Python numpy.max() Examples

def test_accuracy_full_batch(tokens, features, mini_batch_size, word_attn, sent_attn, th=0.5):
    p = []
    l = []
    cnt = 0
    g = gen_minibatch1(tokens, features, mini_batch_size, False)
    for token, feature in g:
        if cnt % 100 == 0:
            print cnt
        cnt +=1
#         print token.size()
#         y_pred = get_predictions(token, word_attn, sent_attn)
#         print y_pred
        y_pred = get_predictions(token, feature, word_attn, sent_attn)
#         print y_pred
#         _, y_pred = torch.max(y_pred, 1)
#         y_pred = y_pred[:, 1]
#         print y_pred
        p.append(np.ndarray.flatten(y_pred.data.cpu().numpy()))
    p = [item for sublist in p for item in sublist]
    p = np.array(p)
    return p 

def _zero_one_normalize(predictions, epsilon=1e-7):
    """Normalize the predictions to the range between 0.0 and 1.0.

    For some predictions like SVM predictions, we need to normalize them before
    calculate the interpolated average precision. The normalization will not
    change the rank in the original list and thus won't change the average
    precision.

    Args:
      predictions: a numpy 1-D array storing the sparse prediction scores.
      epsilon: a small constant to avoid denominator being zero.

    Returns:
      The normalized prediction.
    """
    denominator = numpy.max(predictions) - numpy.min(predictions)
    ret = (predictions - numpy.min(predictions)) / numpy.max(denominator,
                                                             epsilon)
    return ret 

def mypsd(Rates,time_range,bin_w = 5., nmax = 4000):

      bins = np.arange(0,len(time_range),1)
      #print bins
      a,b = np.histogram(Rates, bins)
      ff = (1./len(bins))*abs(np.fft.fft(Rates- np.mean(Rates)))**2
      Fs = 1./(1*0.001)
      freq2 = np.fft.fftfreq(len(bins))[0:len(bins/2)+1] # d= dt
      freq = np.fft.fftfreq(len(bins))[:len(ff)/2+1]
      px = ff[0:len(ff)/2+1]
      max_px = np.max(px[1:])
      idx = px == max_px
      corr_freq = freq[pl.find(idx)]
      new_px = px
      max_pow = new_px[pl.find(idx)]
      return new_px,freq,corr_freq[0],freq2, max_pow 

def calc_loss(self, states, actions, rewards, next_states, episode_ends):
        qv = self.agent.q(states)
        q_t = self.target(next_states)  # Q(s', *)
        max_q_prime = np.array(list(map(np.max, q_t.data)), dtype=np.float32)  # max_a Q(s', a)

        target = cuda.to_cpu(qv.data.copy())
        for i in range(self.replay_size):
            if episode_ends[i][0] is True:
                _r = np.sign(rewards[i])
            else:
                _r = np.sign(rewards[i]) + self.gamma * max_q_prime[i]
            
            target[i, actions[i]] = _r
        
        td = Variable(self.target.arr_to_gpu(target)) - qv
        td_tmp = td.data + 1000.0 * (abs(td.data) <= 1)  # Avoid zero division
        td_clip = td * (abs(td.data) <= 1) + td/abs(td_tmp) * (abs(td.data) > 1)

        zeros = Variable(self.target.arr_to_gpu(np.zeros((self.replay_size, self.target.n_action), dtype=np.float32)))
        loss = F.mean_squared_error(td_clip, zeros)
        self._loss = loss.data
        self._qv = np.max(qv.data)
        return loss 

def getLargestFaceBoundingBox(self, rgbImg, skipMulti=False):
        """
        Find the largest face bounding box in an image.

        :param rgbImg: RGB image to process. Shape: (height, width, 3)
        :type rgbImg: numpy.ndarray
        :param skipMulti: Skip image if more than one face detected.
        :type skipMulti: bool
        :return: The largest face bounding box in an image, or None.
        :rtype: dlib.rectangle
        """
        assert rgbImg is not None

        faces = self.getAllFaceBoundingBoxes(rgbImg)
        if (not skipMulti and len(faces) > 0) or len(faces) == 1:
            return max(faces, key=lambda rect: rect.width() * rect.height())
        else:
            return None 

def getLargestFaceBoundingBox(self, rgbImg, skipMulti=False):
        """
        Find the largest face bounding box in an image.

