import os
from mot.lib.cl_function import SimpleCLCodeObject
from mot.lib.kernel_data import LocalMemory
from mot.library_functions.base import SimpleCLLibrary, SimpleCLLibraryFromFile, CLLibrary
from pkg_resources import resource_filename
from mot.library_functions.eispack import eispack_tred2, eispack_tql2
from mot.library_functions.unity import log1pmx
from mot.library_functions.polynomials import p1evl, polevl, ratevl, real_zeros_cubic_pol
from mot.library_functions.continuous_distributions.normal import normal_cdf, normal_pdf, normal_logpdf, normal_ppf
from mot.library_functions.continuous_distributions.gamma import gamma_pdf, gamma_logpdf, gamma_ppf, gamma_cdf, \
gamma_cdf_approx, gamma_ppf_approx
from mot.library_functions.error_functions import dawson, CerfImWOfX, erfi
from mot.library_functions.legendre_polynomial import FirstLegendreTerm, LegendreTerms, \
EvenLegendreTerms, OddLegendreTerms
__author__ = 'Robbert Harms'
__date__ = '2018-05-07'
__maintainer__ = 'Robbert Harms'
__email__ = 'robbert.harms@maastrichtuniversity.nl'
__licence__ = 'LGPL v3'
[docs]class Besseli0(SimpleCLLibrary):
def __init__(self):
"""Return the zeroth-order modified Bessel function of the first kind
Original author of C code: M.G.R. Vogelaar
"""
super().__init__('''
double bessel_i0(double x){
double y;
if(fabs(x) < 3.75){
y = (x / 3.75) * (x / 3.75);
return 1.0 + y * (3.5156229
+ y * (3.0899424
+ y * (1.2067492
+ y * (0.2659732
+ y * (0.360768e-1
+ y * 0.45813e-2)))));
}
y = 3.75 / fabs(x);
return (exp(fabs(x)) / sqrt(fabs(x)))
* (0.39894228
+ y * (0.1328592e-1
+ y * (0.225319e-2
+ y * (-0.157565e-2
+ y * (0.916281e-2
+ y * (-0.2057706e-1
+ y * (0.2635537e-1
+ y * (-0.1647633e-1
+ y * 0.392377e-2))))))));
}
''')
[docs]class LogBesseli0(SimpleCLLibrary):
def __init__(self):
"""Return the log of the zeroth-order modified Bessel function of the first kind."""
super().__init__('''
double log_bessel_i0(double x){
if(x < 700){
return log(bessel_i0(x));
}
return x - log(2.0 * M_PI * x)/2.0;
}
''', dependencies=(Besseli0(),))
[docs]class LogCosh(SimpleCLLibrary):
def __init__(self):
"""Computes :math:`log(cosh(x))`
For large x this will try to estimate it without overflow. For small x we use the opencl functions log and cos.
The estimation for large numbers has been taken from:
https://github.com/JaneliaSciComp/tmt/blob/master/basics/logcosh.m
"""
super().__init__('''
double log_cosh(double x){
if(x < 50){
return log(cosh(x));
}
return fabs(x) + log(1 + exp(-2.0 * fabs(x))) - log(2.0);
}
''')
[docs]class Rand123(SimpleCLCodeObject):
def __init__(self):
generator = 'threefry'
src = open(os.path.abspath(resource_filename('mot', 'data/opencl/random123/openclfeatures.h'), ), 'r').read()
src += open(os.path.abspath(resource_filename('mot', 'data/opencl/random123/array.h'), ), 'r').read()
src += open(os.path.abspath(resource_filename('mot', 'data/opencl/random123/{}.h'.format(generator)), ),
'r').read()
src += (open(os.path.abspath(resource_filename('mot', 'data/opencl/random123/rand123.h'), ), 'r').read() % {
'GENERATOR_NAME': (generator)
})
super().__init__(src)
[docs]class EuclidianNormFunction(SimpleCLLibraryFromFile):
def __init__(self, memspace='private', memtype='mot_float_type'):
"""A CL functions for calculating the Euclidian distance between n values.
Args:
memspace (str): The memory space of the memtyped array (private, constant, global).
memtype (str): the memory type to use, double, float, mot_float_type, ...
"""
super().__init__(
memtype,
self.__class__.__name__ + '_' + memspace + '_' + memtype,
[],
resource_filename('mot', 'data/opencl/euclidian_norm.cl'),
var_replace_dict={'MEMSPACE': memspace, 'MEMTYPE': memtype})
[docs]class simpsons_rule(SimpleCLLibrary):
def __init__(self, function_name):
"""Create a CL function for integrating a function using Simpson's rule.
