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  • Concurrent cartesian product algorithm in Clojure

    - by jqno
    Is there a good algorithm to calculate the cartesian product of three seqs concurrently in Clojure? I'm working on a small hobby project in Clojure, mainly as a means to learn the language, and its concurrency features. In my project, I need to calculate the cartesian product of three seqs (and do something with the results). I found the cartesian-product function in clojure.contrib.combinatorics, which works pretty well. However, the calculation of the cartesian product turns out to be the bottleneck of the program. Therefore, I'd like to perform the calculation concurrently. Now, for the map function, there's a convenient pmap alternative that magically makes the thing concurrent. Which is cool :). Unfortunately, such a thing doesn't exist for cartesian-product. I've looked at the source code, but I can't find an easy way to make it concurrent myself. Also, I've tried to implement an algorithm myself using map, but I guess my algorithmic skills aren't what they used to be. I managed to come up with something ugly for two seqs, but three was definitely a bridge too far. So, does anyone know of an algorithm that's already concurrent, or one that I can parallelize myself?

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  • Algorithm to produce Cartesian product of arrays in depth-first order

    - by Yuri Gadow
    I'm looking for an example of how, in Ruby, a C like language, or pseudo code, to create the Cartesian product of a variable number of arrays of integers, each of differing length, and step through the results in a particular order: So given, [1,2,3],[1,2,3],[1,2,3]: [1, 1, 1] [2, 1, 1] [1, 2, 1] [1, 1, 2] [2, 2, 1] [1, 2, 2] [2, 1, 2] [2, 2, 2] [3, 1, 1] [1, 3, 1] etc. Instead of the typical result I've seen (including the example I give below): [1, 1, 1] [2, 1, 1] [3, 1, 1] [1, 2, 1] [2, 2, 1] [3, 2, 1] [1, 3, 1] [2, 3, 1] etc. The problem with this example is that the third position isn't explored at all until all combinations of of the first two are tried. In the code that uses this, that means even though the right answer is generally (the much larger equivalent of) 1,1,2 it will examine a few million possibilities instead of just a few thousand before finding it. I'm dealing with result sets of one million to hundreds of millions, so generating them and then sorting isn't doable here and would defeat the reason for ordering them in the first example, which is to find the correct answer sooner and so break out of the cartesian product generation earlier. Just in case it helps clarify any of the above, here's how I do this now (this has correct results and right performance, but not the order I want, i.e., it creates results as in the second listing above): def cartesian(a_of_a) a_of_a_len = a_of_a.size result = Array.new(a_of_a_len) j, k, a2, a2_len = nil, nil, nil, nil i = 0 while 1 do j, k = i, 0 while k < a_of_a_len a2 = a_of_a[k] a2_len = a2.size result[k] = a2[j % a2_len] j /= a2_len k += 1 end return if j > 0 yield result i += 1 end end UPDATE: I didn't make it very clear that I'm after a solution where all the combinations of 1,2 are examined before 3 is added in, then all 3 and 1, then all 3, 2 and 1, then all 3,2. In other words, explore all earlier combinations "horizontally" before "vertically." The precise order in which those possibilities are explored, i.e., 1,1,2 or 2,1,1, doesn't matter, just that all 2 and 1 are explored before mixing in 3 and so on.

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  • Cartesian product in Scheme

    - by John Retallack
    I've been trying to do a function that returns the Cartesian Product of n sets,in Dr Scheme,the sets are given as a list of lists,I've been stuck at this all day,I would like a few guidelines as where to start,I've wrote a pice of code but it dosen't work. (define cart-n(?(l) (if (null? l) '(()) (map (?(lst) (cons (car ( car(l))) lst)) (cart-n (cdr l) )))))

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  • cartesian product

    - by John Retallack
    I've been trying to do a function that returns the Cartesian Product of n sets,in Dr Scheme,the sets are given as a list of lists,I've been stuck at this all day,I would like a few guidelines as where to start,I've wrote a pice of code but it dosen't work. (define cart-n(?(l) (if (null? l) '(()) (map (?(lst) (cons (car ( car(l))) lst)) (cart-n (cdr l) )))))

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  • Uses for Cartesian Products in MS Access

    Less well known than inner and outer joins is the Cartesian product, which produces every possible combination of records between the two tables. Doug Steele offers four examples to demonstrate some legitimate uses for Cartesian products.

