Python numpy.floor() Examples

def frame(data, window_length, hop_length):
  """Convert array into a sequence of successive possibly overlapping frames.

  An n-dimensional array of shape (num_samples, ...) is converted into an
  (n+1)-D array of shape (num_frames, window_length, ...), where each frame
  starts hop_length points after the preceding one.

  This is accomplished using stride_tricks, so the original data is not
  copied.  However, there is no zero-padding, so any incomplete frames at the
  end are not included.

  Args:
    data: np.array of dimension N >= 1.
    window_length: Number of samples in each frame.
    hop_length: Advance (in samples) between each window.

  Returns:
    (N+1)-D np.array with as many rows as there are complete frames that can be
    extracted.
  """
  num_samples = data.shape[0]
  num_frames = 1 + int(np.floor((num_samples - window_length) / hop_length))
  shape = (num_frames, window_length) + data.shape[1:]
  strides = (data.strides[0] * hop_length,) + data.strides
  return np.lib.stride_tricks.as_strided(data, shape=shape, strides=strides) 

def _transform_col(self, x, i):
        """Encode one numerical feature column to quantiles.

        Args:
            x (pandas.Series): numerical feature column to encode
            i (int): column index of the numerical feature

        Returns:
            Encoded feature (pandas.Series).
        """
        # Map values to the emperical CDF between .1% and 99.9%
        rv = np.ones_like(x) * -1

        filt = ~np.isnan(x)
        rv[filt] = np.floor((self.ecdfs[i](x[filt]) * 0.998 + .001) *
                            self.n_label)

        return rv 

def __init__(self, x0, mu, epsmult = 4.0, noc = False):
        #determine number of planets and validate input
        nplanets = x0.size/6.
        if (nplanets - np.floor(nplanets) > 0):
            raise Exception('The length of x0 must be a multiple of 6.')
        
        if (mu.size != nplanets):
            raise Exception('The length of mu must be the length of x0 divided by 6')
        
        self.nplanets = int(nplanets)
        self.mu = np.squeeze(mu)
        if (self.mu.size == 1):
            self.mu = np.array(mu)
        
        self.epsmult = epsmult
        
        if not(noc) and ('EXOSIMS.util.KeplerSTM_C.CyKeplerSTM' in sys.modules):
            self.havec = True
            self.x0 = np.squeeze(x0)
        else:
            self.havec = False
            self.updateState(np.squeeze(x0)) 

def __call__(self, batch):
        images, labels = zip(*batch)

        imgH = self.imgH
        imgW = self.imgW
        if self.keep_ratio:
            ratios = []
            for image in images:
                w, h = image.size
                ratios.append(w / float(h))
            ratios.sort()
            max_ratio = ratios[-1]
            imgW = int(np.floor(max_ratio * imgH))
            imgW = max(imgH * self.min_ratio, imgW)  # assure imgH >= imgW

        transform = resizeNormalize((imgW, imgH))
        images = [transform(image) for image in images]
        images = torch.cat([t.unsqueeze(0) for t in images], 0)

        return images, labels 

def randomise(self, value):
        """Randomise `value` with the mechanism.

        Parameters
        ----------
        value : int
            The value to be randomised.

        Returns
        -------
        int
            The randomised value.

        """
        self.check_inputs(value)

        # Need to account for overlap of 0-value between distributions of different sign
        unif_rv = random() - 0.5
        unif_rv *= 1 + np.exp(self._scale)
        sgn = -1 if unif_rv < 0 else 1

        # Use formula for geometric distribution, with ratio of exp(-epsilon/sensitivity)
        return int(np.round(value + sgn * np.floor(np.log(sgn * unif_rv) / self._scale))) 

def randomise(self, value):
        self.check_inputs(value)

        if self._scale == 0:
            return value

        tau = 1 / (1 + np.floor(self._scale))
        sigma2 = self._scale ** 2

        while True:
            geom_x = 0
            while self._bernoulli_exp(tau):
                geom_x += 1

            bern_b = np.random.binomial(1, 0.5)
            if bern_b and not geom_x:
                continue

            lap_y = int((1 - 2 * bern_b) * geom_x)
            bern_c = self._bernoulli_exp((abs(lap_y) - tau * sigma2) ** 2 / 2 / sigma2)
            if bern_c:
                return value + lap_y 

def lanczos(dx, a=3):
    """Lanczos kernel

    Parameters
    ----------
    dx: float
        amount to shift image
    a: int
        Lanczos window size parameter

