"""
The POVMEffect class and supporting functionality.
"""
#***************************************************************************************************
# Copyright 2015, 2019 National Technology & Engineering Solutions of Sandia, LLC (NTESS).
# Under the terms of Contract DE-NA0003525 with NTESS, the U.S. Government retains certain rights
# in this software.
# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
# in compliance with the License.  You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0 or in the LICENSE file in the root pyGSTi directory.
#***************************************************************************************************

import numpy as _np

from pygsti.modelmembers import modelmember as _modelmember
from pygsti.tools import optools as _ot
from pygsti.baseobjs.opcalc import bulk_eval_compact_polynomials_complex as _bulk_eval_compact_polynomials_complex


class POVMEffect(_modelmember.ModelMember):
    """
    TODO: update docstring
    A parameterized state preparation OR POVM effect vector (operator).

    This class is the  common base class for all specific
    parameterizations of a POVM effect vector.

    Parameters
    ----------
    rep : object
        A representation object containing the core data for this spam vector.

    evotype : Evotype
        The evolution type of this operator, for matching with forward simulators.

    Attributes
    ----------
    size : int
        The number of independent elements in this POVM effect vector (when viewed as a dense array).
    """

    def __init__(self, rep, evotype):
        """ Initialize a new POVM effect Vector """
        super(POVMEffect, self).__init__(rep.state_space, evotype)
        self._rep = rep

    @property
    def outcomes(self):
        """
        The z-value outcomes corresponding to this effect POVM effect vector.

        (Used in the context of a stabilizer-state simulation.)

        Returns
        -------
        numpy.ndarray
        """
        raise NotImplementedError("'outcomes' property is not implemented for %s objects" % self.__class__.__name__)

    @property
    def dim(self):
        """
        Return the dimension of this effect (when viewed as a dense array)

        Returns
        -------
        int
        """
        return self.state_space.dim

    @property
    def hilbert_schmidt_size(self):
        """
        Return the number of independent elements in this effect as a dense Hilbert-Schmidt super-bra.

        Returns
        -------
        int
        """
        return self.state_space.dim

    def set_dense(self, vec):
        """
        Set the dense-vector value of this POVM effect vector.

        Attempts to modify this POVM effect vector's parameters so that the raw
        POVM effect vector becomes `vec`.  Will raise ValueError if this operation
        is not possible.

        Parameters
        ----------
        vec : array_like or POVMEffect
            A numpy array representing a POVM effect vector, or a POVMEffect object.

        Returns
        -------
        None
        """
        raise ValueError("Cannot set the value of a %s directly!" % self.__class__.__name__)

    def set_time(self, t):
        """
        Sets the current time for a time-dependent operator.

        For time-independent operators (the default), this function does absolutely nothing.

        Parameters
        ----------
        t : float
            The current time.

        Returns
        -------
        None
        """
        pass

    ## PUT term calc methods here if appropriate...

    def frobeniusdist_squared(self, other_spam_vec, transform=None,
                              inv_transform=None):
        """
        Return the squared frobenius difference between this operation and `other_spam_vec`.

        Optionally transforms this vector first using `transform` and
        `inv_transform`.

        Parameters
        ----------
        other_spam_vec : POVMEffect
            The other spam vector

        transform : numpy.ndarray, optional
            Transformation matrix.

        inv_transform : numpy.ndarray, optional
            Inverse of `tranform`.

        Returns
        -------
        float
        """
        vec = self.to_dense()
        if transform is None:
            return _ot.frobeniusdist_squared(vec, other_spam_vec.to_dense())
        else:
            return _ot.frobeniusdist_squared(_np.dot(_np.transpose(transform),
                                                     vec), other_spam_vec.to_dense())

    def residuals(self, other_spam_vec, transform=None, inv_transform=None):
        """
        Return a vector of residuals between this spam vector and `other_spam_vec`.

        Optionally transforms this vector first using `transform` and
        `inv_transform`.

