From a1bee4502e1aca6b53b1e229bd23d339ff01e8f1 Mon Sep 17 00:00:00 2001 From: Peter Norvig Date: Sat, 2 Sep 2017 22:47:11 -0700 Subject: [PATCH] Add files via upload --- Gesture Typing.ipynb | 561 ++++++++++++++++++------------------------- 1 file changed, 235 insertions(+), 326 deletions(-) diff --git a/Gesture Typing.ipynb b/Gesture Typing.ipynb index 8605f87..05f676e 100644 --- a/Gesture Typing.ipynb +++ b/Gesture Typing.ipynb @@ -142,9 +142,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "**Design notes for Point:** Alternative representations for points include an `(x, y)` tuple or namedtuple, or a NumPy two-element array, or a class. \n", + "Alternative representations for points include an `(x, y)` tuple or namedtuple, or a NumPy two-element array, or a class. \n", "\n", - "**Design notes for Keyboard:** Alternatives for `Keyboard` include a subclass of `dict`, or a class that contains a `dict`. \n", + "Alternatives for `Keyboard` include a subclass of `dict`, or a class that contains a `dict`. \n", "\n", "\n", "Now we can check that `Keyboard` works:" @@ -426,10 +426,10 @@ } ], "source": [ - "def print_top(n, sequence, key=None, fmt='{:.1f} {}'):\n", + "def print_top(n, sequence, key=None, formatter='{:.1f} {}'.format):\n", " \"Find the top n elements of sequence as ranked by key function, and print them.\"\n", " for x in sorted(sequence, key=key, reverse=True)[:n]:\n", - " print(fmt.format(key(x), x))\n", + " print(formatter(key(x), x))\n", " \n", "print_top(10, WORDS, path_length)" ] @@ -489,12 +489,8 @@ "Question 3: Average Segment Length on Work Load?\n", "===\n", "\n", - "What is the average segment length for a typical typing work load? To answer that, we need to know what a typical work load is.\n", - "\n", - "Representing Workloads\n", - "---\n", - "\n", - "We will read a file of \"typical\" text, and count up how many times each segment is used. We'll define a `Workload` as a `dict` of the form `{segment: proportion, ...},` e.g. `{'AB': 0.02}`, where each key is a two-letter string representing a segment, and each value is the proportion of time that segment appears in the workload. Since the distance from `A` to `B` on a keyboard is the same as the distance from `B` to `A`, we don't need both `AB` and `BA` as keys; we'll combine the counts for both of them under the alphabetically first one (in this case, `AB`). So `Workload` will first generate all two-letter *bigrams* in the text, then take the `segment` of each bigram, and count up (with `Counter`) how many times each segment occurs, and finally normalize these counts so that they sum to 1.0, but retain their proportion to each other." + "What is the average segment length for a typical typing work load? To answer that, we need to know what a typical work load is. We will read a file of \"typical\" text, and count how many times each segment is used. A `Workload` is a `dict` of the form `{segment: proportion, ...},` e.g. `{'AB': 0.02}`, where each key is a two-letter string (or *bigram*) representing a segment, and each value is the proportion of time that segment appears in the workload. Since the distance from `A` to `B` on a keyboard is the same as the distance from `B` to `A`, we can combine them together into one count;\n", + "I'll arbitrarily choose count them both under the alohabetically first one. I make a `Counter` of all two-letter segments, and `normalize` it so that the counts sum to 1 (and are thus probabilities)." ] }, { @@ -508,11 +504,10 @@ "def Workload(text):\n", " \"\"\"Create a Workload--a dict of the form {'AB': 1000, ...} \n", " saying how often each letter pair occurs in text.\"\"\"\n", - " return normalize(Counter(map(segment, bigrams(text))))\n", + " segments = (min(AB, AB[::-1]) for AB in bigrams(text))\n", + " return normalize(Counter(segments))\n", "\n", "def bigrams(text): return re.findall(r'(?=([A-Z][A-Z]))', text)\n", - " \n", - "def segment(AB): return min(AB, AB[::])\n", "\n", "def normalize(dictionary):\n", " \"Normalize a {key: val} dict so that the sum of the vals is 1.0.\"\n", @@ -526,6 +521,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "*Note:* Some `re` trickiness here: `([A-Z][A-Z])` means a group of two consecutive letters. But if I only looked for that, then in the text `'FOUR'` I would find `['FO', 'UR']`. So I use the `?