QMatrix4x4 *QVector3D Precision is not enough, how to improve it?
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@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
internally everything seems to be done in single-precision floating point (i.e. float) rather than double-precision (double type)
Until a few years back video cards only supported single precision floats, with the exception of cards specifically made for HPC applications, so there was (and there still is) no real reason to have the class use double precision. Furthermore, multiple transformations in sequence will always accumulate error, doesn't matter if you use floats or doubles, or even quadruple precision.
@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
multiple transformations in sequence will always accumulate error, doesn't matter if you use floats or doubles, or even quadruple precision
As @jimfar wrote, you can reduce the magnitude of the accumulated error by using higher-resolution/range number representations, assuming that the algorithms/equations you use are not ill-conditioned.
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do u have the opensource for do this? i wanna to replcae the QT scale ,rotate by QQuaternion ,and move ..
@jimfar
Have a look at the Eigen library: https://eigen.tuxfamily.org/dox/group__Geometry__Module.htmlor build your own vector and matrix classes https://en.wikipedia.org/wiki/Scaling_(geometry), https://en.wikipedia.org/wiki/Rotation_matrix
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thanks for ur two attention,i had already give the suggestion for Improve precision to "https://bugreports.qt.io/".and i now use GLm library. the librarys beecksche suggest i will take it into acount
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yes , multipling transformations in sequence will always accumulate error，but the margin of error is difference ,the vtk use double and its error is smaller than QT, comparing with the same operation
@jimfar said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
but the margin of error is difference ,the vtk use double and its error is smaller than QT, comparing with the same operation
@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
As @jimfar wrote, you can reduce the magnitude of the accumulated error by using higher-resolution/range number representations,
You are wrong.
assuming that the algorithms/equations you use are not ill-conditioned.
Matrix multiplication (and summation, which is what matrix multiplication boils down to) is numerically unstable, unless special care is taken. A bound on the input error of the matrix elements does not translate to a bound on the output error.
Read and abide by the Qt Code of Conduct
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@jimfar said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
but the margin of error is difference ,the vtk use double and its error is smaller than QT, comparing with the same operation
@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
As @jimfar wrote, you can reduce the magnitude of the accumulated error by using higher-resolution/range number representations,
You are wrong.
assuming that the algorithms/equations you use are not ill-conditioned.
Matrix multiplication (and summation, which is what matrix multiplication boils down to) is numerically unstable, unless special care is taken. A bound on the input error of the matrix elements does not translate to a bound on the output error.
@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
You are wrong
From now on, let's do everything in float then. Why did they even bother inventing double precision, I wonder... I'm sure that at CERN they only use floats for their matrix and tensor products.
I don't want to go into the details of numerical precision and stability and of how subtracting two almost identical values can lead to large errors etc... but you can improve such computations using tricks indeed. And once you apply those tricks, you do get better precision by using better resolution number formats.
http://www.oishi.info.waseda.ac.jp/~oishi/papers/OgRuOi05.pdf
The question then is of course if the precision gain you get using doubles is relevant or not for the targeted application.
Anyway... this is a Qt site, not a math forum.@kshegunov by the way: instead of telling people they're wrong, maybe it is more helpful to help with the question at hand, given your extensive expertise...
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@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
You are wrong
From now on, let's do everything in float then. Why did they even bother inventing double precision, I wonder... I'm sure that at CERN they only use floats for their matrix and tensor products.
I don't want to go into the details of numerical precision and stability and of how subtracting two almost identical values can lead to large errors etc... but you can improve such computations using tricks indeed. And once you apply those tricks, you do get better precision by using better resolution number formats.
http://www.oishi.info.waseda.ac.jp/~oishi/papers/OgRuOi05.pdf
The question then is of course if the precision gain you get using doubles is relevant or not for the targeted application.
Anyway... this is a Qt site, not a math forum.@kshegunov by the way: instead of telling people they're wrong, maybe it is more helpful to help with the question at hand, given your extensive expertise...
@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I'm sure that at CERN they only use floats for their matrix and tensor products.
I could ask my colleagues, if you're interested.
I don't want to go into the details of numerical precision and stability and of how subtracting two almost identical values can lead to large errors etc...
Kinda have to, as this is the original question.
but you can improve such computations using tricks indeed. And once you apply those tricks, you do get better precision by using better resolution number formats.
These are by no means tricks. Numerical analysis is a science of itself, but it does not depend on width of the floating point mantissa. You get better precision by using an appropriate algorithm, not by just extending the floating point format. Have you wondered why in the article you duly sourced, so much time is dedicated on the Kahan compensated summation and its related algorithms and not so much on whether a single or double precision is used?
Anyway... this is a Qt site, not a math forum.
Indeed, but the topic is relevant to both.
instead of telling people they're wrong, maybe it is more helpful to help with the question at hand, given your extensive expertise...
I hinted what a correct approach would be, but I could've elaborated, I'll grant you that.
@jimfar, Your problem stems from the following fact:
Each matrix multiplication will accumulate N times the error of each element (here N = 4 is the dimension of the matrix). Do that M times and you'd have total error in each element ofM * N. From the above rudimentary observation I could even estimate how many times you applied the transformation if0.00001is the relative error - roughly 25 times.What you should do is either one of two things:
- Provide a matrix multiplication that's stable, which is somewhat involved as it'd require you to implement compensated summations, and to keep the compensations for each element of the matrices.
