# 1. Code Overview

## 1.1. Computational kernels

At the heart of sasmodels are the individual computational kernels. These functions take a particular $$q$$ value and a set of parameter values and return the expected scattering for that $$q$$. The instructions for writing a kernel are documented in Writing a Plugin Model. The source code for the builtin kernels is stored in sasmodels/models.

The primary interface to the models is through core, which provides functions for listing available models, loading the model definition and compiling the model. Use core.load_model() to load in a model definition and compile it. This makes use of core.load_model_info() to load the model definition and core.build_model() to turn it into a computational kernel model kernel.KernelModel.

The modelinfo.ModelInfo class defines the properties of the model including the available model parameters modelinfo.ParameterTable with individual parameter attributes such as units and hard limits defined in modelinfo.Parameter.

The product.ProductModel and mixture.MixtureModel classes are derived models, created automatically for models with names like “hardsphere*sphere” and “cylinder+sphere”.

In order to test models a minimal set of data management routines is provided in data. In particular, it provides mock data.Data1D and data.Data2D classes which mimic those classes in SasView. The functions data.empty_data1D() and data.empty_data2D() are handy for creating containers with a particular set of $$q$$, $$\Delta q$$ points which can later be evaluated, and data.plot_theory() to show the result. If SasView is available on the path then data.load_data() can be used to load any data type defined in SasView. The function data.plot_data() can plot that data alone without the theory value.

## 1.3. Kernel execution

To execute a computational kernel at a particular set of $$q$$ values, the use kernel.KernelModel.make_kernel(), which returns a callable kernel.Kernel for that $$q$$ vector (or a pair of $$q_x$$, $$q_y$$ for 2-D datasets).

The calculated $$q$$ values should include the measured data points as well as additional $$q$$ values required to properly compute the $$q$$ resolution function. The Resolution subclasses in resolution define the q_calc attribute for this purpose. These are resolution.Perfect1D for perfect resolution, resolution.Pinhole1D for the usual SANS pinhole aperture, resolution.Slit1D for the usual USANS slit aperture and resolution2d.Pinhole2D for 2-D pinhole data. In addition, resolution2d.Slit2D defines 1-D slit smeared data for oriented samples, which require calculation at particular $$q_x$$ and $$q_y$$ values instead of $$|q|$$ as is the case for orientationally averaged USANS. The sesans.SesansTransform class acts like a 1-D resolution, having a q_calc attribute that defines the calculated $$q$$ values for the SANS models that get converted to spin-echo values by the sesans.SesansTransform.apply() method.

Polydispersity is defined by weights.Dispersion classes, weights.RectangleDispersion, weights.ArrayDispersion, weights.LogNormalDispersion, weights.GaussianDispersion, weights.SchulzDispersion. The weights.get_weights() function creates a dispersion object of the class matching weights.Dispersion.type, and calls it with the current value of the parameter. This returns a vector of values and weights for a weighted average polydispersity.

In order to call the kernel.Kernel, the values and weights for all parameters must be composed into a details.CallDetails object. This is a compact vector representation of the entire polydispersity loop that can be passed easily to the kernel. Additionally, the magnetic parameters must be converted from polar to cartesian coordinates. This work is done by the details.make_kernel_args() function, which returns values that can be sent directly to the kernel. It uses details.make_details() to set the details object and details.convert_magnetism() for the coordinate transform.

In the end, making a simple theory function evaluation requires a lot of setup. To make calling them a little easier, the DirectModel and BumpsModel interfaces are provided. See Scripting Interface for an example.

The direct_model.DirectModel interface accepts a data object and a kernel model. Within the class, the _interpret_data() method of direct_model.DataMixin is called to query the data and set the resolution. The _calc_theory() method takes a set of parameter values, builds the kernel arguments, calls the kernel, and applies the resolution function, returning the predicted value for the data $$q$$ values. The bumps_model.Experiment class is like the DirectModel class, but it defines a Fitness class that can be handed directly to the bumps optimization and uncertainty analysis program.

The sasview_model.SasviewModel class defines a SasView 4.x compatible interface to the sasmodels definitions, allowing sasmodels to be used directly from SasView. Over time the SasView shim should disappear as SasView access the modelinfo.ModelInfo and computational kernels directly.

## 1.4. Kernel execution

The kernel functions for the most part do not define polydispersity, resolution or magnetism directly. Instead sasmodels automatically applies these, calling the computation kernel as needed.

The outermost loop is the resolution calculation. For the 1-D case this computes a single vector of $$I(q)$$ values and applies the convolution to the resulting set. Since the same $$I(q)$$ vector is used to compute the convolution at each point, it can be precomputed before the convolution, and so the convolution is reasonably efficient. The 2-D case is not that efficient, and instead recomputes the entire shifted/scaled set of $$q_x$$, $$q_y$$ values many times, or very many times depending on the accuracy requested.