=` operator, which says to check for a match, but don't consume the matched characters. So I can find `['FO', 'OU', 'UR']`, which is what I want.\n", + "\n", "Let's see what a workload looks like for a tiny text:" ] }, @@ -538,14 +535,14 @@ "data": { "text/plain": [ "Counter({'AL': 0.05,\n", + " 'AO': 0.05,\n", + " 'DO': 0.05,\n", " 'GO': 0.1,\n", " 'HO': 0.05,\n", + " 'HS': 0.05,\n", " 'IS': 0.05,\n", - " 'OA': 0.05,\n", - " 'OD': 0.05,\n", " 'OO': 0.55,\n", - " 'OT': 0.05,\n", - " 'SH': 0.05})" + " 'OT': 0.05})" ] }, "execution_count": 17, @@ -592,16 +589,16 @@ { "data": { "text/plain": [ - "[('TH', 0.03945159113049897),\n", - " ('HE', 0.035568108897097696),\n", - " ('IN', 0.02354361103999521),\n", - " ('ER', 0.022218638719780824),\n", - " ('AN', 0.020760670432669128),\n", - " ('RE', 0.018283620549206844),\n", - " ('ON', 0.017146505032234898),\n", - " ('ND', 0.01536269662622481),\n", - " ('EN', 0.014606282064496394),\n", - " ('AT', 0.01432532808442584)]" + "[('HT', 0.04144819308354474),\n", + " ('ER', 0.04050225926898767),\n", + " ('EH', 0.03576926529702987),\n", + " ('IN', 0.02699818128015268),\n", + " ('AN', 0.02320447132440709),\n", + " ('NO', 0.022344984888333263),\n", + " ('EN', 0.021994208025641622),\n", + " ('IT', 0.021467211506811055),\n", + " ('ES', 0.020667573255841017),\n", + " ('DE', 0.020619362217840744)]" ] }, "execution_count": 19, @@ -623,7 +620,9 @@ { "cell_type": "code", "execution_count": 20, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "def workload_average(kbd, workload=WORKLOAD):\n", @@ -640,7 +639,7 @@ { "data": { "text/plain": [ - "3.2333097802127657" + "3.2333097802127653" ] }, "execution_count": 21, @@ -666,7 +665,7 @@ "Aside: Visualizing a Keyboard\n", "---\n", "\n", - "We'll need a way of visualizing what a keyboard looks like. I could just `print` letters, but I think it is more compelling to use IPython's `plot` facility. In the function `plot_kbd` we'll draw a square around the center point of each key, and annotate the square with the key letter. In `show_kbd`, we'll call `plot_kbd` and also print out the keyboard's name and workload average:" + "We'll need a way of visualizing what a keyboard looks like. I could just `print` letters, but I think it is more compelling to use IPython's `matplotlib` module. In the function `show_kbd` we'll draw a square around the center point of each key, and annotate the square with the key letter. " ] }, { @@ -693,7 +692,7 @@ " [y-H, y-H, y+H, y+H, y-H], style) \n", " plt.annotate(label, (x-H/4, y-H/4)) # H/4 seems to place label well.\n", " \n", - "def title(kbd, name): return '{}: avg = {:.1f}'.format(name, workload_average(kbd))" + "def title(kbd, name): return '{}: path length = {:.1f}'.format(name, workload_average(kbd))" ] }, { @@ -703,9 +702,9 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -815,9 +814,9 @@ "Visualizing `improved`\n", "---\n", "\n", - "Let's get a better feeling for what `improved` does. We will keep track of the workload average after each swap, and plot that as a line. (We know this line should be monotonically decreasing, starting at 3.23.) We will then plot a dozen instances of this line (different each time because the swaps are random). \n", + "Let's get a better feeling for what `improved` does. We will keep track of the workload average after each swap, and plot that as a curve. We will repeat that 10 times (because each run has random variation).\n", "\n", - "I'll add another parameter, `scores`, to `improved`, If it is not `None`, accumulate scores into it. Then I'll add a new function, `plot_improvements`, that plots the scores that `improved` accumulates." + "I'll add another parameter, `scores`, to `improved`, If it is not `None`, then it should be a list into which we can accumulate all the scores (after each time step). Then I'll add a new function, `plot_improvements`, that plots the scores that `improved` accumulates." ] }, { @@ -826,7 +825,7 @@ "metadata": {}, "outputs": [], "source": [ - "def improved(kbd, swaps=1000, scorer=workload_average, scores=None):\n", + "def improved(kbd, swaps=1000, scorer=workload_average, scores=[]):\n", " \"Minimize scorer(kbd) by swapping keys and keeping improvements.