"""

<NAME>. & <NAME>. (2013).
Virtual Library of Simulation Experiments: Test Functions and Datasets.
Retrieved April 18, 2016, from http://www.sfu.ca/~ssurjano.
"""
from __future__ import print_function

from functools import reduce, wraps
import inspect

from numpy import sin, cos, linspace, meshgrid, e, pi, sqrt, exp, log, log1p
from scipy.special import gammaln

from bumps.names import *

class ModelFunction(object):
    _registered = {}  # class mutable containing list of registered functions
    def __init__(self, f, xmin, fmin, bounds, dim):
        self.name = f.__name__
        self.xmin = xmin
        self.fmin = fmin
        self.bounds = bounds
        self.dim = dim
        self.f = f

        # register the function in the list of available functions
        ModelFunction._registered[self.name] = self

    def __call__(self, x):
        return self.f(x)

    def fk(self, k, **kw):
        """
        Return a function with *k* arguments f(x, y, z1, z2, ..., zk-2)
        """
        wrapper = wraps(self.f)
        if k == 1:
            calculator = wrapper(lambda x: self.f((x,), **kw))
        elif k == 2:
            calculator = wrapper(lambda x, y: self.f((x, y), **kw))
        else:
            args = ",".join("x%d"%j for j in range(1,k+1))
            context = {'self': self, 'kw': kw}
            calculator = wrapper(eval("lambda %s: self.f((%s), **kw)"
                                      %(args, args), context))
        return calculator

    def fv(self, k, **kw):
        """
        Return a function with arguments f(v) for vector v.
        """
        wrapper = wraps(self.f)
        calculator = wrapper(lambda x: self.f(x, **kw))
        return calculator

    @staticmethod
    def lookup(name):
        return ModelFunction._registered.get(name, None)

    @staticmethod
    def available():
        return list(sorted(ModelFunction._registered.keys()))

def select_function(argv, vector=True):
    if len(sys.argv) == 0:
        raise ValueError("no function provided")

    model = ModelFunction.lookup(argv[0])
    if model is None:
        raise ValueError("unknown model %s"%model)

    dim = int(argv[1]) if len(argv) > 1 else 2

    return model.fv(dim) if vector else model.fk(dim)


def fit_function(xmin=None, fmin=None, bounds=(-inf, inf), dim=None):
    return lambda f: ModelFunction(f, xmin, fmin, bounds, dim)


# ================ Model functions ====================

def prod(L):
    return reduce(lambda x,y: x*y, L, 1)

@fit_function(fmin=0.0, xmin=0.0)
def gauss(x):
    """
    Multivariate gaussian distribution
    """
    #mu, sigma = 100.0, 0.001
    mu, sigma = 3.0, 2.0
    # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p)
    #log_norm = 0.5*len(x)*log(2*pi*sigma**2)
    log_norm = 0
    return 0.5*sum(((xi - mu)/sigma)**2 for xi in x) - log_norm

@fit_function(fmin=0.0, xmin=0.0)
def t(x):
    """
    Multivariate t distribution
    """
    mu, sigma, nu = 3.0, 1.0, 2
    p = len(x)
    S = sum(((xi - mu)/sigma)**2 for xi in x)/nu
    # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p)
    log_norm = gammaln(0.5*(nu+p)) - gammaln(0.5*nu) - 0.5*p*log(nu+pi) - p*log(sigma)
    return (nu+p)/2*log1p(S) - log_norm

@fit_function(fmin=0., xmin=3.)
def laplace(x):
    """
    Product of Laplace distributions, mu=3, b=0.1.
    """
    return sum(abs(xi-3.)/0.1 for xi in x)

@fit_function(fmin=0., xmin=3.)
def sin_plus_quadratic(x, c=3., d=2., m=5., h=2.):
    """
    Sin + quadratic.  Multimodal with global minimum.

    *c* is the center point where the function is minimized.

    *d* is the distance between modes, one per dimension.

    *h* is the sine wave amplitude, on per dimension, which controls
    the height of the barrier between modes.