Polydispersity is handled as a mesh over the polydisperse parameters. This is the next level of the loop. For C kernels run in a DLL or using OpenCL, the polydisperisty loop is generated separately for each model as C code. Inside the polydispersity loop there is a loop over the magnetic cross sections for magnetic models, updating the SLD parameters with the effective magnetic SLD for that particular $$q$$ value. For OpenCL, each $$q$$ value loops over the polydispersity mesh on a separate processor. For DLL, the outer loop cycles through polydispersity, and the inner loop distributes q values amongst the processors. Like the DLL, the Python kernel execution cycles over the polydisperse parameters and the magnetic cross sections, calling the computation kernel with a vector of $$q$$ values. Assuming the kernel code accepts vectors, this can be fast enough (though it is painfully slow if not vectorized).

Further details are provided in the next section, Calculator Interface

## 1.5. Orientation and Numerical Integration

For 2d data from oriented anisotropic particles, the mean particle orientation is defined by angles $$\theta$$, $$\phi$$ and $$\Psi$$, which are not in general the same as similarly named angles in many form factors. The wikipedia page on Euler angles (https://en.wikipedia.org/wiki/Euler_angles) lists the different conventions available. To quote: “Different authors may use different sets of rotation axes to define Euler angles, or different names for the same angles. Therefore, any discussion employing Euler angles should always be preceded by their definition.”

We are using the $$z$$-$$y$$-$$z$$ convention with extrinsic rotations $$\Psi$$-$$\theta$$-$$\phi$$ for the particle orientation and $$x$$-$$y$$-$$z$$ convention with extrinsic rotations $$\Psi$$-$$\theta$$-$$\phi$$ for jitter, with jitter applied before particle orientation.

When computing the orientation dispersity integral, the weights for the individual points depends on the map projection used to translate jitter angles into latitude/longitude. The choice of projection is set by sasmodels.generate.PROJECTION, with the default PROJECTION=1 for equirectangular and PROJECTION=2 for sinusoidal. The more complicated Guyou and Postel projections are not implemented. See jitter.draw_mesh for details.

For numerical integration within form factors etc. sasmodels is mostly using Gaussian quadrature with 20, 76 or 150 points depending on the model. It also makes use of symmetries such as calculating only over one quadrant rather than the whole sphere. There is often a U-substitution replacing $$\theta$$ with $$cos(\theta)$$ which changes the limits of integration from 0 to $$\pi/2$$ to 0 to 1 and also conveniently absorbs the $$sin(\theta)$$ scale factor in the integration. This can cause confusion if checking equations to include in a paper or thesis! Most models use the same core kernel code expressed in terms of the rotated view ($$q_a$$, $$q_b$$, $$q_c$$) for both the 1D and the 2D models, but there are also historical quirks such as the parallelepiped model, which has a useless transformation representing $$j_0(a q_a)$$ as $$j_0(b q_a a/b)$$.

Useful testing routines include:

The sascomp utility is used to view and compare models with different parameters and calculation engines. The usual case is to simply plot a model that you are developing:

python sascomp path/to/model.py


Once the obvious problems are addressed, check the numerical precision across a variety of randomly generated inputs:

python sascomp -engine=single,double path/to/model.py -sets=10


You can compare different parameter values for the same or different models. For example when looking along the long axis of a cylinder ($$\theta=0$$), dispersity in $$\theta$$ should be equivalent to dispersity in $$\phi$$ when $$\phi=90$$:

python sascomp -2d cylinder theta=0 phi=0,90 theta_pd_type=rectangle \\


It turns out that they are not because the equirectangular map projection weights the points by $$\cos(\theta)$$ so $$\Delta\theta$$ is not identical to $$\Delta\phi$$. Setting PROJECTION=2 in sasmodels.generate helps somewhat. Postel would help even more in this case, though leading to distortions elsewhere. See sasmodels.compare for many more details.

sascomp -ngauss=n allows you to set the number of quadrature points used for the 1D integration for any model. For example, a carbon nanotube with length 10 $$\mu$$m and radius 1 nm is not computed correctly at high $$q$$:

python sascomp cylinder length=100000 radius=10 -ngauss=76,500 -double -highq


Note: ticket 702 gives some forms for long rods and thin disks that may be used in place of the integration, depending on $$q$$, radius and length; if the cylinder model is updated with these corrections then above call will show no difference.