    Returns
    -------
    result: array-like
        1D Lanczos kernel
    """
    if np.abs(dx) > 1:
        raise ValueError("The fractional shift dx must be between -1 and 1")
    window = np.arange(-a + 1, a + 1) + np.floor(dx)
    y = np.sinc(dx - window) * np.sinc((dx - window) / a)
    return y, window.astype(int) 

def warpImageFast(im, XXdense, YYdense):
    minX = max(1., np.floor(XXdense.min()) - 1)
    minY = max(1., np.floor(YYdense.min()) - 1)

    maxX = min(im.shape[1], np.ceil(XXdense.max()) + 1)
    maxY = min(im.shape[0], np.ceil(YYdense.max()) + 1)

    im = im[int(round(minY-1)):int(round(maxY)),
            int(round(minX-1)):int(round(maxX))]

    assert XXdense.shape == YYdense.shape
    out_shape = XXdense.shape
    coordinates = [
        (YYdense - minY).reshape(-1),
        (XXdense - minX).reshape(-1),
    ]
    im_warp = np.stack([
        map_coordinates(im[..., c], coordinates, order=1).reshape(out_shape)
        for c in range(im.shape[-1])],
        axis=-1)

    return im_warp 

def paintParameterLine(parameterLine, width, height):
    lines = parameterLine.copy()
    panoEdgeC = np.zeros((height, width))

    num_sample = max(height, width)
    for i in range(len(lines)):
        n = lines[i, :3]
        sid = lines[i, 4] * 2 * np.pi
        eid = lines[i, 5] * 2 * np.pi
        if eid < sid:
            x = np.linspace(sid, eid + 2 * np.pi, num_sample)
            x = x % (2 * np.pi)
        else:
            x = np.linspace(sid, eid, num_sample)
        u = -np.pi + x.reshape(-1, 1)
        v = computeUVN(n, u, lines[i, 3])
        xyz = uv2xyzN(np.hstack([u, v]), lines[i, 3])
        uv = xyz2uvN(xyz, 1)
        m = np.minimum(np.floor((uv[:,0] + np.pi) / (2 * np.pi) * width) + 1,
            width).astype(np.int32)
        n = np.minimum(np.floor(((np.pi / 2) - uv[:, 1]) / np.pi * height) + 1,
            height).astype(np.int32)
        panoEdgeC[n-1, m-1] = i

    return panoEdgeC 

def np_sample(img, coords):
    # a numpy implementation of ImageSample layer
    coords = np.maximum(coords, 0)
    coords = np.minimum(coords, np.array([img.shape[0] - 1, img.shape[1] - 1]))

    lcoor = np.floor(coords).astype('int32')
    ucoor = lcoor + 1
    ucoor = np.minimum(ucoor, np.array([img.shape[0] - 1, img.shape[1] - 1]))
    diff = coords - lcoor
    neg_diff = 1.0 - diff

    lcoory, lcoorx = np.split(lcoor, 2, axis=2)
    ucoory, ucoorx = np.split(ucoor, 2, axis=2)
    diff = np.repeat(diff, 3, 2).reshape((diff.shape[0], diff.shape[1], 2, 3))
    neg_diff = np.repeat(neg_diff, 3, 2).reshape((diff.shape[0], diff.shape[1], 2, 3))
    diffy, diffx = np.split(diff, 2, axis=2)
    ndiffy, ndiffx = np.split(neg_diff, 2, axis=2)

    ret = img[lcoory, lcoorx, :] * ndiffx * ndiffy + \
        img[ucoory, ucoorx, :] * diffx * diffy + \
        img[lcoory, ucoorx, :] * ndiffy * diffx + \
        img[ucoory, lcoorx, :] * diffy * ndiffx
    return ret[:, :, 0, :] 

def _ecg_simulate_derivsecgsyn(t, x, rr, ti, sfint, ai, bi):

    ta = math.atan2(x[1], x[0])
    r0 = 1
    a0 = 1.0 - np.sqrt(x[0] ** 2 + x[1] ** 2) / r0

    ip = np.floor(t * sfint).astype(int)
    w0 = 2 * np.pi / rr[min(ip, len(rr) - 1)]
    # w0 = 2*np.pi/rr[ip[ip <= np.max(rr)]]

    fresp = 0.25
    zbase = 0.005 * np.sin(2 * np.pi * fresp * t)

    dx1dt = a0 * x[0] - w0 * x[1]
    dx2dt = a0 * x[1] + w0 * x[0]

