Python functools.reduce() Examples

def begin_read_samples(self):
        if self.cache:
            return

        self.input.begin_read_samples()
         # copy meta
        if self.output:
            self.output.meta = self.input.meta

        self.multipliers = {}
        self.rngs = {}

        def _mul(split):
            return reduce(operator.mul, map(lambda op: _get_multiplier(split, op), self.ops), 1)

        for split in SPLITS:
            self.multipliers[split] = _mul(split)
            self.cache[split] = self._calculate_num_samples(split)
            self.rngs[split] = self.cache[split] * [None]

        self.input.end_read_samples() 

def _apply_window(da, dims, window_type='hanning'):
    """Creating windows in dimensions dims."""

    if window_type not in ['hanning']:
        raise NotImplementedError("Only hanning window is supported for now.")

    numpy_win_func = getattr(np, window_type)

    if da.chunks:
        def dask_win_func(n):
            return dsar.from_delayed(
                delayed(numpy_win_func, pure=True)(n),
                (n,), float)
        win_func = dask_win_func
    else:
        win_func = numpy_win_func

    windows = [xr.DataArray(win_func(len(da[d])),
               dims=da[d].dims, coords=da[d].coords) for d in dims]

    return da * reduce(operator.mul, windows[::-1]) 

def simplify_source(s):
    s = map(lambda x: x.replace(',(1, 1),(0, 0),1,1,bias=True),#Conv2d',')'),s)
    s = map(lambda x: x.replace(',(0, 0),1,1,bias=True),#Conv2d',')'),s)
    s = map(lambda x: x.replace(',1,1,bias=True),#Conv2d',')'),s)
    s = map(lambda x: x.replace(',bias=True),#Conv2d',')'),s)
    s = map(lambda x: x.replace('),#Conv2d',')'),s)
    s = map(lambda x: x.replace(',1e-05,0.1,True),#BatchNorm2d',')'),s)
    s = map(lambda x: x.replace('),#BatchNorm2d',')'),s)
    s = map(lambda x: x.replace(',(0, 0),ceil_mode=False),#MaxPool2d',')'),s)
    s = map(lambda x: x.replace(',ceil_mode=False),#MaxPool2d',')'),s)
    s = map(lambda x: x.replace('),#MaxPool2d',')'),s)
    s = map(lambda x: x.replace(',(0, 0),ceil_mode=False),#AvgPool2d',')'),s)
    s = map(lambda x: x.replace(',ceil_mode=False),#AvgPool2d',')'),s)
    s = map(lambda x: x.replace(',bias=True)),#Linear',')), # Linear'),s)
    s = map(lambda x: x.replace(')),#Linear',')), # Linear'),s)

    s = map(lambda x: '{},\n'.format(x),s)
    s = map(lambda x: x[1:],s)
    s = reduce(lambda x,y: x+y, s)
    return s 

def row_norms(ii, f=Ellipsis, squared=False):
    '''
    row_norms(ii) yields a potential function h(x) that calculates the vector norms of the rows of
      the matrix formed by [x[i] for i in ii] (ii is a matrix of parameter indices).
    row_norms(ii, f) yield a potential function h(x) equivalent to compose(row_norms(ii), f).
    '''
    try:
        (n,m) = ii
        # matrix shape given
        ii = np.reshape(np.arange(n*m), (n,m))
    except Exception: ii = np.asarray(ii)
    f = to_potential(f)
    if is_const_potential(f):
        q = flattest(f.c)
        q = np.sum([q[i]**2 for i in ii.T], axis=0)
        return PotentialConstant(q if squared else np.sqrt(q))
    F = reduce(lambda a,b: a + b, [part(Ellipsis, col)**2 for col in ii.T])
    F = compose(F, f)
    if not squared: F = sqrt(F)
    return F 

def col_norms(ii, f=Ellipsis, squared=False):
    '''
    col_norms(ii) yields a potential function h(x) that calculates the vector norms of the columns
      of the matrix formed by [x[i] for i in ii] (ii is a matrix of parameter indices).
    col_norms(ii, f) yield a potential function h(x) equivalent to compose(col_norms(ii), f).
    '''
    try:
        (n,m) = ii
        # matrix shape given
        ii = np.reshape(np.arange(n*m), (n,m))
    except Exception: ii = np.asarray(ii)
    f = to_potential(f)
    if is_const_potential(f):
        q = flattest(f.c)
        q = np.sum([q[i]**2 for i in ii], axis=0)
        return PotentialConstant(q if squared else np.sqrt(q))
    F = reduce(lambda a,b: a + b, [part(Ellipsis, col)**2 for col in ii])
    F = compose(F, f)
    if not squared: F = sqrt(F)
    return F 

def cplus(*args):
    '''
    cplus(a, b...) returns the sum of all the values as a numpy array object. Like numpy's add
      function or a+b syntax, plus will thread over the latest dimension possible.

