"""\
##########################################
Partial least sqaures regression (``PLS``)
##########################################

.. index:: regression

.. _`Parital Least Squares Regression`: http://en.wikipedia.org/wiki/Partial_least_squares_regression

`Partial least squares
<http://en.wikipedia.org/wiki/Partial_least_squares_regression>`_
regression is a statistical method for simultaneous prediction of
multiple response variables. Orange's implementation is
based on `Scikit learn python implementation
<https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/pls.py>`_.

The following code shows how to fit a PLS regression model on a multi-target data set.

.. literalinclude:: code/pls-example.py
    :lines: 7,9,13,14

.. autoclass:: PLSRegressionLearner
    :members:

.. autoclass:: PLSRegression
    :members:

Utility functions
-----------------

.. autofunction:: normalize_matrix

.. autofunction:: nipals_xy

.. autofunction:: svd_xy

========
Examples
========

The following code predicts the values of output variables for the
first two instances in ``data``.


.. literalinclude:: code/pls-example.py
    :lines: 16-20

::

    Actual     [<orange.Value 'Y1'='0.490'>, <orange.Value 'Y2'='1.237'>, <orange.Value 'Y3'='1.808'>, <orange.Value 'Y4'='0.422'>]
    Predicted  [<orange.Value 'Y1'='0.613'>, <orange.Value 'Y2'='0.826'>, <orange.Value 'Y3'='1.084'>, <orange.Value 'Y4'='0.534'>]

    Actual     [<orange.Value 'Y1'='0.167'>, <orange.Value 'Y2'='-0.664'>, <orange.Value 'Y3'='-1.378'>, <orange.Value 'Y4'='0.589'>]
    Predicted  [<orange.Value 'Y1'='0.058'>, <orange.Value 'Y2'='-0.706'>, <orange.Value 'Y3'='-1.420'>, <orange.Value 'Y4'='0.599'>]

To see the coefficient of the model, print the model:

.. literalinclude:: code/pls-example.py
    :lines: 22

::

    Regression coefficients:
                       Y1           Y2           Y3           Y4
          X1        0.714        2.153        3.590       -0.078 
          X2       -0.238       -2.500       -4.797       -0.036 
          X3        0.230       -0.314       -0.880       -0.060 

Note that coefficients are stored in a matrix since the model predicts
values of multiple outputs.
"""

import Orange
import numpy

from Orange.regression import base
from numpy import dot, zeros
from numpy import linalg
from numpy.linalg import svd, pinv

from Orange.utils import deprecated_members, deprecated_keywords


def normalize_matrix(X):
    """
    Normalize a matrix column-wise: subtract the means and divide by
    standard deviations. Returns the standardized matrix, sample mean
    and standard deviation

    :param X: data matrix
    :type X: :class:`numpy.array`
   
    """
    mu_x, sigma_x = numpy.mean(X, axis=0), numpy.std(X, axis=0)
    sigma_x[sigma_x == 0] = 1.
    return (X - mu_x)/sigma_x, mu_x, sigma_x

@deprecated_keywords({"maxIter": "max_iter"})
def nipals_xy(X, Y, mode="PLS", max_iter=500, tol=1e-06):
    """
    NIPALS algorithm; returns the first left and rigth singular
    vectors of X'Y.

    :param X, Y: data matrix
    :type X, Y: :class:`numpy.array`

    :param mode: possible values "PLS" (default) or "CCA" 
    :type mode: string

    :param max_iter: maximal number of iterations (default: 500)
    :type max_iter: int

    :param tol: tolerance parameter; if norm of difference
        between two successive left singular vectors is less than tol,
        iteration is stopped
    :type tol: a not negative float
            
    """
    yScore, uOld, ite = Y[:, [0]], 0, 1
    Xpinv = Ypinv = None
    # Inner loop of the Wold algo.
    while True and ite < max_iter:
        # Update u: the X weights
        if mode == "CCA":
            if Xpinv is None:
                Xpinv = linalg.pinv(X) # compute once pinv(X)
            u = dot(Xpinv, yScore)
        else: # mode PLS
        # Mode PLS regress each X column on yScore
            u = dot(X.T, yScore) / dot(yScore.T, yScore)
        # Normalize u
        u /= numpy.sqrt(dot(u.T, u))
        # Update xScore: the X latent scores
        xScore = dot(X, u)

