source: sasmodels/doc/developer/calculator.rst @ 4a72d1a

Calculator Interface
====================

The environment needs to provide the following #defines:

- USE_OPENCL is defined if running in opencl
- KERNEL declares a function to be available externally
- KERNEL_NAME is the name of the function being declared
- MAX_PD is the maximum depth of the polydispersity loop
- NPARS is the number of parameters in the kernel
- 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, pars) 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)

- 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 6 parameters in the model, with two polydisperse::

    0: scale        {scl = constant}
    1: background   {bkg = constant}
    5: length       {l = vector of 30pts}
    4: radius       {r = vector of 10pts}
    3: sld          {s = constant/(radius**2*length)}
    2: sld_solvent  {s2 = constant}

This generates the following call to the kernel (where x stands for an
arbitrary value that is not used by the kernel evaluator)::

    NPARS = 4  // scale and background are in all models
    problem {
        pd_par = {5, 4, x, x}         // parameters *radius* and *length* vary
        pd_length = {30, 10, 0, 0}    // *length* has more, so it is first
        pd_offset = {10, 0, x, x}     // *length* starts at index 10 in weights
        pd_stride = {1, 30, 300, 300} // cumulative product of pd length
        pd_isvol = {1, 1, x, x}       // true if weight is a volume weight
        par_offset = {2, 3, 303, 313}  // parameter offsets
        par_coord = {0, 3, 2, 1} // bitmap of parameter dependencies
        fast_coord_index = {5, 3, x, x}
        fast_coord_count = 2  // two parameters vary with *length* distribution
        theta_var = -1   // no spherical correction
        fast_theta = 0   // spherical correction angle is not pd 1
    }

    weight = { l0, .., l29, r0, .., r9}
    pars = { scl, bkg, l0, ..., l29, r0, r1, ..., r9,
             s[l0,r0], ... s[l0,r9], s[l1,r0], ... s[l29,r9] , s2}

    nq = 130
    q = { q0, q1, ..., q130, x, x }  # pad to 8 element boundary
    result = {r1, ..., r130, norm, vol, vol_norm, x, x, x, x, x, x, 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).
This cuts the size of the structure in half compared to allowing a
separate polydispersity for each parameter.  This will help a little
bit for models with large numbers of parameters, such as the onion model.

Parameters may be coordinated.  That is, we may have the value of one
parameter depend on a set of other parameters, some of which may be
polydisperse.  For example, if sld is inversely proportional to the
volume of a cylinder, and the length and radius are independently
polydisperse, then for each combination of length and radius we need a
separate value for the sld.  The caller must provide a coordination table
for each parameter containing the value for each parameter given the
value of the polydisperse parameters v1, v2, etc.  The tables for each
parameter are arranged contiguously in a vector, with offset[k] giving the
starting location of parameter k in the vector.  Each parameter defines
coord[k] as a bit mask indicating which polydispersity parameters the
parameter depends upon. Usually this is zero, indicating that the parameter
is independent, but for the cylinder example given, the bits for the
radius and length polydispersity parameters would both be set, the result
being a (#radius x #length) table, or maybe a (#length x #radius) table
if length comes first in the polydispersity table.

NB: If we can guarantee that a compiler and OpenCL driver are available,
we could instead create the coordination function on the fly for each
parameter, saving memory and transfer time, but requiring a C compiler
as part of the environment.

In ordering the polydisperse parameters by decreasing length we can
iterate over the longest dispersion weight vector first.  All parameters
coordinated with this weight vector (the 'fast' parameters), can be
updated with a simple increment to the next position in the parameter
value table.  The indices of these parameters is stored in fast_coord_index[],
with fast_coord_count being the number of fast parameters.  A total
of NPARS slots is allocated to allow for the case that all parameters
are coordinated with the fast index, though this will likely be mostly
empty.  When the fast increment count reaches the end of the weight
vector, then the index of the second polydisperse parameter must be
incremented, and all of its coordinated parameters updated.  Because this
operation is not in the inner loop, a slower algorithm can be used.

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 can be allocated and sent in as an integer
array using the read-only flag.  This allows 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 is sent for
each I(q) evaluation.

To protect against expensive evaluations taking all the GPU resource
on large fits, the entire polydispersity will not be computed at once.
Instead, a start and stop location will be sent, indicating where in the
polydispersity loop the calculation should start and where it should
stop.  We can do this for arbitrary start/stop points since we have
unwound the nested loop.  Instead, we use the same technique as array
index translation, using div and mod to figure out the i,j,k,...
indices in the virtual nested loop.

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.

Scale and background cannot be coordinated with other polydisperse parameters

Oriented objects in 2-D need a spherical correction on the angular variation
in order to preserve the 'surface area' of the weight distribution.

TODO: cutoff

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