    Additionally, cplus works correctly with sparse arrays.
    '''
    n = len(args)
    if   n == 0: return np.asarray(0)
    elif n == 1: return np.asarray(args[0])
    elif n >  2: return reduce(plus, args)
    (a,b) = args
    if sps.issparse(a):
        if not sps.issparse(b):
            b = np.asarray(b)
            if len(b.shape) == 0: b = np.reshape(b, (1,1))
    elif sps.issparse(b):
        a = np.asarray(a)
        if len(a.shape) == 0: a = np.reshape(a, (1,1))
    else:
        a = np.asarray(a)
        b = np.asarray(b)
    return a + b 

def ctimes(*args):
    '''
    ctimes(a, b...) returns the product of all the values as a numpy array object. Like numpy's
      multiply function or a*b syntax, times will thread over the latest dimension possible; thus
      if a.shape is (4,2) and b.shape is 2, times(a,b) is a equivalent to a * b.

    Unlike numpy's multiply function, ctimes works with sparse matrices and will reify them.
    '''
    n = len(args)
    if   n == 0: return np.asarray(0)
    elif n == 1: return np.asarray(args[0])
    elif n >  2: return reduce(plus, args)
    (a,b) = args
    if   sps.issparse(a): return a.multiply(b)
    elif sps.issparse(b): return b.multiply(a)
    else:                 return np.asarray(a) * b 

def _column_type(strings, has_invisible=True):
    """The least generic type all column values are convertible to.

    >>> _column_type(["1", "2"]) is _int_type
    True
    >>> _column_type(["1", "2.3"]) is _float_type
    True
    >>> _column_type(["1", "2.3", "four"]) is _text_type
    True
    >>> _column_type(["four", '\u043f\u044f\u0442\u044c']) is _text_type
    True
    >>> _column_type([None, "brux"]) is _text_type
    True
    >>> _column_type([1, 2, None]) is _int_type
    True
    >>> import datetime as dt
    >>> _column_type([dt.datetime(1991,2,19), dt.time(17,35)]) is _text_type
    True

    """
    types = [_type(s, has_invisible) for s in strings ]
    return reduce(_more_generic, types, int) 

def feed_forward_categorical_fun(action_space, config, observations):
  """Feed-forward categorical."""
  if not isinstance(action_space, gym.spaces.Discrete):
    raise ValueError("Expecting discrete action space.")
  flat_observations = tf.reshape(observations, [
      tf.shape(observations)[0], tf.shape(observations)[1],
      functools.reduce(operator.mul, observations.shape.as_list()[2:], 1)])
  with tf.variable_scope("network_parameters"):
    with tf.variable_scope("policy"):
      x = flat_observations
      for size in config.policy_layers:
        x = tf.contrib.layers.fully_connected(x, size, tf.nn.relu)
      logits = tf.contrib.layers.fully_connected(x, action_space.n,
                                                 activation_fn=None)
    with tf.variable_scope("value"):
      x = flat_observations
      for size in config.value_layers:
        x = tf.contrib.layers.fully_connected(x, size, tf.nn.relu)
      value = tf.contrib.layers.fully_connected(x, 1, None)[..., 0]
  policy = tf.contrib.distributions.Categorical(logits=logits)
  return NetworkOutput(policy, value, lambda a: a) 

def dense_bitwise_categorical_fun(action_space, config, observations):
  """Dense network with bitwise input and categorical output."""
  del config
  obs_shape = common_layers.shape_list(observations)
  x = tf.reshape(observations, [-1] + obs_shape[2:])

  with tf.variable_scope("network_parameters"):
    with tf.variable_scope("dense_bitwise"):
      x = discretization.int_to_bit_embed(x, 8, 32)
      flat_x = tf.reshape(
          x, [obs_shape[0], obs_shape[1],
              functools.reduce(operator.mul, x.shape.as_list()[1:], 1)])

