# [Scilab-users] ticks_mark property in Scilab 6.0.1

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## [Scilab-users] ticks_mark property in Scilab 6.0.1

 Dear all,   Since Scilab 6.0.1 the ticks_mark property seems to be broken: the following code works as expected in Scilab 5.5.2 but does not display the formatted ticks in Scilab 6.0.1.   `// test of ticks_format property` `// PM 2019-01-08` ` ` `x = [0:%pi/100:2*%pi]` `plot2d(x,sin(x))` `xgrid` ` ` `af=gca()` `// ticks_format ok, in Scilab 5.5.2 and broken in Scilab 6.0.1` `af.ticks_format = ["%.1e","%.2f","%.1f"]  //x-axis in exp notation with 1 decimal place and y-axis with 2 decimal places`     There is a bug 14790 reported Scilab's Bug Tracker.   For publication it is generally vital to have a specified number of decimal places on the axes. So, will this be be solved in the next release or is there a clue to get the good behavior without using ticks_format?   Thanks a lot.   Patrice MEGRET    _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## [Scilab-users] improve accuracy of roots

 Dear all, Consider this code: // Define polynomial variable p = poly(0, 'p', 'roots'); // Define fourth degree polynomial R = (1 + p)^4; // Find its roots z = roots(R) The result (Scilab 6.0.1) is   z  =    -1.0001886    -1. + 0.0001886i    -1. - 0.0001886i    -0.9998114 It should be something closer to    -1.    -1.    -1.    -1. Using these roots C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4))) yield seemingly accurate coefficients   C  =     1.   4.   6.   4.   1. but C - [1  4  6 4 1] shows the actual error: ans  =     3.775D-15   1.243D-14   1.155D-14   4.441D-15   0. This is acceptable for the coefficients, but the error in the roots is too large. Somehow the errors cancel out when  assembling back the polynomial but each individual zero should be closer to the theoretical value Is there some way to improve the accuracy? Regards, Federico Miyara --- El software de antivirus Avast ha analizado este correo electrónico en busca de virus. https://www.avast.com/antivirus_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: improve accuracy of roots

 Hello, > De : users [mailto:[hidden email]] De la part de Federico Miyara > Envoyé : jeudi 10 janvier 2019 00:32 > > // Define fourth degree polynomial > R = (1 + p)^4; > > // Find its roots > z = roots(R) > [...] > but the error in the roots is too large. The help page mentions that: "This implies that just representing the coefficients as IEEE doubles changes the roots." https://help.scilab.org/docs/6.0.1/en_US/roots.html> Is there some way to improve the accuracy? The "f" option does not work so I have no clue here, sorry. Regards -- Christophe Dang Ngoc Chan Mechanical calculation engineer Public This e-mail may contain confidential and/or privileged information. If you are not the intended recipient (or have received this e-mail in error), please notify the sender immediately and destroy this e-mail. Any unauthorized copying, disclosure or distribution of the material in this e-mail is strictly forbidden. _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: improve accuracy of roots

 In reply to this post by fmiyara Hello, I tried this correction to the initial roots z: z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')  ans  =   -1. - 1.923D-13i   -1. + 1.189D-12i   -1. - 1.189D-12i   -1. - 1.919D-13i // Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1): z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') z2 - Z  ans  =    2.233D-08 - 1.923D-13i   -2.968D-08 + 1.189D-12i   -2.968D-08 - 1.189D-12i    2.131D-08 - 1.919D-13i The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8. HTH Denis -----Message d'origine----- De : users [mailto:[hidden email]] De la part de Federico Miyara Envoyé : jeudi 10 janvier 2019 00:32 À : [hidden email] Objet : [Scilab-users] improve accuracy of roots Dear all, Consider this code: // Define polynomial variable p = poly(0, 'p', 'roots'); // Define fourth degree polynomial R = (1 + p)^4; // Find its roots z = roots(R) The result (Scilab 6.0.1) is   z  =    -1.0001886    -1. + 0.0001886i    -1. - 0.0001886i    -0.9998114 It should be something closer to    -1.    -1.    -1.    -1. Using these roots C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4))) yield seemingly accurate coefficients   C  =     1.   4.   6.   4.   1. but C - [1  4  6 4 1] shows the actual error: ans  =     3.775D-15   1.243D-14   1.155D-14   4.441D-15   0. This is acceptable for the coefficients, but the error in the roots is too large. Somehow the errors cancel out when  assembling back the polynomial but each individual zero should be closer to the theoretical value Is there some way to improve the accuracy? Regards, Federico Miyara --- El software de antivirus Avast ha analizado este correo electrónico en busca de virus. https://www.avast.com/antivirus_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users Denis Crété
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## Re: improve accuracy of roots