\"\n", " kbd = kbd.copy()\n", " score = scorer(kbd)\n", @@ -839,8 +838,7 @@ " score = score2 # (and record the new best total)\n", " else:\n", " swap(kbd, B, A) # Step 4: swap back if not better\n", - " if scores is not None: \n", - " scores.append(score) # <<< NEW\n", + " scores.append(score) # <<< NEW\n", " return kbd" ] }, @@ -851,9 +849,9 @@ "outputs": [ { "data": { - "image/png": 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W7dWqF3OvncusX8zirflvMXXFVOvYZ4wxAQUZGiRXVcdXf1DVQhHJbcxORCQP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\nIJYwjDHGBGIJwxhjTCD/H1BNf11J8jcSAAAAAElFTkSuQmCC\n", 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Nwl4ldU4aYmlVVhYkcDm8D8gycKJNDmprjDEmBcJcJfVbEekUnI56R0TWisi56QiusYgL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\n9mN84YX+KbTGFwJcdBF85zt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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -879,8 +877,8 @@ "source": [ "This plot is interesting. I note the following:\n", "\n", - "* Each line follows a slightly different path (because the swaps are random).\n", - "* The lines are grouped very tightly together; the variance is small. Almost everywhere, the difference between the best line and the worst line is about 0.2 or less. By the end, almost all the lines are between 1.9 and 2.0.\n", + "* Each curve follows a slightly different path (because the swaps are random).\n", + "* The curves are grouped very tightly together; the variance is small. Almost everywhere, the difference between the best and the worst is about 0.2 or less. By the end, almost all the curves are between 1.9 and 2.0.\n", "* We make rapid progress, decreasing from 3.2 to around 2.2 in about 200 swaps, and to around 2.0 in about 500 swaps.\n", "* After 1000 swaps, progress is slow, and after 2000, even slower." ] @@ -916,10 +914,10 @@ " 'T U V W X Y Z')),\n", "\n", " '5-by-6': Keyboard((' A B C D E ',\n", - " ' F G H I J ',\n", - " 'K L M N O P',\n", - " ' Q R S T U ',\n", - " ' V W X Y Z '))\n", + " 'F G H I J K',\n", + " 'L M N O P Q',\n", + " ' R S T U V',\n", + " ' W X Y Z '))\n", " }" ] }, @@ -927,7 +925,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Here is a function to report on these keyboards (after improving them):" + "Here is a function to report on a collection of keyboards such as this (after improving them):" ] }, { @@ -937,9 +935,9 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -970,7 +968,8 @@ "def report(keyboards=keyboards, swaps=3000, scorer=workload_average):\n", " \"Iterate through a dict of {name: kbd} pairs, showing kbd before and after repeated_improved(kbd).\"\n", " for (name, kbd) in keyboards.items():\n", - " show_kbd(improved(kbd, swaps=swaps, scorer=scorer), 'improved ' + name)\n", + " show_kbd(improved(kbd, swaps=swaps, scorer=scorer), \n", + " ('improved ' if swaps else '') + name)\n", " \n", "report()" ] @@ -988,14 +987,14 @@ "source": [ "\n", "\n", - "So the more compact keyboards with a smaller diameter (`4-by-7` and `5-by-6`) perform slightly better than `qwerty`. \n" + "So the more compact keyboards with a smaller diameter (`4-by-7` and `5-by-6`) seem to perform slightly better than `qwerty`. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Question 5: How often are two words confused because they have similar paths?\n", + "Question 5: How often are two words confused because of similar paths?\n", "===\n", "\n", "When can one word be confused with another? When their paths are similar (which means that their corresponding letters are in similar locations). For example, on a Qwerty keyboard, the paths for \"HELLO\" and \"JELLO\" are similar, because **H** and **J** are adjacent, and the other letters are the same.\n", @@ -1114,15 +1113,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "These are five columns of letters, and if we pick one letter from each column, we get a path that is formed by letters that are each confusions of letters in the original word, and so the whole path is a confusion for the original word. So \"JELLO\" is a confusion for \"HELLO\", as would be \"BDKKI\" and \"YWPPP\", except they are not words.