Python numpy.insert() Examples

def predict_seq_mul(model, data, win_size, pred_len):
    """
    Predicts multiple sequences
    Input: keras model, testing data, window size, prediction length
    Output: Predicted sequence

    Note: Run from timeSeriesPredict.py
    """
    pred_seq = []
    for i in range(len(data)//pred_len):
        current = data[i * pred_len]
        predicted = []
        for j in range(pred_len):
            predicted.append(model.predict(current[None, :, :])[0, 0])
            current = current[1:]
            current = np.insert(current, [win_size - 1], predicted[-1], axis=0)
        pred_seq.append(predicted)
    return pred_seq 

def predict_all(X, all_theta):
    rows = X.shape[0]
    params = X.shape[1]
    num_labels = all_theta.shape[0]
    
    # same as before, insert ones to match the shape
    X = np.insert(X, 0, values=np.ones(rows), axis=1)
    
    # convert to matrices
    X = np.matrix(X)
    all_theta = np.matrix(all_theta)
    
    # compute the class probability for each class on each training instance
    h = sigmoid(X * all_theta.T)
    
    # create array of the index with the maximum probability
    h_argmax = np.argmax(h, axis=1)
    
    # because our array was zero-indexed we need to add one for the true label prediction
    h_argmax = h_argmax + 1
    
    return h_argmax 

def prepare_poly_data(*args, power):
    """
    args: keep feeding in X, Xval, or Xtest
        will return in the same order
    """
    def prepare(x):
        # expand feature
        df = poly_features(x, power=power)

        # normalization
        ndarr = normalize_feature(df).as_matrix()

        # add intercept term
        return np.insert(ndarr, 0, np.ones(ndarr.shape[0]), axis=1)

    return [prepare(x) for x in args] 

def collect(self, index, dataDict, check=True):
        """
        Collect atom given its index.

        :Parameters:
            #. index (int): The atom index to collect.
            #. dataDict (dict): The atom data dict to collect.
            #. check (boolean):  Whether to check dataDict keys before
               collecting. If set to False, user promises that collected
               data is a dictionary and contains the needed keys.
        """
        assert not self.is_collected(index), LOGGER.error("attempting to collect and already collected atom of index '%i'"%index)
        # add data
        if check:
            assert isinstance(dataDict, dict), LOGGER.error("dataDict must be a dictionary of data where keys are dataKeys")
            assert tuple(sorted(dataDict)) == self.__dataKeys, LOGGER.error("dataDict keys don't match promised dataKeys")
        self.__collectedData[index] = dataDict
        # set indexes sorted array
        idx = np.searchsorted(a=self.__indexesSortedArray, v=index, side='left')
        self.__indexesSortedArray = np.insert(self.__indexesSortedArray, idx, index)
        # set state
        self.__state = str(uuid.uuid1()) 

def release(self, index):
        """
        Release atom from list of collected atoms and return its
        collected data.

        :Parameters:
            #. index (int): The atom index to release.

        :Returns:
            #. dataDict (dict): The released atom collected data.
        """
        if not self.is_collected(index):
            LOGGER.warn("Attempting to release atom %i that is not collected."%index)
            return
        index = self.__collectedData.pop(index)
        # set indexes sorted array
        idx = np.searchsorted(a=self.__indexesSortedArray, v=index, side='left')
        self.__indexesSortedArray = np.insert(self.__indexesSortedArray, idx, index)
        # set state
        self.__state = str(uuid.uuid1())
        # return
        return index 

def regression_data():
    f = open(path + "regression_data1.txt")
    data = np.loadtxt(f, delimiter=",")
    x1 = np.insert(data[:, 0].reshape(len(data), 1), 0, np.ones(len(data)), axis=1)
    y1 = data[:, 1]
    f = open(path + "regression_data2.txt")
    data = np.loadtxt(f, delimiter=",")
    x2 = np.insert(data[:, 0].reshape(len(data), 1), 0, np.ones(len(data)), axis=1)
    y2 = data[:, 1]
    x1 = np.vstack((x1, x2))
    y1 = np.hstack((y1, y2))

