Calculator Interface

.. currentmodule:: sasmodels

This document describes the layer between the form factor kernels and the model calculator which implements the polydispersity and magnetic SLD calculations. There are three separate implementations of this layer, kernelcl.py for OpenCL, which operates on a single Q value at a time, kerneldll.c for the DLL, which loops over a vector of Q values, and kernelpy.py for python models which operates on vector Q values.

Each implementation provides three different calls Iq, Iqxy and Imagnetic for 1-D, 2-D and 2-D magnetic kernels respectively.

The C code is defined in kernel_iq.c and kernel_iq.cl for DLL and OpenCL respectively. The kernel call looks as follows:

kernel void KERNEL_NAME(
    int nq,                  // Number of q values in the q vector
    int pd_start,            // Starting position in the polydispersity loop
    int pd_stop,             // Ending position in the polydispersity loop
    ProblemDetails *details, // Polydispersity info
    double *values,          // Value and weights vector
    double *q,               // q or (qx,qy) vector
    double *result,          // returned I(q), with result[nq] = pd_weight
    double cutoff)           // polydispersity weight cutoff

The details for OpenCL and the python loop are slightly different, but these data structures are common.

nq indicates the number of q values that will be calculated.

The pd_start and pd_stop parameters set the range of the polydispersity loop to compute for the current kernel call. Give a polydispersity calculation with 30 weights for length and 30 weights for radius for example, there are a total of 900 calls to the form factor required to compute the kernel. These might be done in chunks of 100, so the first call would start at zero and stop after 100 iterations. The second call would then have to set the length index to 3 and the radius index to 10 for a position of 3*30+10=100, and could then proceed to position 200. This allows us to interrupt the calculation in the middle of a long polydispersity loop without having to do special tricks with the C code. More importantly, it stops the OpenCL kernel in a reasonable time; because the GPU is used by the operating system to show its windows, if a GPU kernel runs too long then it will be automatically killed and no results will be returned to the caller.

The ProblemDetails structure is a direct map of the :class:`details.CallDetails` buffer. This indicates which parameters are polydisperse, and where in the values vector the values and weights can be found. For each polydisperse parameter there is a parameter id, the length of the polydispersity loop for that parameter, the offset of the parameter values in the pd value and pd weight vectors and the 'stride' from one index to the next, which is used to translate between the position in the polydispersity loop and the particular parameter indices. The num_eval field is the total size of the polydispersity loop. num_weights is the number of elements in the pd value and pd weight vectors. num_active is the number of non-trivial pd loops (polydisperse parameters should be ordered by decreasing pd vector length, with a length of 1 meaning no polydispersity). Oriented objects in 2-D need a cos(theta) spherical correction on the angular variation in order to preserve the 'surface area' of the weight distribution. theta_par is the id of the polar coordinate parameter if there is one.

The values vector consists of the fixed values for the model plus pd value and pd weight vectors. There are NUM_VALUES fixed values for the model, which includes the initial two slots for scale and background, the NUM_PARS values for the kernel parameters, three slots for the applied magnetism, and three slots for each of the SLD parameters for the sample magnetiziation (Mx, My, Mz). Sample magnetization is translated from (M, theta, phi) to (Mx, My, Mz) before the kernel is called. After the fixed values comes the pd value vector, with the polydispersity values for each parameter stacked one after the other. The order isn't important since the location for each parameter is stored in the pd_offset field of the ProblemDetails structure, but the values do need to be contiguous. After num_weights values, the pd weight vector is stored, with the same configuration as the pd value vector. Note that the pd vectors can contain values that are not in the polydispersity loop; this is used by :class:`mixture.MixtureKernel` to make it easier to call the various component kernels.

The q vector contains one value for each q for Iq kernels, or a pair of (qx,qy) values for each q for Iqxy and Imagnetic kernels. OpenCL pads all vectors to 32 value boundaries just to be safe, including the values vector and the the results vector.