\n", + "These are five columns of letters, and if we pick one letter from each column, we get a path that is formed by letters that are each confusions of letters in the original word, and so the whole path is a confusion for the original word. So \"JELLO\" is a confusion for \"HELLO\", as would be \"BDKKI\" and \"YWPPP\", except those are not words.\n", "\n", - "It turns out that there is a library function, `itertools.product`, that will take an iterable of alternative choices, and generate all possible ways of assembling a sequence consisting of one selection (letter) from each alternative choice." + "It turns out that there is a library function, `itertools.product`, that will take alternative choices, and generate all possible ways of assembling a sequence consisting of one selection (letter) from each alternative choice." ] }, { "cell_type": "code", "execution_count": 33, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "paths = {cat(picks) for picks in itertools.product(*columns)}" @@ -1170,7 +1171,7 @@ { "data": { "text/plain": [ - "['BEKMI', 'VWOPI', 'JELLI', 'GWPMO', 'NRLPP', 'JSMKI', 'VELMK', 'YRPKP']" + "['NWPOO', 'HEOOP', 'JRMLI', 'HWPKL', 'VEMKO', 'UWOPI', 'VDOMK', 'HELLI']" ] }, "execution_count": 35, @@ -1304,25 +1305,65 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So far, so good. But I'm worried about the efficiency of `confusions` for long words. \n", + "So far, so good. But I'm worried about the efficiency of `confusions`.\n", "\n", - "More Efficient `confusions`\n", - "---\n", - "\n", - "Consider:" + "My first concern is that `WORDS` has 178,691 words, including many unusual words, so there might be too many confusions. I will read in a smaller word set, with only common words:" ] }, { "cell_type": "code", "execution_count": 41, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "! [ -e words.js ] || curl -O https://xkcd.com/simplewriter/words.js\n", + " \n", + "COMMON = set(re.findall('[A-Z]+', open('words.js').read().upper()))" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(3614, 'SPECIALS', 'UNDERSTANDINGS')" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(COMMON), max(COMMON, key=path_length), max(COMMON, key=len)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "More Efficient `confusions`\n", + "---\n", + "\n", + "Another issue is that `confusions` is really slow:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 3.11 s, sys: 370 ms, total: 3.48 s\n", - "Wall time: 3.49 s\n" + "CPU times: user 3.14 s, sys: 306 ms, total: 3.44 s\n", + "Wall time: 3.45 s\n" ] }, { @@ -1331,7 +1372,7 @@ "{'SOMETHING'}" ] }, - "execution_count": 41, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -1349,7 +1390,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 44, "metadata": {}, "outputs": [ { @@ -1358,7 +1399,7 @@ "[7, 5, 5, 5, 5, 8, 5, 6, 8]" ] }, - "execution_count": 42, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -1371,16 +1412,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There are 7 × 5 × 5 × 5 × 5 × 8 × 5 × 6 × 8 = 8,400,000 paths for `confusions` to consider. Looking at them all takes 3 seconds, but for most of these paths, we're wasting our time. For example, one choice for the first two neighboring letters of 'SOMETHING' is 'XP', but 'XP' does not start any word in the dictionary. Nevertheless, `itertools.product` will generate 240,000 combinations that start with 'XP', and will then rule them out one at a time. It would be better to stop as soon as we see 'XP', and never consider continuations of this path.\n", + "There are 7 × 5 × 5 × 5 × 5 × 8 × 5 × 6 × 8 = 8,400,000 paths for `confusions` to consider. `'PALEOMAGNETISMS'` would have about 10,000 times more paths. Looking at every path is slow, but for most paths, we're wasting our time. For example, one choice for the first two neighboring letters of 'SO' is 'XP', but 'XP' does not start any word in the dictionary. Nevertheless, `itertools.product` will generate 240,000 combinations that start with 'XP', and will then rule them out one at a time. It would be better to stop as soon as we see 'XP', and never consider continuations of this path.\n", "\n", - "So that gives us the key idea for a more efficient version of `confusions`: *only follow paths that form a prefix of at least one word.