I feel the inverse of a matrix should be part of the mathematical functions in stock openSCAD. That is not too difficult to do I suppose and makes the calculations related to linear algebra much simpler. I realised this while trying to calculate the intersection point between 2 straight lines, where 2 simple equations with 2 unknowns need to be calculated. It is possible to do such calculations by hand but would be much simpler if that can be part of the software algorithm. Thanks

I implemented QR factorization in BOSL2, which makes it possible to solve linear systems of equations, and in the rare case you need it, to compute a matrix inverse as well. (Note: matrix inverses should generally be avoided because they are computationally inefficient and also less accurate.) On Fri, Feb 7, 2025 at 11:43 PM Sanjeev Prabhakar via Discuss < discuss@lists.openscad.org> wrote: > I feel the inverse of a matrix should be part of the mathematical > functions in stock openSCAD. > > That is not too difficult to do I suppose and makes the calculations > related to linear algebra much simpler. > > I realised this while trying to calculate the intersection point between 2 > straight lines, where 2 simple equations with 2 unknowns need to be > calculated. > > It is possible to do such calculations by hand but would be much simpler > if that can be part of the software algorithm. > > Thanks > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Only when the determinant is zero it is not possible to calculate inverse. But there is a way to avoid that easily if you Rotate the model by very small amount maybe .0001 deg. On Sat, 8 Feb, 2025, 10:17 am Adrian Mariano via Discuss, < discuss@lists.openscad.org> wrote: > I implemented QR factorization in BOSL2, which makes it possible to solve > linear systems of equations, and in the rare case you need it, to compute a > matrix inverse as well. (Note: matrix inverses should generally be avoided > because they are computationally inefficient and also less accurate.) > > On Fri, Feb 7, 2025 at 11:43 PM Sanjeev Prabhakar via Discuss < > discuss@lists.openscad.org> wrote: > >> I feel the inverse of a matrix should be part of the mathematical >> functions in stock openSCAD. >> >> That is not too difficult to do I suppose and makes the calculations >> related to linear algebra much simpler. >> >> I realised this while trying to calculate the intersection point between >> 2 straight lines, where 2 simple equations with 2 unknowns need to be >> calculated. >> >> It is possible to do such calculations by hand but would be much simpler >> if that can be part of the software algorithm. >> >> Thanks >> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

In pythonscad there has been "divmatrix" next to multmatrix for a long time and it exactly serves that purpose On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < discuss@lists.openscad.org> wrote: > I feel the inverse of a matrix should be part of the mathematical > functions in stock openSCAD. > > That is not too difficult to do I suppose and makes the calculations > related to linear algebra much simpler. > > I realised this while trying to calculate the intersection point between 2 > straight lines, where 2 simple equations with 2 unknowns need to be > calculated. > > It is possible to do such calculations by hand but would be much simpler > if that can be part of the software algorithm. > > Thanks > > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Sanjeev, you can calculate the inverse, sure, but if you are trying to solve an equation like Ax=b you should NOT calculate the inverse and compute inverse(A)*b because this is an inaccurate and slow way to get the solution to that problem. It is a numerically unstable method for solving the problem. And computing the inverse actually requires solving a whole series of Ax=b problems. On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < discuss@lists.openscad.org> wrote: > In pythonscad there has been "divmatrix" next to multmatrix for a long > time and it exactly serves that purpose > > > > > On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < > discuss@lists.openscad.org> wrote: > >> I feel the inverse of a matrix should be part of the mathematical >> functions in stock openSCAD. >> >> That is not too difficult to do I suppose and makes the calculations >> related to linear algebra much simpler. >> >> I realised this while trying to calculate the intersection point between >> 2 straight lines, where 2 simple equations with 2 unknowns need to be >> calculated. >> >> It is possible to do such calculations by hand but would be much simpler >> if that can be part of the software algorithm. >> >> Thanks >> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