    *m* is the curvature of the quadratic, one per dimension.
    """
    n = len(x)
    if np.isscalar(c): c = [c]*n
    if np.isscalar(d): d = [d]*n
    if np.isscalar(h): h = [h]*n
    if np.isscalar(m): m = [m]*n
    return (sum(hi*(sin((2*pi/di)*xi-ci)+1.) for xi,ci,di,hi in zip(x, c, d, h))
            + sum(((xi-ci)/float(mi))**2 for xi,ci,mi in zip(x, c, m)))

@fit_function(fmin=0.0, xmin=0.0)
def stepped_well(x):
    return sum(np.floor(abs(xi)) for xi in x)

@fit_function(xmin=0.0, fmin=0.0, bounds=(-32.768, 32.768))
def ackley(x, a=20., b=0.2, c=2*pi):
    """
    Multimodal with deep global minimum.
    """
    n = len(x)
    return (-a*exp(-b*sqrt(sum(xi**2 for xi in x)/n))
            - exp(sum(cos(c*xi) for xi in x)/n) + a + e)

@fit_function(dim=2, xmin=(3, 0.5), fmin=0.0, bounds=(-4.5, 4.5))
def beale(xy):
    x, y = xy
    return (1.5 - x*y)**2 + (2.25 - x + x*y**2)**2 + (2.625 - x + x*y**3)**2

_TRAY=1.34941
@fit_function(dim=2, fmin=-2.06261, bounds=(-10, 10),
              xmin=((_TRAY, _TRAY), (_TRAY, -_TRAY),
                      (-_TRAY, _TRAY), (-_TRAY, -_TRAY)))
def cross_in_tray(xy):
    x, y = xy
    return -0.0001*(abs(sin(x)*sin(y)*exp(abs(100-sqrt(x**2+y**2)/pi)))+1)**0.1

@fit_function(bounds=(-600, 600), xmin=0.0, fmin=0.0)
def griewank(x):
    return (1 + sum(xi**2 for xi in x)**2/4000
            - prod(cos(xi/sqrt(i+1)) for i,xi in enumerate(x)))


@fit_function(bounds=(-5.12, 5.12), xmin=0.0, fmin=0.0)
def rastrigin(x, A=10.):
    """
    Multimodal with global minimum near local minima.
    """
    n = len(x)
    return A*n + sum(xi**2 - A*cos(2*pi*xi) for xi in x)


# could also use bounds=(-2.048, 2.048)
@fit_function(bounds=(-5, 10), xmin=1., fmin=0.)
def rosenbrock(x):
    """
    Unimodal with narrow parabolic valley.
    """
    return sum(100*(xn-xp**2)**2 + (xp-1)**2 for xp, xn in zip(x[:-1], x[1:]))


# ========================== wrapper ==================

def plot2d(fn, args=None, range=(-10,10)):
    """
    Return a mesh plotter for the given function.

    *args* are the function arguments that are to be meshed (usually the
    first two arguments to the function).  *range* is the bounding box
    for the 2D mesh.

    All arguments except the meshed arguments are held fixed.
    """
    fnargs, _, _, _ = inspect.getargspec(fn)
    if len(fnargs) < 2:
        args = fnargs[:1]
        def plot1d(view=None, **kw):
            import pylab
            x = kw[args[0]]
            r = linspace(range[0], range[1], 500)
            kw[args[0]] = x+r
            pylab.plot(x+r, fn(**kw))
            pylab.xlabel(args[0])
            pylab.ylabel("-log P(%s)"%args[0])
        return plot1d

    if args is None:
        args = fnargs[:2]
    if not all(k in fnargs for k in args):
        raise ValueError("args %s not part of function"%str(args))

    def plotter(view=None, **kw):
        import pylab
        x, y = kw[args[0]], kw[args[1]]
        r = linspace(range[0], range[1], 200)
        X, Y = meshgrid(x+r, y+r)
        kw[args[0]], kw[args[1]] = X, Y
        pylab.pcolormesh(x+r, y+r, fn(**kw))
        pylab.plot(x, y, 'o', hold=True, markersize=6,
                   markerfacecolor='red', markeredgecolor='black',
                   markeredgewidth=1, alpha=0.7)
        pylab.xlabel(args[0])
        pylab.ylabel(args[1])
    return plotter


def columnize(L, indent="", width=79):
    # type: (List[str], str, int) -> str
    """
    Format a list of strings into columns.

