double math - Page 64 - Developer IT

How to implement Horner's scheme for multivariate polynomials?

- by gsreynolds

Background I need to solve polynomials in multiple variables using Horner's scheme in Fortran90/95. The main reason for doing this is the increased efficiency and accuracy that occurs when using Horner's scheme to evaluate polynomials. I currently have an implementation of Horner's scheme for univariate/single variable polynomials. However, developing a function to evaluate multivariate polynomials using Horner's scheme is proving to be beyond me. An example bivariate polynomial would be: 12x^2y^2+8x^2y+6xy^2+4xy+2x+2y which would factorised to x(x(y(12y+8))+y(6y+4)+2)+2y and then evaluated for particular values of x & y. Research I've done my research and found a number of papers such as: staff.ustc.edu.cn/~xinmao/ISSAC05/pages/bulletins/articles/147/hornercorrected.pdf citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.8637&rep=rep1&type=pdf www.is.titech.ac.jp/~kojima/articles/B-433.pdf Problem However, I'm not a mathematician or computer scientist, so I'm having trouble with the mathematics used to convey the algorithms and ideas. As far as I can tell the basic strategy is to turn a multivariate polynomial into separate univariate polynomials and compute it that way. Can anyone help me? If anyone could help me turn the algorithms into pseudo-code that I can implement into Fortran myself, I would be very grateful.

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Fastest primality test

- by Grigory Javadyan

Hi. Could you suggest a fast, deterministic method that is usable in practice, for testing if a large number is prime or not? Also, I would like to know how to use non-deterministic primality tests correctly. For example, if I'm using such a method, I can be sure that a number is not prime if the output is "no", but what about the other case, when the output is "probably"? Do I have to test for primality manually in this case? Thanks in advance.

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Python rounding problem

- by pocoa

>>> num = 4.123456 >>> round(num, 3) # expecting 4.123 4.1230000000000002 I'm expecting 4.123 as a result, Am I wrong?

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How to get bit rotation function to accept any bit size?

- by calccrypto

i have these 2 functions i got from some other code def ROR(x, n): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (32 - n)) def ROL(x, n): return ROR(x, 32 - n) and i wanted to use them in a program, where 16 bit rotations are required. however, there are also other functions that require 32 bit rotations, so i wanted to leave the 32 in the equation, so i got: def ROR(x, n, bits = 32): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (bits - n)) def ROL(x, n, bits = 32): return ROR(x, bits - n) however, the answers came out wrong when i tested this set out. yet, the values came out correctly when the code is def ROR(x, n): mask = (2L**n) - 1 mask_bits = x & mask return (x >> n) | (mask_bits << (16 - n)) def ROL(x, n,bits): return ROR(x, 16 - n) what is going on and how do i fix this?

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How to compute the cross-product?

- by WizardOfOdds

I have the following piece of pseudo-C/Java/C# code: int a[]= { 30, 20 }; int b[] = { 40, 50 }; int c[] = {12, 12}; How do I compute the cross-product ABxAC?

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Help with PHP function that will take $bytes and $rate (per GB) and return $total

- by stormist

I was hoping someone might help with a function that given two parameters: @param $bytes : total amount in bytes of data consumed @param $rate : rate per GB, example .22 (for 22 cents) @returns Total amount owed Rounded to nearest cent of course. Thanks in advance for any help.

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Is there any valid reason radians are used as the inputs to trig function in many modern languages?

- by johnmortal

Is there any pressing reason trig functions should use radian inputs in modern programming languages? As far as I know radians are typically ugly to deal with except in three cases: (1) You want to compute an arc length and you know the angle of the arc and (2) You need to do symbolic calculus with trig functions (3) certain infinite series expansion look prettier if the input is in radians. None of these scenarios seem like a worthy justification for every programming language I am familiar with using radian inputs for Sin, Cos, Tangent, etc... The third one sounds good because it might mean one gets faster computations using radians (very slightly faster- the cost of one additional floating point multiplication ) , but I am dubious even of that because most commonly the developer had to take an extra step to put the angle in radians in the first place. The other two are ridiculous justifications for all the added obscurity.

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Calculus? Need help solving for a time-dependent variable given some other variables.