    # matlab rem and numpy rem are different
    # dti = np.remainder(ta - ti, 2*np.pi)
    dti = (ta - ti) - np.round((ta - ti) / 2 / np.pi) * 2 * np.pi
    dx3dt = -np.sum(ai * dti * np.exp(-0.5 * (dti / bi) ** 2)) - 1 * (x[2] - zbase)

    dxdt = np.array([dx1dt, dx2dt, dx3dt])
    return dxdt 

def scoreatpercentile(a, per, limit=(), interpolation_method='lower'):
    """
    This function is grabbed from scipy

    """
    values = np.sort(a, axis=0)
    if limit:
        values = values[(limit[0] <= values) & (values <= limit[1])]

    idx = per /100. * (values.shape[0] - 1)
    if (idx % 1 == 0):
        score = values[int(idx)]
    else:
        if interpolation_method == 'fraction':
            score = _interpolate(values[int(idx)], values[int(idx) + 1],
                                 idx % 1)
        elif interpolation_method == 'lower':
            score = values[int(np.floor(idx))]
        elif interpolation_method == 'higher':
            score = values[int(np.ceil(idx))]
        else:
            raise ValueError("interpolation_method can only be 'fraction', " \
                             "'lower' or 'higher'")
    return score 

def forward(self, features, rois):
        batch_size, num_channels, data_height, data_width = features.size()
        num_rois = rois.size()[0]
        outputs = Variable(torch.zeros(num_rois, num_channels, self.pooled_height, self.pooled_width)).cuda()

        for roi_ind, roi in enumerate(rois):
            batch_ind = int(roi[0].data[0])
            roi_start_w, roi_start_h, roi_end_w, roi_end_h = np.round(
                roi[1:].data.cpu().numpy() * self.spatial_scale).astype(int)
            roi_width = max(roi_end_w - roi_start_w + 1, 1)
            roi_height = max(roi_end_h - roi_start_h + 1, 1)
            bin_size_w = float(roi_width) / float(self.pooled_width)
            bin_size_h = float(roi_height) / float(self.pooled_height)

            for ph in range(self.pooled_height):
                hstart = int(np.floor(ph * bin_size_h))
                hend = int(np.ceil((ph + 1) * bin_size_h))
                hstart = min(data_height, max(0, hstart + roi_start_h))
                hend = min(data_height, max(0, hend + roi_start_h))
                for pw in range(self.pooled_width):
                    wstart = int(np.floor(pw * bin_size_w))
                    wend = int(np.ceil((pw + 1) * bin_size_w))
                    wstart = min(data_width, max(0, wstart + roi_start_w))
                    wend = min(data_width, max(0, wend + roi_start_w))

                    is_empty = (hend <= hstart) or(wend <= wstart)
                    if is_empty:
                        outputs[roi_ind, :, ph, pw] = 0
                    else:
                        data = features[batch_ind]
                        outputs[roi_ind, :, ph, pw] = torch.max(
                            torch.max(data[:, hstart:hend, wstart:wend], 1)[0], 2)[0].view(-1)

        return outputs 

def create_from_images(tfrecord_dir, image_dir, label_dir, shuffle):
    print('Loading images from "%s"' % image_dir)
    image_filenames = sorted(glob.glob(os.path.join(image_dir, '*')))
    if len(image_filenames) == 0:
        error('No input images found')
        
    img = np.asarray(PIL.Image.open(image_filenames[0]))
    resolution = img.shape[0]
    channels = img.shape[2] if img.ndim == 3 else 1
    if img.shape[1] != resolution:
        error('Input images must have the same width and height')
    if resolution != 2 ** int(np.floor(np.log2(resolution))):
        error('Input image resolution must be a power-of-two')
    if channels not in [1, 3]:
        error('Input images must be stored as RGB or grayscale')

