Python math.sqrt() Examples

def __init__(self, block, layers, num_classes=1000):
        self.inplanes = 64
        super(MyResNet, self).__init__()
        self.conv1 = nn.Conv2d(3, 64, kernel_size=7, stride=2, padding=3,
                               bias=False)
        self.bn1 = nn.BatchNorm2d(64)
        self.relu = nn.ReLU(inplace=True)
        self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
        # note the increasing dilation
        self.layer1 = self._make_layer(block, 64, layers[0])
        self.layer2 = self._make_layer(block, 128, layers[1], stride=2, dilation=1)
        self.layer3 = self._make_layer(block, 256, layers[2], stride=1, dilation=2)
        self.layer4 = self._make_layer(block, 512, layers[3], stride=1, dilation=4)

        # these layers will not be used
        self.avgpool = nn.AvgPool2d(7)
        self.fc = nn.Linear(512 * block.expansion, num_classes)

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_() 

def __init__(self, block, layers, num_classes=1000):
    self.inplanes = 64
    super(ResNet, self).__init__()
    self.conv1 = nn.Conv2d(3, 64, kernel_size=7, stride=2, padding=3,
                 bias=False)
    self.bn1 = nn.BatchNorm2d(64)
    self.relu = nn.ReLU(inplace=True)
    # maxpool different from pytorch-resnet, to match tf-faster-rcnn
    self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
    self.layer1 = self._make_layer(block, 64, layers[0])
    self.layer2 = self._make_layer(block, 128, layers[1], stride=2)
    self.layer3 = self._make_layer(block, 256, layers[2], stride=2)
    # use stride 1 for the last conv4 layer (same as tf-faster-rcnn)
    self.layer4 = self._make_layer(block, 512, layers[3], stride=1)

    for m in self.modules():
      if isinstance(m, nn.Conv2d):
        n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
        m.weight.data.normal_(0, math.sqrt(2. / n))
      elif isinstance(m, nn.BatchNorm2d):
        m.weight.data.fill_(1)
        m.bias.data.zero_() 

def distance(origin, destination):
	"""Determine distance between 2 sets of [lat,lon] in km"""

	lat1, lon1 = origin
	lat2, lon2 = destination
	radius = 6371  # km

	dlat = math.radians(lat2 - lat1)
	dlon = math.radians(lon2 - lon1)
	a = (math.sin(dlat / 2) * math.sin(dlat / 2) +
		 math.cos(math.radians(lat1)) *
		 math.cos(math.radians(lat2)) * math.sin(dlon / 2) *
		 math.sin(dlon / 2))
	c = 2 * math.atan2(math.sqrt(a), math.sqrt(1 - a))
	d = radius * c

	return d 

def get_privacy_spent(self, sess, target_eps=None):
    """Report the spending so far.

    Args:
      sess: the session to run the tensor.
      target_eps: the target epsilon. Unused.
    Returns:
      the list containing a single EpsDelta, with values as Python floats (as
      opposed to numpy.float64). This is to be consistent with
      MomentAccountant which can return a list of (eps, delta) pair.
    """

    # pylint: disable=unused-argument
    unused_target_eps = target_eps
    eps_squared_sum, delta_sum = sess.run([self._eps_squared_sum,
                                           self._delta_sum])
    return [EpsDelta(math.sqrt(eps_squared_sum), float(delta_sum))] 

def update(self, index, weight, grad, state):
        self._update_count(index)
        wd = self._get_wd(index)
        lr = self._get_lr(index)
        num_rows = weight.shape[0]

        dn, n = state
        for row in range(num_rows):
            all_zeros = mx.test_utils.almost_equal(grad[row].asnumpy(), np.zeros_like(grad[row].asnumpy()))
            if all_zeros and self.lazy_update:
                continue
            grad[row] = grad[row] * self.rescale_grad
            if self.clip_gradient is not None:
                mx.nd.clip(grad[row], -self.clip_gradient, self.clip_gradient, out=grad[row])

            #update dn, n
            dn[row] += grad[row] - (mx.nd.sqrt(n[row] + grad[row] * grad[row]) - mx.nd.sqrt(n[row])) * weight[row] / lr
            n[row] += grad[row] * grad[row]

