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function [x0,kerA]=linsolve(A,b,x0)
// Copyright INRIA
%tol=1.D-10;
// Finds all x solution to Ax+b=0;
// x0=particular solution; kerA=nullspace of A
// Any x=x0+kerA*w with arbitrary w solves A*x+b=0
[LHS,RHS]=argn(0);
select type(A)
case 1 then //full matrix
Ab=[A,b];[ma,na]=size(Ab);
[W,rk]=colcomp(Ab);
W=W(:,1:na-rk);last=W(na,:);
[W2,rk1]=colcomp(last);
if rk1==0 then
warning('Conflicting linear constraints!');x0=[];kerA=[];return;
end
W=W*W2;
kerA=W(1:na-1,1:na-rk-1);
if RHS==3 then
if norm(A*x0+b,1)<%tol then
return;
end
disp('recomputing initial guess');
end
piv=W(na,na-rk);x0=W(1:na-1,na-rk)/piv;
case 5 then //sparse matrix
[ma,na]=size(A);
%tol=1.D-10*maxi(abs(A))*max(ma,na);
if ma<na then
A=[A;sparse([],[],[na-ma,na])];b=[b;zeros(na-ma,1)];end
if ma>na then
//A=[A,sparse([],[],[ma,ma-na])];x0=[x0;zeros(ma-na,1)];
b=A'*b;A=A'*A;ma=na;
end
[ptr,rkA]=lufact(A,[%tol,0.001]);
[P,L,U,Q]=luget(ptr);
if RHS==3 then
if norm(A*x0+b,1)>%tol then
x0=lusolve(ptr,-b);
disp('recomputing initial guess');
end
end
if RHS==2 then
x0=lusolve(ptr,-b);
end
ludel(ptr);
U=clean(U);
[ptrU,rk]=lufact(U,[%tol,.001]);
nma=max(na,ma);
Y=[sparse([],[],[rkA,nma-rkA]);speye(nma-rkA,nma-rkA)];
kerA=[];
for k=1:na-rkA
bb=full(Y(:,k));
ww=sparse(lusolve(ptrU,bb));
kerA=[kerA,ww];
end
if na<>rkA then
kerA=clean(Q'*kerA);
end
if norm(A*x0+b,1)>%tol then
warning('Possible Conflicting linear constraints, error in the order of '+...
string(norm(A*x0+b,1)));
end
if ma>na then kerA=kerA(1:na,:);x0=x0(1:na,1);end
ludel(ptrU);
end
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