgs)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:11.619722", | |
"start_time": "2017-03-12T17:11:10.619683" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
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Y99a4l7uq3uV1OX4r4Ju1/OLcP+z8kT/XlpIxhsTERB588EE6duzIihUrOHjw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HAAAg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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x112f01748>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(10, 8))\n", | |
"plt.plot(range_n, avgtime_bfgs, '-x', label='BFGS')\n", | |
"plt.plot(range_n, avgtime_bfgs_ineficient, '-o', label='Ineficient BFGS')\n", | |
"plt.xlabel(\"Matrix Size\", fontsize=20)\n", | |
"plt.ylabel(\"Average Execution Time\", fontsize=20)\n", | |
"plt.legend(loc=2, fontsize=20)\n", | |
"plt.grid()\n", | |
"plt.savefig('comparison.png')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 6, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:12.504721", | |
"start_time": "2017-03-12T17:11:11.621885" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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ts0/4kPDss8PRGp07Ry4cLfI+nMJw//1hcNdOO8WuKP+YamiIxgtZtXSptPba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\nT7ml6VWRAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x11381fbe0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(10, 8))\n", | |
"plt.plot(range_n, avgtime_bfgs_ineficient/avgtime_bfgs, '--o')\n", | |
"plt.xlabel(\"Matrix Size\", fontsize=20)\n", | |
"plt.ylabel(\"Execution Time Ratio\", fontsize=20)\n", | |
"plt.grid()\n", | |
"plt.savefig('comparison2.png')\n", | |
"plt.show()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:13.095963", | |
"start_time": "2017-03-12T17:11:12.507093" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
" 6 function calls in 0.193 seconds\n", | |
"\n", | |
" Ordered by: standard name\n", | |
"\n", | |
" ncalls tottime percall cumtime percall filename:lineno(function)\n", | |
" 1 0.189 0.189 0.190 0.190 <ipython-input-3-a1774bb19283>:1(BFGS)\n", | |
" 1 0.004 0.004 0.193 0.193 <string>:1(<module>)\n", | |
" 1 0.000 0.000 0.193 0.193 {built-in method builtins.exec}\n", | |
" 1 0.000 0.000 0.000 0.000 {built-in method numpy.core.multiarray.dot}\n", | |
" 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}\n", | |
" 1 0.000 0.000 0.000 0.000 {method 'dot' of 'numpy.ndarray' objects}\n", | |
"\n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"n = 2000\n", | |
"I = np.eye(n, dtype=int)\n", | |
"C = np.random.uniform(size=(n, n))\n", | |
"H = np.dot(C.T, C)\n", | |
"s = np.random.uniform(size=n)\n", | |
"y = np.random.uniform(size=n)\n", | |
"g = np.random.uniform(size=n)\n", | |
"aux = np.triu(H)\n", | |
"\n", | |
"\n", | |
"cProfile.run(\"BFGS(aux, s, y, g)\")" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": { | |
"ExecuteTime": { | |
"end_time": "2017-03-12T17:11:14.040099", | |
"start_time": "2017-03-12T17:11:13.098539" | |
}, | |
"collapsed": false, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
" 8 function calls in 0.935 seconds\n", | |
"\n", | |
" Ordered by: standard name\n", | |
"\n", | |
" ncalls tottime percall cumtime percall filename:lineno(function)\n", | |
" 1 0.152 0.152 0.924 0.924 <ipython-input-2-e3c30c7e7eb4>:1(BFGS_ineficient)\n", | |
" 1 0.011 0.011 0.935 0.935 <string>:1(<module>)\n", | |
" 1 0.000 0.000 0.935 0.935 {built-in method builtins.exec}\n", | |
" 4 0.771 0.193 0.771 0.193 {built-in method numpy.core.multiarray.dot}\n", | |
" 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects}\n", | |
"\n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"cProfile.run(\"BFGS_ineficient(H, s, y, g, I)\")" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"metadata": { | |
"collapsed": true, | |
"run_control": { | |
"frozen": false, | |
"read_only": false | |
} | |
}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"hide_input": false, | |
"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": "3.5.1" | |
}, | |
"latex_envs": { | |
"bibliofile": "biblio.bib", | |
"cite_by": "apalike", | |
"current_citInitial": 1, | |
"eqLabelWithNumbers": true, | |
"eqNumInitial": 0 | |
}, | |
"toc": { | |
"nav_menu": { | |
"height": "12px", | |
"width": "252px" | |
}, | |
"navigate_menu": true, | |
"number_sections": true, | |
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"toc_section_display": "block", | |
"toc_window_display": true | |
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"widgets": { | |
"state": {}, | |
"version": "1.1.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 0 | |
} |
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