            # update weight
            weight[row] = (mx.nd.sign(dn[row]) * self.lamda1 - dn[row]) / \
                          ((self.beta + mx.nd.sqrt(n[row])) / lr + wd) * (mx.nd.abs(dn[row]) > self.lamda1) 

def update(self, index, weight, grad, state):
        assert(isinstance(weight, NDArray))
        assert(isinstance(grad, NDArray))
        wd = self._get_wd(index)
        self._update_count(index)

        # preprocess grad
        grad *= self.rescale_grad
        if self.clip_gradient is not None:
            grad = clip(grad, -self.clip_gradient, self.clip_gradient)

        # accumulated g and delta initlization
        acc_g, acc_delta = state

        # update g, delta
        acc_g[:] = self.rho * acc_g + (1. - self.rho) * grad * grad
        current_delta = sqrt(acc_delta + self.epsilon) / sqrt(acc_g + self.epsilon) * grad
        acc_delta[:] = self.rho * acc_delta + (1. - self.rho) * current_delta * current_delta

        # update weight
        weight[:] -= current_delta + wd * weight

#pylint: disable=invalid-name
#pylint: disable=line-too-long 

def _compute_dE(self, pos=None, lengths=None, weights=None, m=None):
        dEx = 0
        dEy = 0
        d2Ex2 = 0
        d2Ey2 = 0
        d2Exy = 0
        d2Eyx = 0
        for i in pos:
            if i != m:
                xmi = pos[m][0] - pos[i][0]
                ymi = pos[m][1] - pos[i][1]
                xmi2 = xmi * xmi
                ymi2 = ymi * ymi
                xmi_ymi2 = xmi2 + ymi2
                lmi = lengths[m][i]
                kmi = weights[m][i] / (lmi * lmi)
                dEx += kmi * (xmi - (lmi * xmi) / math.sqrt(xmi_ymi2))
                dEy += kmi * (ymi - (lmi * ymi) / math.sqrt(xmi_ymi2))
                d2Ex2 += kmi * (1 - (lmi * ymi2) / math.pow(xmi_ymi2, 1.5))
                d2Ey2 += kmi * (1 - (lmi * xmi2) / math.pow(xmi_ymi2, 1.5))
                res = kmi * (lmi * xmi * ymi) / math.pow(xmi_ymi2, 1.5)
                d2Exy += res
                d2Eyx += res
        return dEx, dEy, d2Ex2, d2Ey2, d2Exy, d2Eyx 

def swirl(x, y, step):
    x -= (u_width / 2)
    y -= (u_height / 2)
    dist = math.sqrt(pow(x, 2) + pow(y, 2)) / 2.0
    angle = (step / 10.0) + (dist * 1.5)
    s = math.sin(angle)
    c = math.cos(angle)
    xs = x * c - y * s
    ys = x * s + y * c
    r = abs(xs + ys)
    r = r * 12.0
    r -= 20
    return (r, r + (s * 130), r + (c * 130))


# roto-zooming checker board 

def update(self, index, weight, grad, state):
        assert(isinstance(weight, NDArray))
        assert(isinstance(grad, NDArray))
        self._update_count(index)
        lr = self._get_lr(index)
        wd = self._get_wd(index)

        is_sparse = grad.stype == 'row_sparse'
        history = state

        if is_sparse:
            kwargs = {'epsilon': self.float_stable_eps,
                      'rescale_grad': self.rescale_grad}
            if self.clip_gradient:
                kwargs['clip_gradient'] = self.clip_gradient
            sparse.adagrad_update(weight, grad, history, out=weight, lr=lr, wd=wd, **kwargs)
        else:
            grad = grad * self.rescale_grad
            if self.clip_gradient is not None:
                grad = clip(grad, -self.clip_gradient, self.clip_gradient)
            history[:] += square(grad)
            div = grad / sqrt(history + self.float_stable_eps)
            weight[:] += (div + weight * wd) * -lr 

