C++ for Scientists - Technische Universität Dresden

Vector p(resource(x)), q(resource(x)), r(resource(x)), z(resource(x));
r = b − A∗x;
while (! iter.finished(r)) {
z = solve(L, r);
rho = dot(r, z);
if (iter.first())
p = z;
else
p = z + (rho / rho 1) ∗ p;
q = A ∗ p;
alpha = rho / dot(p, q);
x += alpha ∗ p;
r −= alpha ∗ q;
rho 1 = rho;
++iter;
}
return iter;
}
int main (int argc, char∗ argv[])
{
int size;
}
// set size
mtl::compressed2D A(size, size);
mtl::dense vector x(size), b(size);
// set A and b
// Create preconditioner
itl::pc::ic 0 L(A);
// Object that controls iteration, terminate if residual is below 10ˆ−9 or decrease
// by 6 orders of magnitude, abord after 30 iterations if not converged
itl::basic iteration iter(b, 30, 1.e−6, 1.e−9);
conjugate gradient(A, x, b, L, iter);
return 0 ;
Listing 1.2: High Abstraction Implementation of CG
The first thing you might realize is that the CG implementation is readable without comments.
As a thumb of rule, if other people’s comments look like your program sources then you are
a really good programmer. If you compare the mathematical notation in Algorithm 1 with
Listing 1.2 you will realize that — except for the type and variable declarations at the beginnig
— they are identical. Some readers might think that it looks more like Matlab or Mathematica
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