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  • Multiple many-to-many JOINs in a single mysql query without Cartesian Product

    - by VWD
    At the moment I can get the results I need with two seperate SELECT statements SELECT COUNT(rl.refBiblioID) FROM biblioList bl LEFT JOIN refList rl ON bl.biblioID = rl.biblioID GROUP BY bl.biblioID SELECT GROUP_CONCAT( CONCAT_WS( ':', al.lastName, al.firstName ) ORDER BY al.authorID ) FROM biblioList bl LEFT JOIN biblio_author ba ON ba.biblioID = bl.biblioID JOIN authorList al ON al.authorID = ba.authorID GROUP BY bl.biblioID Combining them like this however SELECT GROUP_CONCAT( CONCAT_WS( ':', al.lastName, al.firstName ) ORDER BY al.authorID ), COUNT(rl.refBiblioID) FROM biblioList bl LEFT JOIN biblio_author ba ON ba.biblioID = bl.biblioID JOIN authorList al ON al.authorID = ba.authorID LEFT JOIN refList rl ON bl.biblioID = rl.biblioID GROUP BY bl.biblioID causes the author result column to have duplicate names. How can I get the desired results from one SELECT statement without using DISTINCT? With subqueries?

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  • Polar and Cartesian calculations not completely working?

    - by Smoka
    double testx, testy, testdeg, testrad, endx, endy; testx = 1; testy = 1; testdeg = atan2( testx, testy) / Math::PI* 180; testrad = sqrt(pow(testx,2) + pow(testy,2)); endx = testrad * cos(testdeg); endy = testrad * sin(testdeg); All parts of this seem to equate properly, except endx and endy should = testx and testy they do when calculating by hand.

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  • how to get cartesian products between database and local sequences in linq?

    - by JD
    I saw this similar question here but can't figure out how to use Contains in Cartesian product desired result situation: http://stackoverflow.com/questions/1712105/linq-to-sql-exception-local-sequence-cannot-be-used-in-linq-to-sql-implementatio Let's say I have following: var a = new [] { 1, 4, 7 }; var b = new [] { 2, 5, 8 }; var test = from i in a from j in b select new { A = i, B = j, AB = string.Format("{0:00}a{1:00}b", i, j), }; foreach (var t in test) Console.Write("{0}, ", t.AB); This works great and I get a dump like so (note, I want the cartesian product): 01a02b, 01a05b, 01a08b, 04a02b, 04a05b, 04a08b, 07a02b, 07a05b, 07a08b, Now what I really want is to take this and cartesian product it again against an ID from a database table I have. But, as soon as I add in one more from clause that instead of referencing objects, references SQL table, I get an error. So, altering above to something like so where db is defined as a new DataContext (i.e., class deriving from System.Data.Linq.DataContext): var a = new [] { 1, 4, 7 }; var b = new [] { 2, 5, 8 }; var test = from symbol in db.Symbols from i in a from j in b select new { A = i, B = j, AB = string.Format("{0}{1:00}a{2:00}b", symbol.ID, i, j), }; foreach (var t in test) Console.Write("{0}, ", t.AB); The error I get is following: Local sequence cannot be used in LINQ to SQL implementations of query operators except the Contains operator Its related to not using Contains apparently but I'm unsure how Contains would be used when I don't really want to constrict the results - I want the Cartesian product for my situation. Any ideas of how to use Contains above and still yield the Cartesian product when joining database and local sequences?