        # Update v: the Y weights
        if mode == "CCA":
            if Ypinv is None:
                Ypinv = linalg.pinv(Y) # compute once pinv(Y)
            v = dot(Ypinv, xScore)
        else:
            # Mode PLS regress each X column on yScore
            v = dot(Y.T, xScore) / dot(xScore.T, xScore)
        # Normalize v
        v /= numpy.sqrt(dot(v.T, v))
        # Update yScore: the Y latent scores
        yScore = dot(Y, v)

        uDiff = u - uOld
        if dot(uDiff.T, uDiff) < tol or Y.shape[1] == 1:
            break
        uOld = u
        ite += 1
    return u, v

def svd_xy(X, Y):
    """ Return the first left and right singular
    vectors of X'Y.

    :param X, Y: data matrix
    :type X, Y: :class:`numpy.array`    
    
    """
    U, s, V = svd(dot(X.T, Y), full_matrices=False)
    u = U[:, [0]]
    v = V.T[:, [0]]
    return u, v


def select_attrs(table, attributes, class_var=None, metas=None):
    """ Select ``attributes`` from the ``table`` and return a new data table.
    """
    domain = Orange.data.Domain(attributes, class_var)
    if metas:
        domain.add_metas(metas)
    return Orange.data.Table(domain, table)


class PLSRegressionLearner(base.BaseRegressionLearner):
    """
    Fit the partial least squares regression model, i.e. learn the
    regression parameters. The implementation is based on `Scikit
    learn python implementation`_
    
    The class is derived from
    :class:`Orange.regression.base.BaseRegressionLearner` that is
    used for preprocessing the data (continuization and imputation)
    before fitting the regression parameters
    
    """

    def __init__(self, n_comp=2, deflation_mode="regression", mode="PLS",
                 algorithm="nipals", max_iter=500, 
                 imputer=None, continuizer=None,
                 **kwds):
        """
        .. attribute:: n_comp
    
            number of components to keep (default: 2)

        .. attribute:: deflation_mode
    
            "canonical" or "regression" (default)

        .. attribute:: mode
    
            "CCA" or "PLS" (default)


        .. attribute:: algorithm
    
            The algorithm for estimating the weights:
            "nipals" or "svd" (default)


        """        
        self.n_comp = n_comp
        self.deflation_mode = deflation_mode
        self.mode = mode
        self.algorithm = algorithm
        self.max_iter = max_iter
        self.set_imputer(imputer=imputer)
        self.set_continuizer(continuizer=continuizer)
        self.__dict__.update(kwds)

    @deprecated_keywords({"xVars": "x_vars", "yVars": "y_vars"})
    def __call__(self, table, weight_id=None, x_vars=None, y_vars=None):
        """
        :param table: data instances.
        :type table: :class:`Orange.data.Table`

        :param x_vars, y_vars: List of input and response variables
            (:obj:`Orange.feature.Continuous` or
            :obj:`Orange.feature.Discrete`). If ``None`` (default) it is
            assumed that the data domain provides information which variables
            are reponses and which are not. If data has
            :obj:`~Orange.data.Domain.class_var` defined in its domain, a
            single-target regression learner is constructed. Otherwise a
            multi-target learner predicting response variables defined by
            :obj:`~Orange.data.Domain.class_vars` is constructed.
        :type x_vars, y_vars: list            

        """     
        domain = table.domain
        multitarget = False
        if x_vars is None and y_vars is None:
            # Response variables are defined in the table.
            x_vars = domain.features
            if domain.class_var:
                y_vars = [domain.class_var]
            elif domain.class_vars:
                y_vars = domain.class_vars
                multitarget = True
            else:
                raise TypeError('Class-less domain (x-vars and y-vars needed).')

        elif not (x_vars and y_vars):
            raise ValueError("Both x_vars and y_vars must be defined.")
        else:
            multitarget = True

        x_table = select_attrs(table, x_vars)
        y_table = select_attrs(table, y_vars)

        # dicrete values are continuized        
        x_table = self.continuize_table(x_table)
        y_table = self.continuize_table(y_table)
        # missing values are imputed
        x_table = self.impute_table(x_table)
        y_table = self.impute_table(y_table)
        