* \n", - "\n", - "So, first we need to define the set of prefixes:" + "So that gives us the key idea for a more efficient version of `confusions`: *only follow paths that form a prefix of some word.* I'll make a set of all the prefixes of the `COMMON` words:" ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 45, "metadata": { "collapsed": true }, @@ -1388,12 +1427,14 @@ "source": [ "def prefixes(words):\n", " \"Return a set of prefixes (1 to N characters) of this collection of words.\"\n", - " return {word[:i] for word in words for i in range(1, len(word)+1)}" + " return {word[:i] for word in words for i in range(1, len(word)+1)}\n", + "\n", + "PREFIXES = prefixes(COMMON)" ] }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 46, "metadata": {}, "outputs": [ { @@ -1402,7 +1443,7 @@ "{'T', 'TH', 'THE', 'THES', 'THESE', 'THEY', 'THO', 'THOS', 'THOSE'}" ] }, - "execution_count": 44, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -1411,38 +1452,6 @@ "prefixes(['THESE', 'THEY', 'THOSE'])" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I'm worried that our dictionary of words includes too many weird words, so there would be too many confusions. So I will read in a smaller word set, with only common words:" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(7005, 3614, 'SPECIALS', 'UNDERSTANDINGS')" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "! [ -e words.js ] || curl -O https://xkcd.com/simplewriter/words.js\n", - " \n", - "COMMON = set(re.findall('[A-Z]+', open('words.js').read().upper()))\n", - "PREFIXES = prefixes(COMMON)\n", - "\n", - "len(PREFIXES), len(COMMON), max(COMMON, key=path_length), max(COMMON, key=len)" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -1451,12 +1460,14 @@ "\n", "1. Maintain a queue of partial paths, where a partial path is a string representing choices for neighboring letters for a prefix of the word. For example, 'HE' and 'JE' are both partial paths for the word 'HELLO'. Initialize the queue to have just one partial path, the empty string.\n", "2. Remove a partial path from the queue. Find all possible ways to extend the path by adding a neighboring letter, but only if doing so creates a path that is a prefix of some word in the dictionary. For example, given the word 'HELLO', and the partial path 'JE', consider all the neighbors of 'L' (namely, 'K', 'M', 'L', 'O', or 'P'), but only 'JEM', 'JEL', and 'JEO' are prefixes of words, so add just those to the queue.\n", - "3. When a partial path reaches the same length as the word ('HELLO' in this example), then don't extend it any farther; instead check to see if the path is a word. If it is, add it to the set of paths/words that form the result." + "3. When a partial path reaches the same length as the word ('HELLO' in this example), then don't extend it any farther; instead check to see if the path is a word. If it is, yield it as a result.\n", + "\n", + "A word is `confusable` if it has a confusion word (other than itself)." ] }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 47, "metadata": { "collapsed": true }, @@ -1476,44 +1487,14 @@ "\n", "def confusable(word, neighbors=neighboring_keys(qwerty)) -> bool: \n", " \"Is this word confusable with another, given this keyboard's neighboring keys?\"\n", - " for w in confusions(word, neighbors):\n", - " if w != word: return True\n", - " return False" + " return any(c != word for c in confusions(word, neighbors))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let's check the speed (the old version took over 3 seconds):" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 91 µs, sys: 1 µs, total: 92 µs\n", - "Wall time: 93.9 µs\n" - ] - }, - { - "data": { - "text/plain": [ - "{'SOMETHING'}" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "%time set(confusions('SOMETHING'))" + "Let's check the speed (remember the old version took over 3 seconds):" ] }, { @@ -1525,14 +1506,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 92 µs, sys: 0 ns, total: 92 µs\n", - "Wall time: 94.2 µs\n" + "CPU times: user 94 µs, sys: 0 ns, total: 94 µs\n", + "Wall time: 95.8 µs\n" ] }, { "data": { "text/plain": [ - "False" + "{'SOMETHING'}" ] }, "execution_count": 48, @@ -1541,14 +1522,14 @@ } ], "source": [ - "%time confusable('SOMETHING')" + "%time