 Hi, This behavior has already been discussed here : http://bugzilla.scilab.org/show_bug.cgi?id=15349S. Le 10/01/2019 à 14:32, CRETE Denis a écrit : > Hello, > I tried this correction to the initial roots z: > > z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') >   ans  = > >    -1. - 1.923D-13i >    -1. + 1.189D-12i >    -1. - 1.189D-12i >    -1. - 1.919D-13i > > // Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1): > z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') > z2 - Z >   ans  = > >     2.233D-08 - 1.923D-13i >    -2.968D-08 + 1.189D-12i >    -2.968D-08 - 1.189D-12i >     2.131D-08 - 1.919D-13i > > The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8. > > HTH > Denis > > -----Message d'origine----- > De : users [mailto:[hidden email]] De la part de Federico Miyara > Envoyé : jeudi 10 janvier 2019 00:32 > À : [hidden email] > Objet : [Scilab-users] improve accuracy of roots > > > Dear all, > > Consider this code: > > // Define polynomial variable > p = poly(0, 'p', 'roots'); > > // Define fourth degree polynomial > R = (1 + p)^4; > > // Find its roots > z = roots(R) > > The result (Scilab 6.0.1) is > >    z  = > >     -1.0001886 >     -1. + 0.0001886i >     -1. - 0.0001886i >     -0.9998114 > > It should be something closer to > >     -1. >     -1. >     -1. >     -1. > > Using these roots > > C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4))) > > yield seemingly accurate coefficients >    C  = > >      1.   4.   6.   4.   1. > > > but > > C - [1  4  6 4 1] > > shows the actual error: > > ans  = > >      3.775D-15   1.243D-14   1.155D-14   4.441D-15   0. > > This is acceptable for the coefficients, but the error in the roots is > too large. Somehow the errors cancel out when  assembling back the > polynomial but each individual zero should be closer to the theoretical > value > > Is there some way to improve the accuracy? > > Regards, > > Federico Miyara > > > > > --- > El software de antivirus Avast ha analizado este correo electrónico en busca de virus. > https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/www.avast.com/antivirus> > _______________________________________________ > users mailing list > [hidden email] > https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users> _______________________________________________ > users mailing list > [hidden email] > https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users-- Stéphane Mottelet Ingénieur de recherche EA 4297 Transformations Intégrées de la Matière Renouvelable Département Génie des Procédés Industriels Sorbonne Universités - Université de Technologie de Compiègne CS 60319, 60203 Compiègne cedex Tel : +33(0)344234688 http://www.utc.fr/~mottelet_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: improve accuracy of roots

In reply to this post by Denis Crété

Denis,

Thank you.

If this were really a general solution it would be great, since it improves the root accuracy by several orders, but I don't fully get the rationale behind this method.

It seems you are trying to apply a variant of the Raphson-Newton method, aren't you?

However, in cases like this, in which there are repeated roots, the derivative approaches zero as you get closer to the root, but the polynomial goes to zero faster.

In that case the factor 4 may imlpy that the next approximation gets closer to the actual root. But this is speculation. It   could also overshoot.