    try:
        with open(label_dir, 'rb') as file:
            labels = pickle.load(file)
    except:
        error('Label file was not found')
    
    with TFRecordExporter(tfrecord_dir, len(image_filenames)) as tfr:
        order = tfr.choose_shuffled_order() if shuffle else np.arange(len(image_filenames))
        reordered_names = []
        for idx in range(order.size):
            image_filename = image_filenames[order[idx]]
            img = np.asarray(PIL.Image.open(image_filename))
            if channels == 1:
                img = img[np.newaxis, :, :] # HW => CHW
            else:
                img = img.transpose(2, 0, 1) # HWC => CHW
            tfr.add_image(img)
            reordered_names.append(os.path.basename(image_filename))
        reordered_labels = []
        for key in reordered_names:
            reordered_labels += [labels[key]]
        reordered_labels = np.stack(reordered_labels, 0)
        tfr.add_labels(reordered_labels)

#---------------------------------------------------------------------------- 

def process_reals(x, lod, mirror_augment, drange_data, drange_net):
    with tf.name_scope('ProcessReals'):
        with tf.name_scope('DynamicRange'):
            x = tf.cast(x, tf.float32)
            x = misc.adjust_dynamic_range(x, drange_data, drange_net)
        if mirror_augment:
            with tf.name_scope('MirrorAugment'):
                s = tf.shape(x)
                mask = tf.random_uniform([s[0], 1, 1, 1], 0.0, 1.0)
                mask = tf.tile(mask, [1, s[1], s[2], s[3]])
                x = tf.where(mask < 0.5, x, tf.reverse(x, axis=[3]))
        with tf.name_scope('FadeLOD'): # Smooth crossfade between consecutive levels-of-detail.
            s = tf.shape(x)
            y = tf.reshape(x, [-1, s[1], s[2]//2, 2, s[3]//2, 2])
            y = tf.reduce_mean(y, axis=[3, 5], keep_dims=True)
            y = tf.tile(y, [1, 1, 1, 2, 1, 2])
            y = tf.reshape(y, [-1, s[1], s[2], s[3]])
            x = tfutil.lerp(x, y, lod - tf.floor(lod))
        with tf.name_scope('UpscaleLOD'): # Upscale to match the expected input/output size of the networks.
            s = tf.shape(x)
            factor = tf.cast(2 ** tf.floor(lod), tf.int32)
            x = tf.reshape(x, [-1, s[1], s[2], 1, s[3], 1])
            x = tf.tile(x, [1, 1, 1, factor, 1, factor])
            x = tf.reshape(x, [-1, s[1], s[2] * factor, s[3] * factor])
        return x

#----------------------------------------------------------------------------
# Just-in-time processing of masks before feeding them to the networks. 

def configure(self, minibatch_size, lod=0):
        lod = int(np.floor(lod))
        assert minibatch_size >= 1 and lod in self._tf_datasets
        if self._cur_minibatch != minibatch_size or self._cur_lod != lod:
            self._tf_init_ops[lod].run({self._tf_minibatch_in: minibatch_size})
            self._cur_minibatch = minibatch_size
            self._cur_lod = lod

    # Get next minibatch as TensorFlow expressions. 

def _coords2idx(self, coords):
        c = coords.transform_to('galactic').represent_as('cartesian')
        
        idx = np.empty((3,) + c.shape, dtype='i4')
        mask = np.zeros(c.shape, dtype=np.bool)

        for i,x in enumerate((c.x, c.y, c.z)):
            idx[i,...] = np.floor(x.to('pc').value + 300) * 256/600.
            mask |= (idx[i] < 0) | (idx[i] >= self._shape[i])

        for i in range(3):
            idx[i, mask] = -1

        return idx, mask 

def make_data_iter_plan(self):
        "make a random data iteration plan"
        # truncate each bucket into multiple of batch-size
        bucket_n_batches = []
        for i in range(len(self.data)):
            bucket_n_batches.append(np.floor((self.data[i]) / self.batch_size))
            self.data[i] = self.data[i][:int(bucket_n_batches[i]*self.batch_size)]