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  • Math Question: Is it possible to calculate the row position as you loop through a cartesian product

    - by Kuyenda
    Is it possible to calculate the row position in the cartesian product of two arrays? For example if you have one array of two rows and another of three rows it's easy to calculate the size of the cartesian product (Array1.Rows.Count * Array2.Rows.Count = 6), but you can't iterate through each array and just use the product of the respective row positions to calculate the row position in the cartesian product. Array1.Row * Array2.Row 1 * 1 = 1 1 * 2 = 2 2 * 1 = 2 2 * 2 = 4 3 * 1 = 3 3 * 2 = 6 Is there a formula to obtain the result 1, 2, 3, 4, 5, 6 from Array1.Row and Array2.Row as you iterate through them in the following fashion: For 1 To Array1.Rows.Count For 1 To Array2.Rows.Count 'some formula here to get cartesian row position' Next Array2.Row Next Array1.Row Thanks!

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  • F#: how to find Cartesian power

    - by Nike
    I have a problem with writing a Cartesian power function. I found many examples about calculating Cartesian Product, but no one about Cartesian power. For example, [1;2] raised to power 3 = [ [1;1;1] ; [1;1;2] ; [1;2;1] ; [1;2;2] ; [2;1;1] ; [2;1;2] ; [2;2;1]; [2;2;2] ] I use following code to calculate Cartesian Product: let Cprod U V = let mutable res = [] for u in U do for v in V do res <- res @ [[u;v]] res And trying to calculate Cartesian power. I use following code to calculate Cartesian Product: let Cpower U n = let mutable V = U for i=0 to n-1 do V <- Dprod U V V Visual Studio said: Error The resulting type would be infinite when unifying ''a' and ''a list'. I will thankful for any help and links.

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  • HTML5 Canvas Converting between cartesian and isometric coordinates

    - by Amir
    I'm having issues wrapping my head around the Cartesian to Isometric coordinate conversion in HTML5 canvas. As I understand it, the process is two fold: (1) Scale down the y-axis by 0.5, i.e. ctx.scale(1,0.5); or ctx.setTransform(1,0,0,0.5,0,0); This supposedly produces the following matrix: [x; y] x [1, 0; 0, 0.5] (2) Rotate the context by 45 degrees, i.e. ctx.rotate(Math.PI/4); This should produce the following matrix: [x; y] x [cos(45), -sin(45); sin(45), cos(45)] This (somehow) results in the final matrix of ctx.setTransform(2,-1,1,0.5,0,0); which I cannot seem to understand... How is this matrix derived? I cannot seem to produce this matrix by multiplying the scaling and rotation matrices produced earlier... Also, if I write out the equation for the final transformation matrix, I get: newX = 2x + y newY = -x + y/2 But this doesn't seem to be correct. For example, the following code draws an isometric tile at cartesian coordinates (500, 100). ctx.setTransform(2,-1,1,0.5,0,0); ctx.fillRect(500, 100, width*2, height); When I check the result on the screen, the actual coordinates are (285, 215) which do not satisfy the equations I produced earlier... So what is going on here? I would be very grateful if you could: (1) Help me understand how the final isometric transformation matrix is derived; (2) Help me produce the correct equation for finding the on-screen coordinates of an isometric projection. Many thanks and kind regards

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  • Spherical to Cartesian Coordinates