        Parameters
        ----------
        other_spam_vec : POVMEffect
            The other spam vector

        transform : numpy.ndarray, optional
            Transformation matrix.

        inv_transform : numpy.ndarray, optional
            Inverse of `tranform`.

        Returns
        -------
        float
        """
        vec = self.to_dense()
        if transform is None:
            return _ot.residuals(vec, other_spam_vec.to_dense())
        else:
            return _ot.residuals(_np.dot(_np.transpose(transform),
                                         vec), other_spam_vec.to_dense())

    def transform_inplace(self, s):
        """
        Update POVM effect (column) vector V => s^T * V

        Note that this is equivalent to the *transpose* of effect vectors
        being mapped as `E^T -> E^T * s`.

        Generally, the transform function updates the *parameters* of
        the POVM effect vector such that the resulting vector is altered as
        described above.  If such an update cannot be done (because
        the gate parameters do not allow for it), ValueError is raised.

        Parameters
        ----------
        s : GaugeGroupElement
            A gauge group element which specifies the "s" matrix
            (and it's inverse) used in the above similarity transform.

        typ : { 'prep', 'effect' }
            Which type of POVM effect vector is being transformed (see above).

        Returns
        -------
        None
        """
        #Evec^T --> ( Evec^T * s )^T
        Smx = s.transform_matrix
        self.set_dense(_np.dot(_np.transpose(Smx), self.to_dense()))

    @property
    def num_params(self):
        """
        Get the number of independent parameters which specify this POVM effect vector.

        Returns
        -------
        int
            the number of independent parameters.
        """
        return 0  # no parameters

    def to_vector(self):
        """
        Get the POVM effect vector parameters as an array of values.

        Returns
        -------
        numpy array
            The parameters as a 1D array with length num_params().
        """
        return _np.array([], 'd')  # no parameters

    def from_vector(self, v, close=False, dirty_value=True):
        """
        Initialize the POVM effect vector using a 1D array of parameters.

        Parameters
        ----------
        v : numpy array
            The 1D vector of POVM effect vector parameters.  Length
            must == num_params()

        close : bool, optional
            Whether `v` is close to this POVM effect vector's current
            set of parameters.  Under some circumstances, when this
            is true this call can be completed more quickly.

        dirty_value : bool, optional
            The value to set this object's "dirty flag" to before exiting this
            call.  This is passed as an argument so it can be updated *recursively*.
            Leave this set to `True` unless you know what you're doing.

        Returns
        -------
        None
        """
        assert(len(v) == 0)  # should be no parameters, and nothing to do

    def deriv_wrt_params(self, wrt_filter=None):
        """
        The element-wise derivative this POVM effect vector.

        Construct a matrix whose columns are the derivatives of the POVM effect vector
        with respect to a single param.  Thus, each column is of length
        dimension and there is one column per POVM effect vector parameter.

        Parameters
        ----------
        wrt_filter : list or numpy.ndarray
            List of parameter indices to take derivative with respect to.
            (None means to use all the this operation's parameters.)

        Returns
        -------
        numpy array
            Array of derivatives, shape == (dimension, num_params)
        """
        dtype = complex if self._evotype == 'statevec' else 'd'
        derivMx = _np.zeros((self.dim, 0), dtype)
        if wrt_filter is None:
            return derivMx
        else:
            return _np.take(derivMx, wrt_filter, axis=1)

    def has_nonzero_hessian(self):
        """
        Whether this POVM effect vector has a non-zero Hessian with respect to its parameters.

        Returns
        -------
        bool
        """
        #Default: assume Hessian can be nonzero if there are any parameters
        return self.num_params > 0

    def hessian_wrt_params(self, wrt_filter1=None, wrt_filter2=None):
        """
        Construct the Hessian of this POVM effect vector with respect to its parameters.

        This function returns a tensor whose first axis corresponds to the
        flattened operation matrix and whose 2nd and 3rd axes correspond to the
        parameters that are differentiated with respect to.