        :param rgbImg: RGB image to process. Shape: (height, width, 3)
        :type rgbImg: numpy.ndarray
        :param skipMulti: Skip image if more than one face detected.
        :type skipMulti: bool
        :return: The largest face bounding box in an image, or None.
        :rtype: dlib.rectangle
        """
        assert rgbImg is not None

        faces = self.getAllFaceBoundingBoxes(rgbImg)
        if (not skipMulti and len(faces) > 0) or len(faces) == 1:
            return max(faces, key=lambda rect: rect.width() * rect.height())
        else:
            return None 

def test_accuracy_full_batch(tokens, features, mini_batch_size, word_attn, sent_attn, th=0.5):
    p = []
    l = []
    cnt = 0
    g = gen_minibatch1(tokens, features, mini_batch_size, False)
    for token, feature in g:
        if cnt % 100 == 0:
            print(cnt)
        cnt +=1
#         print token.size()
#         y_pred = get_predictions(token, word_attn, sent_attn)
#         print y_pred
        y_pred = get_predictions(token, feature, word_attn, sent_attn)
#         print y_pred
#         _, y_pred = torch.max(y_pred, 1)
#         y_pred = y_pred[:, 1]
#         print y_pred
        p.append(np.ndarray.flatten(y_pred.data.cpu().numpy()))
    p = [item for sublist in p for item in sublist]
    p = np.array(p)
    return p 

def getRectArrangements(n):
    p = prime.Prime()
    f = p.getPrimeFactors(n)
    f_count = len(f)
    ma = multiplyArray(f)
    arrangements = set([(1,ma)])

    if (f_count > 1):
        perms = set(p.getPermutations(f))
        for perm in perms:
            for i in range(1,f_count):
                v1 = multiplyArray(perm[0:i])
                v2 = multiplyArray(perm[i:])
                arrangements.add((min(v1, v2),max(v1, v2)))

    return sorted(list(arrangements), cmp=proportion_sort, reverse=True) 

def update_sort_idcs(self):
        # The selected points are sorted before all the other points -- an easy
        # way to achieve this is to add the maximum score to their score
        if self.current_order == 0:
            score = self.score_x
        elif self.current_order == 1:
            score = self.score_y
        elif self.current_order == 2:
            score = self.score_z
        else:
            raise AssertionError(self.current_order)
        score = score.copy()
        if len(self.selected_points):
            score[np.array(sorted(self.selected_points))] += score.max()

        self.sort_idcs = np.argsort(score) 

def update_data_sort_order(self, new_sort_order=None):
        if new_sort_order is not None:
            self.current_order = new_sort_order
        self.update_sort_idcs()
        self.data_image.set_extent((self.raw_lags[0], self.raw_lags[-1],
                            0, len(self.sort_idcs)))
        self.data_ax.set_ylim(0, len(self.sort_idcs))
        all_raw_data  = self.raw_data
        all_raw_data /= (1 + self.raw_data.mean(1)[:, np.newaxis])
        if len(all_raw_data) > 0:
            cmax          = 0.5*all_raw_data.max()
            cmin          = 0.5*all_raw_data.min()
            all_raw_data  = all_raw_data[self.sort_idcs, :]
        else:
            cmin = 0
            cmax = 1
        self.data_image.set_data(all_raw_data)
        self.data_image.set_clim(cmin, cmax)
        self.data_selection.set_y(len(self.sort_idcs)-len(self.selected_points))
        self.data_selection.set_height(len(self.selected_points))
        self.update_data_plot() 

def __init__(self, top_n=None):
    """Construct an AveragePrecisionCalculator to calculate average precision.

    This class is used to calculate the average precision for a single label.

    Args:
      top_n: A positive Integer specifying the average precision at n, or
        None to use all provided data points.

    Raises:
      ValueError: An error occurred when the top_n is not a positive integer.
    """
    if not ((isinstance(top_n, int) and top_n >= 0) or top_n is None):
      raise ValueError("top_n must be a positive integer or None.")

    self._top_n = top_n  # average precision at n
    self._total_positives = 0  # total number of positives have seen
    self._heap = []  # max heap of (prediction, actual) 

def __init__(self, top_n=None):
    """Construct an AveragePrecisionCalculator to calculate average precision.

    This class is used to calculate the average precision for a single label.

    Args:
      top_n: A positive Integer specifying the average precision at n, or
        None to use all provided data points.

    Raises:
      ValueError: An error occurred when the top_n is not a positive integer.
    """
    if not ((isinstance(top_n, int) and top_n >= 0) or top_n is None):
      raise ValueError("top_n must be a positive integer or None.")

    self._top_n = top_n  # average precision at n
    self._total_positives = 0  # total number of positives have seen
    self._heap = []  # max heap of (prediction, actual) 

def _zero_one_normalize(predictions, epsilon=1e-7):
    """Normalize the predictions to the range between 0.0 and 1.0.

    For some predictions like SVM predictions, we need to normalize them before
    calculate the interpolated average precision. The normalization will not
    change the rank in the original list and thus won't change the average
    precision.

    Args:
      predictions: a numpy 1-D array storing the sparse prediction scores.
      epsilon: a small constant to avoid denominator being zero.