      x = tf.contrib.layers.fully_connected(flat_x, 256, tf.nn.relu)
      x = tf.contrib.layers.fully_connected(flat_x, 128, tf.nn.relu)

      logits = tf.contrib.layers.fully_connected(x, action_space.n,
                                                 activation_fn=None)

      value = tf.contrib.layers.fully_connected(
          x, 1, activation_fn=None)[..., 0]
      policy = tf.contrib.distributions.Categorical(logits=logits)

  return NetworkOutput(policy, value, lambda a: a) 

def gather_indices_2d(x, block_shape, block_stride):
  """Getting gather indices."""
  # making an identity matrix kernel
  kernel = tf.eye(block_shape[0] * block_shape[1])
  kernel = reshape_range(kernel, 0, 1, [block_shape[0], block_shape[1], 1])
  # making indices [1, h, w, 1] to appy convs
  x_shape = common_layers.shape_list(x)
  indices = tf.range(x_shape[2] * x_shape[3])
  indices = tf.reshape(indices, [1, x_shape[2], x_shape[3], 1])
  indices = tf.nn.conv2d(
      tf.cast(indices, tf.float32),
      kernel,
      strides=[1, block_stride[0], block_stride[1], 1],
      padding="VALID")
  # making indices [num_blocks, dim] to gather
  dims = common_layers.shape_list(indices)[:3]
  if all([isinstance(dim, int) for dim in dims]):
    num_blocks = functools.reduce(operator.mul, dims, 1)
  else:
    num_blocks = tf.reduce_prod(dims)
  indices = tf.reshape(indices, [num_blocks, -1])
  return tf.cast(indices, tf.int32) 

def setup_critic_optimizer(self):
        logger.info('setting up critic optimizer')
        normalized_critic_target_tf = tf.clip_by_value(normalize(self.critic_target, self.ret_rms), self.return_range[0], self.return_range[1])
        self.critic_loss = tf.reduce_mean(tf.square(self.normalized_critic_tf - normalized_critic_target_tf))
        if self.critic_l2_reg > 0.:
            critic_reg_vars = [var for var in self.critic.trainable_vars if 'kernel' in var.name and 'output' not in var.name]
            for var in critic_reg_vars:
                logger.info('  regularizing: {}'.format(var.name))
            logger.info('  applying l2 regularization with {}'.format(self.critic_l2_reg))
            critic_reg = tc.layers.apply_regularization(
                tc.layers.l2_regularizer(self.critic_l2_reg),
                weights_list=critic_reg_vars
            )
            self.critic_loss += critic_reg
        critic_shapes = [var.get_shape().as_list() for var in self.critic.trainable_vars]
        critic_nb_params = sum([reduce(lambda x, y: x * y, shape) for shape in critic_shapes])
        logger.info('  critic shapes: {}'.format(critic_shapes))
        logger.info('  critic params: {}'.format(critic_nb_params))
        self.critic_grads = U.flatgrad(self.critic_loss, self.critic.trainable_vars, clip_norm=self.clip_norm)
        self.critic_optimizer = MpiAdam(var_list=self.critic.trainable_vars,
            beta1=0.9, beta2=0.999, epsilon=1e-08) 

def normalize(md):
    '''Normalize anchors.'''
    def on_match(link):
        desc = link.group(1)
        old = link.group(2)
        href = (link.group(2)
                .lower()
                .replace('%20', '-')
                .replace(" ", "-")
                .replace("~", "")
                .replace(".", ""))
        old, new = f'[{desc}]({old})', f'[{desc}]({href})'
        print(old, new)
        return old, new

    replacers = set((on_match(x) for x in re.finditer(r'\[([^\]\[]*)\]\((#[^\)]*)\)', md)))
    return ft.reduce(lambda md, x: md.replace(x[0], x[1]), replacers, md) 