This creates a CL function specifically meant for integrating the function of the given name.
The name of the generated CL function will be 'simpsons_rule_<function_name>'.
Args:
function_name (str): the name of the function to integrate, accepting the arguments:
- a: the lower bound of the integral
- b: the upper bound of the integral
- n: the number of steps, i.e. the number of approximations to make
- data: a pointer to some data, this is passed on to the function we are integrating.
"""
super().__init__('''
double simpsons_rule_{f}(double a, double b, uint n, void* data){{
double h = (b - a) / n;
double sum_odds = {f}(a + h/2.0, data);
double sum_evens = 0.0;
double x;
for(uint i = 1; i < n; i++){{
sum_odds += {f}(a + h * i + h / 2.0, data);
sum_evens += {f}(a + h * i, data);
}}
return h / 6.0 * ({f}(a, data) + {f}(b, data) + 4.0 * sum_odds + 2.0 * sum_evens);
}}
'''.format(f=function_name))
[docs]class linear_cubic_interpolation(SimpleCLLibrary):
def __init__(self):
"""Cubic interpolation for a one-dimensional grid.
This uses the theory of Cubic Hermite splines for interpolating a one-dimensional grid of values.
At the borders, it will clip the values to the nearest border.
For more information on this method, see https://en.wikipedia.org/wiki/Cubic_Hermite_spline.
Example usage:
constant float data[] = {1.0, 2.0, 5.0, 6.0};
linear_cubic_interpolation(1.5, 4, data);
"""
super().__init__('''
double linear_cubic_interpolation(double x, int y_len, constant float* y_values){
int n = x;
double u = x - n;
double p0 = y_values[min(max((int)0, n - 1), y_len - 1)];
double p1 = y_values[min(max((int)0, n ), y_len - 1)];
double p2 = y_values[min(max((int)0, n + 1), y_len - 1)];
double p3 = y_values[min(max((int)0, n + 2), y_len - 1)];
double a = 0.5 * (-p0 + 3.0 * p1 - 3.0 * p2 + p3);
double b = 0.5 * (2.0 * p0 - 5.0 * p1 + 4.0 * p2 - p3);
double c = 0.5 * (-p0 + p2);
double d = p1;
return d + u * (c + u * (b + u * a));
}
''')
[docs]class eigenvalues_3x3_symmetric(SimpleCLLibrary):
def __init__(self):
"""Calculate the eigenvalues of a symmetric 3x3 matrix.
This simple algorithm only works in case of a real and symmetric matrix.
The input to this function is an array with the upper triangular elements of the matrix.
The output are the eigenvalues such that eig1 >= eig2 >= eig3, i.e. from large to small.
Args:
A: the upper triangle of an 3x3 matrix
v: the output eigenvalues as a vector of three elements.
References:
[1]: https://en.wikipedia.org/wiki/Eigenvalue_algorithm#3.C3.973_matrices
[2]: Smith, Oliver K. (April 1961), "Eigenvalues of a symmetric 3 × 3 matrix.", Communications of the ACM,
4 (4): 168, doi:10.1145/355578.366316
"""
super().__init__('''
void eigenvalues_3x3_symmetric(double* A, double* v){
double p1 = (A[1] * A[1]) + (A[2] * A[2]) + (A[4] * A[4]);
if (p1 == 0.0){
v[0] = A[0];
v[1] = A[3];
v[2] = A[5];
return;
}
double q = (A[0] + A[3] + A[5]) / 3.0;
double p = sqrt(((A[0] - q)*(A[0] - q) + (A[3] - q)*(A[3] - q) + (A[5] - q)*(A[5] - q) + 2*p1) / 6.0);
double r = (
((A[0] - q)/p) * ((((A[3] - q)/p) * ((A[5] - q)/p)) - ((A[4]/p) * (A[4]/p)))
- (A[1]/p) * ((A[1]/p) * ((A[5] - q)/p) - (A[2]/p) * (A[4]/p))
+ (A[2]/p) * ((A[1]/p) * (A[4]/p) - (A[2]/p) * ((A[3] - q)/p))
) / 2.0;
double phi;
if(r <= -1){
phi = M_PI / 3.0;
}
else if(r >= 1){
phi = 0;
}
else{
phi = acos(r) / 3;
}
v[0] = q + 2 * p * cos(phi);
v[2] = q + 2 * p * cos(phi + (2*M_PI/3.0));
v[1] = 3 * q - v[0] - v[2];
}
''')
[docs]class multiply_square_matrices(SimpleCLLibrary):
def __init__(self):
"""Matrix multiplication of two square matrices.
