//-----------------------------------------------------------------------------
// TestMatrixAdd_aM
//-----------------------------------------------------------------------------
bool TestMatrixAdd_aM()
{
Matrix A("1,2,3;4,5,6");
Matrix B;
Add_aM(2,A,B);
Matrix Ap2("3,4,5;6,7,8");
return ApproxEqual(B,Ap2,TOLERANCE);
}
//=============================================================================
bool minres
(
const CPPL::dsymatrix& A,
CPPL::dcovector& x,
const double& eps
)
{
const CPPL::dcovector y(x);
CPPL::dcovector r(y);
double beta2(nrm2(r)), beta3;
double rho0(1.0), rho1(beta2), rho2;
double rhop(0.0);
double c0(0.0), c1(-1.0), c2;
double s0(0.0), s1(0.0), s2;
double f(beta2);
CPPL::dcovector p1(x.l), p2(r/beta2), p3;
CPPL::dcovector q0(x.l), q1(x.l), q2;
x.zero();
p1.zero();
q0.zero();
q1.zero();
int itc(0);
const int itmax(2*x.l);
while( (fabs(f)>eps || fabs(damax(y-A*x))>eps) && itc<itmax){
std::cout << itc << " " << fabs(damax(y-A*x)) << std::endl;
//std::cerr << "itc=" << itc << ", fabs(f)=" << fabs(f) << std::endl;
CPPL::dcovector Ap2(A*p2), z;
z =Ap2-beta2*p1;
double alpha;
alpha =Ap2%p2;
p3 =z-alpha*p2;
beta3 =nrm2(p3);
p3 /=beta3;
double d, h;
d =(alpha-rhop*c0)*s1;
h =beta2*s0;
rhop =-beta2*c0*s1 -alpha*c1;
rho2 =sqrt(pow(rhop,2)+pow(beta3,2));
c2 =rhop/rho2;
s2 =beta3/rho2;
CPPL::dcovector zp;
zp =p2 -(h/rho0)*q0;
q2 =zp -(d/rho1)*q1;
double t;
t =f*c2;
f *=s2;
x +=(t/rho2)*q2;
beta2=beta3;
rho0=rho1; rho1=rho2;
c0=c1; c1=c2;
s0=s1; s1=s2;
swap(p1,p2); swap(p2,p3);
swap(q0,q1); swap(q1,q2);
itc++;
}
std::cerr << "itc=" << itc << " fabs(damax(y-A*x))=" << fabs(damax(y-A*x)) << std::endl;
//std::cerr << "itc=" << itc << " fabs(f)=" << fabs(f) << std::endl;
if(itc<itmax){ return 0; }
else{ return 1; }
}