    f = open(path + "regression_data_test1.txt")
    data = np.loadtxt(f, delimiter=",")
    x1_test = np.insert(data[:, 0].reshape(len(data), 1), 0, np.ones(len(data)), axis=1)
    y1_test = data[:, 1]
    f = open(path + "regression_data_test2.txt")
    data = np.loadtxt(f, delimiter=",")
    x2_test = np.insert(data[:, 0].reshape(len(data), 1), 0, np.ones(len(data)), axis=1)
    y2_test = data[:, 1]
    x1_test = np.vstack((x1_test, x2_test))
    y1_test = np.hstack((y1_test, y2_test))
    return x1, y1, x1_test, y1_test 

def ex3(replication=2):
    f = open(path + "ex3.txt")
    train_data = np.loadtxt(f, delimiter=",")
    f = open(path + "ex3_test.txt")
    test_data = np.loadtxt(f, delimiter=",")

    x_train = np.insert(train_data[:, (0, 1)], 0, np.ones(len(train_data)), axis=1)
    y_train = train_data[:, 2]
    x_test = np.insert(test_data[:, (0, 1)], 0, np.ones(len(test_data)), axis=1)
    y_test = test_data[:, 2]

    for i in range(replication - 1):
        x_train = np.vstack((x_train, np.insert(train_data[:, (0, 1)], 0, np.ones(len(train_data)), axis=1)))
        y_train = np.hstack((y_train, train_data[:, 2]))

        x_test = np.vstack((x_test, np.insert(test_data[:, (0, 1)], 0, np.ones(len(test_data)), axis=1)))
        y_test = np.hstack((y_test, test_data[:, 2]))

    return x_train, y_train, x_test, y_test 

def _correct_missed(missed_idcs, peaks):

    corrected_peaks = peaks.copy()
    missed_idcs = np.array(missed_idcs)
    # Calculate the position(s) of new beat(s). Make sure to not generate
    # negative indices. prev_peaks and next_peaks must have the same
    # number of elements.
    valid_idcs = np.logical_and(missed_idcs > 1, missed_idcs < len(corrected_peaks))  # pylint: disable=E1111
    missed_idcs = missed_idcs[valid_idcs]
    prev_peaks = corrected_peaks[[i - 1 for i in missed_idcs]]
    next_peaks = corrected_peaks[missed_idcs]
    added_peaks = prev_peaks + (next_peaks - prev_peaks) / 2
    # Add the new peaks before the missed indices (see numpy docs).
    corrected_peaks = np.insert(corrected_peaks, missed_idcs, added_peaks)

    return corrected_peaks 

def _interpolate_missing(peaks, interval, interval_max, sampling_rate):
    outliers = interval > interval_max
    outliers_loc = np.where(outliers)[0]
    if np.sum(outliers) == 0:
        return peaks, False

    # Delete large interval and replace by two unknown intervals
    interval[outliers] = np.nan
    interval = np.insert(interval, outliers_loc, np.nan)
    #    new_peaks_location = np.where(np.isnan(interval))[0]

    # Interpolate values
    interval = pd.Series(interval).interpolate().values
    peaks_corrected = _period_to_location(interval, sampling_rate, first_location=peaks[0])
    peaks = np.insert(peaks, outliers_loc, peaks_corrected[outliers_loc + np.arange(len(outliers_loc))])
    return peaks, True 

def _RLFindRoots(nump, denp, kvect):
    """Find the roots for the root locus."""
    # Convert numerator and denominator to polynomials if they aren't
    roots = []
    for k in kvect:
        curpoly = denp + k * nump
        curroots = curpoly.r
        if len(curroots) < denp.order:
            # if I have fewer poles than open loop, it is because i have
            # one at infinity
            curroots = np.insert(curroots, len(curroots), np.inf)

        curroots.sort()
        roots.append(curroots)

    mymat = row_stack(roots)
    return mymat 

def SetDistribution(self, distinct_values):
        """This is all the values this column will ever see."""
        assert self.all_distinct_values is None
        # pd.isnull returns true for both np.nan and np.datetime64('NaT').
        is_nan = pd.isnull(distinct_values)
        contains_nan = np.any(is_nan)
        dv_no_nan = distinct_values[~is_nan]
        # NOTE: np.sort puts NaT values at beginning, and NaN values at end.
        # For our purposes we always add any null value to the beginning.
        vs = np.sort(np.unique(dv_no_nan))
        if contains_nan and np.issubdtype(distinct_values.dtype, np.datetime64):
            vs = np.insert(vs, 0, np.datetime64('NaT'))
        elif contains_nan:
            vs = np.insert(vs, 0, np.nan)
        if self.distribution_size is not None:
            assert len(vs) == self.distribution_size
        self.all_distinct_values = vs
        self.distribution_size = len(vs)
        return self 