def _get_lbmult(self, nup):
        """Returns lr scaling factor for large batch according to warmup schedule
        (to be implemented)
        """
        nwup = self.warmup_epochs * self.updates_per_epoch
        strategy = self.warmup_strategy
        maxmult = float(self.batch_scale)
        if nup >= nwup:
            mult = maxmult
        elif nwup <= 1:
            mult = 1.0
        else:
            if (strategy == 'linear'):
                mult = 1.0 + (maxmult - 1) * nup / nwup
            elif (strategy == 'power2'):
                mult = 1.0 + (maxmult-1) * (nup*nup)/(nwup*nwup)
            elif (strategy == 'sqrt'):
                mult = 1.0 + (maxmult - 1) * math.sqrt(float(nup) / nwup)
            else:
                mult = 1.0
        return mult 

def _init_weight(self, name, arr):
        shape = arr.shape
        hw_scale = 1.
        if len(shape) < 2:
            raise ValueError('Xavier initializer cannot be applied to vector {0}. It requires at'
                             ' least 2D.'.format(name))
        if len(shape) > 2:
            hw_scale = np.prod(shape[2:])
        fan_in, fan_out = shape[1] * hw_scale, shape[0] * hw_scale
        factor = 1.
        if self.factor_type == "avg":
            factor = (fan_in + fan_out) / 2.0
        elif self.factor_type == "in":
            factor = fan_in
        elif self.factor_type == "out":
            factor = fan_out
        else:
            raise ValueError("Incorrect factor type")
        scale = np.sqrt(self.magnitude / factor)
        if self.rnd_type == "uniform":
            random.uniform(-scale, scale, out=arr)
        elif self.rnd_type == "gaussian":
            random.normal(0, scale, out=arr)
        else:
            raise ValueError("Unknown random type") 

def set_verbosity(self, verbose=False, print_func=None):
        """Switch on/off verbose mode

        Parameters
        ----------
        verbose : bool
            switch on/off verbose mode
        print_func : function
            A function that computes statistics of initialized arrays.
            Takes an `NDArray` and returns an `str`. Defaults to mean
            absolute value str((|x|/size(x)).asscalar()).
        """
        self._verbose = verbose
        if print_func is None:
            def asum_stat(x):
                """returns |x|/size(x), async execution."""
                return str((ndarray.norm(x)/sqrt(x.size)).asscalar())
            print_func = asum_stat
        self._print_func = print_func
        return self 

def matthewscc(self):
        """
        Calculate the Matthew's Correlation Coefficent
        """
        if not self.total_examples:
            return 0.

        true_pos = float(self.true_positives)
        false_pos = float(self.false_positives)
        false_neg = float(self.false_negatives)
        true_neg = float(self.true_negatives)
        terms = [(true_pos + false_pos),
                 (true_pos + false_neg),
                 (true_neg + false_pos),
                 (true_neg + false_neg)]
        denom = 1.
        for t in filter(lambda t: t != 0., terms):
            denom *= t
        return ((true_pos * true_neg) - (false_pos * false_neg)) / math.sqrt(denom) 

def __init__(self, interval, stat_func=None, pattern='.*', sort=False):
        if stat_func is None:
            def asum_stat(x):
                """returns |x|/size(x), async execution."""
                return ndarray.norm(x)/sqrt(x.size)
            stat_func = asum_stat
        self.stat_func = stat_func
        self.interval = interval
        self.activated = False
        self.queue = []
        self.step = 0
        self.exes = []
        self.re_prog = re.compile(pattern)
        self.sort = sort
        def stat_helper(name, array):
            """wrapper for executor callback"""
            array = ctypes.cast(array, NDArrayHandle)
            array = NDArray(array, writable=False)
            if not self.activated or not self.re_prog.match(py_str(name)):
                return
            self.queue.append((self.step, py_str(name), self.stat_func(array)))
        self.stat_helper = stat_helper 

def __init__(self, block, layers, in_channels=3):
        self.inplanes = 64
        super(ResNet, self).__init__()
        self.conv1 = nn.Conv2d(in_channels, 64, kernel_size=7, stride=2, padding=3,
                               bias=False)
        self.bn1 = nn.BatchNorm2d(64)
        self.relu = nn.ReLU(inplace=True)
        self.maxpool = nn.MaxPool2d(kernel_size=3, stride=2, padding=1)
        self.layer1 = self._make_layer(block, 64, layers[0])
        self.layer2 = self._make_layer(block, 128, layers[1], stride=2)
        self.layer3 = self._make_layer(block, 256, layers[2], stride=2)
        self.layer4 = self._make_layer(block, 512, layers[3], stride=2)