    Returns a string with carriage returns ready for printing.
    """
    column_width = max(len(w) for w in L) + 1
    num_columns = (width - len(indent)) // column_width
    num_rows = len(L) // num_columns
    L = L + [""] * (num_rows*num_columns - len(L))
    columns = [L[k*num_rows:(k+1)*num_rows] for k in range(num_columns)]
    lines = [" ".join("%-*s"%(column_width, entry) for entry in row)
             for row in zip(*columns)]
    output = indent + ("\n"+indent).join(lines)
    return output

USAGE = """\
Given the name of the test function followed by dimension.  Dimension
defaults to 2.  Available models are:

""" + columnize(ModelFunction.available(), indent="    ")

try:
    nllf = select_function(sys.argv[1:], vector=False)
except:
    print(USAGE, file=sys.stderr)
    sys.exit(1)

plot=plot2d(nllf, range=(-10,10))

M = PDF(nllf, plot=plot)

for p in M.parameters().values():
    # TODO: really should pull value and range out of the bounds for the
    # function, if any are provided.
    p.value = 400*(np.random.rand()-0.5)
    #p.range(-1,1)
    p.range(-200,200)
    #p.range(-inf,inf)

problem = FitProblem(M)

"""

<NAME>. & <NAME>. (2013).
Virtual Library of Simulation Experiments: Test Functions and Datasets.
Retrieved April 18, 2016, from http://www.sfu.ca/~ssurjano.
"""
from __future__ import print_function

from functools import reduce, wraps
import inspect

from numpy import sin, cos, linspace, meshgrid, e, pi, sqrt, exp, log, log1p
from scipy.special import gammaln

from bumps.names import *

class ModelFunction(object):
    _registered = {}  # class mutable containing list of registered functions
    def __init__(self, f, xmin, fmin, bounds, dim):
        self.name = f.__name__
        self.xmin = xmin
        self.fmin = fmin
        self.bounds = bounds
        self.dim = dim
        self.f = f

        # register the function in the list of available functions
        ModelFunction._registered[self.name] = self

    def __call__(self, x):
        return self.f(x)

    def fk(self, k, **kw):
        """
        Return a function with *k* arguments f(x, y, z1, z2, ..., zk-2)
        """
        wrapper = wraps(self.f)
        if k == 1:
            calculator = wrapper(lambda x: self.f((x,), **kw))
        elif k == 2:
            calculator = wrapper(lambda x, y: self.f((x, y), **kw))
        else:
            args = ",".join("x%d"%j for j in range(1,k+1))
            context = {'self': self, 'kw': kw}
            calculator = wrapper(eval("lambda %s: self.f((%s), **kw)"
                                      %(args, args), context))
        return calculator

    def fv(self, k, **kw):
        """
        Return a function with arguments f(v) for vector v.
        """
        wrapper = wraps(self.f)
        calculator = wrapper(lambda x: self.f(x, **kw))
        return calculator

    @staticmethod
    def lookup(name):
        return ModelFunction._registered.get(name, None)

    @staticmethod
    def available():
        return list(sorted(ModelFunction._registered.keys()))

def select_function(argv, vector=True):
    if len(sys.argv) == 0:
        raise ValueError("no function provided")

    model = ModelFunction.lookup(argv[0])
    if model is None:
        raise ValueError("unknown model %s"%model)

    dim = int(argv[1]) if len(argv) > 1 else 2

    return model.fv(dim) if vector else model.fk(dim)


def fit_function(xmin=None, fmin=None, bounds=(-inf, inf), dim=None):
    return lambda f: ModelFunction(f, xmin, fmin, bounds, dim)


# ================ Model functions ====================

def prod(L):
    return reduce(lambda x,y: x*y, L, 1)

@fit_function(fmin=0.0, xmin=0.0)
def gauss(x):
    """
    Multivariate gaussian distribution
    """
    #mu, sigma = 100.0, 0.001
    mu, sigma = 3.0, 2.0
    # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p)
    #log_norm = 0.5*len(x)*log(2*pi*sigma**2)
    log_norm = 0
    return 0.5*sum(((xi - mu)/sigma)**2 for xi in x) - log_norm