def setup_critic_optimizer(self):
        logger.info('setting up critic optimizer')
        normalized_critic_target_tf = tf.clip_by_value(normalize(self.critic_target, self.ret_rms), self.return_range[0], self.return_range[1])
        self.critic_loss = tf.reduce_mean(tf.square(self.normalized_critic_tf - normalized_critic_target_tf))
        if self.critic_l2_reg > 0.:
            critic_reg_vars = [var for var in self.critic.trainable_vars if 'kernel' in var.name and 'output' not in var.name]
            for var in critic_reg_vars:
                logger.info('  regularizing: {}'.format(var.name))
            logger.info('  applying l2 regularization with {}'.format(self.critic_l2_reg))
            critic_reg = tc.layers.apply_regularization(
                tc.layers.l2_regularizer(self.critic_l2_reg),
                weights_list=critic_reg_vars
            )
            self.critic_loss += critic_reg
        critic_shapes = [var.get_shape().as_list() for var in self.critic.trainable_vars]
        critic_nb_params = sum([reduce(lambda x, y: x * y, shape) for shape in critic_shapes])
        logger.info('  critic shapes: {}'.format(critic_shapes))
        logger.info('  critic params: {}'.format(critic_nb_params))
        self.critic_grads = U.flatgrad(self.critic_loss, self.critic.trainable_vars, clip_norm=self.clip_norm)
        self.critic_optimizer = MpiAdam(var_list=self.critic.trainable_vars,
            beta1=0.9, beta2=0.999, epsilon=1e-08) 

def extract(iid, bindir):
    print('Extracting binaries......')
    query = '''select filename from object_to_image where iid=''' + iid + ''' and score>0 and (mime='application/x-executable; charset=binary' or mime='application/x-object; charset=binary' or mime='application/x-sharedlib; charset=binary') order by score DESC;'''
    wanted = dbquery(query)
    wanted = reduce((lambda a, b: a + b), wanted)
    wanted = map((lambda a: '.' + a), wanted)
    wanted = reduce((lambda a, b: a + ' ' + b), wanted)
    cmd = 'tar xf ' + bindir + '/../../../../images/' + iid + '.tar.gz -C ' + bindir + ' ' + wanted
    subprocess.run([cmd], shell=True)

    print('Extracting library links......')
    query = '''select filename from object_to_image where iid=''' + iid + ''' and regular_file='f';'''
    wanted = dbquery(query)
    wanted = reduce((lambda a, b: a + b), wanted)
    wanted = filter((lambda a: 'lib' in a), wanted)
    wanted = map((lambda a: '.' + a), wanted)
    wanted = reduce((lambda a, b: a + ' ' + b), wanted)
    cmd = 'tar xf ' + bindir + '/../../../../images/' + iid + '.tar.gz -C ' + bindir + ' ' + wanted
    subprocess.run([cmd], shell=True) 

def _get_r(s, snesc):
    # R^dag \tilde{S} R = S
    # R = S^{-1/2} [S^{-1/2}\tilde{S}S^{-1/2}]^{-1/2} S^{1/2}
    w, v = numpy.linalg.eigh(s)
    idx = w > 1e-14
    v = v[:,idx]
    w_sqrt = numpy.sqrt(w[idx])
    w_invsqrt = 1 / w_sqrt

    # eigenvectors of S as the new basis
    snesc = reduce(numpy.dot, (v.conj().T, snesc, v))
    r_mid = numpy.einsum('i,ij,j->ij', w_invsqrt, snesc, w_invsqrt)
    w1, v1 = numpy.linalg.eigh(r_mid)
    idx1 = w1 > 1e-14
    v1 = v1[:,idx1]
    r_mid = numpy.dot(v1/numpy.sqrt(w1[idx1]), v1.conj().T)
    r = numpy.einsum('i,ij,j->ij', w_invsqrt, r_mid, w_sqrt)
    # Back transform to AO basis
    r = reduce(numpy.dot, (v, r, v.conj().T))
    return r 

def _sqrt2(a0, a1i, a1j, a2ij):
    '''Solving second order derivative of x^2 = a'''
    w, v = scipy.linalg.eigh(a0)
    w = numpy.sqrt(w)
    a1i = reduce(numpy.dot, (v.conj().T, a1i, v))
    x1i = a1i / (w[:,None] + w)

    a1j = reduce(numpy.dot, (v.conj().T, a1j, v))
    x1j = a1j / (w[:,None] + w)

    a2ij = reduce(numpy.dot, (v.conj().T, a2ij, v))
    tmp = x1i.dot(x1j)
    a2ij -= tmp + tmp.conj().T
    x2 = a2ij / (w[:,None] + w)
    x2 = reduce(numpy.dot, (v, x2, v.conj().T))
    return x2 

def fast_iao_mullikan_pop(mf,cell,a=None):
    '''
    Input: mf -- a preconverged mean fild object
    Returns: mullikan populaion analysis in the basisIAO a
    '''

