MPI Basic Examples:
1. MPI Example 1: MPI_Init() and MPI_Finalize()
2. MPI Example 2: MPI_Send() and MPI_Recv()
2-1. MPI Example 3: Integral of a function by Trapezoidal rule
2-2. MPI Example 4: Integral of a function by Simpson's rule
2-3. MPI Example 5: Integral of a function by Gaussian quadrature (n=6)
3. MPI Example 6: MPI_Wtime() and MPI_Barrier()
4. MPI Example 7: MPI_Reduce()
5. MPI Example 8: MPI_Bcast() - N x N Matrix multiplication
6. MPI Example 9: MPI_Allreduce() - Simple addition
Exercise:
Correlation function:
1. Cross correlation of two real functions / two complex functions
2. Matrix auto-correlation function [4]
3. Fast auto-correlation of a complex function [5] and Fast cross-correlation of two complex functions [6]
Transform:
1. Discrete Fourier Transform : 1D, 2D, 3D [7,8]
2. Fast Fourier Transform (Radix-2) - 1D [7,9], 2D [10,11], 3D [10,12]
3. Chirp z-transform - 1D, 2D, 3D [10,13]
Time frequency analysis:
1. Short-time Fourier transform [14] ( STFT Viewer )
2. Wavelet transform [15] ( WT Viewer )
Interpolation:
Other methods / algorithms:
Bit-reversal and fast bit-reversal algorithm (for Fast Fourier Transform)
Gaussian Elimination (for solving AX=B)
References:
[1] 多核心高效能程式開發：使用OpenMP及OpenCL實例, Chapter 2 (2013), ISBN 978-968-86398-6-7.
[2] 王致悅, 計算物理手冊（Fortran, C與MPI）, 2nd Ed., Chapter 26-27, Page 302-345 (2010), ISBN 978-986-144-084-2.
[3] 鄭守成, C語言MPI平行計算程式設計, (2002).
[4] http://mathworld.wolfram.com/Autocorrelation.html
[5] Chris Chatfield, The Analysis of Time Series: An Introduction, ISBN 9781584883173.
[6] https://en.wikipedia.org/wiki/Autocorrelation
[7] J. F. James, A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering, 3rd Ed. (2011), Chapter 9.
[8] http://fourier.eng.hmc.edu/e101/lectures/Image_Processing/node6.html
[9] E. Oran Brigham, Fast Fourier Transform and Its Applications, 1st Ed. Chapter 8 Fast Fourier transform (1988).
[10] http://www.originlab.com/doc/Origin-Help/FFT2-Algorithm
[11] http://paulbourke.net/miscellaneous/dft/
[12] R. Schulz, 3D FFT with 2D decomposition, CS project report, (2008).
[13] 具再熙, 數位訊號處理-使用MATLAB, Chapter 6-6 Chirp-Z transform, Page 6-20~6-24 (2007), ISBN 978-9574998043.
[14] Y. T. Lee, J. S. Lin, Journal of Computational Chemistry 34 (31), 2697-2706 (2013). [ Link ]
[15] Y. T. Lee, J. S. Lin, Royal Society of Chemistry Advances 6 (2), 1491-1502 (2016). [ Link ]