def estimate_norm(lmk, image_size = 112, mode='arcface'):
  assert lmk.shape==(5,2)
  tform = trans.SimilarityTransform()
  lmk_tran = np.insert(lmk, 2, values=np.ones(5), axis=1)
  min_M = []
  min_index = []
  min_error = float('inf') 
  if mode=='arcface':
    assert image_size==112
    src = arcface_src
  else:
    src = src_map[image_size]
  for i in np.arange(src.shape[0]):
    tform.estimate(lmk, src[i])
    M = tform.params[0:2,:]
    results = np.dot(M, lmk_tran.T)
    results = results.T
    error = np.sum(np.sqrt(np.sum((results - src[i]) ** 2,axis=1)))
#         print(error)
    if error< min_error:
        min_error = error
        min_M = M
        min_index = i
  return min_M, min_index 

def estimate_norm(lmk, image_size = 112, mode='arcface'):
  assert lmk.shape==(5,2)
  tform = trans.SimilarityTransform()
  lmk_tran = np.insert(lmk, 2, values=np.ones(5), axis=1)
  min_M = []
  min_index = []
  min_error = float('inf') 
  if mode=='arcface':
    assert image_size==112
    src = arcface_src
  else:
    src = src_map[image_size]
  for i in np.arange(src.shape[0]):
    tform.estimate(lmk, src[i])
    M = tform.params[0:2,:]
    results = np.dot(M, lmk_tran.T)
    results = results.T
    error = np.sum(np.sqrt(np.sum((results - src[i]) ** 2,axis=1)))
#         print(error)
    if error< min_error:
        min_error = error
        min_M = M
        min_index = i
  return min_M, min_index 

def _build_paramvec(self):
        """ Resizes self._paramvec and updates gpindices & parent members as needed,
            and will initialize new elements of _paramvec, but does NOT change
            existing elements of _paramvec (use _update_paramvec for this)"""
        v = _np.empty(0, 'd'); off = 0

        # Step 2: add parameters that don't exist yet
        for obj in self.values():
            if obj.gpindices is None or obj.parent is not self:
                #Assume all parameters of obj are new independent parameters
                v = _np.insert(v, off, obj.to_vector())
                num_new_params = obj.allocate_gpindices(off, self)
                off += num_new_params
            else:
                inds = obj.gpindices_as_array()
                M = max(inds) if len(inds) > 0 else -1; L = len(v)
                if M >= L:
                    #Some indices specified by obj are absent, and must be created.
                    w = obj.to_vector()
                    v = _np.concatenate((v, _np.empty(M + 1 - L, 'd')), axis=0)  # [v.resize(M+1) doesn't work]
                    for ii, i in enumerate(inds):
                        if i >= L: v[i] = w[ii]
                off = M + 1
        return v 

def calc_axon_contribution(self, axons):
        xyret = np.column_stack((self.grid.xret.ravel(),
                                 self.grid.yret.ravel()))
        # Only include axon segments that are < `max_d2` from the soma. These
        # axon segments will have `sensitivity` > `self.min_ax_sensitivity`:
        max_d2 = -2.0 * self.axlambda ** 2 * np.log(self.min_ax_sensitivity)
        axon_contrib = []
        for xy, bundle in zip(xyret, axons):
            idx = np.argmin((bundle[:, 0] - xy[0]) ** 2 +
                            (bundle[:, 1] - xy[1]) ** 2)
            # Cut off the part of the fiber that goes beyond the soma:
            axon = np.flipud(bundle[0: idx + 1, :])
            # Add the exact location of the soma:
            axon = np.insert(axon, 0, xy, axis=0)
            # For every axon segment, calculate distance from soma by
            # summing up the individual distances between neighboring axon
            # segments (by "walking along the axon"):
            d2 = np.cumsum(np.diff(axon[:, 0], axis=0) ** 2 +
                           np.diff(axon[:, 1], axis=0) ** 2)
            idx_d2 = d2 < max_d2
            sensitivity = np.exp(-d2[idx_d2] / (2.0 * self.axlambda ** 2))
            idx_d2 = np.insert(idx_d2, 0, False)
            contrib = np.column_stack((axon[idx_d2, :], sensitivity))
            axon_contrib.append(contrib)
        return axon_contrib 