@fit_function(fmin=0.0, xmin=0.0)
def t(x):
    """
    Multivariate t distribution
    """
    mu, sigma, nu = 3.0, 1.0, 2
    p = len(x)
    S = sum(((xi - mu)/sigma)**2 for xi in x)/nu
    # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p)
    log_norm = gammaln(0.5*(nu+p)) - gammaln(0.5*nu) - 0.5*p*log(nu+pi) - p*log(sigma)
    return (nu+p)/2*log1p(S) - log_norm

@fit_function(fmin=0., xmin=3.)
def laplace(x):
    """
    Product of Laplace distributions, mu=3, b=0.1.
    """
    return sum(abs(xi-3.)/0.1 for xi in x)

@fit_function(fmin=0., xmin=3.)
def sin_plus_quadratic(x, c=3., d=2., m=5., h=2.):
    """
    Sin + quadratic.  Multimodal with global minimum.

    *c* is the center point where the function is minimized.

    *d* is the distance between modes, one per dimension.

    *h* is the sine wave amplitude, on per dimension, which controls
    the height of the barrier between modes.

    *m* is the curvature of the quadratic, one per dimension.
    """
    n = len(x)
    if np.isscalar(c): c = [c]*n
    if np.isscalar(d): d = [d]*n
    if np.isscalar(h): h = [h]*n
    if np.isscalar(m): m = [m]*n
    return (sum(hi*(sin((2*pi/di)*xi-ci)+1.) for xi,ci,di,hi in zip(x, c, d, h))
            + sum(((xi-ci)/float(mi))**2 for xi,ci,mi in zip(x, c, m)))

@fit_function(fmin=0.0, xmin=0.0)
def stepped_well(x):
    return sum(np.floor(abs(xi)) for xi in x)

@fit_function(xmin=0.0, fmin=0.0, bounds=(-32.768, 32.768))
def ackley(x, a=20., b=0.2, c=2*pi):
    """
    Multimodal with deep global minimum.
    """
    n = len(x)
    return (-a*exp(-b*sqrt(sum(xi**2 for xi in x)/n))
            - exp(sum(cos(c*xi) for xi in x)/n) + a + e)

@fit_function(dim=2, xmin=(3, 0.5), fmin=0.0, bounds=(-4.5, 4.5))
def beale(xy):
    x, y = xy
    return (1.5 - x*y)**2 + (2.25 - x + x*y**2)**2 + (2.625 - x + x*y**3)**2

_TRAY=1.34941
@fit_function(dim=2, fmin=-2.06261, bounds=(-10, 10),
              xmin=((_TRAY, _TRAY), (_TRAY, -_TRAY),
                      (-_TRAY, _TRAY), (-_TRAY, -_TRAY)))
def cross_in_tray(xy):
    x, y = xy
    return -0.0001*(abs(sin(x)*sin(y)*exp(abs(100-sqrt(x**2+y**2)/pi)))+1)**0.1

@fit_function(bounds=(-600, 600), xmin=0.0, fmin=0.0)
def griewank(x):
    return (1 + sum(xi**2 for xi in x)**2/4000
            - prod(cos(xi/sqrt(i+1)) for i,xi in enumerate(x)))


@fit_function(bounds=(-5.12, 5.12), xmin=0.0, fmin=0.0)
def rastrigin(x, A=10.):
    """
    Multimodal with global minimum near local minima.
    """
    n = len(x)
    return A*n + sum(xi**2 - A*cos(2*pi*xi) for xi in x)


# could also use bounds=(-2.048, 2.048)
@fit_function(bounds=(-5, 10), xmin=1., fmin=0.)
def rosenbrock(x):
    """
    Unimodal with narrow parabolic valley.
    """
    return sum(100*(xn-xp**2)**2 + (xp-1)**2 for xp, xn in zip(x[:-1], x[1:]))


# ========================== wrapper ==================

def plot2d(fn, args=None, range=(-10,10)):
    """
    Return a mesh plotter for the given function.

    *args* are the function arguments that are to be meshed (usually the
    first two arguments to the function).  *range* is the bounding box
    for the 2D mesh.

