[Bugzilla] [Bug 13822] New: strong regression with linear system solving

[bugzilla.admin at scilab.org]

http://bugzilla.scilab.org/show_bug.cgi?id=13822
--------- Bug Summary -----------
strong regression with linear system solving

---------- Changed by ------------
marc.derumaux at free.fr

---------- What changed ----------
bug_id, short_desc, product, version, rep_platform, op_sys, bug_status, bug_severity, priority, component, assigned_to, reporter


            Bug ID: 13822
           Summary: strong regression with linear system solving
           Product: Scilab software
           Version: 5.5.2 final version
          Hardware: PC
                OS: All OS
            Status: NEW
          Severity: Major
          Priority: P5
         Component: Scilab
          Assignee: bugzilla.admin at scilab.org
          Reporter: marc.derumaux at free.fr

BUG DESCRIPTION:
----------------
A=M\B operation gives wrong result and warn for bad conditionning on 5.5.1 and 5.5.2 version.
Same test case on 5.4.1 version works perfectly, with same result as python/numpy.

ERROR LOG:
----------
Attention :
La matrice est presque singulière ou mal conditionnée. rcond =    2.3968D-19

HOW TO REPRODUCE THE BUG:
-------------------------
I discovered that bug by working on an old code that did work, and do not on 5.5.1 and 5.5.2. The code should solve a mean square approximation based
on polynomes.

I could make a test case pretty simple to try :

// cas simplifié faisant apparaitre le bug

h=[0. 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. ]
press =[ 0.988 0.774 0.608 0.466 0.351 0.261 0.191 0.139 0.102 0.074 0.0545]

n=6;

M=[]
B=[]
for j=1:n+1
    for i=1:n+1
        M(j,i)=sum(h.^(i-1).*h.^(j-1));
    end
    B(j)=sum(h.^(j-1).*press);
end

// Résolution du système
A=M\B

// Calcul de la courbe approximée (évaluation du polynome)
y=0;
for i=0:n
    y=y+A(i+1)*h.^i;
end

// Tracé de la courbe polynomiale
figure(1);clf
plot(h,press,"+r");
plot(h,y,"k")

This code will work perfectly on 5.4.1, and gives wrong result on 5.5.2.
For n=4 only, result is OK on 5.5.2.
Same problem if the code is launch with h=h*1000 : Ok on 5.4.1 and bad result for 5.5.2 except for n=2 !

Is it a 32 bits float type used for calculation ?

OTHER INFORMATION:
------------------

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