[math] "equals" in "Vector3D" Classic List Threaded 12 messages Open this post in threaded view
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[math] "equals" in "Vector3D"

 Hello. Could we have a  boolean equals(Vector3D other,                 double tolerance) method? Or even   static boolean equals(Vector3D v1,                         Vector3D v2,                         double tolerance) that would return true if the components are equal within the given tolerance. Best, Gilles P.S. It seems that checking for exact equality (as the "equal(Object)"      method does) is not very useful: If the two vectors being compared      come from different computations, they will (most of the time) be      different although, at the precision-level, they should be considered      equal. --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] "equals" in "Vector3D"

 This is a generally useful thing to have, but there are multiple definitions for how you apply the tolerance.  You should file a JIRA and add a patch! Among the definitions that are commonly used, you will find: L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance All are useful. Which did you think you wanted? On Tue, Apr 28, 2009 at 6:23 AM, Gilles Sadowski < [hidden email]> wrote: > > Could we have a > >  boolean equals(Vector3D other, >                double tolerance) > > method? > Or even > >  static boolean equals(Vector3D v1, >                        Vector3D v2, >                        double tolerance) > > that would return true if the components are equal within the given > tolerance. > > > Best, > Gilles > > P.S. It seems that checking for exact equality (as the "equal(Object)" >     method does) is not very useful: If the two vectors being compared >     come from different computations, they will (most of the time) be >     different although, at the precision-level, they should be considered >     equal. > > --------------------------------------------------------------------- > To unsubscribe, e-mail: [hidden email] > For additional commands, e-mail: [hidden email] > > -- Ted Dunning, CTO DeepDyve 111 West Evelyn Ave. Ste. 202 Sunnyvale, CA 94086 www.deepdyve.com 858-414-0013 (m) 408-773-0220 (fax)
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Re: [math] "equals" in "Vector3D"

 Ted Dunning a écrit : > This is a generally useful thing to have, but there are multiple definitions > for how you apply the tolerance.  You should file a JIRA and add a patch! > > Among the definitions that are commonly used, you will find: > > L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance > L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance > L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance > > All are useful. I'll guess for 3D vector the L2-norm is the more useful as it is invariant when physical orthonormal frames are changed. I'll check in the variant you prefer. Luc > > Which did you think you wanted? > > On Tue, Apr 28, 2009 at 6:23 AM, Gilles Sadowski < > [hidden email]> wrote: > >> Could we have a >> >>  boolean equals(Vector3D other, >>                double tolerance) >> >> method? >> Or even >> >>  static boolean equals(Vector3D v1, >>                        Vector3D v2, >>                        double tolerance) >> >> that would return true if the components are equal within the given >> tolerance. >> >> >> Best, >> Gilles >> >> P.S. It seems that checking for exact equality (as the "equal(Object)" >>     method does) is not very useful: If the two vectors being compared >>     come from different computations, they will (most of the time) be >>     different although, at the precision-level, they should be considered >>     equal. >> >> --------------------------------------------------------------------- >> To unsubscribe, e-mail: [hidden email] >> For additional commands, e-mail: [hidden email] >> >> > > --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] "equals" in "Vector3D"

 That sounds very reasonable, but I wasn't the person with the need. Also, for equality checking, especially in 3D, all of these will be very, very close to the same.  For very high numbers of dimensions, the differences between boxes and balls becomes fairly extreme.  In particular, the corners of unit cubes (with a side length of 1) will begin to stick out of the unit sphere (with a DIAmeter of 2).  Beyond that point, things get very strange. On Tue, Apr 28, 2009 at 11:41 AM, Luc Maisonobe <[hidden email]>wrote: > Ted Dunning a écrit : > > This is a generally useful thing to have,... > > I'll guess for 3D vector the L2-norm is the more useful as it is > invariant when physical orthonormal frames are changed. > I'll check in the variant you prefer. >
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Re: [math] "equals" in "Vector3D"

