source: sasmodels/sasmodels/generate.py @ b3f6bc3

"""
SAS model constructor.

Small angle scattering models are defined by a set of kernel functions:

    *Iq(q, p1, p2, ...)* returns the scattering at q for a form with
    particular dimensions averaged over all orientations.

    *Iqxy(qx, qy, p1, p2, ...)* returns the scattering at qx,qy for a form
    with particular dimensions for a single orientation.

    *Imagnetic(qx, qy, result[], p1, p2, ...)* returns the scattering for the
    polarized neutron spin states (up-up, up-down, down-up, down-down) for
    a form with particular dimensions for a single orientation.

    *form_volume(p1, p2, ...)* returns the volume of the form with particular
    dimension.

    *ER(p1, p2, ...)* returns the effective radius of the form with
    particular dimensions.

    *VR(p1, p2, ...)* returns the volume ratio for core-shell style forms.

These functions are defined in a kernel module .py script and an associated
set of .c files.  The model constructor will use them to create models with
polydispersity across volume and orientation parameters, and provide
scale and background parameters for each model.

*Iq*, *Iqxy*, *Imagnetic* and *form_volume* should be stylized C-99
functions written for OpenCL.  All functions need prototype declarations
even if the are defined before they are used.  OpenCL does not support
*#include* preprocessor directives, so instead the list of includes needs
to be given as part of the metadata in the kernel module definition.
The included files should be listed using a path relative to the kernel
module, or if using "lib/file.c" if it is one of the standard includes
provided with the sasmodels source.  The includes need to be listed in
order so that functions are defined before they are used.

Floating point values should be declared as *double*.  For single precision
calculations, *double* will be replaced by *float*.  The single precision
conversion will also tag floating point constants with "f" to make them
single precision constants.  When using integral values in floating point
expressions, they should be expressed as floating point values by including
a decimal point.  This includes 0., 1. and 2.

OpenCL has a *sincos* function which can improve performance when both
the *sin* and *cos* values are needed for a particular argument.  Since
this function does not exist in C99, all use of *sincos* should be
replaced by the macro *SINCOS(value,sn,cn)* where *sn* and *cn* are
previously declared *double* variables.  When compiled for systems without
OpenCL, *SINCOS* will be replaced by *sin* and *cos* calls.   If *value* is
an expression, it will appear twice in this case; whether or not it will be
evaluated twice depends on the quality of the compiler.

If the input parameters are invalid, the scattering calculator should
return a negative number. Particularly with polydispersity, there are
some sets of shape parameters which lead to nonsensical forms, such
as a capped cylinder where the cap radius is smaller than the
cylinder radius.  The polydispersity calculation will ignore these points,
effectively chopping the parameter weight distributions at the boundary
of the infeasible region.  The resulting scattering will be set to
background.  This will work correctly even when polydispersity is off.

*ER* and *VR* are python functions which operate on parameter vectors.
The constructor code will generate the necessary vectors for computing
them with the desired polydispersity.

The available kernel parameters are defined as a list, with each parameter
defined as a sublist with the following elements:

    *name* is the name that will be used in the call to the kernel
    function and the name that will be displayed to the user.  Names
    should be lower case, with words separated by underscore.  If
    acronyms are used, the whole acronym should be upper case.

    *units* should be one of *degrees* for angles, *Ang* for lengths,
    *1e-6/Ang^2* for SLDs.

    *default value* will be the initial value for  the model when it
    is selected, or when an initial value is not otherwise specified.

    [*lb*, *ub*] are the hard limits on the parameter value, used to limit
    the polydispersity density function.  In the fit, the parameter limits
    given to the fit are the limits  on the central value of the parameter.
    If there is polydispersity, it will evaluate parameter values outside
    the fit limits, but not outside the hard limits specified in the model.
    If there are no limits, use +/-inf imported from numpy.

    *type* indicates how the parameter will be used.  "volume" parameters
    will be used in all functions.  "orientation" parameters will be used
    in *Iqxy* and *Imagnetic*.  "magnetic* parameters will be used in
    *Imagnetic* only.  If *type* is the empty string, the parameter will
    be used in all of *Iq*, *Iqxy* and *Imagnetic*.

    *description* is a short description of the parameter.  This will
    be displayed in the parameter table and used as a tool tip for the
    parameter value in the user interface.

The kernel module must set variables defining the kernel meta data:

    *name* is the model name

    *title* is a short description of the model, suitable for a tool tip,
    or a one line model summary in a table of models.