    - by user1258455
    Well I'm reading the Frank's Luna DirectX10 book and, while I'm trying to understand the first demo, I found something that's not very clear at least for me. In the updateScene method, when I press A, S, W or D, the angles mTheta and mPhi change, but after that, there are three lines of code that I don't understand exactly what they do: // Convert Spherical to Cartesian coordinates: mPhi measured from +y // and mTheta measured counterclockwise from -z. float x = 5.0f*sinf(mPhi)*sinf(mTheta); float z = -5.0f*sinf(mPhi)*cosf(mTheta); float y = 5.0f*cosf(mPhi); I mean, this explains that they do, it says that it converts the spherical coordinates to cartesian coordinates, but, mathematically, why? why the x value is calculated by the product of the sins of both angles? And the z by the product of the sine and cosine? and why the y just uses the cosine? After that, those values (x, y and z) are used to build the view matrix. The book doesn't explain (mathematically) why those values are calculated like that (and I didn't find anything to help me to understand it at the first Part of the book: "Mathematical prerequisites"), so it would be good if someone could explain me what exactly happen in those code lines or just give me a link that helps me to understand the math part. Thanks in advance!

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  • Transform between two 3d cartesian coordinate systems

    - by Pris
    I'd like to know how to get the rotation matrix for the transformation from one cartesian coordinate system (X,Y,Z) to another one (X',Y',Z'). Both systems are defined with three orthogonal vectors as one would expect. No scaling or translation occurs. I'm using OpenSceneGraph and it offers a Matrix convenience class, if it makes finding the matrix easier: http://www.openscenegraph.org/documentation/OpenSceneGraphReferenceDocs/a00403.html.

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  • Euler angles to Cartesian Coordinates for use with gluLookAt

    - by notrodash
    I have searched all of the internet but just couldn't find the answer. I am using LibGDX and this is part of my code that loops over and over: public void render() { GL11 gl = Gdx.gl11; float centerX = (float)Math.cos(yaw) * (float)Math.cos(pitch); float centerY = (float)Math.sin(yaw) * (float)Math.cos(pitch); float centerZ = (float)Math.sin(pitch); System.out.println(centerX+" "+centerY+" "+centerZ+" ~ "+GDXRacing.camera.position.x+" "+GDXRacing.camera.position.y+" "+GDXRacing.camera.position.z); Gdx.glu.gluLookAt(gl, GDXRacing.camera.position.x, GDXRacing.camera.position.y, GDXRacing.camera.position.z, centerX, centerY, centerZ, 0, 1, 0); if(Gdx.input.isKeyPressed(Keys.A)) { yaw--; } if(Gdx.input.isKeyPressed(Keys.D)) { yaw++; } } I might just be bad at the math, but I dont get it. Does someone have a good explanation and an idea about how to deal with this? I am trying to make a first person camera. By the way, the camera is translated by +10 on the Z axis. Currently when I run the application, this is what I get: Watch video in browser | Download video (for those who cant download the video, everything shakes in a clockwise/anticlockwise action, depending on if I increase or decrease the Yaw value) -Thank you. [edit] and with this code: public void render() { GL11 gl = Gdx.gl11; float centerX = (float)(MathUtils.cosDeg(yaw)*4); float centerY = 0; float centerZ = (float)(MathUtils.sinDeg(yaw)*4); System.out.println(centerX+" "+centerY+" "+centerZ+" ~ "+GDXRacing.camera.position.x+" "+GDXRacing.camera.position.y+" "+GDXRacing.camera.position.z); Gdx.glu.gluLookAt(gl, GDXRacing.camera.position.x, GDXRacing.camera.position.y, GDXRacing.camera.position.z, centerX, centerY, centerZ, 0, 1, 0); if(Gdx.input.isKeyPressed(Keys.A)) { yaw--; } if(Gdx.input.isKeyPressed(Keys.D)) { yaw++; } } it slowly swings from the left to the right. This approach worked for turning left and right for 2d games though. What am I doing wrong?