def test_AxonMapModel_calc_axon_contribution(engine):
    model = AxonMapModel(xystep=2, engine=engine, n_axons=10,
                         xrange=(-20, 20), yrange=(-15, 15),
                         axons_range=(-30, 30))
    model.build()
    xyret = np.column_stack((model.spatial.grid.xret.ravel(),
                             model.spatial.grid.yret.ravel()))
    bundles = model.spatial.grow_axon_bundles()
    axons = model.spatial.find_closest_axon(bundles)
    contrib = model.spatial.calc_axon_contribution(axons)

    # Check lambda math:
    for ax, xy in zip(contrib, xyret):
        axon = np.insert(ax, 0, list(xy) + [0], axis=0)
        d2 = np.cumsum(np.diff(axon[:, 0], axis=0) ** 2 +
                       np.diff(axon[:, 1], axis=0) ** 2)
        sensitivity = np.exp(-d2 / (2.0 * model.spatial.axlambda ** 2))
        npt.assert_almost_equal(sensitivity, ax[:, 2]) 

def get_xs_in_range(x_array, x_min, x_max):
    """
    获取分割坐标点
    :param x_array: 宽度方向分割坐标点数组；0~image_width,间隔16 ；如:[0,16,32,...608]
    :param x_min: 四边形x最小值
    :param x_max: 四边形x最大值
    :return:
    """
    indices = np.logical_and(x_array >= x_min, x_array <= x_max)
    xs = x_array[indices]
    # 处理两端的值
    if xs.shape[0] == 0 or xs[0] > x_min:
        xs = np.insert(xs, 0, x_min)
    if xs.shape[0] == 0 or xs[-1] < x_max:
        xs = np.append(xs, x_max)
    return xs 

def test_basic(self):
        a = [1, 2, 3]
        assert_equal(insert(a, 0, 1), [1, 1, 2, 3])
        assert_equal(insert(a, 3, 1), [1, 2, 3, 1])
        assert_equal(insert(a, [1, 1, 1], [1, 2, 3]), [1, 1, 2, 3, 2, 3])
        assert_equal(insert(a, 1, [1, 2, 3]), [1, 1, 2, 3, 2, 3])
        assert_equal(insert(a, [1, -1, 3], 9), [1, 9, 2, 9, 3, 9])
        assert_equal(insert(a, slice(-1, None, -1), 9), [9, 1, 9, 2, 9, 3])
        assert_equal(insert(a, [-1, 1, 3], [7, 8, 9]), [1, 8, 2, 7, 3, 9])
        b = np.array([0, 1], dtype=np.float64)
        assert_equal(insert(b, 0, b[0]), [0., 0., 1.])
        assert_equal(insert(b, [], []), b)
        # Bools will be treated differently in the future:
        # assert_equal(insert(a, np.array([True]*4), 9), [9, 1, 9, 2, 9, 3, 9])
        with warnings.catch_warnings(record=True) as w:
            warnings.filterwarnings('always', '', FutureWarning)
            assert_equal(
                insert(a, np.array([True] * 4), 9), [1, 9, 9, 9, 9, 2, 3])
            assert_(w[0].category is FutureWarning) 

def test_place(self):
        # Make sure that non-np.ndarray objects
        # raise an error instead of doing nothing
        assert_raises(TypeError, place, [1, 2, 3], [True, False], [0, 1])

        a = np.array([1, 4, 3, 2, 5, 8, 7])
        place(a, [0, 1, 0, 1, 0, 1, 0], [2, 4, 6])
        assert_array_equal(a, [1, 2, 3, 4, 5, 6, 7])

        place(a, np.zeros(7), [])
        assert_array_equal(a, np.arange(1, 8))

        place(a, [1, 0, 1, 0, 1, 0, 1], [8, 9])
        assert_array_equal(a, [8, 2, 9, 4, 8, 6, 9])
        assert_raises_regex(ValueError, "Cannot insert from an empty array",
                            lambda: place(a, [0, 0, 0, 0, 0, 1, 0], []))

