# Mesh-Based Source Sampling¶

The source sampling module implements mesh-based source sampling (both Cartesian and tetrahedral) which can be used as a component within Monte Carlo radiation transport codes. A MOAB mesh tagged with energy-wise source densities (and optional biased source densities) is supplied by the user. The user can then supply six pseudorandom numbers in order to generate a random sample of the particle birth parameters (position, energy, statistical weight and cell number). The source sampling module is written in C++ and has fully-supported C++, Fortran, and Python interfaces, which facilitates its use within physics codes. The source sampling module allows for six sampling modes:

DEFAULT_ANALOG (mode 0)

Particle birth parameters are sampled directly from a unmodified probability distribution function created from the source density mesh voxels (i.e. positions/energies with high source density are sampled more often than those of low source density).

DEFAULT_UNIFORM (mode 1)

All mesh volume elements are sampled with equal probability. Energy bins are sampled in analog from the distribution within a given mesh volume element. Statistical weights of particles are modified accordingly.

DEFAULT_USER (mode 2)

In addition to source densities, the user supplies (on the same mesh) biased source densities. Particle birth parameters are then sampled on the basis of the biased source densities, and the statistical weight of particles is modified accordingly. The biased source density tag has the same length as the source density tag. Alternatively, the tag may have a length of 1, in which case the bias is only applied spatially and energy groups are sampled in analog.

SUBVOXEL_ANALOG (mode 3)

Similar to DEFAULT_ANALOG, but the probability distribution function is created from the source density of mesh subvoxels.

SUBVOXEL_UNIFORM (mode 4)

Similar to DEFAULT_UNIFORM, but the probability distribution function is created from the source density of mesh subvoxels.

SUBVOXEL_USER (mode 5)

Similar to DEFAULT_USER, but the probability distribution function is created from the source density of mesh subvoxels. The tag may have a length of 1, number of photon energy groups, or maximum cells number in a voxel multiplied by the number of photon energy groups.

A complete description of the theory involved can be found in the source_sampling entry in the PyNE theory manual.

## C++ interface¶

An object of the Sampler class is first instantiated using a constructor:

constructor
Sampler(std::string filename,

std::map<std::string, std::string> tag_names, std::vector<double> e_bounds, int mode)

The “filename” is a MOAB mesh file (.h5m). The “tag_names” is a map that stores all the tag names need in the problem, such as the “src_tag_name” (required for all modes), “bias_tag_name” (required in mode 2 and 5), “cell_number_tag_name” (required for mode 3, 4, 5), “cell_fracs_tag_name” (required for mode 3, 4, 5). The source density can be specified for an arbitrary number of energy groups, stored as a MOAB vector tag. The “e_bounds” parameter describes the upper and lower bounds of these energy groups. For example if the src_tag_name tag is a vector of length 24 (for 24 energy groups), e_bounds should be of length 25. The final parameter determins the source sampling mode.

Once a Sampler object is created the Sampler.particle_birth() method is called. This method takes a single argument: a vector of 6 pseudorandom number between 0 and 1. This method returns a source particle containing the sampled x position, y position, z position, energy, weight and cell number respectively.

An example C++ program is supplied below. This program requires a mesh file named “source.h5m” with a tag named “source_density” of length 1.

#include "stdlib.h"
#include  <iostream>
#include "pyne/source_sampling.h"

int main(){

std::string filename("source.h5m");
std::map<std::string, std::string> tag_names;
tag_names.insert(std::pair<std::string, std::string>  ("src_tag_name",
"source_density"));
std::vector<double> e_bounds;
e_bounds.push_back(0); // 1 energy group, lower bound of 0 upper bound of 1
e_bounds.push_back(1);

pyne::Sampler sampler(filename, tag_names, e_bounds, 0);

std::vector<double> rands;
int i;
for(i=0; i<6; i++) rands.push_back((double)rand()/RAND_MAX);

pyne::SourceParticle s = sampler.particle_birth(rands);

std::cout<<"x: "<<s.get_x()<<std::endl;
std::cout<<"y: "<<s.get_y()<<std::endl;
std::cout<<"z: "<<s.get_z()<<std::endl;
std::cout<<"e: "<<s.get_e()<<std::endl;
std::cout<<"w: "<<s.get_w()<<std::endl;
std::cout<<"c: "<<s.get_c()<<std::endl;

return 0;
}


This program can be complied with:

g++ test.cpp pyne/source_sampling.cpp pyne/measure.cpp -o test -lMOAB -lpyne


## Python interface¶

The Python interface mainly exists for the purpose of testing the Sampler class with python.nose. It can be used in the same manner as the C++ class:

import numpy as np
from random import uniform
from pyne.source_sampling import Sampler, SourceParticle

tag_names = {"src_tag_name": "source_density"}
sampler = Sampler("source.h5m", tag_names, np.array([0, 1]), 0)
s = sampler.particle_birth([uniform(0, 1) for x in range(6)])

print("x: {0}\ny: {1}\nz: {2}\ne: {3}\nw: {4}\nc: {5}".format(
s.x, s.y, s.z, s.e, s.w, s.c))


