I wrote a javascript version of Lagrange algorithm, but it kept going wrong when I run it, I don't know what went wrong.
I use this to calculate time.
When I pass a cSeconds as a variable, sometimes it returns a minus value which is obviously wrong...
function LagrangeForCat(cSeconds){
var y = [2592000,7776000,15552000,31104000,93312000,155520000,279936000,404352000,528768000,622080000,715392000,870912000,995328000,1119744000,1244160000,1368576000,1492992000,1617408000,1741824000,1866240000,1990656000,2115072000,2239488000,2363904000,2488320000,2612736000,2737152000,2861568000,2985984000,3110400000,3234816000,3359232000,3483648000,3608064000];
var x = [604800,1209600,1814400,2592000,5184000,7776000,15552000,23328000,31104000,46656000,62208000,93312000,124416000,155520000,186624000,217728000,248832000,279936000,311040000,342144000,373248000,404352000,435456000,466560000,497664000,528768000,559872000,590976000,622080000,653184000,684288000,715392000,746496000,777600000];
var l = 0.0;
for (var j = 0; j < 34; j++) {
var s = 1.0;
for (var i = 0; i < 34; i++) {
if (i != j)
s = s * ((cSeconds - x[i]) / (x[j] - x[i]));
}
l = l + s * y[j];
}
var result = l / (24 * 60 * 60);
var Days = Math.floor(result);
//get float seconds data
var littleData = String(result).split(".")[1];
var floatData = parseFloat("0."+littleData);
var second = floatData *60*60*24;
var hours = Math.floor(second/(60*60));
var minutes = Math.floor(second % 3600/60);
var seconds = Math.floor(second % 3600) % 60;
var returnData = {days:Days,hours: hours + ':' + minutes + ':' + seconds}
return returnData;
}
I don't believe the issue is with your code but with the data set.
I tried a few things, for instance if you have cSeconds = one of the x values, then you get the correct result (I could check that it was equal to the matching y value).
I put all the data in open office and drew the graph it was like the square root function but more extreme (the 'straight' part look very straight) then I remembered that when you interpolate you usually get a polynomial that crosses the points you want but can be very wild outside between the point.
To test my theory I modified the algorithm to control at which x/y index to start and tried for all the values:
for (let i = 0; i < 35; ++i) {
LagrangeForCat(63119321, i, 34)
}
Together with a console.log inside LagrangeForCat it gives me the interpolated y value if I use all the x/y arrays (i=0), if I ignore the first x/y point (i=1), the first two (i=2), ...
00-34 -6850462776.278063
01-34 549996977.0003194
02-34 718950902.7592317
03-34 723883771.1443908
04-34 723161627.795225
05-34 721857113.1756063
06-34 721134873.0889213
07-34 720845478.4754647
08-34 720897871.7910147
09-34 721241470.2886044
10-34 722280314.1033486
11-34 750141284.0070543
12-34 750141262.289736
13-34 750141431.2562406
14-34 750141089.6980047
15-34 750141668.8768387
16-34 750142353.3267975
17-34 750141039.138794
18-34 750141836.251831
19-34 750138039.6240234
20-34 750141696.7529297
21-34 750141120.300293
22-34 750141960.4248047
23-34 750140874.0966797
24-34 750141337.5
25-34 750141237.4694824
26-34 750141289.2150879
27-34 750141282.5408936
28-34 750141284.2094421
29-34 750141283.987999
30-34 750141284.0002298
31-34 750141284.0000689
32-34 750141283.9999985
33-34 3608064000
34-34 0
Exclude 33-34 and 34-34 (there's just not enough data to interpolate).
For the example x=63119321 you'd expect y to be between 715392000 and 870912000 you can see that if you ignore the first 2-3 values the interpolation is "believable", if you ignore more values you interpolate based off the very straight part of the curve (see how consistent the interpolation is from 11-34 onward).
I use to work on a project where interpolation was needed, to avoid those pathological cases we opted for linear interpolation trading accuracy for security (and we could generate all the x/y points we wanted). In your case I'd try to use a smaller set, for instance only two values smaller than cSeconds and two greater like this:
function LagrangeForCat(cSeconds) {
var x = [...];
var y = [...];
let begin = 0,
end = 34
for (let i = 0; i < 34; ++i) {
if (cSeconds < x[i]) {
begin = (i < 3) ? 0 : i - 2
end = (i > (x.length - 1)) ? x.length : i + 1
break
}
}
let result = 0.0;
for (let i = begin; i < end; ++i) {
let term = y[i] / (24 * 60 * 60)
for (let j = begin; j < end; ++j) {
if (i != j)
term *= (cSeconds - x[j]) / (x[i] - x[j]);
}
result += term
}
var Days = Math.floor(result);
// I didn't change the rest of the function didn't even looked at it
}
If you find this answer useful please consider marking it as answered it'd be much appreciated.