Regards,

Federico Miyara

On 10/01/2019 10:32, CRETE Denis wrote:
```Hello,
I tried this correction to the initial roots z:

z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
ans  =

-1. - 1.923D-13i
-1. + 1.189D-12i
-1. - 1.189D-12i
-1. - 1.919D-13i

// Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1):
z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
z2 - Z
ans  =

2.233D-08 - 1.923D-13i
-2.968D-08 + 1.189D-12i
-2.968D-08 - 1.189D-12i
2.131D-08 - 1.919D-13i

The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8.

HTH
Denis

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : jeudi 10 janvier 2019 00:32
À : [hidden email]
Objet : [Scilab-users] improve accuracy of roots

Dear all,

Consider this code:

// Define polynomial variable
p = poly(0, 'p', 'roots');

// Define fourth degree polynomial
R = (1 + p)^4;

// Find its roots
z = roots(R)

The result (Scilab 6.0.1) is

z  =

-1.0001886
-1. + 0.0001886i
-1. - 0.0001886i
-0.9998114

It should be something closer to

-1.
-1.
-1.
-1.

Using these roots

C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4)))

yield seemingly accurate coefficients
C  =

1.   4.   6.   4.   1.

but

C - [1  4  6 4 1]

shows the actual error:

ans  =

3.775D-15   1.243D-14   1.155D-14   4.441D-15   0.

This is acceptable for the coefficients, but the error in the roots is
too large. Somehow the errors cancel out when  assembling back the
polynomial but each individual zero should be closer to the theoretical
value

Is there some way to improve the accuracy?

Regards,

Federico Miyara

---
El software de antivirus Avast ha analizado este correo electrónico en busca de virus.
https://www.avast.com/antivirus

_______________________________________________
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[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
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[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```

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## Re: improve accuracy of roots

 In reply to this post by Denis Crété Denis, I've found the correction here, https://en.wikipedia.org/wiki/Newton%27s_methodIt is useful to accelerate convergence in case of multiple roots, but I guess it is not valid to apply it once to improve accuracy because of the risk of overshoot. Regards, Federico Miyara On 10/01/2019 10:32, CRETE Denis wrote: > Hello, > I tried this correction to the initial roots z: > > z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') >   ans  = > >    -1. - 1.923D-13i >    -1. + 1.189D-12i >    -1. - 1.189D-12i >    -1. - 1.919D-13i > > // Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1): > z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') > z2 - Z >   ans  = > >     2.233D-08 - 1.923D-13i >    -2.968D-08 + 1.189D-12i >    -2.968D-08 - 1.189D-12i >     2.131D-08 - 1.919D-13i > > The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8. > > HTH > Denis > > -----Message d'origine----- > De : users [mailto:[hidden email]] De la part de Federico Miyara > Envoyé : jeudi 10 janvier 2019 00:32 > À : [hidden email] > Objet : [Scilab-users] improve accuracy of roots > > > Dear all, > > Consider this code: > > // Define polynomial variable > p = poly(0, 'p', 'roots'); > > // Define fourth degree polynomial > R = (1 + p)^4; > > // Find its roots > z = roots(R) > > The result (Scilab 6.0.1) is > >    z  = > >     -1.0001886 >     -1. + 0.0001886i >     -1. - 0.0001886i >     -0.9998114 > > It should be something closer to > >     -1. >     -1. >     -1. >     -1. > > Using these roots > > C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4))) > > yield seemingly accurate coefficients >    C  = > >      1.   4.   6.   4.   1. > > > but > > C - [1  4  6 4 1] > > shows the actual error: > > ans  = > >      3.775D-15   1.243D-14   1.155D-14   4.441D-15   0. > > This is acceptable for the coefficients, but the error in the roots is > too large. Somehow the errors cancel out when  assembling back the > polynomial but each individual zero should be closer to the theoretical > value > > Is there some way to improve the accuracy? > > Regards, > > Federico Miyara > > > > > --- > El software de antivirus Avast ha analizado este correo electrónico en busca de virus. > https://www.avast.com/antivirus> > _______________________________________________ > users mailing list > [hidden email] > http://lists.scilab.org/mailman/listinfo/users> _______________________________________________ > users mailing list > [hidden email] > http://lists.scilab.org/mailman/listinfo/users> > _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: improve accuracy of roots