I agree on speed but I am really wondering what has lead you to such a conclusion about the accuracy. Although I use 2 different ways to calculate intersections. Inverse matrix method takes longer but the results are comparable with direct calculation method by a derived formulae and it is much simpler to work with, atleast in python. I am not sure about openscad. If there is any other method, which is better and faster, it will be interesting to know. On Sat, 8 Feb, 2025, 6:28 pm Adrian Mariano via Discuss, < discuss@lists.openscad.org> wrote: > Sanjeev, you can calculate the inverse, sure, but if you are trying to > solve an equation like Ax=b you should NOT calculate the inverse and > compute inverse(A)*b because this is an inaccurate and slow way to get the > solution to that problem. It is a numerically unstable method for solving > the problem. And computing the inverse actually requires solving a whole > series of Ax=b problems. > > On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < > discuss@lists.openscad.org> wrote: > >> In pythonscad there has been "divmatrix" next to multmatrix for a long >> time and it exactly serves that purpose >> >> >> >> >> On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < >> discuss@lists.openscad.org> wrote: >> >>> I feel the inverse of a matrix should be part of the mathematical >>> functions in stock openSCAD. >>> >>> That is not too difficult to do I suppose and makes the calculations >>> related to linear algebra much simpler. >>> >>> I realised this while trying to calculate the intersection point between >>> 2 straight lines, where 2 simple equations with 2 unknowns need to be >>> calculated. >>> >>> It is possible to do such calculations by hand but would be much simpler >>> if that can be part of the software algorithm. >>> >>> Thanks >>> >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

I am Wondering after all, why you need Matrix Inversion in Openscad, when there Is in numpy. Am Samstag, 8. Februar 2025 schrieb Sanjeev Prabhakar via Discuss < discuss@lists.openscad.org>: > I agree on speed but I am really wondering what has lead you to such a > conclusion about the accuracy. > > Although I use 2 different ways to calculate intersections. Inverse matrix > method takes longer but the results are comparable with direct calculation > method by a derived formulae and it is much simpler to work with, atleast > in python. > > I am not sure about openscad. > > If there is any other method, which is better and faster, it will be > interesting to know. > > > On Sat, 8 Feb, 2025, 6:28 pm Adrian Mariano via Discuss, < > discuss@lists.openscad.org> wrote: > >> Sanjeev, you can calculate the inverse, sure, but if you are trying to >> solve an equation like Ax=b you should NOT calculate the inverse and >> compute inverse(A)*b because this is an inaccurate and slow way to get the >> solution to that problem. It is a numerically unstable method for solving >> the problem. And computing the inverse actually requires solving a whole >> series of Ax=b problems. >> >> On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < >> discuss@lists.openscad.org> wrote: >> >>> In pythonscad there has been "divmatrix" next to multmatrix for a long >>> time and it exactly serves that purpose >>> >>> >>> >>> >>> On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < >>> discuss@lists.openscad.org> wrote: >>> >>>> I feel the inverse of a matrix should be part of the mathematical >>>> functions in stock openSCAD. >>>> >>>> That is not too difficult to do I suppose and makes the calculations >>>> related to linear algebra much simpler. >>>> >>>> I realised this while trying to calculate the intersection point >>>> between 2 straight lines, where 2 simple equations with 2 unknowns need to >>>> be calculated. >>>> >>>> It is possible to do such calculations by hand but would be much >>>> simpler if that can be part of the software algorithm. >>>> >>>> Thanks >>>> >>>> _______________________________________________ >>>> OpenSCAD mailing list >>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>> >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> > -- Null