    Returns:
      The normalized prediction.
    """
    denominator = numpy.max(predictions) - numpy.min(predictions)
    ret = (predictions - numpy.min(predictions)) / numpy.max(denominator,
                                                             epsilon)
    return ret 

def _zero_one_normalize(predictions, epsilon=1e-7):
    """Normalize the predictions to the range between 0.0 and 1.0.

    For some predictions like SVM predictions, we need to normalize them before
    calculate the interpolated average precision. The normalization will not
    change the rank in the original list and thus won't change the average
    precision.

    Args:
      predictions: a numpy 1-D array storing the sparse prediction scores.
      epsilon: a small constant to avoid denominator being zero.

    Returns:
      The normalized prediction.
    """
    denominator = numpy.max(predictions) - numpy.min(predictions)
    ret = (predictions - numpy.min(predictions)) / numpy.max(denominator,
                                                             epsilon)
    return ret 

def getTrainKernel(self, params):
		self.checkParams(params)
		if (self.sameParams(params)): return self.cache['getTrainKernel']
		
		ell = np.exp(params[0])
		if (self.K_sq is None): K = sq_dist(self.X_scaled.T / ell)	#precompute squared distances
		else: K = self.K_sq / ell**2		
		self.cache['K_sq_scaled'] = K

		# # # #manual computation (just for sanity checks)
		# # # K1 = np.exp(-K / 2.0)
		# # # K2 = np.zeros((self.X_scaled.shape[0], self.X_scaled.shape[0]))
		# # # for i1 in xrange(self.X_scaled.shape[0]):
			# # # for i2 in xrange(i1, self.X_scaled.shape[0]):
				# # # diff = self.X_scaled[i1,:] - self.X_scaled[i2,:]
				# # # K2[i1, i2] = np.exp(-np.sum(diff**2) / (2*ell))
				# # # K2[i2, i1] = K2[i1, i2]				
		# # # print np.max((K1-K2)**2)
		# # # sys.exit(0)
		
		K_exp = np.exp(-K / 2.0)
		self.cache['getTrainKernel'] = K_exp
		self.saveParams(params)
		return K_exp 

def Kdim(self, kdimParams):
		if (self.prevKdimParams is not None and np.max(np.abs(kdimParams-self.prevKdimParams)) < self.epsilon): return self.cache['Kdim']
			
		K = np.zeros((self.n, self.n, len(self.kernels)))
		params_ind = 0
		for k_i, k in enumerate(self.kernels):
			numHyp = k.getNumParams()
			kernelParams_range = np.array(xrange(params_ind, params_ind+numHyp), dtype=np.int)			
			kernel_params = kdimParams[kernelParams_range]			
			if ((numHyp == 0 and 'Kdim' in self.cache) or (numHyp>0 and self.prevKdimParams is not None and np.max(np.abs(kernel_params-self.prevKdimParams[kernelParams_range])) < self.epsilon)):
				K[:,:,k_i] = self.cache['Kdim'][:,:,k_i]
			else:
				K[:,:,k_i] = k.getTrainKernel(kernel_params)				
			params_ind += numHyp
		self.prevKdimParams = kdimParams.copy()
		self.cache['Kdim'] = K
		return K 

def removeTopPCs(X, numRemovePCs):	
	t0 = time.time()
	X_mean = X.mean(axis=0)
	X -= X_mean
	XXT = symmetrize(blas.dsyrk(1.0, X, lower=0))
	s,U = la.eigh(XXT)
	if (np.min(s) < -1e-4): raise Exception('Negative eigenvalues found')
	s[s<0]=0
	ind = np.argsort(s)[::-1]
	U = U[:, ind]
	s = s[ind]
	s = np.sqrt(s)
		
	#remove null PCs
	ind = (s>1e-6)
	U = U[:, ind]
	s = s[ind]
	
	V = X.T.dot(U/s)	
	#print 'max diff:', np.max(((U*s).dot(V.T) - X)**2)
	X = (U[:, numRemovePCs:]*s[numRemovePCs:]).dot((V.T)[numRemovePCs:, :])
	X += X_mean
	
	return X 

def resample(image, scan, new_spacing=[1,1,1]):
    # Determine current pixel spacing
    spacing = map(float, ([scan[0].SliceThickness] + scan[0].PixelSpacing))
    spacing = np.array(list(spacing))

    resize_factor = spacing / new_spacing
    new_real_shape = image.shape * resize_factor
    new_shape = np.round(new_real_shape)
    real_resize_factor = new_shape / image.shape
    new_spacing = spacing / real_resize_factor
    
    #image = scipy.ndimage.interpolation.zoom(image, real_resize_factor)   # nor mode= "wrap"/xxx, nor cval=-1024 can ensure that the min and max values are unchanged .... # cval added
    image = scipy.ndimage.interpolation.zoom(image, real_resize_factor, mode='nearest')  ### early orig modified 
    #image = scipy.ndimage.zoom(image, real_resize_factor, order=1)    # order=1 bilinear , preserves the min and max of the image -- pronbably better for us (also faster than spkine/order=2)
    