explore/check1d.py uses sasmodels 1D integration and compares that with a rectangle distribution in $$\theta$$ and $$\phi$$, with $$\theta$$ limits set to $$\pm 90/\sqrt(3)$$ and $$\phi$$ limits set to $$\pm 180/\sqrt(3)$$ [The rectangle weight function uses the fact that the distribution width column is labelled sigma to decide that the 1-$$\sigma$$ width of a rectangular distribution needs to be multiplied by $$\sqrt(3)$$ to get the corresponding gaussian equivalent, or similar reasoning.] This should rotate the sample through the entire $$\theta$$-$$\phi$$ surface according to the pattern that you see in jitter.py when you use ‘rectangle’ rather than ‘gaussian’ for its distribution without changing the viewing angle. In order to match the 1-D pattern for an arbitrary viewing angle on triaxial shapes, we need to integrate over $$\theta$$, $$\phi$$ and $$\Psi$$.

sascomp -sphere=n uses the same rectangular distribution as check1d to compute the pattern of the $$q_x$$-$$q_y$$ grid. This ought to produce a spherically symmetric pattern.

explore/precision.py investigates the accuracy of individual functions on the different execution platforms. This includes the basic special functions as well as more complex expressions used in scattering. In many cases the OpenCL function in sasmodels will use a polynomial approximation over part of the range to improve accuracy, as shown in:

python explore/precision.py 3j1/x


explore/realspace.py allows you to set up a Monte Carlo simulation of your model by sampling random points within and computing the 1D and 2D scattering patterns. This was used to check the core shell parallelepiped example. This is similar to the general sas calculator in sasview, though it uses different code.

sasmodels/jitter.py is for exploring different options for handling orientation and orientation dispersity. It uses sasmodels/guyou.py to generate the Guyou projection.

explore/asymint.py is a direct implementation of the 1D integration for a number of different models. It calculates the integral for a particular $$q$$ using several different integration schemes, including mpmath with 100 bits of precision (33 digits), so you can use it to check the target values for the 1D model tests. This is not a general purpose tool; you will need to edit the file to change the model parameters. It does not currently apply the $$u=cos(\theta)$$ substitution that many models are using internally so the 76-point gaussian quadrature may not match the value produced by the eqivalent model from sasmodels.

explore/symint.py is for rotationally symmetric models (just cylinder for now), so it can compute an entire curve rather than a single $$q$$ point. It includes code to compare the long cylinder approximation to cylinder.

explore/rpa.py is for checking different implementations of the RPA model against calculations for specific blends. This is a work in (suspended) progress.

There are a few modules left over in explore that can probably be removed. angular_pd.py was an early version of jitter.py. sc.py and sc.c was used to explore different calculations for paracrystal models; it has been absorbed into asymint.py. transform_angles.py translates orientation parameters from the SasView 3.x definition to sasmodels.

explore/angles.py generates code for the view and jitter transformations. Keep this around since it may be needed if we add new projections.

## 1.6. Testing

Individual models should all have test values to make sure that the evaluation is correct. This is particularly important in the context of OpenCL since sasmodels doesn’t control the compiler or the hardware, and since GPUs are notorious for preferring speed over precision. The tests can be run as a group using model_test as main:

$python -m sasmodels.model_test all  Individual models can be listed instead of all, which is convenient when adding new models. The compare module, usually invoked using ./sascomp provides a rich interface for exploring model accuracy, execution speed and parameter ranges. It also allows different models to be compared. The compare_many module does batch comparisons, keeping a list of the particular random seeds which lead to large differences in output between different computing platforms. The rst2html module provides tools for converting model docs to html and viewing the html. This is used by compare to display the model description, such as: $ ./sascomp -html sphere


This makes debugging the latex much faster, though this may require Qt in order for mathjax to work correctly.

When run as main, it can display arbitrary ReStructuredText files. E.g.,

\$ python -m sasmodels.rst2html doc/developer/overview.rst


This is handy for sorting out rst and latex syntax. With some work the results could be improved so that it recognizes sphinx roles such as mod, class and func, and so that it uses the style sheets from the sasmodels docs.

The list_pars module lists all instances of parameters across all models. This helps to make sure that similar parameters have similar names across the different models. With the verbose flag, the particular models which use each named parameter are listed.

## 1.7. Model conversion

Model definitions are not static. As needs change or problems are found, models may be updated with new model names or may be reparameterized with new parameter definitions. For example, in translating the Teubner-Strey model from SasView 3.x to sasmodels, the definition in terms of drho, k, c1, c2, a2 and prefactor was replaced by the defintion in terms of volfraction_a, xi, d, sld_a and sld_b. Within convert, the _hand_convert_3_1_2_to_4_1 function must be called when loading a 3.x model definition to update it to 4.1, and then the model should be further updated to 4.2, 5.0, and so on. The convert.convert_model() function does this, using the conversion table in conversion_table (which handled the major renaming from SasView 3.x to sasmodels), and using the internal _hand_convert function for the more complicated cases.

## 1.8. Other

The exception.annotate_exception() function annotates the current exception with a context string, such as “while opening myfile.dat” without adjusting the traceback.

The alignment.py module is unused.