        # See Issue #6974
        a = np.array(['12', '34'])
        place(a, [0, 1], '9')
        assert_array_equal(a, ['12', '9']) 

def test_out(self):
        mat = np.random.rand(3, 3)
        nan_mat = np.insert(mat, [0, 2], np.nan, axis=1)
        resout = np.zeros(3)
        tgt = np.median(mat, axis=1)
        res = np.nanmedian(nan_mat, axis=1, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        # 0-d output:
        resout = np.zeros(())
        tgt = np.median(mat, axis=None)
        res = np.nanmedian(nan_mat, axis=None, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        res = np.nanmedian(nan_mat, axis=(0, 1), out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt) 

def test_out(self):
        mat = np.random.rand(3, 3)
        nan_mat = np.insert(mat, [0, 2], np.nan, axis=1)
        resout = np.zeros(3)
        tgt = np.percentile(mat, 42, axis=1)
        res = np.nanpercentile(nan_mat, 42, axis=1, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        # 0-d output:
        resout = np.zeros(())
        tgt = np.percentile(mat, 42, axis=None)
        res = np.nanpercentile(nan_mat, 42, axis=None, out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt)
        res = np.nanpercentile(nan_mat, 42, axis=(0, 1), out=resout)
        assert_almost_equal(res, resout)
        assert_almost_equal(res, tgt) 

def __init__(self, ops, dtype=None):
        self.ops = ops
        mops = np.zeros(len(ops), dtype=np.int)
        nops = np.zeros(len(ops), dtype=np.int)
        for iop, oper in enumerate(ops):
            if not isinstance(oper, (LinearOperator, spLinearOperator)):
                self.ops[iop] = MatrixMult(oper, dtype=oper.dtype)
            nops[iop] = self.ops[iop].shape[0]
            mops[iop] = self.ops[iop].shape[1]
        self.nops = nops.sum()
        self.mops = mops.sum()
        self.nnops = np.insert(np.cumsum(nops), 0, 0)
        self.mmops = np.insert(np.cumsum(mops), 0, 0)
        self.shape = (self.nops, self.mops)
        if dtype is None:
            self.dtype = _get_dtype(ops)
        else:
            self.dtype = np.dtype(dtype)
        self.explicit = False 

def __init__(self, ops, dtype=None):
        self.ops = ops
        nops = np.zeros(len(self.ops), dtype=np.int)
        for iop, oper in enumerate(ops):
            if not isinstance(oper, (LinearOperator, spLinearOperator)):
                self.ops[iop] = MatrixMult(oper, dtype=oper.dtype)
            nops[iop] = self.ops[iop].shape[0]
        self.nops = nops.sum()
        mops = [oper.shape[1] for oper in self.ops]
        if len(set(mops)) > 1:
            raise ValueError('operators have different number of columns')
        self.mops = mops[0]
        self.nnops = np.insert(np.cumsum(nops), 0, 0)
        self.shape = (self.nops, self.mops)
        if dtype is None:
            self.dtype = _get_dtype(self.ops)
        else:
            self.dtype = np.dtype(dtype)
        self.explicit = False 

def sum_of_squares_error(xlist, tlist, w1, w2):
    """二乗誤差和を計算する"""
    error = 0.0
    for n in range(N):
        z = np.zeros(NUM_HIDDEN)
        y = np.zeros(NUM_OUTPUT)
        # バイアスの1を先頭に挿入
        x = np.insert(xlist[n], 0, 1)
        # 順伝播で出力を計算
        for j in range(NUM_HIDDEN):
            a = np.zeros(NUM_HIDDEN)
            for i in range(NUM_INPUT):
                a[j] += w1[j, i] * x[i]
            z[j] = np.tanh(a[j])

        for k in range(NUM_OUTPUT):
            for j in range(NUM_HIDDEN):
                y[k] += w2[k, j] * z[j]
        # 二乗誤差を計算
        for k in range(NUM_OUTPUT):
            error += 0.5 * (y[k] - tlist[n, k]) * (y[k] - tlist[n, k])
    return error 