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  • Precision loss when transforming from cartesian to isometric

    - by Justin Skiles
    My goal is to display a tile map in isometric projection. This tile map has 25 tiles across and 25 tiles down. Each tile is 32x32. See below for how I'm accomplishing this. World Space World Space to Screen Space Rotation (45 degrees) Using a 2D rotation matrix, I use the following: double rotation = Math.PI / 4; double rotatedX = ((tileWorldX * Math.Cos(rotation)) - ((tileWorldY * Math.Sin(rotation))); double rotatedY = ((tileWorldX * Math.Sin(rotation)) + (tileWorldY * Math.Cos(rotation))); World Space to Screen Space Scale (Y-axis reduced by 50%) Here I simply scale down the Y value by a factor of 0.5. Problem And it works, kind of. There are some tiny 1px-2px gaps between some of the tiles when rendering. I think there's some precision loss somewhere, or I'm not understanding how to get these tiles to fit together perfectly. I'm not truncating or converting my values to non-decimal types until I absolutely have to (when I pass to the render method, which only takes integers). I'm not sure how to guarantee pixel perfect rendering precision when I'm rotating and scaling on a level of higher precision. Any advice? Do I need to supply for information?

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  • How to avoid Cartesian product in an INNER JOIN query?

    - by flhe
    I have 6 tables, let's call them a,b,c,d,e,f. Now I want to search all the colums (except the ID columns) of all tables for a certain word, let's say 'Joe'. What I did was, I made INNER JOINS over all the tables and then used LIKE to search the columns. INNER JOIN ... ON INNER JOIN ... ON.......etc. WHERE a.firstname ~* 'Joe' OR a.lastname ~* 'Joe' OR b.favorite_food ~* 'Joe' OR c.job ~* 'Joe'.......etc. The results are correct, I get all the colums I was looking for. But I also get some kind of cartesian product, I get 2 or more lines with almost the same results. How can i avoid this? I want so have each line only once, since the results should appear on a web search.

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  • SQL Cartesian product joining table to itself and inserting into existing table

    - by Emma
    I am working in phpMyadmin using SQL. I want to take the primary key (EntryID) from TableA and create a cartesian product (if I am using the term correctly) in TableB (empty table already created) for all entries which share the same value for FieldB in TableA, except where TableA.EntryID equals TableA.EntryID So, for example, if the values in TableA were: TableA.EntryID TableA.FieldB 1 23 2 23 3 23 4 25 5 25 6 25 The result in TableB would be: Primary key EntryID1 EntryID2 FieldD (Default or manually entered) 1 1 2 Default value 2 1 3 Default value 3 2 1 Default value 4 2 3 Default value 5 3 1 Default value 6 3 2 Default value 7 4 5 Default value 8 4 6 Default value 9 5 4 Default value 10 5 6 Default value 11 6 4 Default value 12 6 5 Default value I am used to working in Access and this is the first query I have attempted in SQL. I started trying to work out the query and got this far. I know it's not right yet, as I’m still trying to get used to the syntax and pieced this together from various articles I found online. In particular, I wasn’t sure where the INSERT INTO text went (to create what would be an Append Query in Access). SELECT EntryID FROM TableA.EntryID TableA.EntryID WHERE TableA.FieldB=TableA.FieldB TableA.EntryID<>TableA.EntryID INSERT INTO TableB.EntryID1 TableB.EntryID2 After I've got that query right, I need to do a TRIGGER query (I think), so if an entry changes it's value in TableA.FieldB (changing it’s membership of that grouping to another grouping), the cartesian product will be re-run on THAT entry, unless TableB.FieldD = valueA or valueB (manually entered values). I have been using the Designer Tab. Does there have to be a relationship link between TableA and TableB. If so, would it be two links from the EntryID Primary Key in TableA, one to each EntryID in TableB? I assume this would not work because they are numbered EntryID1 and EntryID2 and the name needs to be the same to set up a relationship? If you can offer any suggestions, I would be very grateful. Research: http://www.fluffycat.com/SQL/Cartesian-Joins/ Cartesian Join example two Q: You said you can have a Cartesian join by joining a table to itself. Show that! Select * From Film_Table T1, Film_Table T2;

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  • In Perl, how can I iterate over the Cartesian product of multiple sets?