- by user451527

Long story short, I'm making a platform game. I'm not old enough to have taken Calculus yet, so I know not of derivatives or integrals, but I know of them. The desired behavior is for my character to automagically jump when there is a block to either side of him that is above the one he's standing on; for instance, stairs. This way the player can just hold left / right to climb stairs, instead of having to spam the jump key too. The issue is with the way I've implemented jumping; I've decided to go mario-style, and allow the player to hold 'jump' longer to jump higher. To do so, I have a 'jump' variable which is added to the player's Y velocity. The jump variable increases to a set value when the 'jump' key is pressed, and decreases very quickly once the 'jump' key is released, but decreases less quickly so long as you hold the 'jump' key down, thus providing continuous acceleration up as long as you hold 'jump.' This also makes for a nice, flowing jump, rather than a visually jarring, abrupt acceleration. So, in order to account for variable stair height, I want to be able to calculate exactly what value the 'jump' variable should get in order to jump exactly to the height of the stair; preferably no more, no less, though slightly more is permissible. This way the character can jump up steep or shallow flights of stairs without it looking weird or being slow. There are essentially 5 variables in play: h -the height the character needs to jump to reach the stair top j -the jump acceleration variable v -the vertical velocity of the character p -the vertical position of the character d -initial vertical position of the player minus final position Each timestep: j -= 1.5; //the jump variable's deceleration v -= j; //the jump value's influence on vertical speed v *= 0.95; //friction on the vertical speed v += 1; //gravity p += v; //add the vertical speed to the vertical position v-initial is known to be zero v-final is known to be zero p-initial is known p-final is known d is known to be p-initial minus p-final j-final is known to be zero j-initial is unknown Given all of these facts, how can I make an equation that will solve for j? tl;dr How do I Calculus? Much thanks to anyone who's made it this far and decides to plow through this problem.

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Finding the Formula for a Curve

- by Mystagogue

Is there a program that will take "response curve" values from me, and provide a formula that approximates the response curve? It would be cool if such a program would take a numeric "percent correct" (perhaps with a standard deviation) so that it returns simplified formulas when laxity is permissable, and more precise (viz. complex) formulas when the curve needs to be approximated closely. My interest is to play with the response curve values and "laxity" factor, until such a tool spits out a curve-fit formula simple enough that I know it will be high performance during machine computations.

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Flipping issue when interpolating Rotations using Quaternions

- by uhuu

I use slerp to interpolate between two quaternions representing rotations. The resulting rotation is then extracted as Euler angles to be fed into a graphics lib. This kind of works, but I have the following problem; when rotating around two (one works just fine) axes in the direction of the green arrow as shown in the left frame here the rotation soon jumps around to rotate from the opposite site to the opposite visual direction, as indicated by the red arrow in the right frame. This may be logical from a mathematical perspective (although not to me), but it is undesired. How could I achieve an interpolation with no visual flipping and changing of directions when rotating around more than one axis, following the green arrow at all times until the interpolation is complete? Thanks in advance.

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CenterPoint in CGContextAddArc ?

- by Mikhail Naimy

Hi , i am drawing Arc through CGCOntext.I want to draw a string in the center Point of Arc.how can i fond the center point in the Arc which has been drawn through CGContext. CGContextSetAlpha(ctx, 0.5); CGContextSetRGBFillColor(ctx, color.red, color.green, color.blue, color.alpha ); CGContextMoveToPoint(ctx, cX, cY); CGContextAddArc(ctx, cX, cY, radious+10, (startDeg-90)*M_PI/180.0, (endDeg-90)*M_PI/180.0, 0); CGContextClosePath(ctx); CGContextFillPath(ctx);

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How to make scipy.interpolate give a an extrapolated result beyond the input range?

- by Salim Fadhley

I'm trying to port a program which uses a hand-rolled interpolator (developed by a mathematitian colleage) over to use the interpolators provided by scipy. I'd like to use or wrap the scipy interpolator so that it has as close as possible behavior to the old interpolator. A key difference between the two functions is that in our original interpolator - if the input value is above or below the input range, our original interpolator will extrapolate the result. If you try this with the scipy interpolator it raises a ValueError. Consider this program as an example: import numpy as np from scipy import interpolate x = np.arange(0,10) y = np.exp(-x/3.0) f = interpolate.interp1d(x, y) print f(9) print f(11) # Causes ValueError, because it's greater than max(x) Is there a sensible way to make it so that instead of crashing, the final line will simply do a linear extrapolate, continuing the gradients defined by the first and last two pouints to infinity. Note, that in the real software I'm not actually using the exp function - that's here for illustration only!