Related
I've been working on this program for a few hours, and I finally got it to output - NaN. I dont know how this could be, I'm pushing a product of real numbers into the array... Somebody help! What did I miss? The problem is to find the largest product produced by 13 adjacent digits within the 1000 digit number assigned to _1000digits.
// what is the largest product of 13 adjacent digits within this 1000 digit number
function largestProduct() {
_1000digits = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450;
separateDigits = _1000digits.toString().split("");
products = [];
var a = 0;
var b = 1;
var c = 2;
var d = 3;
var e = 4;
var f = 5;
var g = 6;
var h = 7;
var i = 8;
var j = 9;
var k = 10;
var l = 11;
var m = 12;
while (m <= 999) {
products.push(
separateDigits[a] *
separateDigits[b] *
separateDigits[c] *
separateDigits[d] *
separateDigits[e] *
separateDigits[f] *
separateDigits[g] *
separateDigits[h] *
separateDigits[i] *
separateDigits[j] *
separateDigits[k] *
separateDigits[l] *
separateDigits[m]
);
a++;
b++;
c++;
d++;
e++;
f++;
g++;
h++;
i++;
j++;
k++;
l++;
m++;
}
products.sort((a, b) => a - b);
console.log(products.pop());
}
largestProduct();
Short:
To work with such huge numbers you'll want to use a special data structure, like BigInt.
Long:
There are a few issues with your code, the first one is trying to store such a huge number in a variable without any treatment. A JavaScript number can only store values up to 25^3 - 1, your number is a lot bigger than that.
If you run:
_1000digits = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450
console.log(_1000digits)
You'll see the output is "Infinity" because that's such a huge number JavaScript doesn't know how to store it entirely.
You're also not checking if the numbers you're accessing actually exist, so if you put a smaller number in _1000digits you'll end up multiplying by undefined, which will result in NaN:
_1000digits = 700
separateDigits = _1000digits.toString().split("")
var f = 5
console.log(separateDigits[f])
It's kind of math problem. I want to fire specific number of setTimeout (the number is based on an array length) in a specific period of time (say, 5 seconds).
The first setTimeout should start at 0 sec. and the last at 5 sec.. All timeouts between should start with an ease-in effect, so that each timeout starts faster.
There's an example which ilustrates what I want to achieve exactly.
I'm struggling around this line:
next += timePeriod/3.52/(i+1);
which works almost perfect in demo example (for any timePeriod), but obviously it doesn't work for a different letters.length as I have used static number 3.52.
How do I calculate next?
var letters = [
'A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T'
];
var div = $('#container');
var timePeriod = 5000; // 5 seconds;
var perLetter = timePeriod/(letters.length-1); // it gives equal time between letters
var next = 0;
for(var i=0; i<letters.length; i++){
setTimeout(function(letter){
//div.append('<span class="letter">' + letter + '</span>');
// Used "|" instead of letter, For better redability:
div.append('<span class="letter">|</span>');
}, next, letters[i]);
// Can't find the logic here:
next += timePeriod/3.52/(i+1);
};
///////////////// FOR DEMO: ///////////////
var sec = timePeriod/1000;
var secondsInterval = setInterval(seconds, 1000);
var demoInterval = setInterval(function(){
sec >= 0 || clearInterval(demoInterval);
div.append('\'');
}, 30);
function seconds(){
sec || clearInterval(secondsInterval);
$('#sec').text(sec-- || 'DONE');
}
seconds();
.letter{
color : red;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<span id=container></span>
<span id=sec class=letter></span>
var steps = letters.length;
var target = timePeriod;
function easeOutQuad(t, b, c, d) {
t /= d;
return -c * t*(t-2) + b;
};
var arrayOfTimeouts = new Array(steps);
var n;
var prev = 0;
for(var i = 1; i <= steps; i++){
n = easeOutQuad(i, 0.0, target, steps);
arrayOfTimeouts[i-1] = n-prev;
prev = n;
}
This one should work with any input value.
fiddle
Note that the graph appears to be slightly too fast but I believe that discrepancy to be a product of timing imperfections, as the sum of my array equals the timePeriod exactly.
more on easing equations
Here's a solution based on a geometric series. It's a bit goofy but it works. It generates an array with your timeout values.
Steps = size of your array.