## Fortran Interface¶

Because Fortran cannot store an instance of the Sampler class, to perform source sampling from Fortran, a free-standing function “sampling_setup” is called to create a global instance of the sampling class. This function takes a single argument: an integer representing the problem mode (0: DEFAULT_USER, 1: DEFAULT_UNIFORM, 2: DEFAULT_USER, 3: SUBVOXEL_ANALOG, 4: SUBVOXEL_UNIFORM, 5: SUBVOXEL_USER). This function assumes the mesh file is “source.h5m” and that the tag names are “source_density”, “biased_source_density”, “cell_number_tag_name” and “cell_fracs_tag_name”. In addition, this function assumes that a file “e_bounds” is present which is a plain text file containing the energy boundaries.

An example program using the Fortran interface is shown below:

program test
implicit none
double precision :: x, y, z, e, w
double precision, dimension(6) :: rands
integer:: i, j, mode, c

mode = 1
call sampling_setup(mode)

do j=1,6
rands(j) = RAND()
end do

call particle_birth(rands, x, y, z, e, w, c)
print*, "x: ", x
print*, "y: ", y
print*, "x: ", z
print*, "e: ", e
print*, "w: ", w
print*, "c: ", c

end program test


This program can be compiled like:

gfortran test.F90 -lpyne -lstdc++ -o test


## Source Sampling in MCNP5¶

Standard MCNP5 ships with an empty source subroutine “source.F90” which can be completed by the user in order to implement any form of custom source sampling. A source.F90 file has been written to allow for the use of PyNE source sampling within MCNP5. This file is found in pyne/share/source.F90. The simplest way to compile MCNP5 with the source subroutine is as follows:

1. Obtain a copy of the MCNP5 source code.

2. Navigate to the folder MCNP5/Source/src: cd MCNP5/Source/src

3. Symlink the following files into this folder:

1. ln -s /path/to/pyne/src/source_sampling.cpp .

2. ln -s /path/to/pyne/src/source_sampling.h .

3. ln -s /path/to/pyne/src/measure.cpp .

4. ln -s /path/to/pyne/src/measure.h .

4. Remove the pre-existing empty source.F90 file.

5. Symlink source.F90: ln -s /path/to/pyne/share/source.F90 .

6. Open the file MCNP/Source/src/FILE.list and edit line 78 to include the additional source files. It should look like CXX_SRC := measure.cpp source_sampling.cpp.

7. Compile MCNP5 using the standard build method.

Once MCNP5 is compiled, MCNP5 can be run normally. The file “source.h5m” and “e_bounds” must be present in the working directory that MCNP5 is run from. The file “source.h5m” should contain source densities (on the “source_density” tag) and optionally biased source densities (the “biased_source_density” tag). The file “e_bounds” should contain the energy boundaries of the photon energy groups used in the activation calculations. An “idum” card must be used in the MCNP5 input file. This card should have three arguments. The first is the sampling mode (0: DEFAULT_ANALOG, 1: DEFAULT_UNIFORM, 2: DEFAULT_USER, 3: SUBVOXEL_ANALOG, 4: SUBVOXEL_UNIFORM, 5: SUBVOXEL_USER). The second is the resample limit for void and cell rejections. If the second argument is set to be a postive integer, the void rejection will be applied, i.e., for a given particle, if a source position is selected in void (MCNP material 0) or in a cell that disagrees with the cell number, the source position is resampled within the selected mesh volume element until either a correct position is found, or this user-specified limit is researched. If the second argument is set to be 0, then the void rejection will be disabled. The third argument should specify the particle type: 1 for neutrons, 2 for photons.

For example, this “idum” card specifies uniform sampling with a resample limit of 100 with source particles specified as photons:

idum 1 100 2


## Source Sampling in MCNP6¶

Another version of the source.F90 file was produced for use with MCNP6. The instructions for how to use it are identical to those for the MCNP5 version except for one difference: the file that should be symlinked is called pyne/share/source_mcnp6.F90 instead. It should still be called source.F90 inside the MCNP source directory. For example:

cd MCNP6/Source/src
ln -s /path/to/pyne/share/source_mcnp6.F90 source.F90