Having this as a special function is slightly faster than a more generic matrix multiplication algorithm.
All matrices are expected to be in c/row-major order.
Parameters:
n: the rectangular size of the matrix (the number of rows / the number of columns).
A[n*n]: the left matrix
B[n*n]: the right matrix
C[n*n]: the output matrix
"""
super().__init__('''
void multiply_square_matrices(uint n, double* A, double* B, double* C){
int i, j, z;
double sum;
for(int ind = 0; ind < n*n; ind++){
i = ind / n;
j = ind - n * i;
sum = 0;
for(z = 0; z < n; z++){
sum += A[i * n + z] * B[z * n + j];
}
C[ind] = sum;
}
}
''')
[docs]class eigen_decompose_real_symmetric_matrix(SimpleCLLibrary):
def __init__(self):
"""Computes eigenvalues and eigenvectors of real symmetric matrix.
This uses the RS routine from the EISPACK code, to be found at:
https://people.sc.fsu.edu/~jburkardt/c_src/eispack/eispack.html
It first tri-diagonalizes the matrix using Householder transformations and then computes the diagonal
using QR transformations.
This routine only works with real symmetric matrices as input.
Parameters:
n: input, the order of the matrix.
A[n*n]: input, the real symmetric matrix to invert
W[n]: output, the eigenvalues in ascending order.
Z[n*n]: output, the eigenvectors, can coincide with A[n*n].
scratch[n]: input, scratch data
Output:
error code: the error for the the TQL2 routine (see EISPACK).
The no-error, normal completion code is zero.
"""
super().__init__('''
int eigen_decompose_real_symmetric_matrix(int n, double* A, double* w, double* Z, double* scratch){
// tri-diagonalize the matrix
eispack_tred2 ( n, A, w, scratch, Z );
// QR decompose the tri-diagonal
return eispack_tql2 ( n, w, scratch, Z );
}
''', dependencies=[eispack_tred2(), eispack_tql2()])
[docs]class pseudo_inverse_real_symmetric_matrix_upper_triangular(SimpleCLLibrary):
def __init__(self):
"""Compute the pseudo-inverse of a real symmetric matrix stored as an upper triangular vector.
Results are placed in the upper triangular input vector.
Parameters:
n: the size of the symmetric matrix
A[n*(n+1)/2]: on input, the matrix to inverse. On output, the inverse of the matrix.
scratch[2*n + 2*n*n]: scratch data
"""
super().__init__('''
void pseudo_inverse_real_symmetric_matrix_upper_triangular(uint n, double* A, double* scratch){
int i, j, z, ind_counter;
double sum;
double* w = scratch;
double* Z = w + n;
double* decomposition_scratch = Z + n * n;
double* Z_transpose_w = decomposition_scratch + n;
ind_counter = 0;
for (j = 0; j < n; j++){
for (i = j; i < n; i++){
Z[i+j*n] = A[ind_counter];
ind_counter++;
}
}
eigen_decompose_real_symmetric_matrix(n, Z, w, Z, decomposition_scratch);
// inverse the eigenvalues
for(i = 0; i < n; i++){
if(w[i] == 0.){
w[i] = 0;
}
else{
w[i] = fabs(1/w[i]);
}
}
// prepare the left matrix Z.T*w
for(i = 0; i < n; i++){
for(j = 0; j < n; j++){
Z_transpose_w[i * n + j] = Z[j * n + i] * w[j];
}
}
// matrix multiplication of (Z.T*w) * Z
ind_counter = 0;
for(i = 0; i < n; i++){
for(j = i; j < n; j++){
sum = 0;
for(z = 0; z < n; z++){
sum += Z_transpose_w[i * n + z] * Z[z * n + j];
}
A[ind_counter] = sum;
ind_counter++;
}
}
}
''', dependencies=[eigen_decompose_real_symmetric_matrix()])
[docs]class Powell(SimpleCLLibraryFromFile):
def __init__(self, eval_func, nmr_parameters, patience=2, patience_line_search=None,
reset_method='EXTRAPOLATED_POINT', **kwargs):
"""The Powell CL implementation.
Args:
eval_func (mot.lib.cl_function.CLFunction): the function we want to optimize, Should be of signature:
``double evaluate(local mot_float_type* x, void* data_void);``
nmr_parameters (int): the number of parameters in the model, this will be hardcoded in the method
patience (int): the patience of the Powell algorithm
patience_line_search (int): the patience of the line search algorithm. If None, we set it equal to the
patience.
reset_method (str): one of ``RESET_TO_IDENTITY`` or ``EXTRAPOLATED_POINT``. The method used to
reset the search directions every iteration.