    - by nubie2
    I want to do permutation in Perl. For example I have three arrays: ["big", "tiny", "small"] and then I have ["red", "yellow", "green"] and also ["apple", "pear", "banana"]. How do I get: ["big", "red", "apple"] ["big", "red", "pear"] ..etc.. ["small", "green", "banana"] I understand this is called permutation. But I am not sure how to do it. Also I don't know how many arrays I can have. There may be three or four, so I don't want to do nested loop.

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  • Why would this query cause a Merge Cartesian Join in Oracle

    - by decompiled
    I have a query that was recently required to be modified. Here's the original SELECT RTRIM (position) AS "POSITION", . // Other fields . . FROM schema.table x WHERE hours > 0 AND pay = 'RGW' AND NOT EXISTS( SELECT position FROM schema.table2 y where y.position = x.position ) Here's the new version SELECT RTRIM (position) AS "POSITION", . // Other fields . . FROM schema.table x WHERE hours > 0 AND pay = 'RGW' AND NOT EXISTS( SELECT position FROM schema.table2 y where y.date = get_fiscal_year_start_date (SYSDATE) AND y.position = x.position ) The UDF get_fiscal_year_start_date() returns the fiscal year start date of the date parameter. The first query runs fine, but the second creates a merge Cartesian join. I looked at the indexes on the tables and found that position and date were both indexed. My question for you stackoverflow is why would the addition of 'y.date = get_fiscal_year_start_date (SYSDATE)' cause a merge cartesian join in Oracle 10g.

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  • is NATURAL JOIN any better than SELECT FROM WHERE in terms of performance ?

    - by ashy_32bit
    Today I got into a debate with my project manager about Cartesian products. He says a 'natural join' is somehow much better than using 'select from where' because the later cause the db engine to internally perform a Cartesian product but the former uses another approach that prevents this. As far as I know, the natural join syntax is not any different in anyway than 'select from where' in terms of performance or meaning, I mean you can use either based on your taste. SELECT * FROM table1,table2 WHERE table1.id=table2.id SELECT * FROM table1 NATURAL JOIN table2 please elaborate about the first query causing a Cartesian product but the second one being somehow more smart

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  • Polygon area calculation using Latitude and Longitude generated from Cartesian space and a world fil

    - by Heath
    Given a series of GPS coordinate pairs, I need to calculate the area of a polygon (n-gon). This is relatively small (not larger than 50,000 sqft). The geocodes are created by applying an affine transform with data from a world file. I have tried to use a two step approach by doing converting the geocodes to cartesian coordinates: double xPos = (lon-lonAnchor)*( Math.toRadians( 6378137 ) )*Math.cos( latAnchor ); double yPos = (lat-latAnchor)*( Math.toRadians( 6378137 ) ); then I use a cross product calculation to determine the area. The issue is that the results are a bit off in accuracy (around 1%). Is there anything I can look into to improve this? Thanks.

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  • Cartesian Plane

    - by NuNu
    I'm trying to define a function in Haskell that takes an integer argument c and returns the list of all points on the cartesian plane of the form (x/c,y/c) where x and y are integers. x/c is between -2 and 1 and y/r is between -1 and 1 This is what I've gotten so far which I'm almost sure is right but I'm getting a parse error on input = when I run it particularly at this line: cart xs ys c = [(y/c,x/c) | x <- xs, y <- ys] plane :: Int -> [a] plane c = cart [-1*c .. 1*c] [-2*c .. 1*c] c cart xs ys c = [(y/c,x/c) | x <- xs, y <- ys] A sample output would be: plane 1 would generate: [(-2.0, -1.0), (-1.0, -1.0), ( 0.0, -1.0), ( 1.0, -1.0), (-2.0, 0.0), (-1.0, 0.0), ( 0.0, 0.0), ( 1.0, 0.0), (-2.0, 1.0), (-1.0, 1.0), ( 0.0, 1.0), ( 1.0, 1.0)] Anyone have any idea how I can fix this! Thanks

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