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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) ????-2008 - INRIA - Francois DELBECQUE
//
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
function res=determ(W,k)
// determinant of a polynomial or rational matrix by FFT
// W=square polynomial matrix
// k=``predicted'' degree of the determinant of W i.e. k is
// an integer larger or equal to the actual degree of W.
// Method: evaluate the determinant of W for the Fourier frequencies
// and apply inverse fft to the coefficients of the determinant.
// See also detr
if and(typeof(W)<>['rational','polynomial','constant']) then
error(msprintf(gettext("%s: Wrong type for input argument #%d: A floating point number or polynomial or rational fraction array expected.\n"),"determ",1))
end
if size(W,1)<>size(W,2) then
error(msprintf(gettext("%s: Wrong size for input argument #%d: A square matrix expected.\n"),"determ",1))
end
if W==[] then
res=1;
return;
end;
n1=size(W,1)
// small cases
if n1==1 then
res=W;
return;
elseif n1==2 then
res = W(1,1)*W(2,2) - W(1,2)*W(2,1);
return;
end
//upper bound of the determinant degree
maj = n1*maxi(degree(W))+1;
if argn(2)==1 then
k=1;
while k < maj,
k=2*k;
end
end
if n1>8 then
mprintf(gettext("Computing determinant: Be patient...\n"));
end
// Default Values
e=0*ones(k,1);
e(2)=1;
// Paramtres de clean
epsa=1.d-10;
epsr=0;//no relative rounding
if k==1 then
ksi=1;
else
ksi=fft(e,-1);
end
fi=[];
if ~isreal(W,0) then
// Cas Complexe
for kk=1:k,
fi=[fi,det(horner(W,ksi(kk)))];
end
Temp0 = poly(fft(fi,1),varn(W),'c');
Temp1 = clean(real(Temp0),epsa,epsr)+%i*clean(imag(Temp0),epsa,epsr);
else
// Cas Rel
for kk=1:k,fi=[fi,det(freq(W,ones(W),ksi(kk)))];end
Temp1 = clean(real(poly(fft(fi,1),varn(W),'c')),epsa,epsr);
end
if argn(2)==1 then
// Cas o k est dfini dans les paramtres d'entre.
// On va maintenant annuler tous les coefficients
// dont le degr est suprieur maj
Temp2 = coeff(Temp1);
for i=1:maj,
Temp2(i) = 0;
end
res = Temp1 - poly(Temp2,varn(W),"coeff");
return;
else
// Cas o k n'est pas dfini dans les paramtres d'entre
res = Temp1;
return;
end
endfunction
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