        Parameters
        ----------
        wrt_filter1 : list or numpy.ndarray
            List of parameter indices to take 1st derivatives with respect to.
            (None means to use all the this operation's parameters.)

        wrt_filter2 : list or numpy.ndarray
            List of parameter indices to take 2nd derivatives with respect to.
            (None means to use all the this operation's parameters.)

        Returns
        -------
        numpy array
            Hessian with shape (dimension, num_params1, num_params2)
        """
        if not self.has_nonzero_hessian():
            return _np.zeros(self.size, self.num_params, self.num_params)

        # FUTURE: create a finite differencing hessian method?
        raise NotImplementedError("hessian_wrt_params(...) is not implemented for %s objects" % self.__class__.__name__)

    def taylor_order_terms(self, order, max_polynomial_vars=100, return_coeff_polys=False):
        """
        Get the `order`-th order Taylor-expansion terms of this effect vector.

        This function either constructs or returns a cached list of the terms at
        the given order.  Each term is "rank-1", meaning that it is a state
        preparation followed by or POVM effect preceded by actions on a
        density matrix `rho` of the form:

        `rho -> A rho B`

        The coefficients of these terms are typically polynomials of the
        State's parameters, where the polynomial's variable indices index the
        *global* parameters of the State's parent (usually a :class:`Model`)
        , not the State's local parameter array (i.e. that returned from
        `to_vector`).

        Parameters
        ----------
        order : int
            The order of terms to get.

        max_polynomial_vars : int, optional
            maximum number of variables the created polynomials can have.

        return_coeff_polys : bool
            Whether a parallel list of locally-indexed (using variable indices
            corresponding to *this* object's parameters rather than its parent's)
            polynomial coefficients should be returned as well.

        Returns
        -------
        terms : list
            A list of :class:`RankOneTerm` objects.

        coefficients : list
            Only present when `return_coeff_polys == True`.
            A list of *compact* polynomial objects, meaning that each element
            is a `(vtape,ctape)` 2-tuple formed by concatenating together the
            output of :method:`Polynomial.compact`.
        """
        #NOTE: exact copy of State method - consolidate in FUTURE?
        raise NotImplementedError("taylor_order_terms(...) not implemented for %s objects!" %
                                  self.__class__.__name__)

    def highmagnitude_terms(self, min_term_mag, force_firstorder=True, max_taylor_order=3, max_polynomial_vars=100):
        """
        Get terms with magnitude above `min_term_mag`.

        Get the terms (from a Taylor expansion of this state vector) that have
        magnitude above `min_term_mag` (the magnitude of a term is taken to
        be the absolute value of its coefficient), considering only those
        terms up to some maximum Taylor expansion order, `max_taylor_order`.

        Note that this function also *sets* the magnitudes of the returned
        terms (by calling `term.set_magnitude(...)`) based on the current
        values of this state vector's parameters.  This is an essential step
        to using these terms in pruned-path-integral calculations later on.

        Parameters
        ----------
        min_term_mag : float
            the threshold for term magnitudes: only terms with magnitudes above
            this value are returned.

        force_firstorder : bool, optional
            if True, then always return all the first-order Taylor-series terms,
            even if they have magnitudes smaller than `min_term_mag`.  This
            behavior is needed for using GST with pruned-term calculations, as
            we may begin with a guess model that has no error (all terms have
            zero magnitude!) and still need to compute a meaningful jacobian at
            this point.

        max_taylor_order : int, optional
            the maximum Taylor-order to consider when checking whether term-
            magnitudes exceed `min_term_mag`.

        max_polynomial_vars : int, optional
            maximum number of variables the created polynomials can have.