See the answer in https://math.stackexchange.com/questions/4297923/reasoning-behind-choosing-appropriate-decomposition-when-solving-linear-equation, it is quite detailed. Long story short: Computing the inverse is numerically unstable, there are better approaches. On Sat, Feb 8, 2025, 11:15 PM Guenther Sohler via Discuss < discuss@lists.openscad.org> wrote: > I am Wondering after all, why you need Matrix Inversion in Openscad, when > there Is in numpy. > > > Am Samstag, 8. Februar 2025 schrieb Sanjeev Prabhakar via Discuss < > discuss@lists.openscad.org>: > >> I agree on speed but I am really wondering what has lead you to such a >> conclusion about the accuracy. >> >> Although I use 2 different ways to calculate intersections. Inverse >> matrix method takes longer but the results are comparable with direct >> calculation method by a derived formulae and it is much simpler to work >> with, atleast in python. >> >> I am not sure about openscad. >> >> If there is any other method, which is better and faster, it will be >> interesting to know. >> >> >> On Sat, 8 Feb, 2025, 6:28 pm Adrian Mariano via Discuss, < >> discuss@lists.openscad.org> wrote: >> >>> Sanjeev, you can calculate the inverse, sure, but if you are trying to >>> solve an equation like Ax=b you should NOT calculate the inverse and >>> compute inverse(A)*b because this is an inaccurate and slow way to get the >>> solution to that problem. It is a numerically unstable method for solving >>> the problem. And computing the inverse actually requires solving a whole >>> series of Ax=b problems. >>> >>> On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < >>> discuss@lists.openscad.org> wrote: >>> >>>> In pythonscad there has been "divmatrix" next to multmatrix for a long >>>> time and it exactly serves that purpose >>>> >>>> >>>> >>>> >>>> On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < >>>> discuss@lists.openscad.org> wrote: >>>> >>>>> I feel the inverse of a matrix should be part of the mathematical >>>>> functions in stock openSCAD. >>>>> >>>>> That is not too difficult to do I suppose and makes the calculations >>>>> related to linear algebra much simpler. >>>>> >>>>> I realised this while trying to calculate the intersection point >>>>> between 2 straight lines, where 2 simple equations with 2 unknowns need to >>>>> be calculated. >>>>> >>>>> It is possible to do such calculations by hand but would be much >>>>> simpler if that can be part of the software algorithm. >>>>> >>>>> Thanks >>>>> >>>>> _______________________________________________ >>>>> OpenSCAD mailing list >>>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>>> >>>> _______________________________________________ >>>> OpenSCAD mailing list >>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>> >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> > > -- > Null > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

Not for me, i thought this is trivial to do in openscad and can help openscad community for the people who don't want to experiment with other languages. On Sat, 8 Feb, 2025, 8:45 pm Guenther Sohler via Discuss, < discuss@lists.openscad.org> wrote: > I am Wondering after all, why you need Matrix Inversion in Openscad, when > there Is in numpy. > > > Am Samstag, 8. Februar 2025 schrieb Sanjeev Prabhakar via Discuss < > discuss@lists.openscad.org>: > >> I agree on speed but I am really wondering what has lead you to such a >> conclusion about the accuracy. >> >> Although I use 2 different ways to calculate intersections. Inverse >> matrix method takes longer but the results are comparable with direct >> calculation method by a derived formulae and it is much simpler to work >> with, atleast in python. >> >> I am not sure about openscad. >> >> If there is any other method, which is better and faster, it will be >> interesting to know. >> >> >> On Sat, 8 Feb, 2025, 6:28 pm Adrian Mariano via Discuss, < >> discuss@lists.openscad.org> wrote: >> >>> Sanjeev, you can calculate the inverse, sure, but if you are trying to >>> solve an equation like Ax=b you should NOT calculate the inverse and >>> compute inverse(A)*b because this is an inaccurate and slow way to get the >>> solution to that problem. It is a numerically unstable method for solving >>> the problem. And computing the inverse actually requires solving a whole >>> series of Ax=b problems. >>> >>> On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < >>> discuss@lists.openscad.org> wrote: >>> >>>> In pythonscad there has been "divmatrix" next to multmatrix for a long >>>> time and it exactly serves that purpose >>>> >>>> >>>> >>>> >>>> On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < >>>> discuss@lists.openscad.org> wrote: >>>> >>>>> I feel the inverse of a matrix should be part of the mathematical >>>>> functions in stock openSCAD. >>>>> >>>>> That is not too difficult to do I suppose and makes the calculations >>>>> related to linear algebra much simpler. >>>>> >>>>> I realised this while trying to calculate the intersection point >>>>> between 2 straight lines, where 2 simple equations with 2 unknowns need to >>>>> be calculated. >>>>> >>>>> It is possible to do such calculations by hand but would be much >>>>> simpler if that can be part of the software algorithm. >>>>> >>>>> Thanks >>>>> >>>>> _______________________________________________ >>>>> OpenSCAD mailing list >>>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>>> >>>> _______________________________________________ >>>> OpenSCAD mailing list >>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>> >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> > > -- > Null > _______________________________________________ > OpenSCAD mailing list > To unsubscribe send an email to discuss-leave@lists.openscad.org >