Target = the total time.
var steps = 50;
var target = 5000;
var fraction = 1.5 + steps / 7;
var ratio = (fraction-1) / fraction;
var n = target / fraction;
var sum = 0;
var arrayOfTimeouts = new Array(steps);
for(var i = 0; i < steps; i++){
sum += n;
arrayOfTimeouts[i] = n;
n *= ratio;
}
console.log(arrayOfTimeouts, sum);
Say I have array [1,2,5,18,17,8] and I want to turn that into an array of length 40 that follows the same path.
a = [1,2,5,18,17,8];
stepSize = 1 / (40 / a.length);
then i think i could do something like
steps = [];
for( var i = 0; i < 1; i+= stepSize) {
steps.push(d3.interpolate(a[0],a[1])(i));
}
and then repeat that for all the elements. My question is there a better way to do this?
I can only guess what your real problem is but I think you want to plot these values and have a smooth curve. In that case use line.interpolate() https://github.com/mbostock/d3/wiki/SVG-Shapes#line_interpolate
In case you DO know what you need and your solution works for you, take this tip:
Never iterate over stepSize. Calculate it once and multiply it with i in every loop where i goes from 0 to 40. This way you work around precision problems.
Your algorithm cleaned up, tested and working:
var a = [1,5,12,76,1,2];
var steps = 24;
var ss = (a.length-1) / (steps-1);
var result = new Array(steps);
for (var i=0; i<steps; i++) {
var progress = ss * i;
var left = Math.floor(progress);
var right = Math.ceil(progress);
var factor = progress - left;
result[i] = (1 - factor) * a[left] + (factor) * a[right];
// alternative that actually works the same:
//result[i] = d3.interpolateNumber(a[left], a[right], factor);
}
console.log(result);
I've written the following Javascript:
(function () {
var computationModule = (function foo1(stdlib, foreign, heap) {
"use asm";
var sqrt = stdlib.Math.sqrt,
heapArray = new stdlib.Int32Array(heap),
outR = 0.0,
outI = 0.0;
function computeRow(canvasWidth, canvasHeight, limit, max, rowNumber, minR, maxR, minI, maxI) {
canvasWidth = +canvasWidth;
canvasHeight = +canvasHeight;
limit = +limit;
max = max | 0;
rowNumber = +rowNumber;
minR = +minR;
maxR = +maxR;
minI = +minI;
maxI = +maxI;
var columnNumber = 0.0,
zReal = 0.0,
zImaginary = 0.0,
numberToEscape = 0;
var columnNumberInt = 0;
// Compute the imaginary part of the numbers that correspond to pixels in this row.
zImaginary = +(((maxI - minI) * +rowNumber) / +canvasHeight + minI);
// Iterate over the pixels in this row.
// Compute the number of iterations to escape for each pixel that will determine its color.
for (columnNumber = +0; + columnNumber < +canvasWidth; columnNumber = +(+columnNumber + 1.0)) {
// Compute the real part of the number for this pixel.
zReal = +(((maxR - minR) * +columnNumber) / +canvasWidth + minR);
numberToEscape = howManyToEscape(zReal, zImaginary, max, limit) | 0;
columnNumberInt = columnNumberInt + 1 | 0;
heapArray[(columnNumberInt * 4) >> 2] = numberToEscape | 0;
}
}
// Function to determine how many iterations for a point to escape.
function howManyToEscape(r, i, max, limit) {
r = +r;
i = +i;
max = max | 0;
limit = +limit;
var j = 0,
ar = 0.0,
ai = 0.0;
ar = +r;
ai = +i;
for (j = 0;
(j | 0) < (max | 0); j = (j + 1) | 0) {
iteratingFunction(ar, ai, r, i)
ar = outR;
ai = outI;
if (+(ar * ar + ai * ai) >= +(limit * limit))
return j | 0;
}
return j | 0;
}
// The iterating function defining the fractal to draw
// r and i are the real and imaginary parts of the value from the previous iteration
// r0 and i0 are the starting points
function iteratingFunction(r, i, r0, i0) {
r = +r;
i = +i;
r0 = +r0;
i0 = +i0;
computePower(r, i, 2);
// Set the output from this function to t
outR = +(r0 + outR);
outI = +(i0 + outI);
}
// Compute the result of [r,i] raised to the power n.