        # Collect the new transformed x_vars/y_vars 
        x_vars = list(x_table.domain.variables)
        y_vars = list(y_table.domain.variables)
        
        domain = Orange.data.Domain(x_vars + y_vars, False)

        x = x_table.to_numpy()[0]
        y = y_table.to_numpy()[0]
        
        kwargs = self.fit(x, y)
        return PLSRegression(domain=domain, x_vars=x_vars, y_vars=y_vars,
                             multitarget=multitarget, **kwargs)

    def fit(self, X, Y):
        """ Fit all unknown parameters, i.e.
        weights, scores, loadings (for x and y) and regression coefficients.
        Return a dict with all of the parameters.
        """
        # copy since this will contain the residuals (deflated) matrices

        X, Y = X.copy(), Y.copy()
        if Y.ndim == 1:
            Y = Y.reshape((Y.size, 1))
        n, p = X.shape
        q = Y.shape[1]

        # normalization of data matrices
        X, muX, sigmaX = normalize_matrix(X)
        Y, muY, sigmaY = normalize_matrix(Y)
        # Residuals (deflated) matrices
        Xk, Yk = X, Y
        # Results matrices
        T, U = zeros((n, self.n_comp)), zeros((n, self.n_comp))
        W, C = zeros((p, self.n_comp)), zeros((q, self.n_comp))
        P, Q = zeros((p, self.n_comp)), zeros((q, self.n_comp))      

        # NIPALS over components
        for k in xrange(self.n_comp):
            # Weights estimation (inner loop)
            if self.algorithm == "nipals":
                u, v = nipals_xy(X=Xk, Y=Yk, mode=self.mode, 
                                 max_iter=self.max_iter)
            elif self.algorithm == "svd":
                u, v = svd_xy(X=Xk, Y=Yk)
            # compute scores
            xScore, yScore = dot(Xk, u), dot(Yk, v)
            # Deflation (in place)
            # - regress Xk's on xScore
            xLoadings = dot(Xk.T, xScore) / dot(xScore.T, xScore)
            # - substract rank-one approximations to obtain remainder matrix
            Xk -= dot(xScore, xLoadings.T)
            if self.deflation_mode == "canonical":
                # - regress Yk's on yScore, then substract rank-one approx.
                yLoadings = dot(Yk.T, yScore) / dot(yScore.T, yScore)
                Yk -= dot(yScore, yLoadings.T)
            if self.deflation_mode == "regression":
                # - regress Yk's on xScore, then substract rank-one approx.
                yLoadings = dot(Yk.T, xScore) / dot(xScore.T, xScore)
                Yk -= dot(xScore, yLoadings.T)
            # Store weights, scores and loadings 
            T[:, k] = xScore.ravel() # x-scores
            U[:, k] = yScore.ravel() # y-scores
            W[:, k] = u.ravel() # x-weights
            C[:, k] = v.ravel() # y-weights
            P[:, k] = xLoadings.ravel() # x-loadings
            Q[:, k] = yLoadings.ravel() # y-loadings
        # X = TP' + E and Y = UQ' + E

        # Rotations from input space to transformed space (scores)
        # T = X W(P'W)^-1 = XW* (W* : p x k matrix)
        # U = Y C(Q'C)^-1 = YC* (W* : q x k matrix)
        xRotations = dot(W, pinv(dot(P.T, W)))
        if Y.shape[1] > 1:
            yRotations = dot(C, pinv(dot(Q.T, C)))
        else:
            yRotations = numpy.ones(1)

        if True or self.deflation_mode == "regression":
            # Estimate regression coefficient
            # Y = TQ' + E = X W(P'W)^-1Q' + E = XB + E
            # => B = W*Q' (p x q)
            coefs = dot(xRotations, Q.T)
            coefs = 1. / sigmaX.reshape((p, 1)) * \
                    coefs * sigmaY
        
        return {"mu_x": muX, "mu_y": muY, "sigma_x": sigmaX,
                "sigma_y": sigmaY, "T": T, "U":U, "W":U, 
                "C": C, "P":P, "Q":Q, "x_rotations": xRotations,
                "y_rotations": yRotations, "coefs": coefs}

deprecated_members({"nComp": "n_comp",
                    "deflationMode": "deflation_mode",
                    "maxIter": "max_iter"},
                   wrap_methods=["__init__"],
                   in_place=True)(PLSRegressionLearner)

class PLSRegression(Orange.classification.Classifier):
    """ Predict values of the response variables
    based on the values of independent variables.
    