    *description* is an extended description of the model to be displayed
    while the model parameters are being edited.

    *parameters* is the list of parameters.  Parameters in the kernel
    functions must appear in the same order as they appear in the
    parameters list.  Two additional parameters, *scale* and *background*
    are added to the beginning of the parameter list.  They will show up
    in the documentation as model parameters, but they are never sent to
    the kernel functions.

    *source* is the list of C-99 source files that must be joined to
    create the OpenCL kernel functions.  The files defining the functions
    need to be listed before the files which use the functions.

    *ER* is a python function defining the effective radius.  If it is
    not present, the effective radius is 0.

    *VR* is a python function defining the volume ratio.  If it is not
    present, the volume ratio is 1.

    *form_volume*, *Iq*, *Iqxy*, *Imagnetic* are strings containing the
    C source code for the body of the volume, Iq, and Iqxy functions
    respectively.  These can also be defined in the last source file.

An *info* dictionary is constructed from the kernel meta data and
returned to the caller.  It includes the additional fields


The model evaluator, function call sequence consists of q inputs and the return vector,
followed by the loop value/weight vector, followed by the values for
the non-polydisperse parameters, followed by the lengths of the
polydispersity loops.  To construct the call for 1D models, the
categories *fixed-1d* and *pd-1d* list the names of the parameters
of the non-polydisperse and the polydisperse parameters respectively.
Similarly, *fixed-2d* and *pd-2d* provide parameter names for 2D models.
The *pd-rel* category is a set of those parameters which give
polydispersitiy as a portion of the value (so a 10% length dispersity
would use a polydispersity value of 0.1) rather than absolute
dispersity such as an angle plus or minus 15 degrees.

The *volume* category lists the volume parameters in order for calls
to volume within the kernel (used for volume normalization) and for
calls to ER and VR for effective radius and volume ratio respectively.

The *orientation* and *magnetic* categories list the orientation and
magnetic parameters.  These are used by the sasview interface.  The
blank category is for parameters such as scale which don't have any
other marking.

The doc string at the start of the kernel module will be used to
construct the model documentation web pages.  Embedded figures should
appear in the subdirectory "img" beside the model definition, and tagged
with the kernel module name to avoid collision with other models.  Some
file systems are case-sensitive, so only use lower case characters for
file names and extensions.


The function :func:`make` loads the metadata from the module and returns
the kernel source.  The function :func:`doc` extracts the doc string
and adds the parameter table to the top.  The function :func:`sources`
returns a list of files required by the model.
"""

# TODO: identify model files which have changed since loading and reload them.

__all__ = ["make, doc", "sources", "use_single"]

import sys
import os
import os.path
import re

import numpy as np

F64 = np.dtype('float64')
F32 = np.dtype('float32')

# Scale and background, which are parameters common to every form factor
COMMON_PARAMETERS = [
    [ "scale", "", 1, [0, np.inf], "", "Source intensity" ],
    [ "background", "1/cm", 0, [0, np.inf], "", "Source background" ],
    ]


# Conversion from units defined in the parameter table for each model
# to units displayed in the sphinx documentation.
RST_UNITS = {
    "Ang": "|Ang|",
    "1/Ang^2": "|Ang^-2|",
    "1e-6/Ang^2": "|1e-6Ang^-2|",
    "degrees": "degree",
    "1/cm": "|cm^-1|",
    "": "None",
    }

# Headers for the parameters tables in th sphinx documentation
PARTABLE_HEADERS = [
    "Parameter",
    "Description",
    "Units",
    "Default value",
    ]

# Minimum width for a default value (this is shorter than the column header
# width, so will be ignored).
PARTABLE_VALUE_WIDTH = 10

# Header included before every kernel.
# This makes sure that the appropriate math constants are defined, and does
# whatever is required to make the kernel compile as pure C rather than
# as an OpenCL kernel.
KERNEL_HEADER = """\
// GENERATED CODE --- DO NOT EDIT ---
// Code is produced by sasmodels.gen from sasmodels/models/MODEL.c