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_() 

def _attn(self, q, k, v, sequence_mask):
        w = torch.matmul(q, k)
        if self.scale:
            w = w / math.sqrt(v.size(-1))

        b_subset = self.b[:, :, :w.size(-2), :w.size(-1)]

        if sequence_mask is not None:
            b_subset = b_subset * sequence_mask.view(
                sequence_mask.size(0), 1, -1)
            b_subset = b_subset.permute(1, 0, 2, 3)

        w = w * b_subset + -1e9 * (1 - b_subset)
        w = nn.Softmax(dim=-1)(w)
        w = self.attn_dropout(w)
        return torch.matmul(w, v) 

def __call__(self, video):
    for attempt in range(10):
      area = video.shape[-3]*video.shape[-2]
      target_area = random.uniform(0.08, 1.0)*area
      aspect_ratio = random.uniform(3./4, 4./3)

      w = int(round(math.sqrt(target_area*aspect_ratio)))
      h = int(round(math.sqrt(target_area/aspect_ratio)))

      if random.random() < 0.5:
        w, h = h, w

      if w <= video.shape[-2] and h <= video.shape[-3]:
        x1 = random.randint(0, video.shape[-2]-w)
        y1 = random.randint(0, video.shape[-3]-h)

        video = video[..., y1:y1+h, x1:x1+w, :]

        return resize(video, (self.size, self.size), self.interpolation)

    # Fallback
    scale = Scale(self.size, interpolation=self.interpolation)
    crop = CenterCrop(self.size)
    return crop(scale(video)) 

def genCubeVector(x, y, z, x_mult=1, y_mult=1, z_mult=1):
    """Generates a map of vector lengths from the center point to each coordinate

    x - width of matrix to generate
    y - height of matrix to generate
    z - depth of matrix to generate
    x_mult - value to scale x-axis by
    y_mult - value to scale y-axis by
    z_mult - value to scale z-axis by
    """
    cX = (x - 1) / 2.0
    cY = (y - 1) / 2.0
    cZ = (z - 1) / 2.0

    def vect(_x, _y, _z):
        return int(math.sqrt(math.pow(_x - cX, 2 * x_mult) +
                             math.pow(_y - cY, 2 * y_mult) +
                             math.pow(_z - cZ, 2 * z_mult)))

    return [[[vect(_x, _y, _z) for _z in range(z)] for _y in range(y)] for _x in range(x)] 

def __init__(self, depth, num_classes=1000):
        super(ResNet, self).__init__()
        # Model type specifies number of layers for CIFAR-10 model
        assert (depth - 2) % 6 == 0, 'depth should be 6n+2'
        n = (depth - 2) / 6

        block = Bottleneck if depth >=44 else BasicBlock

        self.inplanes = 16
        self.conv1 = nn.Conv2d(1, 16, kernel_size=3, padding=1,
                               bias=False)
        self.bn1 = nn.BatchNorm2d(16)
        self.relu = nn.ReLU(inplace=True)
        self.layer1 = self._make_layer(block, 16, n)
        self.layer2 = self._make_layer(block, 32, n, stride=2)
        self.layer3 = self._make_layer(block, 64, n, stride=2)
        self.avgpool = nn.AvgPool2d(7)
        self.fc = nn.Linear(64 * block.expansion, num_classes)

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_() 

def time_tensorflow_run(session, target, info_string):
  """Run the computation to obtain the target tensor and print timing stats.

  Args:
    session: the TensorFlow session to run the computation under.
    target: the target Tensor that is passed to the session's run() function.
    info_string: a string summarizing this run, to be printed with the stats.

