An Introduction to Parallel Programming by Tobias Wittwer PDF
By Tobias Wittwer
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Additional resources for An Introduction to Parallel Programming
The speedup should be even better when processing larger problems. 46 CHAPTER 5. 5 Parallelisation with MPI The direct method was parallelised for distributed memory systems using ScaLAPACK. ScaLAPACK was the ideal method, as most of the workload was performed by the BLAS and LAPACK routines DSYRK and DPOSV. As could be seen in the previous section, the conjugate gradient method behaves quite differently. Only small vectors are processed, with most of the runtime being consumed by the linewise setup of the design matrix A.
1) where GM is the geocentric gravitational constant, R is the earth radius, n is the spherical harmonic degree, m is the spherical harmonic order, l is the longitude and J the colatitude (polar distance) of a point on the sphere, the P¯n,m are the normalised associated Legendre functions of the first kind, and c¯n,m and s¯n,m are the unknown spherical harmonic coefficients which we want to estimate. 2) unknown coefficients. 1 after the unknowns, we get the entries for the design matrix A that links observations i and unknowns c¯n,m , s¯n,m : 27 28 CHAPTER 5.
When using the Goto BLAS, you may need to set the environment variable GOTO_NUM_THREADS to 1. 0d0, N2(1,threadnum),nmax+1) ... Note that a_block has the dimensions u × blocksize, and not blocksize × u. This is due to Fortran’s column-major array storage (arrays are stored column by column, not line by line as in C). build_a_line needs only one row of A at a time, which is achieved by making the rows the columns. This has to be kept in mind when building the product AT A, which has to be done as A j ATj .
An Introduction to Parallel Programming by Tobias Wittwer