    #image = scipy.ndimage.zoom(image, real_resize_factor, mode='nearest', order=1)    # order=1 bilinear , preserves the min and max of the image -- pronbably better for us (also faster than spkine/order=2)
    
    return image, new_spacing 

def spec_entropy(Rates,time_range=[],bin_w = 5.,freq_range = []):
	'''Function to calculate the spectral entropy'''

        power,freq,dfreq,dummy,dummy = mypsd(Rates,time_range,bin_w = bin_w)
        if freq_range != []:
                power = power[(freq>=freq_range[0]) & (freq <= freq_range[1])]
                freq = freq[(freq>=freq_range[0]) & (freq <= freq_range[1])]
		maxFreq = freq[np.where(power==np.max(power))]*1000*100
		perMax = (np.max(power)/np.sum(power))*100
        k = len(freq)
        power = power/sum(power)
        sum_power = 0
        for ii in range(k):
                sum_power += (power[ii]*np.log(power[ii]))
        spec_ent = -(sum_power/np.log(k))
        return spec_ent,dfreq,maxFreq,perMax 

def testStartStopModulation(self):
        radiusInMilliRad= 12.4
        frequencyInHz= 100.
        centerInMilliRad= [-10, 15]
        self._tt.setTargetPosition(centerInMilliRad)
        self._tt.startModulation(radiusInMilliRad,
                                 frequencyInHz,
                                 centerInMilliRad)
        self.assertTrue(
            np.allclose(
                [1, 1, 0],
                self._ctrl.getWaveGeneratorStartStopMode()))
        waveform= self._ctrl.getWaveform(1)
        wants= self._tt._milliRadToGcsUnitsOneAxis(-10, self._tt.AXIS_A)
        got= np.mean(waveform)
        self.assertAlmostEqual(
            wants, got, msg="wants %g, got %g" % (wants, got))
        wants= self._tt._milliRadToGcsUnitsOneAxis(-10 + 12.4, self._tt.AXIS_A)
        got= np.max(waveform)
        self.assertAlmostEqual(
            wants, got, msg="wants %g, got %g" % (wants, got))

        self._tt.stopModulation()
        self.assertTrue(
            np.allclose(centerInMilliRad, self._tt.getTargetPosition())) 

def getLatLonRange(pbo_info, station_list):
    '''
    Retrive the range of latitude and longitude occupied by a set of stations

    @param pbo_info: PBO Metadata
    @param station_list: List of stations

    @return list containg two tuples, lat_range and lon_range
    '''

    coord_list = getStationCoords(pbo_info, station_list)

    lat_list = []
    lon_list = []
    for coord in coord_list:
        lat_list.append(coord[0])
        lon_list.append(coord[1])

    lat_range = (np.min(lat_list), np.max(lat_list))
    lon_range = (np.min(lon_list), np.max(lon_list))

    return [lat_range, lon_range] 

def conv1(model):
    n1, n2, x, y, z = model.conv1.W.shape
    fig = plt.figure()
    for nn in range(0, n1):
        ax = fig.add_subplot(4, 5, nn+1, projection='3d')
        ax.set_xlim(0.0, x)
        ax.set_ylim(0.0, y)
        ax.set_zlim(0.0, z)
        ax.set_xticklabels([])
        ax.set_yticklabels([])
        ax.set_zticklabels([])
        for xx in range(0, x):
            for yy in range(0, y):
                for zz in range(0, z):
                    max = np.max(model.conv1.W.data[nn, :])
                    min = np.min(model.conv1.W.data[nn, :])
                    step = (max - min) / 1.0
                    C = (model.conv1.W.data[nn, 0, xx, yy, zz] - min) / step
                    color = cm.cool(C)
                    C = abs(1.0 - C)
                    ax.plot(np.array([xx]), np.array([yy]), np.array([zz]), "o", color=color, ms=7.0*C, mew=0.1)

    plt.savefig("result/graph_conv1.png") 

def create_graph():
    logfile = 'result/log'
    xs = []
    ys = []
    ls = []
    f = open(logfile, 'r')
    data = json.load(f)

    print(data)

    for d in data:
        xs.append(d["iteration"])
        ys.append(d["main/accuracy"])
        ls.append(d["main/loss"])

    plt.clf()
    plt.cla()
    plt.hlines(1, 0, np.max(xs), colors='r', linestyles="dashed")  # y=-1, 1??????
    plt.title(r"loss/accuracy")
    plt.plot(xs, ys, label="accuracy")
    plt.plot(xs, ls, label="loss")
    plt.legend()
    plt.savefig("result/log.png") 