  Returns:
    None
  """
  num_steps_burn_in = 10
  total_duration = 0.0
  total_duration_squared = 0.0
  for i in xrange(FLAGS.num_batches + num_steps_burn_in):
    start_time = time.time()
    _ = session.run(target)
    duration = time.time() - start_time
    if i >= num_steps_burn_in:
      if not i % 10:
        print ('%s: step %d, duration = %.3f' %
               (datetime.now(), i - num_steps_burn_in, duration))
      total_duration += duration
      total_duration_squared += duration * duration
  mn = total_duration / FLAGS.num_batches
  vr = total_duration_squared / FLAGS.num_batches - mn * mn
  sd = math.sqrt(vr)
  print ('%s: %s across %d steps, %.3f +/- %.3f sec / batch' %
         (datetime.now(), info_string, FLAGS.num_batches, mn, sd)) 

def __init__(self, depth, num_classes=1000):
        super(ResNet, self).__init__()
        # Model type specifies number of layers for CIFAR-10 model
        assert (depth - 2) % 6 == 0, 'depth should be 6n+2'
        n = (depth - 2) // 6

        block = Bottleneck if depth >=44 else BasicBlock

        self.inplanes = 16
        self.conv1 = nn.Conv2d(3, 16, kernel_size=3, padding=1,
                               bias=False)
        self.bn1 = nn.BatchNorm2d(16)
        self.relu = nn.ReLU(inplace=True)
        self.layer1 = self._make_layer(block, 16, n)
        self.layer2 = self._make_layer(block, 32, n, stride=2)
        self.layer3 = self._make_layer(block, 64, n, stride=2)
        self.avgpool = nn.AvgPool2d(8)
        self.fc = nn.Linear(64 * block.expansion, num_classes)

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_() 

def __init__(self, depth, num_classes, widen_factor=1, dropRate=0.0):
        super(WideResNet, self).__init__()
        nChannels = [16, 16*widen_factor, 32*widen_factor, 64*widen_factor]
        assert (depth - 4) % 6 == 0, 'depth should be 6n+4'
        n = (depth - 4) / 6
        block = BasicBlock
        # 1st conv before any network block
        self.conv1 = nn.Conv2d(3, nChannels[0], kernel_size=3, stride=1,
                               padding=1, bias=False)
        # 1st block
        self.block1 = NetworkBlock(n, nChannels[0], nChannels[1], block, 1, dropRate)
        # 2nd block
        self.block2 = NetworkBlock(n, nChannels[1], nChannels[2], block, 2, dropRate)
        # 3rd block
        self.block3 = NetworkBlock(n, nChannels[2], nChannels[3], block, 2, dropRate)
        # global average pooling and classifier
        self.bn1 = nn.BatchNorm2d(nChannels[3])
        self.relu = nn.ReLU(inplace=True)
        self.fc = nn.Linear(nChannels[3], num_classes)
        self.nChannels = nChannels[3]

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_()
            elif isinstance(m, nn.Linear):
                m.bias.data.zero_() 

def tunnel(x, y, step):
    speed = step / 100.0
    x -= (u_width / 2)
    y -= (u_height / 2)
    xo = math.sin(step / 27.0) * 2
    yo = math.cos(step / 18.0) * 2
    x += xo
    y += yo
    if y == 0:
        if x < 0:
            angle = -(math.pi / 2)
        else:
            angle = (math.pi / 2)
    else:
        angle = math.atan(x / y)
    if y > 0:
        angle += math.pi
    angle /= 2 * math.pi  # convert angle to 0...1 range
    hyp = math.sqrt(math.pow(x, 2) + math.pow(y, 2))
    shade = hyp / 2.1
    shade = 1 if shade > 1 else shade
    angle += speed
    depth = speed + (hyp / 10)
    col1 = hue_to_rgb[step % 255]
    col1 = (col1[0] * 0.8, col1[1] * 0.8, col1[2] * 0.8)
    col2 = hue_to_rgb[step % 255]
    col2 = (col2[0] * 0.3, col2[1] * 0.3, col2[2] * 0.3)
    col = col1 if int(abs(angle * 6.0)) % 2 == 0 else col2
    td = .3 if int(abs(depth * 3.0)) % 2 == 0 else 0
    col = (col[0] + td, col[1] + td, col[2] + td)
    col = (col[0] * shade, col[1] * shade, col[2] * shade)
    return (col[0] * 255, col[1] * 255, col[2] * 255) 