        bucket_plan = np.hstack([np.zeros(n, int)+i for i, n in enumerate(bucket_n_batches)])
        np.random.shuffle(bucket_plan)

        bucket_idx_all = [np.random.permutation(len(x)) for x in self.data]

        self.bucket_plan = bucket_plan
        self.bucket_idx_all = bucket_idx_all
        self.bucket_curr_idx = [0 for x in self.data]

        self.data_buffer = []
        self.label_buffer = []
        for i_bucket in range(len(self.data)):
            if not self.model_parallel:
                data = np.zeros((self.batch_size, self.buckets[i_bucket]))
                label = np.zeros((self.batch_size, self.buckets[i_bucket]))
                self.data_buffer.append(data)
                self.label_buffer.append(label)
            else:
                data = np.zeros((self.buckets[i_bucket], self.batch_size))
                self.data_buffer.append(data)

        if self.model_parallel:
            # Transpose data if model parallel
            for i in range(len(self.data)):
                bucket_data = self.data[i]
                self.data[i] = np.transpose(bucket_data) 

def __init__(self, in_channels, out_channels, kernel_size, stride):
        super(ConvLayer, self).__init__()
        padding = int(np.floor(kernel_size / 2))
        self.pad = ReflectancePadding(pad_width=(0,0,0,0,padding,padding,padding,padding))
        self.conv2d = nn.Conv2D(in_channels=in_channels, channels=out_channels, 
                                kernel_size=kernel_size, strides=(stride,stride),
                                padding=0) 

def __init__(self, in_channels, out_channels, kernel_size, 
            stride, upsample=None):
        super(UpsampleConvLayer, self).__init__()
        self.upsample = upsample
        self.reflection_padding = int(np.floor(kernel_size / 2))
        self.conv2d = nn.Conv2D(in_channels=in_channels, 
                                channels=out_channels, 
                                kernel_size=kernel_size, strides=(stride,stride),
                                padding=self.reflection_padding) 

def _get_xy_bounding_box(vertex, padding):
  """Returns the xy bounding box of the environment."""
  min_ = np.floor(np.min(vertex[:, :2], axis=0) - padding).astype(np.int)
  max_ = np.ceil(np.max(vertex[:, :2], axis=0) + padding).astype(np.int)
  return min_, max_ 

def generate_goal_images(map_scales, map_crop_sizes, n_ori, goal_dist,
                         goal_theta, rel_goal_orientation):
  goal_dist = goal_dist[:,0]
  goal_theta = goal_theta[:,0]
  rel_goal_orientation = rel_goal_orientation[:,0]

  goals = [];
  # Generate the map images.
  for i, (sc, map_crop_size) in enumerate(zip(map_scales, map_crop_sizes)):
    goal_i = np.zeros((goal_dist.shape[0], map_crop_size, map_crop_size, n_ori),
                      dtype=np.float32)
    x = goal_dist*np.cos(goal_theta)*sc + (map_crop_size-1.)/2.
    y = goal_dist*np.sin(goal_theta)*sc + (map_crop_size-1.)/2.

    for j in range(goal_dist.shape[0]):
      gc = rel_goal_orientation[j]
      x0 = np.floor(x[j]).astype(np.int32); x1 = x0 + 1;
      y0 = np.floor(y[j]).astype(np.int32); y1 = y0 + 1;
      if x0 >= 0 and x0 <= map_crop_size-1:
        if y0 >= 0 and y0 <= map_crop_size-1:
          goal_i[j, y0, x0, gc] = (x1-x[j])*(y1-y[j])
        if y1 >= 0 and y1 <= map_crop_size-1:
          goal_i[j, y1, x0, gc] = (x1-x[j])*(y[j]-y0)

      if x1 >= 0 and x1 <= map_crop_size-1:
        if y0 >= 0 and y0 <= map_crop_size-1:
          goal_i[j, y0, x1, gc] = (x[j]-x0)*(y1-y[j])
        if y1 >= 0 and y1 <= map_crop_size-1:
          goal_i[j, y1, x1, gc] = (x[j]-x0)*(y[j]-y0)