def reshapeWeights(self, weights, normalize=True, modifier=None):
        # reshape the weights matrix to a grid for visualization
        n_rows = int(np.sqrt(weights.shape[1]))
        n_cols = int(np.sqrt(weights.shape[1]))
        kernel_size = int(np.sqrt(weights.shape[0]/3))
        weights_grid = np.zeros((int((np.sqrt(weights.shape[0]/3)+1)*n_rows), int((np.sqrt(weights.shape[0]/3)+1)*n_cols), 3), dtype=np.float32)
        for i in range(weights_grid.shape[0]/(kernel_size+1)):
            for j in range(weights_grid.shape[1]/(kernel_size+1)):
                index = i * (weights_grid.shape[0]/(kernel_size+1))+j
                if not np.isclose(np.sum(weights[:, index]), 0):
                    if normalize:
                        weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size]=\
                            (weights[:, index].reshape(kernel_size, kernel_size, 3) - np.min(weights[:, index])) / ((np.max(weights[:, index]) - np.min(weights[:, index])) + 1.e-6)
                    else:
                        weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size] =\
                        (weights[:, index].reshape(kernel_size, kernel_size, 3))
                    if modifier is not None:
                        weights_grid[i * (kernel_size + 1):i * (kernel_size + 1) + kernel_size, j * (kernel_size + 1):j * (kernel_size + 1) + kernel_size] *= modifier[index]

        return weights_grid 

def extract_features_from_roi(roi):
    roi_width = roi.shape[1]
    roi_height = roi.shape[2]
    new_width = roi_width / feature_size
    new_height = roi_height / feature_size
    pooled_values = np.zeros([feature_size, feature_size, 512])
    for j in range(512):
        for i in range(feature_size):
            for k in range(feature_size):
                if k == (feature_size-1) & i == (feature_size-1):
                    patch = roi[j, i * new_width:roi_width, k * new_height:roi_height]
                elif k == (feature_size-1):
                    patch = roi[j, i * new_width:(i + 1) * new_width, k * new_height:roi_height]
                elif i == (feature_size-1):
                    patch = roi[j, i * new_width:roi_width, k * new_height:(k + 1) * new_height]
                else:
                    patch = roi[j, i * new_width:(i + 1) * new_width, k * new_height:(k + 1) * new_height]
                pooled_values[i, k, j] = np.max(patch)
    return pooled_values 

def room2blocks_plus_normalized(data_label, num_point, block_size, stride,
                                random_sample, sample_num, sample_aug):
    """ room2block, with input filename and RGB preprocessing.
        for each block centralize XYZ, add normalized XYZ as 678 channels
    """
    data = data_label[:,0:6]
    data[:,3:6] /= 255.0
    label = data_label[:,-1].astype(np.uint8)
    max_room_x = max(data[:,0])
    max_room_y = max(data[:,1])
    max_room_z = max(data[:,2])
    
    data_batch, label_batch = room2blocks(data, label, num_point, block_size, stride,
                                          random_sample, sample_num, sample_aug)
    new_data_batch = np.zeros((data_batch.shape[0], num_point, 9))
    for b in range(data_batch.shape[0]):
        new_data_batch[b, :, 6] = data_batch[b, :, 0]/max_room_x
        new_data_batch[b, :, 7] = data_batch[b, :, 1]/max_room_y
        new_data_batch[b, :, 8] = data_batch[b, :, 2]/max_room_z
        minx = min(data_batch[b, :, 0])
        miny = min(data_batch[b, :, 1])
        data_batch[b, :, 0] -= (minx+block_size/2)
        data_batch[b, :, 1] -= (miny+block_size/2)
    new_data_batch[:, :, 0:6] = data_batch
    return new_data_batch, label_batch 

def room2samples_plus_normalized(data_label, num_point):
    """ room2sample, with input filename and RGB preprocessing.
        for each block centralize XYZ, add normalized XYZ as 678 channels
    """
    data = data_label[:,0:6]
    data[:,3:6] /= 255.0
    label = data_label[:,-1].astype(np.uint8)
    max_room_x = max(data[:,0])
    max_room_y = max(data[:,1])
    max_room_z = max(data[:,2])
    #print(max_room_x, max_room_y, max_room_z)
    
    data_batch, label_batch = room2samples(data, label, num_point)
    new_data_batch = np.zeros((data_batch.shape[0], num_point, 9))
    for b in range(data_batch.shape[0]):
        new_data_batch[b, :, 6] = data_batch[b, :, 0]/max_room_x
        new_data_batch[b, :, 7] = data_batch[b, :, 1]/max_room_y
        new_data_batch[b, :, 8] = data_batch[b, :, 2]/max_room_z
        #minx = min(data_batch[b, :, 0])
        #miny = min(data_batch[b, :, 1])
        #data_batch[b, :, 0] -= (minx+block_size/2)
        #data_batch[b, :, 1] -= (miny+block_size/2)
    new_data_batch[:, :, 0:6] = data_batch
    return new_data_batch, label_batch 