It is a well-known fact in numerical analysis that the inverse is ill-conditioned and as a result the bounds on error when you use inverse are bad. The error is related to the condition number and the difference may not be apparent or problematic for well-conditioned problems. The MATLAB documentation has an example where the error is 1e-15 with LU decomposition and 1e-6 with inverse. https://www.mathworks.com/help/matlab/ref/inv.html Three methods are commonly used for solving Ax=b that are stable and have better error bounds than matrix inverse. The most stable method is eigenvalue decomposition (or SVD). The other choices are QR factorization and LU decomposition (aka Gaussian elimination). The second two produce a decomposition of A into a triangular matrix so that then the problem can be solved by back-substitution. I implemented QR factorization in OpenSCAD. Note that eigenvalue/svd is very difficult to implement. (I have written an eigenvalue solver in OpenSCAD, but there doesn't seem to be a need for this.) But QR and LU factorization are simple methods that are easy to code. Note to Guenther: I use pure OpenSCAD, so I need linear equation solutions natively. On Sat, Feb 8, 2025 at 10:04 AM Sanjeev Prabhakar <sprabhakar2006@gmail.com> wrote: > I agree on speed but I am really wondering what has lead you to such a > conclusion about the accuracy. > > Although I use 2 different ways to calculate intersections. Inverse matrix > method takes longer but the results are comparable with direct calculation > method by a derived formulae and it is much simpler to work with, atleast > in python. > > I am not sure about openscad. > > If there is any other method, which is better and faster, it will be > interesting to know. > > > On Sat, 8 Feb, 2025, 6:28 pm Adrian Mariano via Discuss, < > discuss@lists.openscad.org> wrote: > >> Sanjeev, you can calculate the inverse, sure, but if you are trying to >> solve an equation like Ax=b you should NOT calculate the inverse and >> compute inverse(A)*b because this is an inaccurate and slow way to get the >> solution to that problem. It is a numerically unstable method for solving >> the problem. And computing the inverse actually requires solving a whole >> series of Ax=b problems. >> >> On Sat, Feb 8, 2025 at 1:51 AM Guenther Sohler via Discuss < >> discuss@lists.openscad.org> wrote: >> >>> In pythonscad there has been "divmatrix" next to multmatrix for a long >>> time and it exactly serves that purpose >>> >>> >>> >>> >>> On Sat, Feb 8, 2025 at 5:44 AM Sanjeev Prabhakar via Discuss < >>> discuss@lists.openscad.org> wrote: >>> >>>> I feel the inverse of a matrix should be part of the mathematical >>>> functions in stock openSCAD. >>>> >>>> That is not too difficult to do I suppose and makes the calculations >>>> related to linear algebra much simpler. >>>> >>>> I realised this while trying to calculate the intersection point >>>> between 2 straight lines, where 2 simple equations with 2 unknowns need to >>>> be calculated. >>>> >>>> It is possible to do such calculations by hand but would be much >>>> simpler if that can be part of the software algorithm. >>>> >>>> Thanks >>>> >>>> _______________________________________________ >>>> OpenSCAD mailing list >>>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>>> >>> _______________________________________________ >>> OpenSCAD mailing list >>> To unsubscribe send an email to discuss-leave@lists.openscad.org >>> >> _______________________________________________ >> OpenSCAD mailing list >> To unsubscribe send an email to discuss-leave@lists.openscad.org >> >