    goals.append(goal_i)
  return goals 

def computePad(dims,depth):
	y1=y2=x1=x2=0; 
	y,x = [numpy.ceil(dims[i]/float(2**depth)) * (2**depth) for i in range(-2,0)]
	x = float(x); y = float(y);
	y1 = int(numpy.floor((y - dims[-2])/2)); y2 = int(numpy.ceil((y - dims[-2])/2))
	x1 = int(numpy.floor((x - dims[-1])/2)); x2 = int(numpy.ceil((x - dims[-1])/2))
	return y1,y2,x1,x2 

def preprocess(self, state):
        scaled_state = self.scale * state
        x_floor, y_floor = np.floor(scaled_state)
        assert x_floor <= self.scale
        assert y_floor <= self.scale
        if x_floor == self.scale:
            x_floor -= 1
        if y_floor == self.scale:
            y_floor -= 1
        index = self.scale*x_floor + y_floor
        return index 

def forward(self, features, rois):
        batch_size, num_channels, data_height, data_width = features.size()
        num_rois = rois.size()[0]
        outputs = Variable(torch.zeros(num_rois, num_channels, self.pooled_height, self.pooled_width)).cuda()

        for roi_ind, roi in enumerate(rois):
            batch_ind = int(roi[0].data[0])
            roi_start_w, roi_start_h, roi_end_w, roi_end_h = np.round(
                roi[1:].data.cpu().numpy() * self.spatial_scale).astype(int)
            roi_width = max(roi_end_w - roi_start_w + 1, 1)
            roi_height = max(roi_end_h - roi_start_h + 1, 1)
            bin_size_w = float(roi_width) / float(self.pooled_width)
            bin_size_h = float(roi_height) / float(self.pooled_height)

            for ph in range(self.pooled_height):
                hstart = int(np.floor(ph * bin_size_h))
                hend = int(np.ceil((ph + 1) * bin_size_h))
                hstart = min(data_height, max(0, hstart + roi_start_h))
                hend = min(data_height, max(0, hend + roi_start_h))
                for pw in range(self.pooled_width):
                    wstart = int(np.floor(pw * bin_size_w))
                    wend = int(np.ceil((pw + 1) * bin_size_w))
                    wstart = min(data_width, max(0, wstart + roi_start_w))
                    wend = min(data_width, max(0, wend + roi_start_w))

                    is_empty = (hend <= hstart) or(wend <= wstart)
                    if is_empty:
                        outputs[roi_ind, :, ph, pw] = 0
                    else:
                        data = features[batch_ind]
                        outputs[roi_ind, :, ph, pw] = torch.max(
                            torch.max(data[:, hstart:hend, wstart:wend], 1)[0], 2)[0].view(-1)

        return outputs 

def __init__(self, x0, mu, epsmult = 4.0, prefVallado = False, noc = False):
        #determine number of planets and validate input
        nplanets = x0.size/6.
        if (nplanets - np.floor(nplanets) > 0):
            raise Exception('The length of x0 must be a multiple of 6.')
        
        if (mu.size != nplanets):
            raise Exception('The length of mu must be the length of x0 divided by 6')
        
        self.nplanets = int(nplanets)
        self.mu = np.squeeze(mu)
        if (self.mu.size == 1):
            self.mu = np.array(mu)
        
        self.epsmult = epsmult
        
        if prefVallado:
            self.algOrder = [self.calcSTM_vallado, self.calcSTM]
        else:
            self.algOrder = [self.calcSTM, self.calcSTM_vallado]

        #create position and velocity index matrices
        tmp = np.reshape(np.arange(self.nplanets*6),(self.nplanets,6)).T
        self.rinds = tmp[0:3]
        self.vinds = tmp[3:6]

        if not(noc) and ('EXOSIMS.util.KeplerSTM_C.CyKeplerSTM' in sys.modules):
            self.havec = True
        else:
            self.havec = False

        self.updateState(np.squeeze(x0)) 

def calcSTM(self,dt,j):
        #allocate
        u = 0
        deltaU = 0
        t = 0
        counter = 0
        
        #For elliptic orbits, calculate period effects
        if self.beta[j] >0:
            P = 2*np.pi*self.mu[j]*self.beta[j]**(-3./2.)
            n = np.floor((dt + P/2 - 2*self.nu0[j]/self.beta[j])/P)
            deltaU = 2*np.pi*n*self.beta[j]**(-5./2.)
        