#ifdef __OPENCL_VERSION__
# define USE_OPENCL
#endif

// If opencl is not available, then we are compiling a C function
// Note: if using a C++ compiler, then define kernel as extern "C"
#ifndef USE_OPENCL
#  ifdef __cplusplus
     #include <cmath>
     #if defined(_MSC_VER)
     #define kernel extern "C" __declspec( dllexport )
     #else
     #define kernel extern "C"
     #endif
     using namespace std;
     inline void SINCOS(double angle, double &svar, double &cvar)
       { svar=sin(angle); cvar=cos(angle); }
#  else
     #include <math.h>
     #if defined(_MSC_VER)
     #define kernel __declspec( dllexport )
     #else
     #define kernel
     #endif
     #define SINCOS(angle,svar,cvar) do {svar=sin(angle);cvar=cos(angle);} while (0)
#  endif
#  define global
#  define local
#  define constant const
#  define powr(a,b) pow(a,b)
#else
#  ifdef USE_SINCOS
#    define SINCOS(angle,svar,cvar) svar=sincos(angle,&cvar)
#  else
#    define SINCOS(angle,svar,cvar) do {svar=sin(angle);cvar=cos(angle);} while (0)
#  endif
#endif

// Standard mathematical constants:
//   M_E, M_LOG2E, M_LOG10E, M_LN2, M_LN10, M_PI, M_PI_2=pi/2, M_PI_4=pi/4,
//   M_1_PI=1/pi, M_2_PI=2/pi, M_2_SQRTPI=2/sqrt(pi), SQRT2, SQRT1_2=sqrt(1/2)
// OpenCL defines M_constant_F for float constants, and nothing if double
// is not enabled on the card, which is why these constants may be missing
#ifndef M_PI
#  define M_PI 3.141592653589793
#endif
#ifndef M_PI_2
#  define M_PI_2 1.570796326794897
#endif
#ifndef M_PI_4
#  define M_PI_4 0.7853981633974483
#endif

// Non-standard pi/180, used for converting between degrees and radians
#ifndef M_PI_180
#  define M_PI_180 0.017453292519943295
#endif
"""


# The I(q) kernel and the I(qx, qy) kernel have one and two q parameters
# respectively, so the template builder will need to do extra work to
# declare, initialize and pass the q parameters.
KERNEL_1D = {
    'fn': "Iq",
    'q_par_decl': "global const double *q,",
    'qinit': "const double qi = q[i];",
    'qcall': "qi",
    'qwork': ["q"],
    }

KERNEL_2D = {
    'fn': "Iqxy",
    'q_par_decl': "global const double *qx,\n    global const double *qy,",
    'qinit': "const double qxi = qx[i];\n    const double qyi = qy[i];",
    'qcall': "qxi, qyi",
    'qwork': ["qx", "qy"],
    }

# Generic kernel template for the polydispersity loop.
# This defines the opencl kernel that is available to the host.  The same
# structure is used for Iq and Iqxy kernels, so extra flexibility is needed
# for q parameters.  The polydispersity loop is built elsewhere and
# substituted into this template.
KERNEL_TEMPLATE = """\
kernel void %(name)s(
    %(q_par_decl)s
    global double *result,
#ifdef USE_OPENCL
    global double *loops_g,
#else
    const int Nq,
#endif
    local double *loops,
    const double cutoff,
    %(par_decl)s
    )
{
#ifdef USE_OPENCL
  // copy loops info to local memory
  event_t e = async_work_group_copy(loops, loops_g, (%(pd_length)s)*2, 0);
  wait_group_events(1, &e);

  int i = get_global_id(0);
  int Nq = get_global_size(0);
#endif

#ifdef USE_OPENCL
  if (i < Nq)
#else
  #pragma omp parallel for
  for (int i=0; i < Nq; i++)
#endif
  {
    %(qinit)s
    double ret=0.0, norm=0.0;
    double vol=0.0, norm_vol=0.0;
%(loops)s
    if (vol*norm_vol != 0.0) {
      ret *= norm_vol/vol;
    }
    result[i] = scale*ret/norm+background;
  }
}
"""

# Polydispersity loop level.
# This pulls the parameter value and weight from the looping vector in order
# in preperation for a nested loop.
LOOP_OPEN="""\
for (int %(name)s_i=0; %(name)s_i < N%(name)s; %(name)s_i++) {
  const double %(name)s = loops[2*(%(name)s_i%(offset)s)];
  const double %(name)s_w = loops[2*(%(name)s_i%(offset)s)+1];\
"""



##########################################################
#                                                        #
#   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   #
#   !!                                              !!   #
#   !!  KEEP THIS CODE CONSISTENT WITH PYKERNEL.PY  !!   #
#   !!                                              !!   #
#   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!   #
#                                                        #
##########################################################