    #
    # here we convert the density matrix to the IAO basis
    #
    if a is None:
        a = numpy.eye(mf.make_rdm1().shape[1])
    #converts the occupied MOs to the IAO basis
    ovlpS = mf.get_ovlp()
    CIb = reduce(numpy.dot, (a.T, ovlpS , mf.make_rdm1()))

    #
    # This is the mullikan population below here
    #

    mo_occ = mf.mo_coeff[:,mf.mo_occ>0]
    mo_occ = reduce(numpy.dot, (a.T, mf.get_ovlp(), mo_occ))
    dm = numpy.dot(mo_occ, mo_occ.T) * 2
    pmol = cell.copy()
    pmol.build(False, False, basis='minao')
    return mf.mulliken_pop(pmol, dm, s=numpy.eye(pmol.nao_nr())) 

def spin_square(self, mo_coeff=None, s=None):
        '''Treating the k-point sampling wfn as a giant Slater determinant,
        the spin_square value is the <S^2> of the giant determinant.
        '''
        nkpts = len(self.kpts)
        if mo_coeff is None:
            mo_a = [self.mo_coeff[0][k][:,self.mo_occ[0][k]>0] for k in range(nkpts)]
            mo_b = [self.mo_coeff[1][k][:,self.mo_occ[1][k]>0] for k in range(nkpts)]
        else:
            mo_a, mo_b = mo_coeff
        if s is None:
            s = self.get_ovlp()

        nelec_a = sum([mo_a[k].shape[1] for k in range(nkpts)])
        nelec_b = sum([mo_b[k].shape[1] for k in range(nkpts)])
        ssxy = (nelec_a + nelec_b) * .5
        for k in range(nkpts):
            sij = reduce(np.dot, (mo_a[k].T.conj(), s[k], mo_b[k]))
            ssxy -= np.einsum('ij,ij->', sij.conj(), sij).real
        ssz = (nelec_b-nelec_a)**2 * .25
        ss = ssxy + ssz
        s = np.sqrt(ss+.25) - .5
        return ss, s*2+1 

def canonicalize(mf, mo_coeff_kpts, mo_occ_kpts, fock=None):
    if fock is None:
        dm = mf.make_rdm1(mo_coeff_kpts, mo_occ_kpts)
        fock = mf.get_fock(dm=dm)
    mo_coeff = []
    mo_energy = []
    for k, mo in enumerate(mo_coeff_kpts):
        mo1 = np.empty_like(mo)
        mo_e = np.empty_like(mo_occ_kpts[k])
        occidx = mo_occ_kpts[k] == 2
        viridx = ~occidx
        for idx in (occidx, viridx):
            if np.count_nonzero(idx) > 0:
                orb = mo[:,idx]
                f1 = reduce(np.dot, (orb.T.conj(), fock[k], orb))
                e, c = scipy.linalg.eigh(f1)
                mo1[:,idx] = np.dot(orb, c)
                mo_e[idx] = e
        mo_coeff.append(mo1)
        mo_energy.append(mo_e)
    return mo_energy, mo_coeff 

def _calculate_num_samples(self, split):
        """Calculate the total number of samples after applying ops.
        """
        num_samples = self.input.num_samples(split)

        # calculate how much the samples will be augmented after going through ops
        multiplier = reduce(operator.mul, map(lambda op: _get_multiplier(split, op), self.ops), 1)

        return int(num_samples * multiplier) 

def download_and_parse_mnist_file(file_name, datadir=None, force=False):
    file_name = maybe_download_mnist_file(file_name, datadir=datadir,
                                          force=force)

    # Open the file and unzip it if necessary
    if os.path.splitext(file_name)[1] == '.gz':
        open_fn = gzip.open
    else:
        open_fn = open