 Thank you Frederico! According to the page you refer to, the method seems to converge more rapidly with this factor equal to the multiplicity of the root. About overshoot, it is well known to occur for |x|^a where a <1. But for a>1, the risk of overshoot with the Newton-Raphson method seems to be very small... Best regards Denis [@@ THALES GROUP INTERNAL @@] Unité Mixte de Physique CNRS / THALES 1 Avenue Augustin Fresnel 91767 Palaiseau CEDEx - France Tel : +33 (0)1 69 41 58 52 Fax : +33 (0)1 69 41 58 78 e-mail :  [hidden email]  http://www.trt.thalesgroup.com/ump-cnrs-thales http://www.research.thalesgroup.com-----Message d'origine----- De : users [mailto:[hidden email]] De la part de Federico Miyara Envoyé : samedi 12 janvier 2019 07:52 À : Users mailing list for Scilab Objet : Re: [Scilab-users] improve accuracy of roots Denis, I've found the correction here, https://en.wikipedia.org/wiki/Newton%27s_methodIt is useful to accelerate convergence in case of multiple roots, but I guess it is not valid to apply it once to improve accuracy because of the risk of overshoot. Regards, Federico Miyara On 10/01/2019 10:32, CRETE Denis wrote: > Hello, > I tried this correction to the initial roots z: > > z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') >   ans  = > >    -1. - 1.923D-13i >    -1. + 1.189D-12i >    -1. - 1.189D-12i >    -1. - 1.919D-13i > > // Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1): > z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))') > z2 - Z >   ans  = > >     2.233D-08 - 1.923D-13i >    -2.968D-08 + 1.189D-12i >    -2.968D-08 - 1.189D-12i >     2.131D-08 - 1.919D-13i > > The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8. > > HTH > Denis > > -----Message d'origine----- > De : users [mailto:[hidden email]] De la part de Federico Miyara > Envoyé : jeudi 10 janvier 2019 00:32 > À : [hidden email] > Objet : [Scilab-users] improve accuracy of roots > > > Dear all, > > Consider this code: > > // Define polynomial variable > p = poly(0, 'p', 'roots'); > > // Define fourth degree polynomial > R = (1 + p)^4; > > // Find its roots > z = roots(R) > > The result (Scilab 6.0.1) is > >    z  = > >     -1.0001886 >     -1. + 0.0001886i >     -1. - 0.0001886i >     -0.9998114 > > It should be something closer to > >     -1. >     -1. >     -1. >     -1. > > Using these roots > > C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4))) > > yield seemingly accurate coefficients >    C  = > >      1.   4.   6.   4.   1. > > > but > > C - [1  4  6 4 1] > > shows the actual error: > > ans  = > >      3.775D-15   1.243D-14   1.155D-14   4.441D-15   0. > > This is acceptable for the coefficients, but the error in the roots is > too large. Somehow the errors cancel out when  assembling back the > polynomial but each individual zero should be closer to the theoretical > value > > Is there some way to improve the accuracy? > > Regards, > > Federico Miyara > > > > > --- > El software de antivirus Avast ha analizado este correo electrónico en busca de virus. > https://www.avast.com/antivirus> > _______________________________________________ > users mailing list > [hidden email] > http://lists.scilab.org/mailman/listinfo/users> _______________________________________________ > users mailing list > [hidden email] > http://lists.scilab.org/mailman/listinfo/users> > _______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users Denis Crété
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## Re: improve accuracy of roots

Denis,

What I meant is that convergence is a limiting process. On average, as the number of iterations rises you´ll be closer to the limit, bu there is no guarantee that any single iteration will bring you any closer; it may be a question of luck. Maybe (though it would require a proof, it is not self-evident for me) in the exact case of a single multiple root as (x - a)^n the convergence process is monotonous, but what if you have (x - a1)* ... * (x  - an) where ak are all very similar but not identical, say, with relative differences of the order of those reported by the application of the regular version  of roots.
Regards,

Federico Miyara

On 14/01/2019 13:47, CRETE Denis wrote:
```Thank you Frederico!
According to the page you refer to, the method seems to converge more rapidly with this factor equal to the multiplicity of the root.
About overshoot, it is well known to occur for |x|^a where a <1. But for a>1, the risk of overshoot with the Newton-Raphson method seems to be very small...
Best regards
Denis