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posmax: like argmax but gives the position(s) of the element x for which f[x] is maximal

- by dreeves

Mathematica has a built-in function ArgMax for functions over infinite domains, based on the standard mathematical definition. The analog for finite domains is a handy utility function. Given a function and a list (call it the domain of the function), return the element(s) of the list that maximize the function. Here's an example of finite argmax in action: http://stackoverflow.com/questions/471029/canonicalize-nfl-team-names/472213#472213 And here's my implementation of it (along with argmin for good measure): (* argmax[f, domain] returns the element of domain for which f of that element is maximal -- breaks ties in favor of first occurrence. *) SetAttributes[{argmax, argmin}, HoldFirst]; argmax[f_, dom_List] := Fold[If[f[#1]>=f[#2], #1, #2]&, First[dom], Rest[dom]] argmin[f_, dom_List] := argmax[-f[#]&, dom] First, is that the most efficient way to implement argmax? What if you want the list of all maximal elements instead of just the first one? Second, how about the related function posmax that, instead of returning the maximal element(s), returns the position(s) of the maximal elements?

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Python - How to find a correlation between two vectors ?

- by psihodelia

Given two vectors X and Y I have to find their correlation, i.e. their linear dependence/independence. Both vectors have equal dimension. A resulted answer should be a floating point number from [-1.0 .. 1.0]. Example: X=[-1, 2, 0] Y=[ 4, 2, -0.3] Find y=cor(X,Y) such that y belongs to [-1.0 .. 1.0]. It should be a simple construction involving a list-comprehension. No external library is allowed. UPDATE: ok, if dot product is enough, then here is my solution: nX = 1/(sum([x*x for x in X]) ** 0.5) nY = 1/(sum([y*y for y in Y]) ** 0.5) cor = sum([(x*nX)*(y*nY) for x,y in zip(X,Y) ]) right?

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mod,prime -> inverse possible

- by Piet

Hi all. I was wondering if one can do the following: We have: X is a product of N-primes, thus I assume unique. C is a constant. We can assure that C is a number that is part of the N-primes or not. Whichever will work best. Thus: X mod C = Z We have Z and C and we know that X was a product of N-primes, where N is restricted lets say first 100 primes. Is there anyway we can get back X?

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Divide and conquer method to compute roots [SOLVED]

- by hellsoul153

Hello, Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ? In other words, I'm wondering if (n exp(1/x)) is more efficient to (n exp(1/y)) for x < y and where x and y are integers.

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finding ALL cycles in a huge sparse matrix

- by Andy

Hi there, First of all I'm quite a Java beginner, so I'm not sure if this is even possible! Basically I have a huge (3+million) data source of relational data (i.e. A is friends with B+C+D, B is friends with D+G+Z (but not A - i.e. unmutual) etc.) and I want to find every cycle within this (not necessarily connected) directed graph. I've found this thread (http://stackoverflow.com/questions/546655/finding-all-cycles-in-graph/549402#549402) which has pointed me to Donald Johnson's (elementary) cycle-finding algorithm which, superficially at least, looks like it'll do what I'm after (I'm going to try when I'm back at work on Tuesday - thought it wouldn't hurt to ask in the meanwhile!). I had a quick scan through the code of the Java implementation of Johnson's algorithm (in that thread) and it looks like a matrix of relations is the first step, so I guess my questions are: a) Is Java capable of handling a 3+million*3+million matrix? (was planning on representing A-friends-with-B by a binary sparse matrix) b) Do I need to find every connected subgraph as my first problem, or will cycle-finding algorithms handle disjoint data? c) Is this actually an appropriate solution for the problem? My understanding of "elementary" cycles is that in the graph below, rather than picking out A-B-C-D-E-F it'll pick out A-B-F, B-C-D etc. but that's not the end of the world given the task. E / \ D---F / \ / \ C---B---A d) If necessary, I can simplify the problem by enforcing mutuality in relations - i.e. A-friends-with-B <== B-friends-with-A, and if really necessary I can maybe cut down the data size, but realistically it is always going to be around the 1mil mark. z) Is this a P or NP task?! Am I biting off more than I can chew? Thanks all, any help appreciated! Andy

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multidimensional vector rotation and angle computation -- how?

- by macias

Input: two multidimensional (for example dim=8) vectors a and b. I need to find out the "directed" angle (0-2*Pi, not 0-Pi) between those vectors a and b. And if they are not parallel I need to rotate vector b in plane a,b by "directed" angle L. If they are parallel, plane does not matter, but angle of rotation is still the same L. For 2d and 3d this is quite easy, but for more dimensions I am lost, I didn't find anything on google, and I prefer using some already proved&tested equations (avoiding errors introduced by my calculations :-D). Thank you in advance for tips, links, etc. Edit: dimension of the space is the same as dimension of the vectors.

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Base 62 conversion in Python

- by mikl

How would you convert an integer to base 62 (like hexadecimal, but with these digits: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'). I have been trying to find a good Python library for it, but they all seems to be occupied with converting strings. The Python base64 module only accepts strings and turns a single digit into four characters. I was looking for something akin to what URL shorteners use.

