Cornell University

Department of Physics

Phys 480/680, Astro 690 April 15, 2005

Computational Physics, Spring 2005

Homework Assignment # 6

(Due Thursday, March 31)

Agenda and readings for the week of April 5:

Goal: Optimize to produce efficient, high-precision software to calculate the electronic structure of atoms within density-functional theory; explore FLOP rates of various operations and cache performance.

Readings marked NR are from Numerical Recipes: The Art of Scientific Computing, 2$^{\mathrm nd}$ edition (in C). Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P480.

Recap of last three weeks:

• 03/08 Lec 14: Recap modified Broyden method; Introduction to numerical linear algebra; Benefits of LAPACK; Solution of linear systems through LU decomposition; Crout's algoritm for LU decomposition
  Reading: NR 2.0, 2.3

• 03/10 Lec 15: Crout's Algorithm with pivoting
  Reading: NR 2.3

• 03/10 Lab 5: ``Hot-wired'' solver for atoms within Hartree theory, reproducing analytic Hydrogenic solutions to Schrödinger's equation ($-(1/2)Z^2/n^2$).

• 03/15 Lec 16: Inner loop tricks; Cache optimization, ....

• 03/17 Lab 6 (Meet in Rock B3): Profiling and real-time optimization of full atomic solver: using gprof; avoiding malloc; inlining optimizations.

• 03/21-03/25: SPRING BREAK

Preview of coming week:

• 03/29 Lec 17 Avoiding cache misses; BLAS1-3; blocked matrix multiplies; Automated empirical optimization of software (AEOS): automatically tuned linear algebra software (ATLAS), fastest Fourier Transform in the West (FFTW).

• 03/31 Lec 18: Solution of Poisson's equation in d>1 dimensions; expressive software

• 03/31 Lab 7: FLOP performance of basic operations; FLOP rates in octave.

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