OR
- Save the original orientation/position and have the changes be accumulated (i.e. rotation around x, y, z, translations and so on) in a numerically stable way (again think stable accumulators) and only at the end should you construct the transformation matrix and apply it. A letter of warning here - matrices in general do not commute so order matters.
Read and abide by the Qt Code of Conduct
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@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I'm sure that at CERN they only use floats for their matrix and tensor products.
I could ask my colleagues, if you're interested.
I don't want to go into the details of numerical precision and stability and of how subtracting two almost identical values can lead to large errors etc...
Kinda have to, as this is the original question.
but you can improve such computations using tricks indeed. And once you apply those tricks, you do get better precision by using better resolution number formats.
These are by no means tricks. Numerical analysis is a science of itself, but it does not depend on width of the floating point mantissa. You get better precision by using an appropriate algorithm, not by just extending the floating point format. Have you wondered why in the article you duly sourced, so much time is dedicated on the Kahan compensated summation and its related algorithms and not so much on whether a single or double precision is used?
Anyway... this is a Qt site, not a math forum.
Indeed, but the topic is relevant to both.
instead of telling people they're wrong, maybe it is more helpful to help with the question at hand, given your extensive expertise...
I hinted what a correct approach would be, but I could've elaborated, I'll grant you that.
@jimfar, Your problem stems from the following fact:
Each matrix multiplication will accumulate N times the error of each element (here N = 4 is the dimension of the matrix). Do that M times and you'd have total error in each element ofM * N. From the above rudimentary observation I could even estimate how many times you applied the transformation if0.00001is the relative error - roughly 25 times.What you should do is either one of two things:
- Provide a matrix multiplication that's stable, which is somewhat involved as it'd require you to implement compensated summations, and to keep the compensations for each element of the matrices.
OR
- Save the original orientation/position and have the changes be accumulated (i.e. rotation around x, y, z, translations and so on) in a numerically stable way (again think stable accumulators) and only at the end should you construct the transformation matrix and apply it. A letter of warning here - matrices in general do not commute so order matters.
@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I could ask my colleagues, if you're interested.
Are you actually on side? I used to live close by, and a friend of mine made his doctoral thesis there, mybe you crossed paths :-)
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@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I could ask my colleagues, if you're interested.
Are you actually on side? I used to live close by, and a friend of mine made his doctoral thesis there, mybe you crossed paths :-)
@J.Hilk said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
Are you actually on side?
No, I work in low energy nuclear, but I have colleagues both from uni and the institute that are doing the CERN dance (mainly with the CMS).
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@kshegunov said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I could ask my colleagues, if you're interested.
Are you actually on side? I used to live close by, and a friend of mine made his doctoral thesis there, mybe you crossed paths :-)
@J-Hilk Sorry for the confusion~~
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@J-Hilk Sorry for the confusion~~
@Diracsbracket
wrong @ target, I just quoted @kshegunov
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@Diracsbracket said in QMatrix4x4 *QVector3D Precision is not enough, how to improve it?:
I'm sure that at CERN they only use floats for their matrix and tensor products.
I could ask my colleagues, if you're interested.
I don't want to go into the details of numerical precision and stability and of how subtracting two almost identical values can lead to large errors etc...
Kinda have to, as this is the original question.
but you can improve such computations using tricks indeed. And once you apply those tricks, you do get better precision by using better resolution number formats.
These are by no means tricks. Numerical analysis is a science of itself, but it does not depend on width of the floating point mantissa. You get better precision by using an appropriate algorithm, not by just extending the floating point format. Have you wondered why in the article you duly sourced, so much time is dedicated on the Kahan compensated summation and its related algorithms and not so much on whether a single or double precision is used?
Anyway... this is a Qt site, not a math forum.
Indeed, but the topic is relevant to both.
instead of telling people they're wrong, maybe it is more helpful to help with the question at hand, given your extensive expertise...
I hinted what a correct approach would be, but I could've elaborated, I'll grant you that.
@jimfar, Your problem stems from the following fact:
Each matrix multiplication will accumulate N times the error of each element (here N = 4 is the dimension of the matrix). Do that M times and you'd have total error in each element ofM * N. From the above rudimentary observation I could even estimate how many times you applied the transformation if0.00001is the relative error - roughly 25 times.What you should do is either one of two things:
- Provide a matrix multiplication that's stable, which is somewhat involved as it'd require you to implement compensated summations, and to keep the compensations for each element of the matrices.
OR
- Save the original orientation/position and have the changes be accumulated (i.e. rotation around x, y, z, translations and so on) in a numerically stable way (again think stable accumulators) and only at the end should you construct the transformation matrix and apply it. A letter of warning here - matrices in general do not commute so order matters.
I could ask my colleagues, if you're interested
Yes please, ask if they use floats a lot, that would be fun to know ^^. Since @jimfar is interested in greater precision, maybe they would be so kind as to explain how they do such matrix operations at high precision...
These are by no means tricks.
Well, to me they are, as they are just tools to get the actual work done.
You get better precision by using an appropriate algorithm, not by just extending the floating point format. Have you wondered why in the article you duly sourced, so much time is dedicated on the Kahan compensated summation and its related algorithms and not so much on whether a single or double precision is used?
My "tricks" also included those algorithms, if you read my post correctly.
matrices in general do not commute so order matters.
Thanks for this reminder of very basic matrix arithmetic.
You always seem to want to have the last word, so I will gladly grant it to you: you are right! And I'm an idiot (that part is really true). I hope this closes the matter and that I can go back and try to learn some QML from this forum ;-)
