More efficient eval_f in RBC on GPU
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#!!!!!!!!!! WARNING: RUFF FAILED !!!!!!!!!!: #pySDC/projects/GPU/analysis_scripts/compare_RBC3D.py:494:9: E722 Do not use bare `except` # | Parallel-in-Time#492 | k[_s > 1e-16], _s[_s > 1e-16], color=last_line.get_color(), ls=last_line.get_linestyle(), label=label Parallel-in-Time#493 | ) Parallel-in-Time#494 | except: # | ^^^^^^ E722 Parallel-in-Time#495 | pass # | # #pySDC/projects/GPU/analysis_scripts/compare_RBC3D.py:593:5: F841 Local variable `Delta_Nu` is assigned to but never used # | Parallel-in-Time#591 | t = data['t'] Parallel-in-Time#592 | avg_Nu = np.array([np.mean(Nu[40 : 40 + i + 1]) for i in range(len(Nu[40:]))]) Parallel-in-Time#593 | Delta_Nu = np.array([abs(avg_Nu[i + 1] - avg_Nu[i]) for i in range(len(avg_Nu) - 1)]) # | ^^^^^^^^ F841 Parallel-in-Time#594 | # ax.plot(data['t'][40:-1], Delta_Nu / avg_Nu[:-1]) Parallel-in-Time#595 | # ax.plot(data['t'], np.abs(avg_Nu - avg_Nu[-1]) / avg_Nu[-1]) # | # = help: Remove assignment to unused variable `Delta_Nu`:
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After profiling the code on GPUs some more, I noticed some efficiency can be gained from reducing the number of matrix multiplications. That is all that I am doing here: Rather than computing derivatives by multiplying each component with the derivative matrix separately, I construct a large matrix containing the derivative matrix multiple times in order to compute all derivatives simultaneously. Also, I cache the$L$ matrix in the basis of Chebychov T polynomials, rather than computing it every time. This is not a huge difference, but saves a few ms in every call of the function on both CPU and GPU.