def mine(self, im, gt_bboxes): 
        """
        Propose bounding boxes using proposer, and
        augment non-overlapping boxes with IoU < 0.1
        to the ground truth set.
        (up to a maximum of num_proposals)
        """
        bboxes = self.proposer_.process(im)

        if len(gt_bboxes): 
            # Determine bboxes that have low IoU with ground truth
            # iou = [N x GT]
            iou = brute_force_match(bboxes, gt_bboxes, 
                                    match_func=lambda x,y: intersection_over_union(x,y))
            # print('Detected {}, {}, {}'.format(iou.shape, len(gt_bboxes), len(bboxes))) # , np.max(iou, axis=1)
            overlap_inds, = np.where(np.max(iou, axis=1) < 0.1)
            bboxes = bboxes[overlap_inds]
            # print('Remaining non-overlapping {}'.format(len(bboxes)))

        bboxes = bboxes[:self.num_proposals_]
        targets = self.generate_targets(len(bboxes))
        return bboxes, targets 

def inc_region(self, dst, y, x, h, w):
    '''Incremets dst in the specified region. Runs fastest on np.int8, but not much slower on
    np.int16.'''

    dh, dw = dst.shape
    h2 = h // 2
    w2 = w // 2
    py = y - h2 
    px = x - w2 
    y_min = max(0, py)
    y_max = min(dh, y + h2)
    x_min = max(0, px)
    x_max = min(dw, x + w2)
    if y_max - y_min <= 0 or x_max - x_min <= 0:
      return

    dst[y_min:y_max, x_min:x_max] += 1 

def compHistDistance(h1, h2):
  def normalize(h):    
    if np.sum(h) == 0: 
        return h
    else:
        return h / np.sum(h)

  def smoothstep(x, x_min=0., x_max=1., k=2.):
      m = 1. / (x_max - x_min)
      b = - m * x_min
      x = m * x + b
      return betainc(k, k, np.clip(x, 0., 1.))

  def fn(X, Y, k):
    return 4. * (1. - smoothstep(Y, 0, (1 - Y) * X + Y + .1)) \
      * np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) \
             + 2. * smoothstep(Y, 0, (1 - Y) * X + Y + .1) \
             * (1. - 2. * np.sqrt(2 * X) * smoothstep(X, 0., 1. / k, 2) - 0.5)

  h1 = normalize(h1)
  h2 = normalize(h2)

  return max(0, np.sum(fn(h2, h1, len(h1))))
  # return np.sum(np.where(h2 != 0, h2 * np.log10(h2 / (h1 + 1e-10)), 0))  # KL divergence 

def effective_sample_size(x, mu, var, logger):
    """
    Calculate the effective sample size of sequence generated by MCMC.
    :param x:
    :param mu: mean of the variable
    :param var: variance of the variable
    :param logger: logg
    :return: effective sample size of the sequence
    Make sure that `mu` and `var` are correct!
    """
    # batch size, time, dimension
    b, t, d = x.shape
    ess_ = np.ones([d])
    for s in range(1, t):
        p = auto_correlation_time(x, s, mu, var)
        if np.sum(p > 0.05) == 0:
            break
        else:
            for j in range(0, d):
                if p[j] > 0.05:
                    ess_[j] += 2.0 * p[j] * (1.0 - float(s) / t)

    logger.info('ESS: max [%f] min [%f] / [%d]' % (t / np.min(ess_), t / np.max(ess_), t))
    return t / ess_ 

def score_fun_first_term(vals_hist,a_mid):
	sum = 0.0
	lim = int(np.max(vals_hist.keys()))
	for i in range(0, lim+1):
		if (vals_hist[i] > 0):
			inner_sum = 0.0
			for j in range(0, i):
				inner_sum += j/(1.0 + a_mid*j)
			sum += vals_hist[i]*inner_sum
    
	return sum 

	
##############################	
## in-line functions
############################## 

def estimate_clipping_rect(projector, size):
    """
    Return:
    rect -- NSRect style 2d-tuple.
    flipped (bool) -- Whether y-axis is flipped.
    """
    # lt -> rt -> lb -> rb
    image_corners = [(0, 0), (size[0], 0), (0, size[1]), size]
    x_points = []
    y_points = []
    for corner in image_corners:
        x, y = map(int, projector.project_point(*corner))
        x_points.append(x)
        y_points.append(y)
    min_x = min(x_points)
    min_y = min(y_points)
    max_x = max(x_points)
    max_y = max(y_points)

    rect = ((min_x, min_y), (max_x - min_x, max_y - min_y))
    flipped = y_points[3] < 0

    return rect, flipped 

def to_dim_times_two(self, bounds):
        """return boundaries in format ``[[lb0, ub0], [lb1, ub1], ...]``,
        as used by ``BoxConstraints...`` class.