# Polydispersity loop body.
# This computes the weight, and if it is sufficient, calls the scattering
# function and adds it to the total.  If there is a volume normalization,
# it will also be added here.
LOOP_BODY="""\
const double weight = %(weight_product)s;
if (weight > cutoff) {
  const double I = %(fn)s(%(qcall)s, %(pcall)s);
  if (I>=0.0) { // scattering cannot be negative
    ret += weight*I%(sasview_spherical)s;
    norm += weight;
    %(volume_norm)s
  }
  //else { printf("exclude qx,qy,I:%%g,%%g,%%g\\n",%(qcall)s,I); }
}
//else { printf("exclude weight:%%g\\n",weight); }\
"""

# Use this when integrating over orientation
SPHERICAL_CORRECTION="""\
// Correction factor for spherical integration p(theta) I(q) sin(theta) dtheta
double spherical_correction = (Ntheta>1 ? fabs(sin(M_PI_180*theta)) : 1.0);\
"""
# Use this to reproduce sasview behaviour
SASVIEW_SPHERICAL_CORRECTION="""\
// Correction factor for spherical integration p(theta) I(q) sin(theta) dtheta
double spherical_correction = (Ntheta>1 ? fabs(cos(M_PI_180*theta))*M_PI_2 : 1.0);\
"""

# Volume normalization.
# If there are "volume" polydispersity parameters, then these will be used
# to call the form_volume function from the user supplied kernel, and accumulate
# a normalized weight.
VOLUME_NORM="""const double vol_weight = %(vol_weight)s;
    vol += vol_weight*form_volume(%(vol_pars)s);
    norm_vol += vol_weight;\
"""

# functions defined as strings in the .py module
WORK_FUNCTION="""\
double %(name)s(%(pars)s);
double %(name)s(%(pars)s)
{
%(body)s
}\
"""

# Documentation header for the module, giving the model name, its short
# description and its parameter table.  The remainder of the doc comes
# from the module docstring.
DOC_HEADER=""".. _%(name)s:

%(label)s
=======================================================

%(title)s

%(parameters)s

The returned value is scaled to units of |cm^-1|.

%(docs)s
"""

def indent(s, depth):
    """
    Indent a string of text with *depth* additional spaces on each line.
    """
    spaces = " "*depth
    sep = "\n"+spaces
    return spaces + sep.join(s.split("\n"))


def kernel_name(info, is_2D):
    """
    Name of the exported kernel symbol.
    """
    return info['name'] + "_" + ("Iqxy" if is_2D else "Iq")


def use_single(source):
    """
    Convert code from double precision to single precision.
    """
    # Convert double keyword to float.  Accept an 'n' parameter for vector
    # values, where n is 2, 4, 8 or 16. Assume complex numbers are represented
    # as cdouble which is typedef'd to double2.
    source = re.sub(r'(^|[^a-zA-Z0-9_]c?)double(([248]|16)?($|[^a-zA-Z0-9_]))',
                    r'\1float\2', source)
    # Convert floating point constants to single by adding 'f' to the end.
    # OS/X driver complains if you don't do this.
    source = re.sub(r'[^a-zA-Z_](\d*[.]\d+|\d+[.]\d*)([eE][+-]?\d+)?',
                    r'\g<0>f', source)
    return source


def make_kernel(info, is_2D):
    """
    Build a kernel call from metadata supplied by the user.

    *info* is the json object defined in the kernel file.

    *form* is either "Iq" or "Iqxy".

    This does not create a complete OpenCL kernel source, only the top
    level kernel call with polydispersity and a call to the appropriate
    Iq or Iqxy function.
    """

    # If we are building the Iqxy kernel, we need to propagate qx,qy
    # parameters, otherwise we can
    dim = "2d" if is_2D else "1d"
    fixed_pars = info['partype']['fixed-'+dim]
    pd_pars = info['partype']['pd-'+dim]
    vol_pars = info['partype']['volume']
    q_pars = KERNEL_2D if is_2D else KERNEL_1D
    fn = q_pars['fn']

    # Build polydispersity loops
    depth = 4
    offset = ""
    loop_head = []
    loop_end = []
    for name in pd_pars:
        subst = { 'name': name, 'offset': offset }
        loop_head.append(indent(LOOP_OPEN%subst, depth))
        loop_end.insert(0, (" "*depth) + "}")
        offset += '+N'+name
        depth += 2

