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Aggregate quantizer-bitrate statistics
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| #!/usr/bin/env python | |
| import matplotlib as mpl | |
| mpl.use('Agg') | |
| from matplotlib import pyplot as plt | |
| import numpy as np | |
| from pprint import pprint | |
| from glob import glob | |
| # Klotz, Jerome H. "UPDATING SIMPLE LINEAR REGRESSION." | |
| # Statistica Sinica 5, no. 1 (1995): 399-403. | |
| # http://www.jstor.org/stable/24305577 | |
| def online_simple_regression(accumulator, x, y): | |
| Ax_, Ay_, Sxy, Sxx, n_, miny, maxy = accumulator or (0, 0, 0, 0, 0, 0, 0) | |
| first = n_ == 0 | |
| n = n_ + x.size | |
| rt_n, rt_n_ = np.sqrt((n, n_), dtype=np.float128) | |
| Ax = (Ax_*n_ + x.sum(dtype=np.float128))/n | |
| Ay = (Ay_*n_ + y.sum(dtype=np.float128))/n | |
| miny = min(miny, y.min()) | |
| maxy = max(maxy, y.max()) | |
| X = Ax if first else (Ax_*rt_n_ + Ax*rt_n)/(rt_n_ + rt_n) | |
| Y = Ay if first else (Ay_*rt_n_ + Ay*rt_n)/(rt_n_ + rt_n) | |
| Sxx += np.sum((x - X)**2) | |
| Sxy += np.sum((x - X)*(y - Y)) | |
| return Ax, Ay, Sxy, Sxx, n, miny, maxy | |
| def conv_px(s): | |
| w, h = s.split(b'x') | |
| return int(w)*int(h) | |
| conv_fti = [b'I', b'P', b'B0', b'B1'].index | |
| def collect(filename, queues): | |
| px, log_target_q, byte_size, frame_type = np.loadtxt( | |
| filename, dtype=np.int64, delimiter=',', | |
| converters={1: conv_px, 4: conv_fti}, | |
| skiprows=1, usecols=range(1, 5), unpack=True) | |
| blog64q57_ibpp = np.round(( | |
| np.log2(px, dtype=np.float128) - np.log2(byte_size*8, dtype=np.float128) | |
| )*2**57).astype(np.int64) | |
| for fti in np.unique(frame_type): | |
| x, y = log_target_q[frame_type==fti], blog64q57_ibpp[frame_type==fti] | |
| queue = queues.get(fti, ([], [])) | |
| queue[0].append(x) | |
| queue[1].append(y) | |
| queues[fti] = queue | |
| def aggregate(queues, partials): | |
| for fti, queue in queues.items(): | |
| x, y = np.concatenate(queue[0]), np.concatenate(queue[1]) | |
| partials[fti] = online_simple_regression(partials.get(fti, None), x, y) | |
| partials = dict() | |
| for base in sorted(glob('*.y4m')): | |
| queues = dict() | |
| for q in range(1, 256): | |
| collect('%s/%d.txt' % (base, q), queues) | |
| aggregate(queues, partials) | |
| pprint(partials) | |
| plt.figure(figsize=(7, 6)) | |
| plt.axis('equal') | |
| plt.xticks([0, 10]) | |
| plt.yticks([0, 10]) | |
| plt.minorticks_on() | |
| plt.grid(b=True, which='major') | |
| plt.grid(b=True, which='minor', alpha=0.2) | |
| for fti, accumulator in partials.items(): | |
| Ax, Ay, Sxy, Sxx, n, miny, maxy = accumulator | |
| beta = Sxy/Sxx | |
| alpha = Ay - beta*Ax | |
| scale = int(np.round(np.exp2(3 - alpha/2**57))) | |
| exp = int(np.round(beta*2**6)) | |
| label = ['I', 'P', 'B0', 'B1'][fti] | |
| print('%2s: exp=%d scale=%d' % (label, exp, scale)) | |
| ys = [miny/2**57, maxy/2**57] | |
| xs = [(ys[0] - alpha/2**57)/beta, (ys[1] - alpha/2**57)/beta] | |
| plt.plot(xs, ys, label=label) | |
| plt.legend() | |
| plt.savefig('log-bitrate_wrt_log-quantizer.png') | |
| plt.clf() |
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "scrolled": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "{0: (5.938885278876450718e+17,\n", | |
| " 1.9137710889304368723e+17,\n", | |