set(confusions('SOMETHING'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We went from about 3 seconds to 100 microseconds: that's 30,000 times faster! We can look at some more confusions:" + "We went from about 3 seconds to about 100 microseconds: that's 30,000 times faster! We can look at some more confusions:" ] }, { @@ -1559,36 +1540,36 @@ { "data": { "text/plain": [ - "{'BORING': 'NOTING HIDING BORING BITING',\n", - " 'BRANCHINGS': 'BRANCHINGS',\n", - " 'DISCOVER': 'DISCOVER',\n", - " 'EVERYONE': 'EVERYONE',\n", - " 'FLASH': 'FLASH DOZEN',\n", - " 'FLIGHT': 'TOOTHY FOUGHT FLIGHT',\n", - " 'FOOTING': 'ROOFING FOOTING',\n", - " 'GATHERED': 'GATHERED FATHERED',\n", - " 'HEART': 'NEWER HEART',\n", - " 'HIGHER': 'HIGHER BOTHER BIGGER',\n", - " 'IGNORE': 'IGNORE',\n", - " 'KILLER': 'LOOKER LOOKED KILLER KILLED JUMPER JUMPED',\n", - " 'LANDERS': 'LANDERS',\n", - " 'MEMORY': 'MEMORY',\n", - " 'MIRROR': 'MIRROR MIDDLE LITTLE',\n", - " 'PAINTINGS': 'PAINTINGS',\n", - " 'PARENT': 'PARENT',\n", - " 'REMEMBER': 'REMEMBER',\n", - " 'REVEALED': 'REVEALED',\n", - " 'RUNS': 'TIME RUNS RUBS FINE FIND',\n", - " 'SCENE': 'SCENE EVENS',\n", - " 'SMILERS': 'SMOKERS SMILERS',\n", - " 'SOUNDS': 'SOUNDS',\n", - " 'SUITED': 'WHITES WHITER WHITED SUITES SUITED',\n", - " 'TEACH': 'TEACH READY REACH',\n", - " 'THEY': 'THEY RUSH',\n", - " 'TIME': 'TONE TOLD TIME RUNS GUNS GONE GOLD FINE FIND',\n", - " 'TRAVELLERS': 'TRAVELLERS',\n", - " 'UPON': 'UPON JOIN',\n", - " 'WASN': 'WASN WASH'}" + "{'BELIEVED': 'BELIEVES BELIEVER BELIEVED',\n", + " 'BENDS': 'BENDS',\n", + " 'BITEY': 'HURRY BITEY',\n", + " 'CEILINGS': 'CEILINGS',\n", + " 'COATING': 'COATING',\n", + " 'COLORERS': 'COLORERS',\n", + " 'COUPLES': 'COUPLES',\n", + " 'DUSTING': 'SHARING DUSTING',\n", + " 'DYING': 'EYING DYING',\n", + " 'ENJOYS': 'ENJOYS',\n", + " 'FREED': 'TREES TREED FREES FREER FREED FEWER FEEDS DRESS',\n", + " 'GET': 'YET TRY HEY HER GET CRY',\n", + " 'GUESSES': 'GUESSES GUESSED',\n", + " 'HOSPITAL': 'HOSPITAL',\n", + " 'IMAGING': 'OKAYING IMAGING',\n", + " 'LETTER': 'LETTER',\n", + " 'LUCKY': 'LUCKY',\n", + " 'MAY': 'MAY LAY',\n", + " 'ONCE': 'ONCE',\n", + " 'PALE': 'PALE',\n", + " 'PARTIES': 'PARTIES PARTIED',\n", + " 'PLAYER': 'PLAYER PLAYED PLATED OKAYED',\n", + " 'REPEAT': 'REPEAT',\n", + " 'RUSHES': 'RUSHES RUSHED FISHES FISHED',\n", + " 'SAMES': 'WAKES WAKED SANDS SAMES ASKED',\n", + " 'SHARP': 'SHARP',\n", + " 'SINGE': 'WINGS SONGS SINGS SINGE SINCE AUNTS',\n", + " 'SPEND': 'WORKS SPEND DOWNS',\n", + " 'TAUGHT': 'TAUGHT',\n", + " 'WALLED': 'WALLED WALKER WALKED'}" ] }, "execution_count": 49, @@ -1608,10 +1589,8 @@ "Visualizing Paths on a Keyboard\n", "----\n", "\n", - "To determine if these `confusions` are good ones, let's build something to visualize paths on a keyboard. \n", - "\n", - "\n", - "I'll add functionality to `show_kbd` to call the new function `plot_paths` and implement that:\n", + "It would be nice to see potentially confusable word paths on a keyboard.\n", + "I'll add functionality to `show_kbd` to call the new function `plot_paths` if any `words` are passed to `show_kbd`:\n", "\n" ] }, @@ -1656,9 +1635,9 @@ "outputs": [ { "data": { - "image/png": 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HbjSz183sjfjv8UkHxe94+kfKfoUbgUlmtn+SOQ3uCx6BQ1rgoYth2RD47C5o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\nfwER8k0EUCMU3wAAAABJRU5ErkJggg==\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1673,18 +1652,20 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "OK, we're on the right track, but I see three problems: \n", - "- The letters are obscured by the circles. \n", - "- When the paths are the same, they overwrite each other. \n", - "- There is no indication what direction the path is going in.. \n", + " OK, we're on the right track, but I see three problems, which I think I can solve: \n", "\n", - "I have an idea to fix the first two problems (and I will ignore the third for now). Instead of plotting the circle in the center of the key, offset it towards one of the corners of the key. That way they won't overlap (at least for up to four paths). " + "- The letters are obscured by the circles. Solution: offset paths away from the center.