        """
        if not bounds:
            b = [[None, None]]
        else:
            l = [None, None]  # figure out lenths
            for i in [0, 1]:
                try:
                    l[i] = len(bounds[i])
                except TypeError:
                    bounds[i] = [bounds[i]]
                    l[i] = 1
            b = []  # bounds in different format
            try:
                for i in range(max(l)):
                    b.append([bounds[0][i] if i < l[0] else None,
                              bounds[1][i] if i < l[1] else None])
            except (TypeError, IndexError):
                print("boundaries must be provided in the form " +
                      "[scalar_of_vector, scalar_or_vector]")
                raise
        return b 

def alleviate_conditioning_in_coordinates(self, condition=1e8):
        """pass scaling from `C` to `sigma_vec`.

        As a result, `C` is a correlation matrix, i.e., all diagonal
        entries of `C` are `1`.
        """
        if max(self.dC) / min(self.dC) > condition:
            # allows for much larger condition numbers, if axis-parallel
            if hasattr(self, 'sm') and isinstance(self.sm, sampler.GaussFullSampler):
                old_coordinate_condition = max(self.dC) / min(self.dC)
                old_condition = self.sm.condition_number
                factors = self.sm.to_correlation_matrix()
                self.sigma_vec *= factors
                self.pc /= factors
                self._updateBDfromSM(self.sm)
                utils.print_message('\ncondition in coordinate system exceeded'
                                    ' %.1e, rescaled to %.1e, '
                                    '\ncondition changed from %.1e to %.1e'
                                      % (old_coordinate_condition, max(self.dC) / min(self.dC),
                                         old_condition, self.sm.condition_number),
                                    iteration=self.countiter) 

def plot_axes_scaling(self, iabscissa=1):
        from matplotlib import pyplot
        if not hasattr(self, 'D'):
            self.load()
        dat = self
        if np.max(dat.D[:, 5:]) == np.min(dat.D[:, 5:]):
            pyplot.text(0, dat.D[-1, 5],
                        'all axes scaling values equal to %s'
                        % str(dat.D[-1, 5]),
                        verticalalignment='center')
            return self  # nothing interesting to plot
        self._enter_plotting()
        pyplot.semilogy(dat.D[:, iabscissa], dat.D[:, 5:], '-b')
        # pyplot.hold(True)
        pyplot.grid(True)
        ax = array(pyplot.axis())
        # ax[1] = max(minxend, ax[1])
        pyplot.axis(ax)
        pyplot.title('Principle Axes Lengths')
        # pyplot.xticks(xticklocs)
        self._xlabel(iabscissa)
        self._finalize_plotting()
        return self 

def initwithsize(self, curshape, dim):
        # DIM-dependent initialization
        if self.dim != dim:
            scale = max(1, dim ** .5 / 8.)
            self.linearTF = scale * compute_rotation(self.rseed, dim)
            # if self.zerox:
            #    self.xopt = zeros(dim) # does not work here
            # else:
            # TODO: clean this line
            self.xopt = np.hstack(dot(self.linearTF, 0.5 * np.ones((dim, 1)) / scale ** 2))

        # DIM- and POPSI-dependent initialisations of DIM*POPSI matrices
        if self.lastshape != curshape:
            self.dim = dim
            self.lastshape = curshape
            self.arrxopt = resize(self.xopt, curshape) 

def update_measure(self):
        """updated noise level measure using two fitness lists ``self.fit`` and
        ``self.fitre``, return ``self.noiseS, all_individual_measures``.

        Assumes that ``self.idx`` contains the indices where the fitness
        lists differ.

        """
        lam = len(self.fit)
        idx = np.argsort(self.fit + self.fitre)
        ranks = np.argsort(idx).reshape((2, lam))
        rankDelta = ranks[0] - ranks[1] - np.sign(ranks[0] - ranks[1])

        # compute rank change limits using both ranks[0] and ranks[1]
        r = np.arange(1, 2 * lam)  # 2 * lam - 2 elements
        limits = [0.5 * (Mh.prctile(np.abs(r - (ranks[0, i] + 1 - (ranks[0, i] > ranks[1, i]))),
                                      self.theta * 50) +
                         Mh.prctile(np.abs(r - (ranks[1, i] + 1 - (ranks[1, i] > ranks[0, i]))),
                                      self.theta * 50))
                    for i in self.idx]
        # compute measurement
        #                               max: 1 rankchange in 2*lambda is always fine
        s = np.abs(rankDelta[self.idx]) - Mh.amax(limits, 1)  # lives roughly in 0..2*lambda
        self.noiseS += self.cum * (np.mean(s) - self.noiseS)
        return self.noiseS, s 

def logscale_img(img_array,
                 cap=255.0,
                 coeff=1000.0):
    '''
    This scales the image according to the relation:

    logscale_img = np.log(coeff*(img/max(img))+1)/np.log(coeff)