| " 2.410941997325506283e+40,\n", | |
| " 2.4723415216574388483e+40,\n", | |
| " 337110,\n", | |
| " -479784840691660528,\n", | |
| " 1428504883828996212),\n", | |
| " 1: (6.505176872133070449e+17,\n", | |
| " 5.7400758576573096778e+17,\n", | |
| " 2.9449582682435935951e+41,\n", | |
| " 1.9503819765026800224e+41,\n", | |
| " 2659395,\n", | |
| " -430456311176036496,\n", | |
| " 2134890862486819534),\n", | |
| " 2: (7.071468465389690206e+17,\n", | |
| " 8.0193697664877629525e+17,\n", | |
| " 2.9225410017825442604e+41,\n", | |
| " 1.9821745679309526856e+41,\n", | |
| " 2702745,\n", | |
| " -392114462299251034,\n", | |
| " 1791224583212461071),\n", | |
| " 3: (7.637760058646309966e+17,\n", | |
| " 9.827995667253292844e+17,\n", | |
| " 5.475769590533601731e+41,\n", | |
| " 3.9548113584334235726e+41,\n", | |
| " 5392485,\n", | |
| " -369660646353102446,\n", | |
| " 1993683613661377668)}\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "%matplotlib inline\n", | |
| "from IPython.display import set_matplotlib_formats\n", | |
| "set_matplotlib_formats('svg')\n", | |
| "\n", | |
| "from glob import glob\n", | |
| "from matplotlib import pyplot as plt\n", | |
| "import numpy as np\n", | |
| "from pprint import pprint\n", | |
| "\n", | |
| "# Klotz, Jerome H. \"UPDATING SIMPLE LINEAR REGRESSION.\"\n", | |
| "# Statistica Sinica 5, no. 1 (1995): 399-403.\n", | |
| "# http://www.jstor.org/stable/24305577\n", | |
| "def online_simple_regression(accumulator, x, y):\n", | |
| " Ax_, Ay_, Sxy, Sxx, n_, miny, maxy = accumulator or (0, 0, 0, 0, 0, 0, 0)\n", | |
| "\n", | |
| " first = n_ == 0\n", | |
| " n = n_ + x.size\n", | |
| " rt_n, rt_n_ = np.sqrt((n, n_), dtype=np.float128)\n", | |
| "\n", | |
| " Ax = (Ax_*n_ + x.sum(dtype=np.float128))/n\n", | |
| " Ay = (Ay_*n_ + y.sum(dtype=np.float128))/n\n", | |
| " \n", | |
| " miny = min(miny, y.min())\n", | |
| " maxy = max(maxy, y.max())\n", | |
| " \n", | |
| " X = Ax if first else (Ax_*rt_n_ + Ax*rt_n)/(rt_n_ + rt_n)\n", | |
| " Y = Ay if first else (Ay_*rt_n_ + Ay*rt_n)/(rt_n_ + rt_n)\n", | |
| "\n", | |
| " Sxx += np.sum((x - X)**2)\n", | |
| " Sxy += np.sum((x - X)*(y - Y))\n", | |
| "\n", | |
| " return Ax, Ay, Sxy, Sxx, n, miny, maxy\n", | |
| "\n", | |
| "def conv_px(s):\n", | |
| " w, h = s.split(b'x')\n", | |
| " return int(w)*int(h)\n", | |
| "\n", | |
| "conv_fti = [b'I', b'P', b'B0', b'B1'].index\n", | |
| "\n", | |
| "def collect(filename, queues):\n", | |
| " px, log_target_q, byte_size, frame_type = np.loadtxt(\n", | |
| " filename, dtype=np.int64, delimiter=',',\n", | |
| " converters={1: conv_px, 4: conv_fti},\n", | |
| " skiprows=1, usecols=range(1, 5), unpack=True)\n", | |
| "\n", | |
| " blog64q57_ibpp = np.round((\n", | |
| " np.log2(px, dtype=np.float128) - np.log2(byte_size*8, dtype=np.float128)\n", | |
| " )*2**57).astype(np.int64)\n", | |
| "\n", | |
| " for fti in np.unique(frame_type):\n", | |
| " x, y = log_target_q[frame_type==fti], blog64q57_ibpp[frame_type==fti]\n", | |
| " queue = queues.get(fti, ([], []))\n", | |
| " queue[0].append(x)\n", | |
| " queue[1].append(y)\n", | |
| " queues[fti] = queue\n", | |
| "\n", | |
| "def aggregate(queues, partials):\n", | |
| " for fti, queue in queues.items():\n", | |
| " x, y = np.concatenate(queue[0]), np.concatenate(queue[1])\n", | |