// Place the resulting real part in outR and the imaginary part in outI.
function computePower(r, i, n) {
// Tell asm.js that r, i are floating point and n is an integer.
r = +r;
i = +i;
n = n | 0;
// Declare and initialize variables to be numbers.
var rResult = 0.0;
var iResult = 0.0;
var j = 0;
var tr = 0.0;
var ti = 0.0;
// Declare and initialize variables that will be used only in the
// event we need to compute the reciprocal.
var abs = 0.0;
var recr = 0.0;
var reci = 0.0;
if ((n | 0) < (0 | 0)) {
// For n less than 0, compute the reciprocal and then raise it to the opposite power.
abs = +sqrt(r * r + i * i);
recr = r / abs;
reci = -i / abs;
r = recr;
i = reci;
n = -n | 0;
}
rResult = r;
iResult = i;
for (j = 1;
(j | 0) < (n | 0); j = (j + 1) | 0) {
tr = rResult * r - iResult * i;
ti = rResult * i + iResult * r;
rResult = tr;
iResult = ti;
}
outR = rResult;
outI = iResult;
} // end computePower
return {
computeRow: computeRow
};
})(self, foreign, heap);
// Return computationModule that we just defined.
return computationModule;
})();
There's nothing particularly unusual about this Javascript, except that I want to make my web application display the Javascript in an ACE text editor (http://ace.c9.io/) so that the user can modify the code at runtime.
I load the Javascript using jQuery AJAX and then set the contents of the ACE Editor to the Javascript code. After the user modifies the code, he can click a button to run the code. (This uses eval)
The problem I'm having is that ACE is displaying strange characters instead of spaces.
Oddly enough, if I try to copy text from the ACE editor, the strange characters disappear and the spaces are normal. Furthermore, the code runs fine even with these strange characters being displayed.
I also noticed that the problem does not appear when using Firefox, but it appears for Chrome and IE 11.
Finally, the problem only occurs when I put the code on a real web server. It doesn't reproduce in my development environment.
Looking at this some more, I can see that it's not just the text I'm loading via AJAX. Even when I type new spaces, more text characters appear!
What could be going wrong so that the text doesn't display properly?
Here's a link to the application: http://danielsadventure.info/html5fractal/
Use charset="utf-8" in the script tag where you include ace.
<script src="path/to/ace.js" charset="utf-8">
This may have something to do with this:
When no explicit charset parameter is provided by the sender, media
subtypes of the "text" type are defined to have a default charset
value of "ISO-8859-1" when received via HTTP. Data in character sets
other than "ISO-8859-1" or its subsets MUST be labeled with an
appropriate charset value. See section 3.4.1 for compatibility
problems.
http://www.w3.org/Protocols/rfc2616/rfc2616-sec3.html#sec3.7.1
So the string passed to the script are in an encoding different than what ACE (or JS in general) expects, which is UTF-8.
I am trying to do following:
Create 2 unique numbers that are both within a certain range and they are at least n bigger/smaller.
In example:
Range is 0-600
Minimum "difference" is 150
So the generated numbers could be: [2,400],[120,310],[82,530]
But Not [900,400] or [200,220].
Thats what I have so far:
var posYArray = [];
for(i=0; i < 2; i++){
var posY = (Math.random() * 200).toFixed();
if(i < 1){
posYArray.push(posY);
}else{
for(i=0; i < posYArray.length; i++){
if(posY < posYArray[i]+100){
posYArray.push(posY);
}else{
//Restart loop??
}
}
}
}
But this randomly crashes the browser and also I didnt know a good way to restart the loop when the numbers are too close...
You could do this in two steps.
Generate your first random number.
Reduce the pool of random numbers which to the only possible valids.
Select your next random number in the reduced pool.
var upperBound = 200,
minDelta = 90,
firstRandom = Math.floor(Math.random() * upperBound);
var validPool = [];
for (var i = 0; i < upperBound; i++) {
if (i < firstRandom - minDelta || i > firstRandom + minDelta) {
validPool.push(i);
}
}
var secondRandom = validPool[Math.floor(Math.random() * validPool.length)];
jsFiddle.
It might be slower than randomly choosing and comparing, but at least it has a guaranteed running time :)
You can shift the gap in which not to choose a number, i.e. pick a random number x between 0 and range - gap, than pick first one between 0 and x and the second between x + gap and range. That would be somewhat more efficient.
var range = 600, gap = 150;
var x = Math.floor(Math.random() * (range - gap));
var posX = (Math.random() * (x)).toFixed();
var posY = (Math.random() * (range - x - gap) + x + gap).toFixed();
Works in O(1).
What about simply trying them? Very easy and when the difference is a lot smaller then the max size (example 150 and 600) you have a good pair in 1/2 of the possibilities.
For example:
var posY = (Math.random() * 600).toFixed();
var posX = (Math.random() * 600).toFixed();
while(abs(poX-posY) < 150){
posX = (Math.random() * 600).toFixed()
}
Not that efficient, but when you only have 2 numbers to generate that wont matter !