    All arguments except the meshed arguments are held fixed.
    """
    fnargs, _, _, _ = inspect.getargspec(fn)
    if len(fnargs) < 2:
        args = fnargs[:1]
        def plot1d(view=None, **kw):
            import pylab
            x = kw[args[0]]
            r = linspace(range[0], range[1], 500)
            kw[args[0]] = x+r
            pylab.plot(x+r, fn(**kw))
            pylab.xlabel(args[0])
            pylab.ylabel("-log P(%s)"%args[0])
        return plot1d

    if args is None:
        args = fnargs[:2]
    if not all(k in fnargs for k in args):
        raise ValueError("args %s not part of function"%str(args))

    def plotter(view=None, **kw):
        import pylab
        x, y = kw[args[0]], kw[args[1]]
        r = linspace(range[0], range[1], 200)
        X, Y = meshgrid(x+r, y+r)
        kw[args[0]], kw[args[1]] = X, Y
        pylab.pcolormesh(x+r, y+r, fn(**kw))
        pylab.plot(x, y, 'o', hold=True, markersize=6,
                   markerfacecolor='red', markeredgecolor='black',
                   markeredgewidth=1, alpha=0.7)
        pylab.xlabel(args[0])
        pylab.ylabel(args[1])
    return plotter


def columnize(L, indent="", width=79):
    # type: (List[str], str, int) -> str
    """
    Format a list of strings into columns.

    Returns a string with carriage returns ready for printing.
    """
    column_width = max(len(w) for w in L) + 1
    num_columns = (width - len(indent)) // column_width
    num_rows = len(L) // num_columns
    L = L + [""] * (num_rows*num_columns - len(L))
    columns = [L[k*num_rows:(k+1)*num_rows] for k in range(num_columns)]
    lines = [" ".join("%-*s"%(column_width, entry) for entry in row)
             for row in zip(*columns)]
    output = indent + ("\n"+indent).join(lines)
    return output

USAGE = """\
Given the name of the test function followed by dimension.  Dimension
defaults to 2.  Available models are:

""" + columnize(ModelFunction.available(), indent="    ")

try:
    nllf = select_function(sys.argv[1:], vector=False)
except:
    print(USAGE, file=sys.stderr)
    sys.exit(1)

plot=plot2d(nllf, range=(-10,10))

M = PDF(nllf, plot=plot)

for p in M.parameters().values():
    # TODO: really should pull value and range out of the bounds for the
    # function, if any are provided.
    p.value = 400*(np.random.rand()-0.5)
    #p.range(-1,1)
    p.range(-200,200)
    #p.range(-inf,inf)

problem = FitProblem(M)

<NAME>. & <NAME>. (2013). Virtual Library of Simulation Experiments: Test Functions and Datasets. Retrieved April 18, 2016, from http://www.sfu.ca/~ssurjano. # class mutable containing list of registered functions # register the function in the list of available functions Return a function with *k* arguments f(x, y, z1, z2, ..., zk-2) Return a function with arguments f(v) for vector v. # ================ Model functions ==================== Multivariate gaussian distribution #mu, sigma = 100.0, 0.001 # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p) #log_norm = 0.5*len(x)*log(2*pi*sigma**2) Multivariate t distribution # note: sqrt(det(Sigma)) = p log(sigma) since Sigma = sigma^2 eye(p) Product of Laplace distributions, mu=3, b=0.1. Sin + quadratic.  Multimodal with global minimum.      *c* is the center point where the function is minimized.      *d* is the distance between modes, one per dimension.      *h* is the sine wave amplitude, on per dimension, which controls     the height of the barrier between modes.      *m* is the curvature of the quadratic, one per dimension. Multimodal with deep global minimum. Multimodal with global minimum near local minima. # could also use bounds=(-2.048, 2.048) Unimodal with narrow parabolic valley. # ========================== wrapper ================== Return a mesh plotter for the given function.      *args* are the function arguments that are to be meshed (usually the     first two arguments to the function).  *range* is the bounding box     for the 2D mesh.      All arguments except the meshed arguments are held fixed. # type: (List[str], str, int) -> str Format a list of strings into columns.      Returns a string with carriage returns ready for printing. \ Given the name of the test function followed by dimension.  Dimension defaults to 2.  Available models are: # TODO: really should pull value and range out of the bounds for the # function, if any are provided. #p.range(-1,1) #p.range(-inf,inf)