[@@ THALES GROUP INTERNAL @@]

Unité Mixte de Physique CNRS / THALES
1 Avenue Augustin Fresnel
91767 Palaiseau CEDEx - France
Tel : +33 (0)1 69 41 58 52 Fax : +33 (0)1 69 41 58 78
e-mail :
[hidden email] [hidden email]
http://www.trt.thalesgroup.com/ump-cnrs-thales
http://www.research.thalesgroup.com

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : samedi 12 janvier 2019 07:52
À : Users mailing list for Scilab
Objet : Re: [Scilab-users] improve accuracy of roots

Denis,

I've found the correction here,

https://en.wikipedia.org/wiki/Newton%27s_method

It is useful to accelerate convergence in case of multiple roots, but I
guess it is not valid to apply it once to improve accuracy because of
the risk of overshoot.

Regards,

Federico Miyara

On 10/01/2019 10:32, CRETE Denis wrote:
```
```Hello,
I tried this correction to the initial roots z:

z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
ans  =

-1. - 1.923D-13i
-1. + 1.189D-12i
-1. - 1.189D-12i
-1. - 1.919D-13i

// Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1):
z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
z2 - Z
ans  =

2.233D-08 - 1.923D-13i
-2.968D-08 + 1.189D-12i
-2.968D-08 - 1.189D-12i
2.131D-08 - 1.919D-13i

The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8.

HTH
Denis

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : jeudi 10 janvier 2019 00:32
À : [hidden email]
Objet : [Scilab-users] improve accuracy of roots

Dear all,

Consider this code:

// Define polynomial variable
p = poly(0, 'p', 'roots');

// Define fourth degree polynomial
R = (1 + p)^4;

// Find its roots
z = roots(R)

The result (Scilab 6.0.1) is

z  =

-1.0001886
-1. + 0.0001886i
-1. - 0.0001886i
-0.9998114

It should be something closer to

-1.
-1.
-1.
-1.

Using these roots

C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4)))

yield seemingly accurate coefficients
C  =

1.   4.   6.   4.   1.

but

C - [1  4  6 4 1]

shows the actual error:

ans  =

3.775D-15   1.243D-14   1.155D-14   4.441D-15   0.

This is acceptable for the coefficients, but the error in the roots is
too large. Somehow the errors cancel out when  assembling back the
polynomial but each individual zero should be closer to the theoretical
value

Is there some way to improve the accuracy?

Regards,

Federico Miyara

---
El software de antivirus Avast ha analizado este correo electrónico en busca de virus.
https://www.avast.com/antivirus

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```
```_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```

 Libre de virus. www.avast.com

_______________________________________________
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## [Scilab-users] Seemingly inconsistent behavior

 Dear all, This statement a = {[%f, %t], {2; poly([3, 2],'v')}} defines a cell array whose first element is a boolean row vector and whose second element in turn is another cell array. Invoking a{1}(1) correctly returns the boolean value F. But a{2}{1} does not return 2, as expected but an error: Error: syntax error, unexpected {, expecting end of file However b  =  a{2} b{1} returns the correct value 2. Why, if a{2} is a cell array, its entries cannot be extracted with the curly brackets {}? Moreover a{2}(1) and a{2}(2) should be the constant 2. and the polynomial             2     6 -5v +v respectively,  but they are reported as cell arrays, since iscell(a{2}(1)) and  iscell(a{2}(2)) are both True Why is a cell array responsive to () at all and why it returns a sub ell array? Thank you in advance. Regards, Federico Miyara --- El software de antivirus Avast ha analizado este correo electrónico en busca de virus. https://www.avast.com/antivirus_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: Seemingly inconsistent behavior

 Hello, This limitation is alreay pointed out here : http://bugzilla.scilab.org/show_bug.cgi?id=15756S. Le 15/01/2019 à 03:36, Federico Miyara a écrit : > > Dear all, > > This statement > > a = {[%f, %t], {2; poly([3, 2],'v')}} > > defines a cell array whose first element is a boolean row vector and > whose second element in turn is another cell array. > > Invoking a{1}(1) correctly returns the boolean value F. > > But a{2}{1} does not return 2, as expected but an error: > > Error: syntax error, unexpected {, expecting end of file > > However > > b  =  a{2} > b{1} > > returns the correct value 2. > > Why, if a{2} is a cell array, its entries cannot be extracted with the > curly brackets {}? > > Moreover a{2}(1) and a{2}(2) should be the constant 2. and the polynomial > >            2 >    6 -5v +v > > respectively,  but they are reported as cell arrays, since > > iscell(a{2}(1)) and  iscell(a{2}(2)) are both True > > Why is a cell array responsive to () at all and why it returns a sub > ell array? > > Thank you in advance. > > Regards, > > Federico Miyara > > > > > --- > El software de antivirus Avast ha analizado este correo electrónico en > busca de virus. > https://antispam.utc.fr/proxy/2/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/www.avast.com/antivirus  > > > _______________________________________________ > users mailing list > [hidden email] > https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users  > -- Stéphane Mottelet Ingénieur de recherche EA 4297 Transformations Intégrées de la Matière Renouvelable Département Génie des Procédés Industriels Sorbonne Universités - Université de Technologie de Compiègne CS 60319, 60203 Compiègne cedex Tel : +33(0)344234688 http://www.utc.fr/~mottelet_______________________________________________ users mailing list [hidden email] http://lists.scilab.org/mailman/listinfo/users
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## Re: improve accuracy of roots

In reply to this post by fmiyara
Hello,

After a quick search on the internet I have found and translated in Scilab "multroot", a Matlab Package computing polynomial roots and multiplicities. If you are interested proceed to this url: http://bugzilla.scilab.org/show_bug.cgi?id=15349#c9

Enjoy !

S.

Le 14/01/2019 à 21:07, Federico Miyara a écrit :

Denis,

What I meant is that convergence is a limiting process. On average, as the number of iterations rises you´ll be closer to the limit, bu there is no guarantee that any single iteration will bring you any closer; it may be a question of luck. Maybe (though it would require a proof, it is not self-evident for me) in the exact case of a single multiple root as (x - a)^n the convergence process is monotonous, but what if you have (x - a1)* ... * (x  - an) where ak are all very similar but not identical, say, with relative differences of the order of those reported by the application of the regular version  of roots.
Regards,

Federico Miyara

On 14/01/2019 13:47, CRETE Denis wrote:
```Thank you Frederico!
According to the page you refer to, the method seems to converge more rapidly with this factor equal to the multiplicity of the root.
About overshoot, it is well known to occur for |x|^a where a <1. But for a>1, the risk of overshoot with the Newton-Raphson method seems to be very small...
Best regards
Denis