"""
dependencies = list(kwargs.get('dependencies', []))
dependencies.append(eval_func)
kwargs['dependencies'] = dependencies
params = {
'FUNCTION_NAME': eval_func.get_cl_function_name(),
'NMR_PARAMS': nmr_parameters,
'RESET_METHOD': reset_method.upper(),
'PATIENCE': patience,
'PATIENCE_LINE_SEARCH': patience if patience_line_search is None else patience_line_search
}
super().__init__(
'int', 'powell', [
'local mot_float_type* model_parameters',
'void* data',
'local mot_float_type* scratch_mot_float_type'
],
resource_filename('mot', 'data/opencl/powell.cl'),
var_replace_dict=params, **kwargs)
[docs] def get_kernel_data(self):
"""Get the kernel data needed for this optimization routine to work."""
return {
'scratch_mot_float_type': LocalMemory(
'mot_float_type', 3 * self._var_replace_dict['NMR_PARAMS'] + self._var_replace_dict['NMR_PARAMS']**2)
}
[docs]class LibNMSimplex(SimpleCLLibraryFromFile):
def __init__(self, function_name):
"""The NMSimplex algorithm as a reusable library component.
Args:
function_name (str): the name of the evaluation function to call, defaults to 'evaluate'.
This should point to a function with signature:
``double evaluate(local mot_float_type* x, void* data_void);``
"""
params = {
'FUNCTION_NAME': function_name
}
super().__init__(
'int', 'lib_nmsimplex', [],
resource_filename('mot', 'data/opencl/lib_nmsimplex.cl'),
var_replace_dict=params)
[docs]class NMSimplex(SimpleCLLibrary):
def __init__(self, function_name, nmr_parameters, patience=200, alpha=1.0, beta=0.5,
gamma=2.0, delta=0.5, scale=0.1, adaptive_scales=True, **kwargs):
self._nmr_parameters = nmr_parameters
if 'dependencies' in kwargs:
kwargs['dependencies'] = list(kwargs['dependencies']) + [LibNMSimplex(function_name)]
else:
kwargs['dependencies'] = [LibNMSimplex(function_name)]
params = {'NMR_PARAMS': nmr_parameters,
'PATIENCE': patience,
'ALPHA': alpha,
'BETA': beta,
'GAMMA': gamma,
'DELTA': delta,
'INITIAL_SIMPLEX_SCALES': '\n'.join('initial_simplex_scale[{}] = {};'.format(ind, scale)
for ind in range(nmr_parameters))}
if adaptive_scales:
params.update(
{'ALPHA': 1,
'BETA': 0.75 - 1.0 / (2 * nmr_parameters),
'GAMMA': 1 + 2.0 / nmr_parameters,
'DELTA': 1 - 1.0 / nmr_parameters}
)
super().__init__('''
int nmsimplex(local mot_float_type* model_parameters, void* data,
local mot_float_type* initial_simplex_scale,
local mot_float_type* nmsimplex_scratch){
if(get_local_id(0) == 0){
%(INITIAL_SIMPLEX_SCALES)s
}
barrier(CLK_LOCAL_MEM_FENCE);
mot_float_type fdiff;
mot_float_type psi = 0;
return lib_nmsimplex(%(NMR_PARAMS)r, model_parameters, data, initial_simplex_scale,
&fdiff, psi, (int)(%(PATIENCE)r * (%(NMR_PARAMS)r+1)),
%(ALPHA)r, %(BETA)r, %(GAMMA)r, %(DELTA)r,
nmsimplex_scratch);
}
''' % params, **kwargs)
[docs] def get_kernel_data(self):
"""Get the kernel data needed for this optimization routine to work."""
return {
'nmsimplex_scratch': LocalMemory(
'mot_float_type', self._nmr_parameters * 2 + (self._nmr_parameters + 1) ** 2 + 1),
'initial_simplex_scale': LocalMemory('mot_float_type', self._nmr_parameters)
}
[docs]class Subplex(SimpleCLLibraryFromFile):
def __init__(self, eval_func, nmr_parameters, patience=10,
patience_nmsimplex=100, alpha=1.0, beta=0.5, gamma=2.0, delta=0.5, scale=1.0, psi=0.001, omega=0.01,
adaptive_scales=True, min_subspace_length='auto', max_subspace_length='auto', **kwargs):
"""The Subplex optimization routines."""
