We attempt to solve a toy LDA problem described in §9.4.3.4 for four electrons on a one-dimensional grid with 12 points and a coupling constant of 20. In this case, we use the first four eigenvectors of the linear problem as a starting point.
>> !cp examples/ldatoy/*.m . >> K = Kinetic(12); >> parameters(K,20); >> Y0 = guess(4); >> [fn,Yn] = sg_min(Y0,'newton','euclidean'); iter grad F(Y) flops step type 0 2.432521e+00 7.750104e+00 4554 none invdgrad: Hessian not positive definite, CG terminating early 1 4.770038e-01 7.546426e+00 367756 steepest step 2 4.664971e-02 7.531450e+00 789739 Newton step 3 3.363736e-04 7.531232e+00 1284452 Newton step 4 1.809273e-07 7.531232e+00 1976096 Newton step 5 1.843536e-07 7.531232e+00 2778377 Newton step
Figure 9.4 shows the convergence curve for this run.