[@@ THALES GROUP INTERNAL @@]

Unité Mixte de Physique CNRS / THALES
1 Avenue Augustin Fresnel
91767 Palaiseau CEDEx - France
Tel : +33 (0)1 69 41 58 52 Fax : +33 (0)1 69 41 58 78
e-mail :
[hidden email] [hidden email]
http://www.trt.thalesgroup.com/ump-cnrs-thales
http://www.research.thalesgroup.com

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : samedi 12 janvier 2019 07:52
À : Users mailing list for Scilab
Objet : Re: [Scilab-users] improve accuracy of roots

Denis,

I've found the correction here,

https://en.wikipedia.org/wiki/Newton%27s_method

It is useful to accelerate convergence in case of multiple roots, but I
guess it is not valid to apply it once to improve accuracy because of
the risk of overshoot.

Regards,

Federico Miyara

On 10/01/2019 10:32, CRETE Denis wrote:
```
```Hello,
I tried this correction to the initial roots z:

z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
ans  =

-1. - 1.923D-13i
-1. + 1.189D-12i
-1. - 1.189D-12i
-1. - 1.919D-13i

// Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1):
z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
z2 - Z
ans  =

2.233D-08 - 1.923D-13i
-2.968D-08 + 1.189D-12i
-2.968D-08 - 1.189D-12i
2.131D-08 - 1.919D-13i

The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8.

HTH
Denis

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : jeudi 10 janvier 2019 00:32
À : [hidden email]
Objet : [Scilab-users] improve accuracy of roots

Dear all,

Consider this code:

// Define polynomial variable
p = poly(0, 'p', 'roots');

// Define fourth degree polynomial
R = (1 + p)^4;

// Find its roots
z = roots(R)

The result (Scilab 6.0.1) is

z  =

-1.0001886
-1. + 0.0001886i
-1. - 0.0001886i
-0.9998114

It should be something closer to

-1.
-1.
-1.
-1.

Using these roots

C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4)))

yield seemingly accurate coefficients
C  =

1.   4.   6.   4.   1.

but

C - [1  4  6 4 1]

shows the actual error:

ans  =

3.775D-15   1.243D-14   1.155D-14   4.441D-15   0.

This is acceptable for the coefficients, but the error in the roots is
too large. Somehow the errors cancel out when  assembling back the
polynomial but each individual zero should be closer to the theoretical
value

Is there some way to improve the accuracy?

Regards,

Federico Miyara

---
El software de antivirus Avast ha analizado este correo electrónico en busca de virus.
https://www.avast.com/antivirus

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```
```_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```

 Libre de virus. www.avast.com

```_______________________________________________
users mailing list
[hidden email]
```

```--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet```

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## Re: improve accuracy of roots

Stéphane,

Thank you very much for your contribution!

Best regards,

Federico Miyara

On 15/01/2019 14:14, Stéphane Mottelet wrote:
Hello,

After a quick search on the internet I have found and translated in Scilab "multroot", a Matlab Package computing polynomial roots and multiplicities. If you are interested proceed to this url: http://bugzilla.scilab.org/show_bug.cgi?id=15349#c9

Enjoy !

