Modelling the earth with Spherical Harmonic functions
Compute a model with the lowest average error
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Geodesy is built with CMake
mkdir build && cd build
cmake ../ -DCMAKE_BUILD_TYPE=Release
cmake --build ./
There are three main executables (among others) that are created by this project, located in build/src. new_model, new_model_mpi, and new_model_omp2 are 3 different implementations of the Numerical Quadrature algorithm to approximate the Laplace Series coefficients of a NASA data set. The CLI is similar to the model that was provided to us, which is now located in old_model.
New model computes the Laplace series coefficients up to a certain degree l via numerical quadrature. The binary data sets are provided in the bin/ directory of geodesy's root folder and unfortunately the paths are hardcoded: therefore we must execute new_model from the /build/src directory.
./new_model --small --lmodel 100
The coefficients are then stored in the file sph_small_100.bin of the current working directory. To validate the model and extract the coefficients into a text file, we can add the parameters --diff and --txt.
./new_model --small --lmodel 100 --txt --diff
The Laplace series coefficients are outputted to sph_small_100.txt in the same format that the old_model provides. The Average Absolute Error (AAE) and the Mean Squared Error (MSE) are printed at the bottom of the screen. Furthermore, notice that since the coefficients were stored in a binary file we don't need to recompute them. Similarly, the predictions have been stored in a binary format and don't need to be recomputed on subsequent computations.
Rerunning
./new_model --small --lmodel 100 --txt --diff
completes almost instantly
If you would like to recompute values then we pass the parameter --recompute
Model using numerical quadrature that is parallelized with omp. new_model_omp tries to parallize the internal integration loop whereas new_model_omp2 parallelizes the loop that computes (l + 1)(l + 2) coefficients. We can compute a model in a nearly identical fashion as new_model but this time we specify the number of threads with the --threads flag.
./new_model_omp2 --small --lmodel 100 --lmax 200 --recompute --threads 2
new_model_omp2 uses an older version of the command line interface so we have to specify the degree of the precomputed Associated Legendre Polynomials with --lmax.
Notice that with two threads the runtime of computing a model of degree 100 is nearly two times faster than with only one thread.
Uses MPI routines to parallelize the computation of Laplace series coefficients.
mpirun --mca opal_warn_on_missing_libcuda 0 -np 2 ./new_model_mpi --small --lmodel 100 --recompute --txt --predict --diff --no-ascii
The AAE printed at the bottom is exactly the same as for new_model and new_model_2 which confirms that the coefficients computed are consistent across different implementations.
To confirm that the AAE computed by our program is exactly the same as by the original validate program, let's compute a degree 20 model.
./new_model --small --lmodel 20 --no-ascii --diff --txt
Which computes a model whose AAE is 641.1. We can use the old model's validation program validate to verify that our validation results are consistent with the provided implementation.
./validate --data ../../csv/ETOPO1_small.csv --model sph_small_20.txt --npoint 64800 --lmax 20
Indeed, the Average error computed by validate is 641.1 and therefore we are confident with the validation of our programs new_model, new_model_omp2, and new_model_mpi.