linear equation solver
[x0,kerA]=linsolve(A,b [,x0])
:A a na x ma real matrix (possibly sparse) : :b a na x 1 vector (same row dimension as A) : :x0 a real vector : :kerA a ma x k real matrix :
linsolve computes all the solutions to A*x+b=0.
x0 is a particular solution (if any) and kerA=`nullspace of `A. Any x=x0+kerA*w with arbitrary w satisfies A*x+b=0.
If compatible x0 is given on entry, x0 is returned. If not a compatible x0, if any, is returned.
A=`rand`_(5,3)*`rand`_(3,8);
b=A*`ones`_(8,1);[x,kerA]=linsolve(A,b);A*x+b //compatible b
b=`ones`_(5,1);[x,kerA]=linsolve(A,b);A*x+b //uncompatible b
A=`rand`_(5,5);[x,kerA]=linsolve(A,b), -`inv`_(A)*b //x is unique
// Benchmark with other linear sparse solver:
[A,descr,ref,mtype] = `ReadHBSparse`_(SCI+"/modules/umfpack/examples/bcsstk24.rsa");
b = `zeros`_(`size`_(A,1),1);
`tic`_();
res = `umfpack`_(A,'\',b);
`mprintf`_('\ntime needed to solve the system with umfpack: %.3f\n',`toc`_());
`tic`_();
res = linsolve(A,b);
`mprintf`_('\ntime needed to solve the system with linsolve: %.3f\n',`toc`_());
`tic`_();
res = A\b;
`mprintf`_('\ntime needed to solve the system with the backslash operator: %.3f\n',`toc`_());