 In reply to this post by Ted Dunning > Among the definitions that are commonly used, you will find: > > L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance > L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance > L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance                    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ I was thinking of that one. [Actually, I use it in unit tests...] [The L2-norm is already available through the "distance" method.] Gilles --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] "equals" in "Vector3D"

 How about: Vector3D {      ...      enum Norm { L_0, L_1, L_2, L_infinity};      static double distance(Vector3D a, Vector3D b, Norm n);      ... } ? You can then use distance(a, b, Vector3D.Norm.L_infinity) < epsilon It gives you what you want and it should be very recognizable to the reader of the code (subject to verification by all the readers out there). On Tue, Apr 28, 2009 at 1:55 PM, Gilles Sadowski < [hidden email]> wrote: > > Among the definitions that are commonly used, you will find: > > > > L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance > > L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance > > L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance >                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > I was thinking of that one. [Actually, I use it in unit tests...] > > [The L2-norm is already available through the "distance" method.] > > > Gilles > > --------------------------------------------------------------------- > To unsubscribe, e-mail: [hidden email] > For additional commands, e-mail: [hidden email] > > -- Ted Dunning, CTO DeepDyve 111 West Evelyn Ave. Ste. 202 Sunnyvale, CA 94086 www.deepdyve.com 858-414-0013 (m) 408-773-0220 (fax)
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Re: [math] "equals" in "Vector3D"

 In reply to this post by Luc Maisonobe > > L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance > > L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance > > L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance > > > > All are useful. > > I'll guess for 3D vector the L2-norm is the more useful as it is > invariant when physical orthonormal frames are changed. > I'll check in the variant you prefer. [Cf. my other reply.] Should I still create an issue? Best, Gilles --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] "equals" in "Vector3D"

 Absolutely. On Tue, Apr 28, 2009 at 2:10 PM, Gilles Sadowski < [hidden email]> wrote: > > I'll guess for 3D vector the L2-norm is the more useful as it is > > invariant when physical orthonormal frames are changed. > > I'll check in the variant you prefer. > > [Cf. my other reply.] > Should I still create an issue? > >
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Re: [math] "equals" in "Vector3D"

 In reply to this post by Gilles Sadowski Gilles Sadowski schrieb: >>> L1 norm: equals(a, b, tolerance) = sum(abs(a-b)) < tolerance >>> L2 norm: equals(a, b, tolerance) = sqrt(sum((a-b)^2)) < tolerance >>> L-infinity norm: equals(a, b, tolerance) = max(abs(a-b)) < tolerance >>> >>> All are useful. >> I'll guess for 3D vector the L2-norm is the more useful as it is >> invariant when physical orthonormal frames are changed. >> I'll check in the variant you prefer. > > [Cf. my other reply.] > Should I still create an issue? I'm currently not invovled in commons-math, but I've written substatntial amount of numeric software. My thought on this point is, that it is generally more feasible to implement a bunch on distance methods like   a.distance1(b)   ... L1-Norm   a.distance(b)    ... L1-Norm (this is usually what the user wants as default)   a.distanceInf(b) ... L∞-Norm and have the user decide on what is equal in his particular situation. There is a very good article on ieee754 equality under   http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htmwhich contains an excessive discussion about various "equality" approaches. IMHO it should be moreover considered to include the "AlomostEquals2sComplement" method of this paper into commons-math if not done so far.   Best regards,    Wolfgang --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]
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Re: [math] "equals" in "Vector3D"

 Hi.   > There is a very good article on ieee754 equality under > >   http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm> > which contains an excessive discussion about various "equality" approaches. > > IMHO it should be moreover considered to include the "AlomostEquals2sComplement" > method of this paper into commons-math if not done so far. It would be a nice addition to "util.MathUtils". I'll open another JIRA issue. Thanks, Gilles --------------------------------------------------------------------- To unsubscribe, e-mail: [hidden email] For additional commands, e-mail: [hidden email]