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Example3_compute_pi.snb
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{
"metadata" : {
"name" : "Example3_compute_pi",
"user_save_timestamp" : "1970-01-01T01:00:00.000Z",
"auto_save_timestamp" : "1970-01-01T01:00:00.000Z",
"language_info" : {
"name" : "scala",
"file_extension" : "scala",
"codemirror_mode" : "text/x-scala"
},
"trusted" : true,
"customLocalRepo" : null,
"customRepos" : null,
"customDeps" : null,
"customImports" : null,
"customArgs" : null,
"customSparkConf" : null
},
"cells" : [ {
"metadata" : {
"id" : "E43A55DDEDE8431C8D50A8C10002BE21"
},
"cell_type" : "markdown",
"source" : "We can compute the number PI by taken random points in a square, and computing how many of them are inside the circle."
}, {
"metadata" : {
"trusted" : true,
"input_collapsed" : false,
"collapsed" : false,
"id" : "6CB4784E97CB4AB0AEC615EB44A40187"
},
"cell_type" : "code",
"source" : "def r = (math.random-0.5)*2 // a random number between -1.0 and 1.0\n\ndef isInsideCircle(x: Double, y: Double): Boolean = x * x + y * y < 1\n\nval points = (1 to 10000).map(p => (r, r)).map { case (x, y) => (x, y, isInsideCircle(x, y)) }\n\nval PI = 4.0 * points.count(_._3) / points.length\nprintln(\"PI: \" + PI)\n\nScatterChart(points.toDF(\"x\", \"y\", \"insideCircle\"), groupField=Some(\"insideCircle\"), sizes=(100,100), maxPoints = points.length)",
"outputs" : [ {
"name" : "stdout",
"output_type" : "stream",
"text" : "PI: 3.1512\nr: Double\nisInsideCircle: (x: Double, y: Double)Boolean\npoints: scala.collection.immutable.IndexedSeq[(Double, Double, Boolean)] = Vector((-0.6345976056592251,-0.00945689901898139,true), (0.37742535857834403,-0.5681786199751127,true), (0.194642822170062,0.2646461333556813,true), (0.5013365804969321,-0.059761430190944376,true), (-0.07891747684300299,0.1067226410117692,true), (0.9163559389729969,-0.7275140926261352,false), (-0.7954325373118782,0.19375978788604886,true), (-0.8447813432918734,0.38455346169786964,true), (-0.8028243311291066,0.028339748196317682,true), (0.8329071925453599,-0.11364034971397174,true), (-0.42168926258936157,-0.6619012421580897,true), (0.07910390226656783,0.4026631759422903,true), (-0.7394339052772423,-0.9210452731994809,false), (0.01583423131061723,-0.6325129161..."
}, {
"metadata" : { },
"data" : {
"text/html" : "<div>\n <script 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type=\"text/x-scoped-javascript\">/*<![CDATA[*/req(['../javascripts/notebook/playground','../javascripts/notebook/magic/scatterChart'], \n function(playground, _magicscatterChart) {\n // data ==> data-this (in observable.js's scopedEval) ==> this in JS => { dataId, dataInit, ... }\n // this ==> scope (in observable.js's scopedEval) ==> this.parentElement ==> div.container below (toHtml)\n\n playground.call(data,\n this\n ,\n {\n \"f\": _magicscatterChart,\n \"o\": {\"x\":\"x\",\"y\":\"y\",\"width\":100,\"height\":100,\"g\":\"insideCircle\"}\n }\n \n \n \n );\n }\n );/*]]>*/</script>\n <div>\n <span class=\"chart-total-item-count\"><p data-bind=\"text: value\"><script data-this=\"{"valueId":"anon0c6e144105445a1c450369dfad401e9d","initialValue":"10000 or more"}\" type=\"text/x-scoped-javascript\">/*<![CDATA[*/\nreq(\n['observable', 'knockout'],\nfunction (O, ko) {\n ko.applyBindings({\n value: O.makeObservable(valueId, initialValue)\n },\n this\n );\n});\n /*]]>*/</script></p> entries total</span>\n <span class=\"chart-sampling-warning\"><p data-bind=\"text: value\"><script data-this=\"{"valueId":"anon12250e00853797497ef4c9604de045ed","initialValue":" (Warning: showing only first 10000 rows)"}\" type=\"text/x-scoped-javascript\">/*<![CDATA[*/\nreq(\n['observable', 'knockout'],\nfunction (O, ko) {\n ko.applyBindings({\n value: O.makeObservable(valueId, initialValue)\n },\n this\n );\n});\n /*]]>*/</script></p></span>\n <div>\n </div>\n </div></div>"
},
"output_type" : "execute_result",
"execution_count" : 1,
"time" : "Took: 1 minute 15 seconds 88 milliseconds, at 2017-2-23 14:32"
} ]
}, {
"metadata" : {
"trusted" : true,
"input_collapsed" : false,
"collapsed" : true,
"id" : "4FEEA4256FE84AC181F80A319CE3D4EB"
},
"cell_type" : "markdown",
"source" : "The more points we use, better the precission. This task can be parallelized among many computers."
}, {
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"id" : "7353E85BAEC8465994A131EE0AC41D1B"
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"cell_type" : "code",
"source" : "val numSamples = 100000000\nval samples = sc.parallelize(1 to numSamples)",
"outputs" : [ {
"name" : "stdout",
"output_type" : "stream",
"text" : "numSamples: Int = 100000000\nsamples: org.apache.spark.rdd.RDD[Int] = ParallelCollectionRDD[0] at parallelize at <console>:68\n"
}, {
"metadata" : { },
"data" : {
"text/html" : ""
},
"output_type" : "execute_result",
"execution_count" : 2,
"time" : "Took: 4 seconds 521 milliseconds, at 2017-2-23 14:32"
} ]
}, {
"metadata" : {
"trusted" : true,
"input_collapsed" : false,
"collapsed" : false,
"id" : "562999D4AF5241758C38FC123296ACF2"
},
"cell_type" : "code",
"source" : "samples.getNumPartitions",
"outputs" : [ {
"name" : "stdout",
"output_type" : "stream",
"text" : "res4: Int = 4\n"
}, {
"metadata" : { },
"data" : {
"text/html" : "4"
},
"output_type" : "execute_result",
"execution_count" : 3,
"time" : "Took: 4 seconds 259 milliseconds, at 2017-2-23 14:32"
} ]
}, {
"metadata" : {
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"input_collapsed" : false,
"collapsed" : false,
"id" : "7EB51A557A78409BB351EBFA6D14899B"
},
"cell_type" : "code",
"source" : "def isInsideCircle(p: Int): Boolean = {\n val x = math.random\n val y = math.random\n x * x + y * y < 1\n}\n\nval numSamplesInsideCircle = samples.filter(isInsideCircle).count()",
"outputs" : [ {
"name" : "stdout",
"output_type" : "stream",
"text" : "isInsideCircle: (p: Int)Boolean\nnumSamplesInsideCircle: Long = 78533957\n"
}, {
"metadata" : { },
"data" : {
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},
"output_type" : "execute_result",
"execution_count" : 4,
"time" : "Took: 38 seconds 511 milliseconds, at 2017-2-23 14:33"
} ]
}, {
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"id" : "8B357F7337A940A59FE69FDEBAFF7C5D"
},
"cell_type" : "code",
"source" : "val PI = 4.0 * numSamplesInsideCircle / numSamples",
"outputs" : [ {
"name" : "stdout",
"output_type" : "stream",
"text" : "PI: Double = 3.14135828\n"
}, {
"metadata" : { },
"data" : {
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},
"output_type" : "execute_result",
"execution_count" : 5,
"time" : "Took: 1 second 216 milliseconds, at 2017-2-23 14:33"
} ]
} ],
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