\n", + "- When the paths are the same, they overwrite each other. Solution: offset each path towards a different corner.\n", + "- There is no indication what direction the path is going in. Solution: put a diamond on the start position.\n", + "\n" ] }, { "cell_type": "code", "execution_count": 52, - "metadata": {}, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "def plot_paths(kbd, K, words):\n", @@ -1694,7 +1675,8 @@ " for (i, word) in enumerate(words):\n", " Xs = [+K * kbd[L].x + offsets[i % 4].x for L in word]\n", " Ys = [-K * kbd[L].y + offsets[i % 4].y for L in word]\n", - " plt.plot(Xs, Ys, '-o')" + " plt.plot(Xs, Ys, '-o')\n", + " plt.plot(Xs[:1], Ys[:1], 'kd')" ] }, { @@ -1704,9 +1686,9 @@ "outputs": [ { "data": { - "image/png": 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CiGTKndXAU/EtOSgmAHuaNbmQIpeCS+vM1nRJergL0Af6bXHWS305MNnus7F0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\nIiISUDCIiEjg/wCN41XMyaDUJgAAAABJRU5ErkJggg==\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1721,7 +1703,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "That looks busier, but it is much easier to follow the paths. Another example:" + "That looks busier, but it is easier to follow the paths. Another example:" ] }, { @@ -1731,29 +1713,9 @@ "outputs": [ { "data": { + "image/png": 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"text/plain": [ - "{'HOUSED', 'HOUSES', 'NOISED', 'NOISES'}" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "set(confusions('HOUSED'))" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1761,7 +1723,7 @@ } ], "source": [ - "show_kbd(qwerty, words=_)" + "show_kbd(qwerty, words={'HOUSED', 'HOUSES', 'NOISES'})" ] }, { @@ -1776,7 +1738,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 55, "metadata": { "collapsed": true }, @@ -1788,24 +1750,24 @@ " return mean([confusable(w, neighbors) for w in COMMON])\n", "\n", "def title(kbd, name): \n", - " return ('{}: avg = {:.1f}, confuse = {:.0%}'\n", + " return ('{}: path length = {:.1f}, confuse = {:.0%}'\n", " .format(name, workload_average(kbd), confusingness(kbd)))" ] }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'4-by-7': 0.4571112340896514,\n", - " '5-by-6': 0.5838406198118429,\n", + " '5-by-6': 0.5282235749861649,\n", " 'qwerty': 0.5398450470392916}" ] }, - "execution_count": 57, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -1818,74 +1780,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "About half the common words are confusable, with a little bit of variation between keyboards.\n", - "\n", - "Remember that `improved` is still working to improve the workload average, not confusingness, so it will be interesting to see how `improved` changes confusingness:" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "report(keyboards)" + "About half the common words are confusable, with a little bit of variation between keyboards." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Confusingness got worse as workload average length got better. Can we make confusingness better?\n", - "\n", "Question 6: Is there a Keyboard that Minimizes Confusion?\n", "===\n", "\n", - "Unfortunately, we won't be able to search as quickly. Consider:" + "Consider this:" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 124 ms, sys: 1.69 ms, total: 125 ms\n", - "Wall time: 125 ms\n" + "CPU times: user 112 ms, sys: 990 µs, total: 113 ms\n", + "Wall time: 112 ms\n" ] }, { @@ -1894,7 +1812,7 @@ "0.5398450470392916" ] }, - "execution_count": 59, + "execution_count": 57, "metadata": {}, "output_type": "execute_result" } @@ -1905,24 +1823,24 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 294 µs, sys: 1 µs, total: 295 µs\n", - "Wall time: 297 µs\n" + "CPU times: user 168 µs, sys: 0 ns, total: 168 µs\n", + "Wall time: 171 µs\n" ] }, { "data": { "text/plain": [ - "3.2333097802127657" + "3.2333097802127653" ] }, - "execution_count": 60, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1940,14 +1858,14 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 59, "metadata": {}, "outputs": [ { "data": { - "image/png": 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DZ22shZi1EJ/TOPcYpHmkH/74JPC62V4WLVzuMUzZQt3aWIhZC/E5mTV/cqadNco9BklS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\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1957,20 +1875,20 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 18.6 s, sys: 43.3 ms, total: 18.7 s\n", - "Wall time: 18.7 s\n" + "CPU times: user 10.4 s, sys: 19.7 ms, total: 10.4 s\n", + "Wall time: 10.4 s\n" ] } ], "source": [ - "%time show_kbd(improved(qwerty, swaps=200, scorer=confusingness))" + "%time show_kbd(improved(qwerty, swaps=100, scorer=confusingness))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This did indeed reduce confusingness (which was 54%); not bad for only 200 swaps. Too bad the workload average got worse." + "This did indeed reduce confusingness (which was 54%); not bad for only 100 swaps." ] }, { @@ -1980,14 +1898,14 @@ "Question 7: Is there a Keyboard that Maximizes User Satisfaction?\n", "===\n", "\n", - "What is user satisfaction? I don't know, but for now I'll approximate satisfaction (or rather, *dissatisfaction*, since lower scores are better) with a combined score that is the average of workload average and 10 times confusingness. Why 10 times? Because our best scores are around 1.8 for workload average and about 1/10 of that for confusingness.\n", + "What is user satisfaction? I don't know, but for now I'll approximate satisfaction (or rather, *dissatisfaction*, since lower scores are better) with a combined score that is the product of workload average and confusingness. Then I (rather arbitrarily) scale the result by 5, just because I think a number like \"2.1\" looks better than \"0.42\".\n", "\n", - "First we'll define the combined scorer function:" + "First we'll define the combined scorer function and incorporate it into `title`:" ] }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 60, "metadata": { "collapsed": true }, @@ -1995,60 +1913,51 @@ "source": [ "def dissatisfaction(kbd):\n", " \"The product of workload average and confusingness, scaled by 5.\"\n", - " return 5 * workload_average(kbd) * confusingness(kbd)" + " return 5 * workload_average(kbd) * confusingness(kbd)\n", + "\n", + "def title(kbd, name): \n", + " return ('{}: path length = {:.1f}, confuse = {:.0%}, overall = {:.1f}'\n", + " .format(name, workload_average(kbd), confusingness(kbd), \n", + " dissatisfaction(kbd)))" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 61, "metadata": {}, "outputs": [ { "data": { + "image/png": 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"text/plain": [ - "8.72743135195781" + "" ] }, - "execution_count": 72, "metadata": {}, - "output_type": "execute_result" + "output_type": "display_data" } ], "source": [ - "dissatisfaction(qwerty)" + "show_kbd(qwerty)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can incorporate the combined score into `title`:" + "Now let'stry to minimize confusion. This should take around 2 minutes:" ] }, { "cell_type": "code", - "execution_count": 63, - "metadata": {}, - "outputs": [], - "source": [ - "def title(kbd, name): \n", - " W = workload_average(kbd)\n", - " C = confusingness(kbd)\n", - " S = dissatisfaction(kbd)\n", - " return ('{}: avg = {:.1f}, confuse = {:.0%}, overall = {:.1f}'\n", - " .format(name, W, C, S))" - ] - }, - { - "cell_type": "code", - "execution_count": 71, + "execution_count": 62, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2078,8 +1987,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 2min 26s, sys: 330 ms, total: 2min 27s\n", - "Wall time: 2min 27s\n" + "CPU times: user 2min 30s, sys: 482 ms, total: 2min 31s\n", + "Wall time: 2min 31s\n" ] } ], @@ -2099,14 +2008,14 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 63, "metadata": {}, "outputs": [ { "data": { - "image/png": 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H4OjSWfqUJO0CfAPYJyL+UDhPNy8C3wR66my0zc3kAiDt+O8A5ktaQ9LywKbAzFLh+pEL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\nP/K3c1luY46PAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2159,14 +2068,14 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 64, "metadata": {}, "outputs": [ { "data": { - "image/png": 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gFrjW3R8uQKxV7t4v9fw0YB93P7/QsQolHcfMjgRuAMa5+8JCxurqlBi6rhOB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\nRCJKDCIiElFiEBGRyP8H9xYYXXi8RJgAAAAASUVORK5CYII=\n", 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