    Basic notations:
    n - number of data instances
    p - number of independent variables
    q - number of reponse variables

    .. attribute:: T
    
        A n x n_comp numpy array of x-scores

    .. attribute:: U
    
        A n x n_comp numpy array of y-scores

    .. attribute:: W
    
        A p x n_comp numpy array of x-weights

    .. attribute:: C
    
        A q x n_comp numpy array of y-weights

    .. attribute:: P
    
        A p x n_comp numpy array of x-loadings

    .. attribute:: Q
    
        A q x n_comp numpy array of y-loading

    .. attribute:: coefs
    
        A p x q numpy array coefficients
        of the linear model: Y = X coefs + E

    .. attribute:: x_vars
    
        Predictor variables

    .. attribute:: y_vars
    
        Response variables 
        
    """
    def __init__(self, domain=None, multitarget=False, coefs=None, sigma_x=None, sigma_y=None,
                 mu_x=None, mu_y=None, x_vars=None, y_vars=None, **kwargs):
        self.domain = domain
        self.multitarget = multitarget
        if multitarget and y_vars:
            self.class_vars = y_vars
        elif y_vars:
            self.class_var = y_vars[0]

        self.coefs = coefs
        self.mu_x, self.mu_y = mu_x, mu_y
        self.sigma_x, self.sigma_y = sigma_x, sigma_y
        self.x_vars, self.y_vars = x_vars, y_vars
            
        for name, val in kwargs.items():
            setattr(self, name, val)

    def __call__(self, instance, result_type=Orange.core.GetValue):
        """
        :param instance: data instance for which the value of the response
            variable will be predicted
        :type instance: :class:`Orange.data.Instance` 
        
        """ 
        instance = Orange.data.Instance(self.domain, instance)
        ins = [instance[v].native() for v in self.x_vars]
        
        if "?" in ins: # missing value -> corresponding coefficient omitted
            def miss_2_0(x): return x if x != "?" else 0
            ins = map(miss_2_0, ins)
        ins = numpy.array(ins)
        xc = (ins - self.mu_x)
        predicted = dot(xc, self.coefs) + self.mu_y
        y_hat = [var(val) for var, val in zip(self.y_vars, predicted)]
        if result_type == Orange.core.GetValue:
            return y_hat if self.multitarget else y_hat[0]
        else:
            from Orange.statistics.distribution import Distribution
            probs = []
            for var, val in zip(self.y_vars, y_hat):
                dist = Distribution(var)
                dist[val] = 1.0
                probs.append(dist)
            if result_type == Orange.core.GetBoth:
                return (y_hat, probs) if self.multitarget else (y_hat[0], probs[0])
            else:
                return probs if self.multitarget else probs[0]
            
    def to_string(self):
        """ Pretty-prints the coefficient of the PLS regression model.
        """       
        x_vars, y_vars = [x.name for x in self.x_vars], [y.name for y in self.y_vars]
        fmt = "%8s " + "%12.3f " * len(y_vars)
        first = [" " * 8 + "%13s" * len(y_vars) % tuple(y_vars)]
        lines = [fmt % tuple([x_vars[i]] + list(coef))
                 for i, coef in enumerate(self.coefs)]
        return '\n'.join(first + lines)
            
    def __str__(self):
        return self.to_string()

    """
    def transform(self, X, Y=None):

        # Normalize
        Xc = (X - self.muX) / self.sigmaX
        if Y is not None:
            Yc = (Y - self.muY) / self.sigmaY
        # Apply rotation
        xScores = dot(Xc, self.xRotations)
        if Y is not None:
            yScores = dot(Yc, self.yRotations)
            return xScores, yScores

        return xScores
    """
              
deprecated_members({"xVars": "x_vars", 
                    "yVars": "y_vars",
                    "muX": "mu_x",
                    "muY": "mu_y",
                    "sigmaX": "sigma_x",
                    "sigmaY": "sigma_y"},
                   wrap_methods=["__init__"],
                   in_place=True)(PLSRegression)
                   
if __name__ == "__main__":

    import Orange
    from Orange.regression import pls

    data = Orange.data.Table("multitarget-synthetic")
    l = pls.PLSRegressionLearner()

    x = data.domain.features
    y = data.domain.class_vars
    print x, y
    # c = l(data, x_vars=x, y_vars=y)
    c = l(data)
    print c