    # Parse the file
    with open_fn(file_name, 'rb') as file_descriptor:
        header = file_descriptor.read(4)
        assert len(header) == 4

        zeros, data_type, n_dims = struct.unpack('>HBB', header)
        assert zeros == 0

        hex_to_data_type = {
            0x08: 'B',
            0x09: 'b',
            0x0b: 'h',
            0x0c: 'i',
            0x0d: 'f',
            0x0e: 'd'}
        data_type = hex_to_data_type[data_type]

        dim_sizes = struct.unpack(
            '>' + 'I' * n_dims,
            file_descriptor.read(4 * n_dims))

        data = array.array(data_type, file_descriptor.read())
        data.byteswap()

        desired_items = functools.reduce(operator.mul, dim_sizes)
        assert len(data) == desired_items
        return np.array(data).reshape(dim_sizes) 

def os_path_exists(f):
    chunks = reduce(lambda accum, x : accum + x.split('/'), f.split('\\'), [])
    if chunks[-1] in ['multibootusb.log', 'loopback.cfg']:
        return True
    if 'arch' in chunks:
        return True
    if chunks[1] in ['rootfs1.gz', 'rootfs2.gz']:
        return True
    if chunks == ['multibootusb', 'debian-sid', 'boot', 'rootfs4.gz']:
        return True
    return False 

def forward(self, input):
        return reduce(self.lambda_func,self.forward_prepare(input)) 

def forward(self, input):
        # result is a Variable
        return reduce(self.lambda_func,self.forward_prepare(input)) 

def forward(self, input):
        return reduce(self.lambda_func,self.forward_prepare(input)) 

def _reduced_filter(self) -> t.Optional[Predicate]:
        """Before evaluation, sum up all filter predicates into a single one"""
        return None if self._is_trivial else reduce(and_, self._filters)

    # lazy queries 

def valid(word):
    # check number
    try:
        numbers = [w2n.word_to_num(it) for it in word.split()]
        if len(numbers) > 1:
            return False
    except ValueError:
        return False
    # check English
    chars = map(lambda c: 'a' <= c <= 'z', word)
    return reduce(lambda a, b: a or b, chars, False) 

def compose(*args):
    '''
    compose(g, h...) yields a potential function f that is the result of composing together all the
      arguments g, h, etc. after calling to_potential() on each. The result is defined such that
      f(x) is equivalent to g(h(...(x))).
    '''
    return reduce(lambda h,g: PotentialComposition(g,h), reversed(list(map(to_potential, args)))) 

def fit_pRF_radius(ctx, retinotopy=Ellipsis, mask=None, weight=Ellipsis, slope_only=False):
    '''
    fit_pRF_radius(ctx) fits a line, m*eccen + b, to the pRF radius and yields the tuple (m, b).

    The following options may be given:
      * retinotopy (default: Ellipsis) specifies the prefix for the retinotopy (passed to
        retinotopy_data() to find the retinotopic dataset).
      * mask (default: None) specifies the mask over which to perform the calculation. This is
        passed to the to_mask() function. In the case that mask is a set or frozenset, then it is
        treated as a conjunction (intersection) of masks.
      * weight (default: None) specifies that a weight should be used; if this is True or Ellipsis,
        will use the variance_explained if it is part of the retinotopy dataset; if this is False or
        None, uses no weight; otherwise, this must be a weight property or property name.
      * slope_only (default: False) may be set to True to instead fit radius = m*eccen and return
        only m.
    '''
    rdat = retinotopy_data(ctx, retinotopy)
    if 'radius' not in rdat: raise ValueError('No pRF radius found in dataset %s' % retinotopy)
    rad = rdat['radius']
    (ang,ecc) = as_retinotopy(rdat, 'visual')
    if isinstance(mask, (set, frozenset)):
        mask = reduce(np.intersect1d, [ctx.mask(m, indices=True) for m in mask])
    else: mask = ctx.mask(mask, indices=True)
    # get a weight if provided:
    if weight in [False, None]: wgt = np.ones(rad.shape)
    elif weight in [True, Ellipsis]:
        if 'variance_explained' in rdat: wgt = rdat['variance_explained']
        else: wgt = np.ones(rad.shape)
    else: wgt = ctx.property(weight)
    # get the relevant eccen and radius values
    (ecc,rad,wgt) = [x[mask] for x in (ecc,rad,wgt)]
    # fit a line...
    if slope_only:
        ecc = np.reshape(ecc * wgt, (len(ecc), 1))
        rad = np.reshape(rad * wgt, (len(rad), 1))
        return np.linalg.lstsq(ecc, rad)[0]
    else:
        return tuple(np.polyfit(ecc, rad, 1, w=wgt))