    # The volume parameters in the inner loop are used to call the volume()
    # function in the kernel, with the parameters defined in vol_pars and the
    # weight product defined in weight.  If there are no volume parameters,
    # then there will be no volume normalization.
    if vol_pars:
        subst = {
            'vol_weight': "*".join(p+"_w" for p in vol_pars),
            'vol_pars': ", ".join(vol_pars),
            }
        volume_norm = VOLUME_NORM%subst
    else:
        volume_norm = ""

    # Define the inner loop function call
    # The parameters to the f(q,p1,p2...) call should occur in the same
    # order as given in the parameter info structure.  This may be different
    # from the parameter order in the call to the kernel since the kernel
    # call places all fixed parameters before all polydisperse parameters.
    fq_pars = [p[0] for p in info['parameters'][len(COMMON_PARAMETERS):]
               if p[0] in set(fixed_pars+pd_pars)]
    if False and "theta" in pd_pars:
        spherical_correction = [indent(SPHERICAL_CORRECTION, depth)]
        weights = [p+"_w" for p in pd_pars]+['spherical_correction']
        sasview_spherical = ""
    elif True and "theta" in pd_pars:
        spherical_correction = [indent(SASVIEW_SPHERICAL_CORRECTION,depth)]
        weights = [p+"_w" for p in pd_pars]
        sasview_spherical = "*spherical_correction"
    else:
        spherical_correction = []
        weights = [p+"_w" for p in pd_pars]
        sasview_spherical = ""
    subst = {
        'weight_product': "*".join(weights),
        'volume_norm': volume_norm,
        'fn': fn,
        'qcall': q_pars['qcall'],
        'pcall': ", ".join(fq_pars), # skip scale and background
        'sasview_spherical': sasview_spherical,
        }
    loop_body = [indent(LOOP_BODY%subst, depth)]
    loops = "\n".join(loop_head+spherical_correction+loop_body+loop_end)

    # declarations for non-pd followed by pd pars
    # e.g.,
    #     const double sld,
    #     const int Nradius
    fixed_par_decl = ",\n    ".join("const double %s"%p for p in fixed_pars)
    pd_par_decl = ",\n    ".join("const int N%s"%p for p in pd_pars)
    if fixed_par_decl and pd_par_decl:
        par_decl = ",\n    ".join((fixed_par_decl, pd_par_decl))
    elif fixed_par_decl:
        par_decl = fixed_par_decl
    else:
        par_decl = pd_par_decl

    # Finally, put the pieces together in the kernel.
    subst = {
        # kernel name is, e.g., cylinder_Iq
        'name': kernel_name(info, is_2D),
        # to declare, e.g., global double q[],
        'q_par_decl': q_pars['q_par_decl'],
        # to declare, e.g., double sld, int Nradius, int Nlength
        'par_decl': par_decl,
        # to copy global to local pd pars we need, e.g., Nradius+Nlength
        'pd_length': "+".join('N'+p for p in pd_pars),
        # the q initializers, e.g., double qi = q[i];
        'qinit': q_pars['qinit'],
        # the actual polydispersity loop
        'loops': loops,
        }
    kernel = KERNEL_TEMPLATE%subst

    # If the working function is defined in the kernel metadata as a
    # string, translate the string to an actual function definition
    # and put it before the kernel.
    if info[fn]:
        subst = {
            'name': fn,
            'pars': ", ".join("double "+p for p in q_pars['qwork']+fq_pars),
            'body': info[fn],
            }
        kernel = "\n".join((WORK_FUNCTION%subst, kernel))
    return kernel

def make_partable(pars):
    """
    Generate the parameter table to include in the sphinx documentation.
    """
    pars = COMMON_PARAMETERS + pars
    column_widths = [
        max(len(p[0]) for p in pars),
        max(len(p[-1]) for p in pars),
        max(len(RST_UNITS[p[1]]) for p in pars),
        PARTABLE_VALUE_WIDTH,
        ]
    column_widths = [max(w, len(h))
                     for w,h in zip(column_widths, PARTABLE_HEADERS)]

    sep = " ".join("="*w for w in column_widths)
    lines = [
        sep,
        " ".join("%-*s"%(w,h) for w,h in zip(column_widths, PARTABLE_HEADERS)),
        sep,
        ]
    for p in pars:
        lines.append(" ".join([
            "%-*s"%(column_widths[0],p[0]),
            "%-*s"%(column_widths[1],p[-1]),
            "%-*s"%(column_widths[2],RST_UNITS[p[1]]),
            "%*g"%(column_widths[3],p[2]),
            ]))
    lines.append(sep)
    return "\n".join(lines)

def _search(search_path, filename):
    """
    Find *filename* in *search_path*.