dependencies = list(kwargs.get('dependencies', []))
dependencies.append(eval_func)
dependencies.append(LibNMSimplex('subspace_evaluate'))
kwargs['dependencies'] = dependencies
params = {
'FUNCTION_NAME': eval_func.get_cl_function_name(),
'PATIENCE': patience,
'PATIENCE_NMSIMPLEX': patience_nmsimplex,
'ALPHA': alpha,
'BETA': beta,
'GAMMA': gamma,
'DELTA': delta,
'PSI': psi,
'OMEGA': omega,
'NMR_PARAMS': nmr_parameters,
'ADAPTIVE_SCALES': int(bool(adaptive_scales)),
'MIN_SUBSPACE_LENGTH': (min(2, nmr_parameters) if min_subspace_length == 'auto' else min_subspace_length),
'MAX_SUBSPACE_LENGTH': (min(5, nmr_parameters) if max_subspace_length == 'auto' else max_subspace_length)
}
s = ''
for ind in range(nmr_parameters):
s += 'initial_simplex_scale[{}] = {};'.format(ind, scale)
params['INITIAL_SIMPLEX_SCALES'] = s
super().__init__(
'int', 'subplex', [
'local mot_float_type* const model_parameters',
'void* data',
'local mot_float_type* initial_simplex_scale',
'local mot_float_type* subplex_scratch_float',
'local int* subplex_scratch_int'
],
resource_filename('mot', 'data/opencl/subplex.cl'), var_replace_dict=params, **kwargs)
[docs] def get_kernel_data(self):
"""Get the kernel data needed for this optimization routine to work."""
return {
'subplex_scratch_float': LocalMemory(
'mot_float_type', 4 + self._var_replace_dict['NMR_PARAMS'] * 2
+ self._var_replace_dict['MAX_SUBSPACE_LENGTH'] * 2
+ (self._var_replace_dict['MAX_SUBSPACE_LENGTH'] * 2
+ self._var_replace_dict['MAX_SUBSPACE_LENGTH']+1)**2 + 1),
'subplex_scratch_int': LocalMemory(
'int', 2 + self._var_replace_dict['NMR_PARAMS']
+ (self._var_replace_dict['NMR_PARAMS'] // self._var_replace_dict['MIN_SUBSPACE_LENGTH'])),
'initial_simplex_scale': LocalMemory('mot_float_type', self._var_replace_dict['NMR_PARAMS'])
}
[docs]class LevenbergMarquardt(SimpleCLLibraryFromFile):
def __init__(self, eval_func, nmr_parameters, nmr_observations, jacobian_func, patience=250,
step_bound=100.0, scale_diag=1, usertol_mult=30, **kwargs):
"""The Powell CL implementation.
Args:
eval_func (mot.lib.cl_function.CLFunction): the function we want to optimize, Should be of signature:
``void evaluate(local mot_float_type* x, void* data_void, local mot_float_type* result);``
nmr_parameters (int): the number of parameters in the model, this will be hardcoded in the method
nmr_observations (int): the number of observations in the model
jacobian_func (mot.lib.cl_function.CLFunction): the function used to compute the Jacobian.
patience (int): the patience of the Powell algorithm
patience_line_search (int): the patience of the line search algorithm
reset_method (str): one of ``RESET_TO_IDENTITY`` or ``EXTRAPOLATED_POINT``. The method used to
reset the search directions every iteration.
"""
dependencies = list(kwargs.get('dependencies', []))
dependencies.append(eval_func)
dependencies.append(jacobian_func)
kwargs['dependencies'] = dependencies
var_replace_dict = {
'FUNCTION_NAME': eval_func.get_cl_function_name(),
'JACOBIAN_FUNCTION_NAME': jacobian_func.get_cl_function_name(),
'NMR_PARAMS': nmr_parameters,
'PATIENCE': patience,
'NMR_OBSERVATIONS': nmr_observations,
'SCALE_DIAG': int(bool(scale_diag)),
'STEP_BOUND': step_bound,
'USERTOL_MULT': usertol_mult
}
super().__init__(
'int', 'lmmin', ['local mot_float_type* const model_parameters',
'void* data',
'mot_float_type* scratch_mot_float_type',
'int* scratch_int'],
resource_filename('mot', 'data/opencl/lmmin.cl'),
var_replace_dict=var_replace_dict, **kwargs)
[docs] def get_kernel_data(self):
"""Get the kernel data needed for this optimization routine to work."""
return {
'scratch_mot_float_type': LocalMemory(
'mot_float_type', 8 +
2 * self._var_replace_dict['NMR_OBSERVATIONS'] +
5 * self._var_replace_dict['NMR_PARAMS'] +
self._var_replace_dict['NMR_PARAMS'] * self._var_replace_dict['NMR_OBSERVATIONS']),
'scratch_int': LocalMemory('int', self._var_replace_dict['NMR_PARAMS'])
}