Like this (I have simplified your script a little bit) for n=1000 there
is a x60 speedup with Cardan's formulas:
clear
n = 1000;
S11 = rand(n,1);
S22 = rand(n,1);
S33 = rand(n,1);
S12 = rand(n,1);
S23 = rand(n,1);
S13 = rand(n,1);
princ = zeros(n,3);
// with a loop
tic();
princ1 = zeros(n,3);
for i = 1 : n
S=[S11(i) S12(i) S13(i)
S12(i) S22(i) S23(i)
S13(i) S23(i) S33(i)];
princ1(i,:) = gsort(spec(S))';
end
duration1 = toc(); printf("Duration 1 = %g\n",duration1);
// using Cardan formulas
tic();
// characteristic polynomial is poly([d c b a],"x","coeff")
S13sq = S13.*S13;
S12sq = S12.*S12;
S23sq = S23.*S23;
//a=1; (not used) b=-S11-S22-S33;
c=S11.*S22+S11.*S33+S22.*S33-S23sq-S13sq-S12sq;
d=S11.*S23sq+S22.*S13sq+S12sq.*S33 - S11.*S22.*S33-2*S13.*S12.*S23;
b2=b.*b;
p=-b2/3+c;
q=b.*(2*b2-9*c)/27+d;
//delta=-(4*p.*p.*p+27*q.*q) (not used since matrix is symetric =>real
eigenvalues)
princ2=zeros(n,3);
theta=acos(1.5*q./p.*sqrt(-3./p))/3;
for k=0:2
princ2(:,k+1)=2*sqrt(-p/3).*cos(theta+2*k*%pi/3)-b/3;
end
princ2=gsort(princ2,"c")
duration2 = toc(); printf("Duration 2 = %g\n",duration2);
disp(norm(princ1-princ2,%inf))
disp(duration1/duration2)
S.
Le 18/01/2019 à 15:21, Stéphane Mottelet a écrit :
Hello Paul,
If you stick to 3x3, you can vectorize the Cardan formulas applied to
the characteristic polynomial of each individual matrix.
S.
Le 15/01/2019 à 09:56, Carrico, Paul a écrit :
clc
mode(0)
clear
function*V*=_eigen_val_(*S11*, *S12*, *S13*, *S22*, *S23*, *S33*)
S_u = [0 *S12* *S13* ; 0 0 *S23* ; 0. 0. 0.];
S_d = [*S11* ; *S22* ; *S33*];
S = S_u + S_u' + diag(S_d);
*V* = gsort(spec(S),'lr','d')'; clear S; clear S_u; clear S_d;
endfunction
n= 10; m = 1;
S11= rand(n,m);
S22= rand(n,m);
S33= rand(n,m);
S12= rand(n,m);
S23= rand(n,m);
S13= rand(n,m);
princ= zeros(n,3);
/// with a loop/
tic();
princ1= zeros(n,3*m);
fori = 1 : n
S_u = [0 S12(i,m) S13(i,m) ; 0 0 S23(i,m) ; 0. 0. 0.];
S_d = [S11(i,m) ; S22(i,1) ; S33(i,m)];
S = S_u + S_u' + diag(S_d);
princ1(i,:) = gsort(spec(S),'lr','d')'; clear S; clear S_u; clear S_d;
end
duration1= toc(); printf("Duration 1 = %g\n",duration1);
/// using a function/
tic();
princ2= zeros(n,3*m);
fori = 1 : n
princ2(i,:) =
_eigen_val_(S11(i,m),S12(i,m),S13(i,m),S22(i,m),S23(i,m),S33(i,m));
end
duration2= toc(); printf("Duration 2 = %g\n",duration2);
isequal(princ1,princ2)
/// using vectorization (in combination with the function ?)/
i= (1:n)';
S= zeros(3,3,n)
--
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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users mailing list
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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
[email protected]
http://lists.scilab.org/mailman/listinfo/users