The results vector contains one slot for each of the nq values, plus one extra slot at the end for the current polydisperse normalization. This is required when the polydispersity loop is broken across several kernel calls.

cutoff is a importance cutoff so that points which contribute negligibly to the total scattering can be skipped without calculating them.

:func:`generate.make_source` defines the following C macros:

• USE_OPENCL is defined if running in opencl

• MAX_PD is the maximum depth of the polydispersity loop [model specific]

• NUM_PARS is the number of parameter values in the kernel. This may be more than the number of parameters if some of the parameters are vector values.

• NUM_VALUES is the number of fixed values, which defines the offset in the value list to the polydisperse value and weight vectors.

• NUM_MAGNETIC is the number of magnetic SLDs

• MAGNETIC_PARS is a comma separated list of the magnetic SLDs, indicating their locations in the values vector.

• MAGNETIC_PAR0 to MAGNETIC_PAR2 are the first three magnetic parameter ids so we can hard code the setting of magnetic values if there are only a few of them.

• KERNEL_NAME is the name of the function being declared

• PARAMETER_TABLE is the declaration of the parameters to the kernel:

  Cylinder:

  #define PARAMETER_TABLE \
  double length; \
  double radius; \
  double sld; \
  double sld_solvent;
  

  Note: scale and background are never included

  Multi-shell cylinder (10 shell max):

  #define PARAMETER_TABLE \
  double num_shells; \
  double length; \
  double radius[10]; \
  double sld[10]; \
  double sld_solvent;
  

• CALL_IQ(q, i, var) is the declaration of a call to the kernel:

  Cylinder:

  #define CALL_IQ(q, i, var) Iq(q[i], \
  var.length, \
  var.radius, \
  var.sld, \
  var.sld_solvent)
  

  Multi-shell cylinder:

  #define CALL_IQ(q, i, var) Iq(q[i], \
  var.num_shells, \
  var.length, \
  var.radius, \
  var.sld, \
  var.sld_solvent)
  

  Cylinder2D:

  #define CALL_IQ(q, i, var) Iqxy(q[2*i], q[2*i+1], \
  var.length, \
  var.radius, \
  var.sld, \
  var.sld_solvent, \
  var.theta, \
  var.phi)
  

• CALL_VOLUME(var) is similar, but for calling the form volume:

  #define CALL_VOLUME(var) \
  form_volume(var.length, var.radius)
  

There is an additional macro that can be defined within the model.c file:

• INVALID(var) is a test for model parameters in the correct range:

  Cylinder:

  #define INVALID(var) 0
  

  BarBell:

  #define INVALID(var) (var.bell_radius < var.radius)
  

  Model with complicated constraints:

  inline bool constrained(p1, p2, p3) { return expression; }
  #define INVALID(var) constrained(var.p1, var.p2, var.p3)
  

Our design supports a limited number of polydispersity loops, wherein we need to cycle through the values of the polydispersity, calculate the I(q, p) for each combination of parameters, and perform a normalized weighted sum across all the weights. Parameters may be passed to the underlying calculation engine as scalars or vectors, but the polydispersity calculator treats the parameter set as one long vector.

Let's assume we have 8 parameters in the model, with two polydisperse. Since this is a 1-D model the orientation parameters won't be used:

0: scale        {scl = constant}
1: background   {bkg = constant}
2: radius       {r = vector of 10pts}
3: length       {l = vector of 30pts}
4: sld          {s = constant/(radius**2*length)}
5: sld_solvent  {s2 = constant}
6: theta        {not used}
7: phi          {not used}

This generates the following call to the kernel. Note that parameters 4 and 5 are treated as polydisperse even though they are not --- this is because it is harmless to do so and simplifies the looping code:

MAX_PD = 4
NUM_PARS = 6          // kernel parameters only
NUM_VALUES = 17       // all values, including scale and background
NUM_MAGNETIC = 2      // two parameters might be magnetic
MAGNETIC_PARS = 4, 5  // they are sld and sld_solvent
MAGNETIC_PAR0 = 4     // sld index
MAGNETIC_PAR1 = 5     // solvent index
details {
    pd_par = {3, 2, 4, 5}         // parameters *radius* and *length* vary
    pd_length = {30, 10, 1, 1}    // *length* has more, so it is first
    pd_offset = {10, 0, 31, 32}   // *length* starts at index 10 in weights
    pd_stride = {1, 30, 300, 300} // cumulative product of pd length
    num_eval = 300   // 300 values in the polydispersity loop
    num_weights = 42 // 42 values in the pd vector
    num_active = 2   // only the first two pd are active
    theta_var =  6   // spherical correction
}
values = { scl, bkg,                                  // universal
           r, l, s, s2, theta, phi,                   // kernel pars
           in spin, out spin, spin angle,             // applied magnetism
           mx s, my s, mz s, mx s2, my s2, mz s2,     // magnetic slds
           r0, .., r9, l0, .., l29, s, s2,            // pd values
           r0, .., r9, l0, .., l29, s, s2}            // pd weights
nq = 130
q = { q0, q1, ..., q130, x, x }  # pad to 8 element boundary
result = {r1, ..., r130, pd_norm, x }

The polydisperse parameters are stored in as an array of parameter indices, one for each polydisperse parameter, stored in pd_par[n]. Non-polydisperse parameters do not appear in this array. Each polydisperse parameter has a weight vector whose length is stored in pd_length[n]. The weights are stored in a contiguous vector of weights for all parameters, with the starting position for the each parameter stored in pd_offset[n]. The values corresponding to the weights are stored together in a separate weights[] vector, with offset stored in par_offset[pd_par[n]]. Polydisperse parameters should be stored in decreasing order of length for highest efficiency.

We limit the number of polydisperse dimensions to MAX_PD (currently 4), though some models may have fewer if they have fewer polydisperse parameters. The main reason for the limit is to reduce code size. Each additional polydisperse parameter requires a separate polydispersity loop. If more than 4 levels of polydispersity are needed, then kernel_iq.c and kernel_iq.cl will need to be extended.

Constraints between parameters are not supported. Instead users will have to define a new model with the constraints built in by making a copy of the existing model. Mac provides OpenCL and we are supplying the tinycc compiler for Windows so this won't be a complete limitation, but it is rather inconvenient. The process could perhaps be automated so that there is no code copying required, just an alternate CALL_IQ macro that implements the constraints. Think carefully about constraining theta since the polar coordinates normalization is tied to this parameter.

If there is no polydispersity we pretend that it is polydisperisty with one parameter, pd_start=0 and pd_stop=1. We may or may not short circuit the calculation in this case, depending on how much time it saves.

The problem details structure could be allocated and sent in as an integer array using the read-only flag. This would allow us to copy it once per fit along with the weights vector, since features such as the number of polydisperity elements per pd parameter or the coordinated won't change between function evaluations. A new parameter vector must be sent for each I(q) evaluation. This is not currently implemented, and would require some resturcturing of the :class:`sasview_model.SasviewModel` interface.

The results array will be initialized to zero for polydispersity loop entry zero, and preserved between calls to [start, stop] so that the results accumulate by the time the loop has completed. Background and scale will be applied when the loop reaches the end. This does require that the results array be allocated read-write, which is less efficient for the GPU, but it makes the calling sequence much more manageable.

For accuracy we may want to introduce Kahan summation into the integration:

double accumulated_error = 0.0;
...
#if USE_KAHAN_SUMMATION
    const double y = next - accumulated_error;
    const double t = ret + y;
    accumulated_error = (t - ret) - y;
    ret = t;
#else
    ret += next;
#endif

This will require accumulated error for each I(q) value to be preserved between kernel calls to implement this fully. The kernel_iq.c code, which loops over q for each parameter set in the polydispersity loop, will need also need the accumalation vector.