def output(x, w1, w2):
    """xを入力したときのニューラルネットワークの出力を計算
    隠れユニットの出力も一緒に返す"""
    # 配列に変換して先頭にバイアスの1を挿入
    x = np.insert(x, 0, 1)
    z = np.zeros(NUM_HIDDEN)
    y = np.zeros(NUM_OUTPUT)
    # 順伝播で出力を計算
    for j in range(NUM_HIDDEN):
        a = np.zeros(NUM_HIDDEN)
        for i in range(NUM_INPUT):
            a[j] += w1[j, i] * x[i]
        z[j] = np.tanh(a[j])
    for k in range(NUM_OUTPUT):
        for j in range(NUM_HIDDEN):
            y[k] += w2[k, j] * z[j]
    return y, z 

def sum_of_squares_error(xlist, tlist, w1, w2):
    """二乗誤差和を計算する"""
    error = 0.0
    for n in range(N):
        z = np.zeros(NUM_HIDDEN)
        y = np.zeros(NUM_OUTPUT)
        # バイアスの1を先頭に挿入
        x = np.insert(xlist[n], 0, 1)
        # 順伝播で出力を計算
        for j in range(NUM_HIDDEN):
            a = np.zeros(NUM_HIDDEN)
            a[j] = np.dot(w1[j, :], x)
            z[j] = np.tanh(a[j])
        for k in range(NUM_OUTPUT):
            y[k] = np.dot(w2[k, :], z)
        # 二乗誤差を計算
        for k in range(NUM_OUTPUT):
            error += 0.5 * (y[k] - tlist[n, k]) * (y[k] - tlist[n, k])
    return error 

def one_vs_all(X, y, num_labels, learning_rate):
    rows = X.shape[0]
    params = X.shape[1]
    
    # k X (n + 1) array for the parameters of each of the k classifiers
    all_theta = np.zeros((num_labels, params + 1))
    
    # insert a column of ones at the beginning for the intercept term
    X = np.insert(X, 0, values=np.ones(rows), axis=1)
    
    # labels are 1-indexed instead of 0-indexed
    for i in range(1, num_labels + 1):
        theta = np.zeros(params + 1)
        y_i = np.array([1 if label == i else 0 for label in y])
        y_i = np.reshape(y_i, (rows, 1))
        
        # minimize the objective function
        fmin = minimize(fun=cost, x0=theta, args=(X, y_i, learning_rate), method='TNC', jac=gradient)
        all_theta[i-1,:] = fmin.x
    
    return all_theta 

def forward_propagate(X, theta1, theta2):
    m = X.shape[0]
    
    a1 = np.insert(X, 0, values=np.ones(m), axis=1)
    z2 = a1 * theta1.T
    a2 = np.insert(sigmoid(z2), 0, values=np.ones(m), axis=1)
    z3 = a2 * theta2.T
    h = sigmoid(z3)
    
    return a1, z2, a2, z3, h 

def prediction(self, input_data='', mode='test_data', with_missing_data=False):

        prediction = {}

        if (self.status != 'train'):
            print("Please load train data and init W then train the W first.")
            return prediction

        if (input_data == ''):
            print("Please input test data for prediction.")
            return prediction

        if mode == 'future_data':
            data = input_data.split()
            input_data_x = [v for v in data]
            input_data_x = np.ravel(input_data_x)
            input_data_x = np.insert(input_data_x, 0, '1')
            prediction = self.score_function(input_data_x, self.W, with_missing_data)
            return {"input_data_x": input_data_x, "input_data_y": None, "prediction": prediction}
        else:
            data = input_data.split()
            input_data_x = [v for v in data[:-1]]
            input_data_x = np.ravel(input_data_x)
            input_data_x = np.insert(input_data_x, 0, '1')
            input_data_y = data[-1]
            prediction = self.score_function(input_data_x, self.W, with_missing_data)
            return {"input_data_x": input_data_x, "input_data_y": input_data_y, "prediction": prediction} 

def weights(self):
        """Current value weights vector."""
        weights = self.__scheme[1:]-self.__scheme[:-1]
        weights = list(weights)
        weights.insert(0,self.__scheme[0])
        return weights