        #loop until convergence of the time array to the time step
        while (np.max(np.abs(t-dt)) > self.epsmult*np.spacing(dt)) and (counter < 1000):
            q = self.beta[j]*u**2./(1+self.beta[j]*u**2.)
            U0w2 = 1. - 2.*q
            U1w2 = 2.*(1.-q)*u
            temp = self.contFrac(q)
            U = 16./15.*U1w2**5.*temp + deltaU
            U0 = 2.*U0w2**2.-1.
            U1 = 2.*U0w2*U1w2
            U2 = 2.*U1w2**2.
            U3 = self.beta[j]*U + U1*U2/3.
            r = self.r0norm[j]*U0 + self.nu0[j]*U1 + self.mu[j]*U2
            t = self.r0norm[j]*U1 + self.nu0[j]*U2 + self.mu[j]*U3
            u = u - (t-dt)/(4.*(1.-q)*r)
            counter += 1
        
        if (counter == 1000):
            raise ValueError('Failed to converge on t: %e/%e'%(np.max(np.abs(t-dt)), self.epsmult*np.spacing(dt)))
        
        #Kepler solution
        f = 1 - self.mu[j]/self.r0norm[j]*U2
        g = self.r0norm[j]*U1 + self.nu0[j]*U2
        F = -self.mu[j]*U1/r/self.r0norm[j]
        G = 1 - self.mu[j]/r*U2
        
        Phi = np.vstack((np.hstack((np.eye(3)*f, np.eye(3)*g)),np.hstack((np.eye(3)*F, np.eye(3)*G))))
       
        return Phi 

def resize_img(img, scale_factor):
    new_size = (np.floor(np.array(img.shape[0:2]) * scale_factor)).astype(int)
    new_img = cv2.resize(img, (new_size[1], new_size[0]))
    # This is scale factor of [height, width] i.e. [y, x]
    actual_factor = [
        new_size[0] / float(img.shape[0]), new_size[1] / float(img.shape[1])
    ]
    return new_img, actual_factor 

def winning_unit(xt):
    global W
    distances = np.linalg.norm(W - xt, ord=2, axis=2)
    max_activation_unit = np.argmax(distances)
    return int(np.floor(max_activation_unit / matrix_side)), max_activation_unit % matrix_side 

def resample1d(inp,inp_space,out_space=1):
    #Output shape
    print inp.size(), inp_space, out_space
    out_shape = list(np.int64(inp.size()[:-1]))+[int(np.floor(inp.size()[-1]*inp_space/out_space))] #Optional for if we expect a float_tensor
    out_shape = [int(item) for item in out_shape]
    # Get output coordinates, deltas, and t (chord distances)
    # torch.cuda.set_device(inp.get_device())
    # Output coordinates in real space
    coords = torch.cuda.HalfTensor(range(out_shape[-1]))*out_space
    delta = coords.fmod(inp_space).div(inp_space).repeat(out_shape[0],out_shape[1],1)
    t = torch.cuda.HalfTensor(4,out_shape[0],out_shape[1],out_shape[2]).zero_()
    t[0] = 1
    t[1] = delta
    t[2] = delta**2
    t[3] = delta**3    
    # Nearest neighbours indices
    nn = coords.div(inp_space).floor().long()    
    # Stack the nearest neighbors into P, the Points Array
    P = torch.cuda.HalfTensor(4,out_shape[0],out_shape[1],out_shape[2]).zero_()
    for i in range(-1,3):
        P[i+1] = inp.index_select(2,torch.clamp(nn+i,0,inp.size()[-1]-1))    
    #Take catmull-rom  spline interpolation:
    return 0.5*t.mul(torch.cuda.HalfTensor([[ 0,  2,  0,  0],
                            [-1,  0,  1,  0],
                            [ 2, -5,  4, -1],
                            [ -1, 3, -3,  1]]).mm(P.view(4,-1))\
                                                              .view(4,
                                                                    out_shape[0],
                                                                    out_shape[1],
                                                                    out_shape[2]))\
                                                              .sum(0)\
                                                              .squeeze()