    Raises ValueError if file does not exist.
    """
    for path in search_path:
        target = os.path.join(path, filename)
        if os.path.exists(target):
            return target
    raise ValueError("%r not found in %s"%(filename, search_path))

def sources(info):
    """
    Return a list of the sources file paths for the module.
    """
    from os.path import abspath, dirname, join as joinpath
    search_path = [ dirname(info['filename']),
                    abspath(joinpath(dirname(__file__),'models')) ]
    return [_search(search_path, f) for f in info['source']]

def make_model(info):
    """
    Generate the code for the kernel defined by info, using source files
    found in the given search path.
    """
    source = [open(f).read() for f in sources(info)]
    # If the form volume is defined as a string, then wrap it in a
    # function definition and place it after the external sources but
    # before the kernel functions.  If the kernel functions are strings,
    # they will be translated in the make_kernel call.
    if info['form_volume']:
        subst = {
            'name': "form_volume",
            'pars': ", ".join("double "+p for p in info['partype']['volume']),
            'body': info['form_volume'],
            }
        source.append(WORK_FUNCTION%subst)
    kernel_Iq = make_kernel(info, is_2D=False) if not callable(info['Iq']) else ""
    kernel_Iqxy = make_kernel(info, is_2D=True) if not callable(info['Iqxy']) else ""
    kernel = "\n\n".join([KERNEL_HEADER]+source+[kernel_Iq, kernel_Iqxy])
    return kernel

def categorize_parameters(pars):
    """
    Build parameter categories out of the the parameter definitions.

    Returns a dictionary of categories.
    """
    partype = {
        'volume': [], 'orientation': [], 'magnetic': [], '': [],
        'fixed-1d': [], 'fixed-2d': [], 'pd-1d': [], 'pd-2d': [],
        'pd-rel': set(),
    }

    for p in pars:
        name,ptype = p[0],p[4]
        if ptype == 'volume':
            partype['pd-1d'].append(name)
            partype['pd-2d'].append(name)
            partype['pd-rel'].add(name)
        elif ptype == 'magnetic':
            partype['fixed-2d'].append(name)
        elif ptype == 'orientation':
            partype['pd-2d'].append(name)
        elif ptype == '':
            partype['fixed-1d'].append(name)
            partype['fixed-2d'].append(name)
        else:
            raise ValueError("unknown parameter type %r"%ptype)
        partype[ptype].append(name)

    return partype

def make(kernel_module):
    """
    Build an OpenCL/ctypes function from the definition in *kernel_module*.

    The module can be loaded with a normal python import statement if you
    know which module you need, or with __import__('sasmodels.model.'+name)
    if the name is in a string.
    """
    # TODO: allow Iq and Iqxy to be defined in python
    from os.path import abspath
    #print kernelfile
    info = dict(
        filename = abspath(kernel_module.__file__),
        name = kernel_module.name,
        title = kernel_module.title,
        description = kernel_module.description,
        parameters = COMMON_PARAMETERS + kernel_module.parameters,
        source = getattr(kernel_module, 'source', []),
        )
    # Fill in attributes which default to None
    info.update((k,getattr(kernel_module, k, None))
                for k in ('ER', 'VR', 'form_volume', 'Iq', 'Iqxy'))
    # Fill in the derived attributes
    info['limits'] = dict((p[0],p[3]) for p in info['parameters'])
    info['partype'] = categorize_parameters(info['parameters'])

    source = make_model(info)

    return source, info

def doc(kernel_module):
    """
    Return the documentation for the model.
    """
    subst = dict(name=kernel_module.name.replace('_','-'),
                 label=" ".join(kernel_module.name.split('_')).capitalize(),
                 title=kernel_module.title,
                 parameters=make_partable(kernel_module.parameters),
                 docs=kernel_module.__doc__)
    return DOC_HEADER%subst



def demo_time():
    import datetime
    from .models import cylinder
    toc = lambda: (datetime.datetime.now()-tic).total_seconds()
    tic = datetime.datetime.now()
    source, info = make(cylinder)
    print "time:",toc()

def demo():
    from .models import cylinder
    source, info = make(cylinder)
    #print doc(cylinder)
    print source

if __name__ == "__main__":
    demo()