S.

Le 14/01/2019 à 21:07, Federico Miyara a écrit :

Denis,

What I meant is that convergence is a limiting process. On average, as the number of iterations rises you´ll be closer to the limit, bu there is no guarantee that any single iteration will bring you any closer; it may be a question of luck. Maybe (though it would require a proof, it is not self-evident for me) in the exact case of a single multiple root as (x - a)^n the convergence process is monotonous, but what if you have (x - a1)* ... * (x  - an) where ak are all very similar but not identical, say, with relative differences of the order of those reported by the application of the regular version  of roots.
Regards,

Federico Miyara

On 14/01/2019 13:47, CRETE Denis wrote:
```Thank you Frederico!
According to the page you refer to, the method seems to converge more rapidly with this factor equal to the multiplicity of the root.
About overshoot, it is well known to occur for |x|^a where a <1. But for a>1, the risk of overshoot with the Newton-Raphson method seems to be very small...
Best regards
Denis

[@@ THALES GROUP INTERNAL @@]

Unité Mixte de Physique CNRS / THALES
1 Avenue Augustin Fresnel
91767 Palaiseau CEDEx - France
Tel : +33 (0)1 69 41 58 52 Fax : +33 (0)1 69 41 58 78
e-mail :
[hidden email] [hidden email]
http://www.trt.thalesgroup.com/ump-cnrs-thales
http://www.research.thalesgroup.com

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : samedi 12 janvier 2019 07:52
À : Users mailing list for Scilab
Objet : Re: [Scilab-users] improve accuracy of roots

Denis,

I've found the correction here,

https://en.wikipedia.org/wiki/Newton%27s_method

It is useful to accelerate convergence in case of multiple roots, but I
guess it is not valid to apply it once to improve accuracy because of
the risk of overshoot.

Regards,

Federico Miyara

On 10/01/2019 10:32, CRETE Denis wrote:
```
```Hello,
I tried this correction to the initial roots z:

z-4*(1+z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
ans  =

-1. - 1.923D-13i
-1. + 1.189D-12i
-1. - 1.189D-12i
-1. - 1.919D-13i

// Evaluation of new error, (and defining Z as the intended root, i.e. here Z=-1):
z2=z-4*(z-Z).^4 ./([ones(z),z,z.^2,z.^3]*(C(2:5).*(1:4))')
z2 - Z
ans  =

2.233D-08 - 1.923D-13i
-2.968D-08 + 1.189D-12i
-2.968D-08 - 1.189D-12i
2.131D-08 - 1.919D-13i

The factor 4 in the correction is a bit obscure to me, but it seems to work also for R=(3+p)^4, again with an accuracy on the roots of a ~2E-8.

HTH
Denis

-----Message d'origine-----
De : users [[hidden email]] De la part de Federico Miyara
Envoyé : jeudi 10 janvier 2019 00:32
À : [hidden email]
Objet : [Scilab-users] improve accuracy of roots

Dear all,

Consider this code:

// Define polynomial variable
p = poly(0, 'p', 'roots');

// Define fourth degree polynomial
R = (1 + p)^4;

// Find its roots
z = roots(R)

The result (Scilab 6.0.1) is

z  =

-1.0001886
-1. + 0.0001886i
-1. - 0.0001886i
-0.9998114

It should be something closer to

-1.
-1.
-1.
-1.

Using these roots

C = coeff((p-z(1))*(p-z(2))*(p-z(3))*(p-z(4)))

yield seemingly accurate coefficients
C  =

1.   4.   6.   4.   1.

but

C - [1  4  6 4 1]

shows the actual error:

ans  =

3.775D-15   1.243D-14   1.155D-14   4.441D-15   0.

This is acceptable for the coefficients, but the error in the roots is
too large. Somehow the errors cancel out when  assembling back the
polynomial but each individual zero should be closer to the theoretical
value

Is there some way to improve the accuracy?

Regards,

Federico Miyara

---
El software de antivirus Avast ha analizado este correo electrónico en busca de virus.
https://www.avast.com/antivirus

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```
```_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users

```

 Libre de virus. www.avast.com

```_______________________________________________
users mailing list
[hidden email]
```

```--
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet```

```_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
```

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users