def __init__(self, depth, num_classes, widen_factor=1, dropRate=0.0):
        super(WideResNet, self).__init__()
        nChannels = [16, 16*widen_factor, 32*widen_factor, 64*widen_factor]
        assert (depth - 4) % 6 == 0, 'depth should be 6n+4'
        n = (depth - 4) // 6
        block = BasicBlock
        # 1st conv before any network block
        self.conv1 = nn.Conv2d(1, nChannels[0], kernel_size=3, stride=1,
                               padding=1, bias=False)
        # 1st block
        self.block1 = NetworkBlock(n, nChannels[0], nChannels[1], block, 1, dropRate)
        # 2nd block
        self.block2 = NetworkBlock(n, nChannels[1], nChannels[2], block, 2, dropRate)
        # 3rd block
        self.block3 = NetworkBlock(n, nChannels[2], nChannels[3], block, 2, dropRate)
        # global average pooling and classifier
        self.bn1 = nn.BatchNorm2d(nChannels[3])
        self.relu = nn.ReLU(inplace=True)
        self.fc = nn.Linear(nChannels[3], num_classes)
        self.nChannels = nChannels[3]

        for m in self.modules():
            if isinstance(m, nn.Conv2d):
                n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels
                m.weight.data.normal_(0, math.sqrt(2. / n))
            elif isinstance(m, nn.BatchNorm2d):
                m.weight.data.fill_(1)
                m.bias.data.zero_()
            elif isinstance(m, nn.Linear):
                m.bias.data.zero_() 

def distance(self, vec1, vec2):
    """
    Compute distance of two vector by square distance
    """
    super(SqrtDistance, self).distance(vec1, vec2)      #super method
    vec=vec1-vec2
    return sqrt(sum([pow(item, 2) for item in vec]))
#end SqrtDistance 

def rmsprop_2d(x1, x2, s1, s2):
    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6
    s1 = gamma * s1 + (1 - gamma) * g1 ** 2
    s2 = gamma * s2 + (1 - gamma) * g2 ** 2
    x1 -= eta / math.sqrt(s1 + eps) * g1
    x2 -= eta / math.sqrt(s2 + eps) * g2
    return x1, x2, s1, s2 

def rmsprop(params, states, hyperparams):
    eps = 1e-6
    gamma = hyperparams['gamma']
    for p, s in zip(params, states):
        s.data = gamma * s.data + (1-gamma) * (p.grad.data)**2
        p.data -= hyperparams['lr'] * p.grad.data / torch.sqrt(s + eps) 

def adagrad_2d(x1, x2, s1, s2):
    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6
    s1 += g1 ** 2
    s2 += g2 ** 2
    x1 -= eta / math.sqrt(s1 + eps) * g1
    x2 -= eta / math.sqrt(s2 + eps) * g2
    return x1, x2, s1, s2 

def distance(self, vec1, vec2):
    """
    Compute distance of two vector by pearson distance
    """
    super(PearsonDistance, self).distance(vec1, vec2)      #super method
    avg1, avg2 = (self._avg(vec1), self._avg(vec2))
    v1, v2 = ([item - avg1 for item in vec1[0]], [item - avg1 for item in vec2[0]])
    sqrt1, sqrt2 = (sqrt(sum([pow(item, 2) for item in v1])), sqrt(sum([pow(item, 2) for item in v2])))
    if sqrt1*sqrt2 == 0:
      return 1
    return - reduce(lambda n,m:n+m, [i*j for i,j in zip(v1, v2)]) \
           /  (sqrt1*sqrt2) 

def adagrad(params, states, hyperparams):
    eps = 1e-6
    for p, s in zip(params, states):
        s.data += (p.grad.data ** 2)
        p.data -= hyperparams['lr'] * p.grad.data / torch.sqrt(s + eps)