        Returns
        -------
        highmag_terms : list
            A list of the high-magnitude terms that were found.  These
            terms are *sorted* in descending order by term-magnitude.

        first_order_indices : list
            A list of the indices into `highmag_terms` that mark which
            of these terms are first-order Taylor terms (useful when
            we're forcing these terms to always be present).
        """
        #NOTE: SAME as for LinearOperator class and State class -- TODO consolidate in FUTURE
        #print("DB: state get_high_magnitude_terms")
        v = self.to_vector()
        taylor_order = 0
        terms = []; last_len = -1; first_order_magmax = 1.0
        while len(terms) > last_len:  # while we keep adding something
            if taylor_order > 1 and first_order_magmax**taylor_order < min_term_mag:
                break  # there's no way any terms at this order reach min_term_mag - exit now!

            MAX_CACHED_TERM_ORDER = 1
            if taylor_order <= MAX_CACHED_TERM_ORDER:
                #print("order ",taylor_order," : ",len(terms), "terms")
                terms_at_order, cpolys = self.taylor_order_terms(taylor_order, max_polynomial_vars, True)
                coeffs = _bulk_eval_compact_polynomials_complex(
                    cpolys[0], cpolys[1], v, (len(terms_at_order),))  # an array of coeffs
                mags = _np.abs(coeffs)
                last_len = len(terms)
                #OLD: terms_at_order = [ t.copy_with_magnitude(abs(coeff)) for coeff, t in zip(coeffs, terms_at_order) ]

                if taylor_order == 1:
                    #OLD: first_order_magmax = max([t.magnitude for t in terms_at_order])
                    first_order_magmax = max(mags)

                    if force_firstorder:
                        terms.extend([(taylor_order, t.copy_with_magnitude(mag))
                                      for coeff, mag, t in zip(coeffs, mags, terms_at_order)])
                    else:
                        for mag, t in zip(mags, terms_at_order):
                            if mag >= min_term_mag:
                                terms.append((taylor_order, t.copy_with_magnitude(mag)))
                else:
                    for mag, t in zip(mags, terms_at_order):
                        if mag >= min_term_mag:
                            terms.append((taylor_order, t.copy_with_magnitude(mag)))

            else:
                eff_min_term_mag = 0.0 if (taylor_order == 1 and force_firstorder) else min_term_mag
                terms.extend([(taylor_order, t) for t in
                              self.taylor_order_terms_above_mag(taylor_order,
                                                                max_polynomial_vars, eff_min_term_mag)])

            taylor_order += 1
            if taylor_order > max_taylor_order: break

        #Sort terms based on magnitude
        sorted_terms = sorted(terms, key=lambda t: t[1].magnitude, reverse=True)
        first_order_indices = [i for i, t in enumerate(sorted_terms) if t[0] == 1]
        return [t[1] for t in sorted_terms], first_order_indices

    def taylor_order_terms_above_mag(self, order, max_polynomial_vars, min_term_mag):
        """
        Get the `order`-th order Taylor-expansion terms of this state vector that have magnitude above `min_term_mag`.

        This function constructs the terms at the given order which have a magnitude (given by
        the absolute value of their coefficient) that is greater than or equal to `min_term_mag`.
        It calls :method:`taylor_order_terms` internally, so that all the terms at order `order`
        are typically cached for future calls.

        Parameters
        ----------
        order : int
            The order of terms to get.

        max_polynomial_vars : int, optional
            maximum number of variables the created polynomials can have.

        min_term_mag : float
            the minimum term magnitude.

        Returns
        -------
        list
        """
        #NOTE: exact copy of State method - consolidate in FUTURE?
        v = self.to_vector()
        terms_at_order, cpolys = self.taylor_order_terms(order, max_polynomial_vars, True)
        coeffs = _bulk_eval_compact_polynomials_complex(
            cpolys[0], cpolys[1], v, (len(terms_at_order),))  # an array of coeffs
        terms_at_order = [t.copy_with_magnitude(abs(coeff)) for coeff, t in zip(coeffs, terms_at_order)]
        return [t for t in terms_at_order if t.magnitude >= min_term_mag]