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st-ordering library function?

- by chang

I'm in the search for an implementation of an ear-decomposition algorithm (http://www.ics.uci.edu/~eppstein/junkyard/euler/ear.html). I examined networkx and didn't find one. Although the algorithm layout is vaguely in my mind, I'd like to see some reference implementation, too. Side problem: First step could be an st-ordering of a graph. Are there any implementations for st-ordering algorithms you know? Thanks for your input. I'd really like to contribute e.g. to networkx by implementing the ear-decomposition algorithm in python.

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Generate RTT values

- by Jean Gauthier

Hi all, I'm writing a Java applet where I should be able to simulate a connection between two hosts. Hence I have to generate packet round-trip times at random. These RTTs can go from ~0 to infinity, but are typically oscillating around some average value (i.e. an extremely large or small value is very improbable but possible). I was wondering if anyone had an idea of how I could do this? Thanks in advance

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Express any number as the sum of 4 prime numbers [Doubts]

- by WarDoGG

I was give a problem to express any number as sum of 4 prime numbers. Conditions: Not allowed to use any kind of database. Maximum execution time : 3 seconds Numbers only till 100,000 If the splitting is NOT possible, then return -1 What i did : using the sieve of eratosthenes, i calculated all prime numbers till the specified number. looked up a concept called goldbach conjecture which expresses an even number as the summation of 2 primes. However, i am stuck beyond that. Can anyone help me on this one as to what approach u might take ? The sieve of eratosthenes is taking 2 seconds to count primes till 100,000 :(((

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Is the binormal of a vertex the cross between its normal and tangent?

- by meds

I'm trying to find out what a binormal is in the context of graphics programming but coming up short, I saw on a site that the binormal was being calculated as the corss between the normal and tangent (i.e. cross(normal, tangent)), is this the correct way to calculate a binormal?

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Can't get my object to point at the mouse.

- by melignus

I'm using a combination of SDL and OpenGL in a sort of crash course project to teach myself how this all works. I'm really only interested in OpenGL as a way to use acceleration in 2D games so I just need this to work in a 2D plane. I have been having a lot of problems today with my current issue, I would like an object to point towards the mouse while the mouse button is clicked and then of course stay pointing in that direction after the mouse is lifted. void Square::handle_input() { //If a key was pressed if( event.type == SDL_KEYDOWN ) { //Adjust the velocity switch( event.key.keysym.sym ) { case SDLK_UP: upUp = false; yVel = -1; break; case SDLK_DOWN: downUp = false; yVel = 1; break; case SDLK_LEFT: leftUp = false; xVel = -1; break; case SDLK_RIGHT: rightUp = false; xVel = 1; break; case SDLK_w: wUp = false; sAng = 1; break; case SDLK_s: sUp = false; sAng = -1; break; } } //If a key was released else if( event.type == SDL_KEYUP ) { //Adjust the velocity switch( event.key.keysym.sym ) { case SDLK_UP: upUp = true; yVel = 0; break; case SDLK_DOWN: downUp = true; yVel = 0; break; case SDLK_LEFT: leftUp = true; xVel = 0; break; case SDLK_RIGHT: rightUp = true; xVel = 0; break; case SDLK_w: wUp = true; sAng = 0; break; case SDLK_s: sUp = true; sAng = 0; break; } } //If a mouse button was pressed if( event.type == SDL_MOUSEBUTTONDOWN ) { switch ( event.type ) { case SDL_MOUSEBUTTONDOWN: mouseUp = false; mousex == event.button.x; mousey == event.button.y; break; case SDL_MOUSEBUTTONUP: mouseUp = true; break; } } } And then this is called at the end of my Object::Move call which also handles x and y translation if (!mouseUp) { xVect = mousex - x; yVect = mousey - y; radAng = atan2 ( mousey - y, mousex - x ); sAng = radAng * 180 / 3.1415926l; } Right now when I click the object turns and faces down to the bottom left but then no longer changes direction. I'd really appreciate any help I could get here. I'm guessing there might be an issue here with state versus polled events but from all the tutorials that I've been through I was pretty sure I had fixed that. I've just hit a wall and I need some advice!

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adding up value of array and getting the average

- by sea_1987

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- by gsreynolds

- by Grigory Javadyan

- by pocoa

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- by WizardOfOdds

- by stormist

- by johnmortal

- by user451527

- by Mystagogue

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- by Mikhail Naimy

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- by dreeves

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- by Piet

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