HotSpot Thermal Floorplan Solver Using Conjugate Gradient to Speed Up

Algorithm 1

: The conjugate gradient algorithm as an iterative method.

Require: f(x): objective function; x0: initial solution;
Ensure: optimal x
(1)	int Iter = 0;
(2)	double α, β, rp, rpold, bnorm, rnorm;
(3)	vector r, p, q, z;
(4)	initial r = b ? A ? x;
(5)	rnorm = (r,r);
(6)	while (rnorm < precision) do
(7)	if using preconditioned then
(8)	z = M^−1r; (using difference preconditioned)
(9)	else
(10)	z = r; (no preconditioned)
(11)	end if
(12)	rp = (r,z);
(13)	if Iter == 1 then
(14)	p0 = z
(15)	else
(16)	β = rp/rpold;
(17)	p = z + β p
(18)	end if
(19)	q = A p;
(20)	α = (r,z)/(p,q);
(21)	x = x + α p;
(22)	r = r − α q;
(23)	rnorm = (r,r);
(24)	rpold = rp;
(25)	end while