| " partials[fti] = online_simple_regression(partials.get(fti, None), x, y)\n", | |
| "\n", | |
| "partials = dict()\n", | |
| "for base in sorted(glob('*.y4m')):\n", | |
| " queues = dict()\n", | |
| " for q in range(1, 256):\n", | |
| " collect('%s/%d.txt' % (base, q), queues)\n", | |
| " aggregate(queues, partials)\n", | |
| "pprint(partials)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| " I: exp=62 scale=52\n", | |
| " P: exp=97 scale=57\n", | |
| "B0: exp=94 scale=25\n", | |
| "B1: exp=89 scale=11\n" | |
| ] | |
| }, | |
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| "<path id=\"i\" d=\"m19.7 64.8v-27.4h12.4q6.89 0 10.6 3.56 3.77 3.56 3.77 10.2 0 6.55-3.77 10.1-3.75 3.56-10.6 3.56zm-9.86 8.11h22.3q12.3 0 18.5-5.55 6.28-5.55 6.28-16.2 0-10.8-6.28-16.3-6.27-5.52-18.5-5.52h-12.4v-29.3h-9.86z\"/>\n", | |
| "</defs>\n", | |
| "<g transform=\"translate(395 42) scale(.1 -.1)\">\n", | |
| "<use xlink:href=\"#i\"/>\n", | |
| "</g>\n", | |
| "<path d=\"m367 53.2h20\" fill=\"none\" stroke=\"#2ca02c\" stroke-linecap=\"square\" stroke-width=\"1.5\"/>\n", | |
| "<defs>\n", | |
| "<path id=\"h\" d=\"m19.7 34.8v-26.7h15.8q7.95 0 11.8 3.3 3.84 3.3 3.84 10.1 0 6.84-3.84 10.1-3.83 3.25-11.8 3.25zm0 30v-22h14.6q7.22 0 10.8 2.7 3.55 2.72 3.55 8.28 0 5.52-3.55 8.25-3.53 2.73-10.8 2.73zm-9.86 8.11h25.2q11.3 0 17.4-4.69 6.11-4.69 6.11-13.3 0-6.7-3.12-10.7t-9.19-4.92q7.28-1.56 11.3-6.53 4.03-4.95 4.03-12.4 0-9.77-6.64-15.1-6.64-5.31-18.9-5.31h-26.2z\"/>\n", | |
| "</defs>\n", | |
| "<g transform=\"translate(395 56.7) scale(.1 -.1)\">\n", | |
| "<use xlink:href=\"#h\"/>\n", | |
| "<use x=\"68.603516\" xlink:href=\"#d\"/>\n", | |
| "</g>\n", | |
| "<path d=\"m367 67.8h20\" fill=\"none\" stroke=\"#d62728\" stroke-linecap=\"square\" stroke-width=\"1.5\"/>\n", | |
| "<g transform=\"translate(395 71.3) scale(.1 -.1)\">\n", | |
| "<use xlink:href=\"#h\"/>\n", | |
| "<use x=\"68.603516\" xlink:href=\"#e\"/>\n", | |
| "</g>\n", | |
| "<defs>\n", | |
| "<clipPath id=\"a\">\n", | |
| "<rect x=\"26.9\" y=\"10.7\" width=\"391\" height=\"326\"/>\n", | |
| "</clipPath>\n", | |
| "</defs>\n", | |
| "</svg>\n" | |
| ], | |
| "text/plain": [ | |
| "<Figure size 504x432 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(7, 6))\n", | |
| "plt.axis('equal')\n", | |
| "plt.xticks([0, 10])\n", | |
| "plt.yticks([0, 10])\n", | |
| "plt.minorticks_on()\n", | |
| "plt.grid(b=True, which='major')\n", | |
| "plt.grid(b=True, which='minor', alpha=0.2)\n", | |
| "\n", | |
| "for fti, accumulator in partials.items():\n", | |
| " Ax, Ay, Sxy, Sxx, n, miny, maxy = accumulator\n", | |
| "\n", | |
| " beta = Sxy/Sxx\n", | |
| " alpha = Ay - beta*Ax\n", | |
| " scale = int(np.round(np.exp2(3 - alpha/2**57)))\n", | |
| " exp = int(np.round(beta*2**6))\n", | |
| " label = ['I', 'P', 'B0', 'B1'][fti]\n", | |
| " print('%2s: exp=%d scale=%d' % (label, exp, scale))\n", | |
| "\n", | |
| " ys = [miny/2**57, maxy/2**57]\n", | |
| " xs = [(ys[0] - alpha/2**57)/beta, (ys[1] - alpha/2**57)/beta]\n", | |
| " plt.plot(xs, ys, label=label)\n", | |
| "\n", | |
| "plt.legend();" | |
| ] | |
| } | |
| ], | |
| "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": "3.7.0" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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