    Taken from the DS9 scaling algorithms page at:

    http://hea-www.harvard.edu/RD/ds9/ref/how.html

    According to that page:

    coeff = 1000.0 works well for optical images
    coeff = 100.0 works well for IR images

    '''

    logscaled_img = np.log(coeff*img_array/np.nanmax(img_array)+1)/np.log(coeff)
    return cap*logscaled_img 

def genplot(x, y, fit, xdata=None, ydata=None, maxpts=10000):
    bin_range = (0, 360)
    a = (np.arange(*bin_range))
    f_a = nuth_func(a, fit[0], fit[1], fit[2])
    nuth_func_str = r'$y=%0.2f*cos(%0.2f-x)+%0.2f$' % tuple(fit)
    if xdata.size > maxpts:
        import random
        idx = random.sample(list(range(xdata.size)), 10000)
    else:
        idx = np.arange(xdata.size)
    f, ax = plt.subplots()
    ax.set_xlabel('Aspect (deg)')
    ax.set_ylabel('dh/tan(slope) (m)')
    ax.plot(xdata[idx], ydata[idx], 'k.', label='Orig pixels')
    ax.plot(x, y, 'ro', label='Bin median')
    ax.axhline(color='k')
    ax.plot(a, f_a, 'b', label=nuth_func_str)
    ax.set_xlim(*bin_range)
    pad = 0.2 * np.max([np.abs(y.min()), np.abs(y.max())])
    ax.set_ylim(y.min() - pad, y.max() + pad)
    ax.legend(prop={'size':8})
    return f 

#Function copied from from openPIV pyprocess 

def center_clipping(x, percent=30):
    """
    Performs center clipping, a spectral whitening process

    need some type of spectrum flattening so that the
    speech signal more closely approximates a periodic impulse train

    Args:
        x       (array): signal data
        percent (float): percent threshold to clip

    Returns:
        cc         (array): center clipped signal
        clip_level (float): value of clipping
    """
    max_amp = np.max(np.abs(x))
    clip_level = max_amp * (percent / 100)
    positive_mask = x > clip_level
    negative_mask = x < -clip_level
    cc = np.zeros(x.shape)
    cc[positive_mask] = x[positive_mask] - clip_level
    cc[negative_mask] = x[negative_mask] + clip_level
    return cc, clip_level 

def calc_tvd(sess,Generator,Data,N=50000,nbins=10):
    Xd=sess.run(Data.X,{Data.N:N})
    step,Xg=sess.run([Generator.step,Generator.X],{Generator.N:N})

    p_gen,_ = np.histogramdd(Xg,bins=nbins,range=[[0,1],[0,1],[0,1]],normed=True)
    p_dat,_ = np.histogramdd(Xd,bins=nbins,range=[[0,1],[0,1],[0,1]],normed=True)
    p_gen/=nbins**3
    p_dat/=nbins**3
    tvd=0.5*np.sum(np.abs( p_gen-p_dat ))
    mvd=np.max(np.abs( p_gen-p_dat ))

    return step,tvd, mvd

    s_tvd=make_summary(Data.name+'_tvd',tvd)
    s_mvd=make_summary(Data.name+'_mvd',mvd)

    return step,s_tvd,s_mvd
    #return make_summary('tvd/'+Generator.name,tvd) 

def scatter2d(x,y,title='2dscatterplot',xlabel=None,ylabel=None):
    fig=plt.figure()
    plt.scatter(x,y)
    plt.title(title)
    if xlabel:
        plt.xlabel(xlabel)
    if ylabel:
        plt.ylabel(ylabel)

    if not 0<=np.min(x)<=np.max(x)<=1:
        raise ValueError('summary_scatter2d title:',title,' input x exceeded [0,1] range.\
                         min:',np.min(x),' max:',np.max(x))
    if not 0<=np.min(y)<=np.max(y)<=1:
        raise ValueError('summary_scatter2d title:',title,' input y exceeded [0,1] range.\
                         min:',np.min(y),' max:',np.max(y))

    plt.xlim([0,1])
    plt.ylim([0,1])
    return fig 

def get_next_batch(experience, model, num_actions, gamma, batch_size):
    batch_indices = np.random.randint(low=0, high=len(experience),
                                      size=batch_size)
    batch = [experience[i] for i in batch_indices]
    X = np.zeros((batch_size, 80, 80, 4))
    Y = np.zeros((batch_size, num_actions))
    for i in range(len(batch)):
        s_t, a_t, r_t, s_tp1, game_over = batch[i]
        X[i] = s_t
        Y[i] = model.predict(s_t)[0]
        Q_sa = np.max(model.predict(s_tp1)[0])
        if game_over:
            Y[i, a_t] = r_t
        else:
            Y[i, a_t] = r_t + gamma * Q_sa
    return X, Y


############################# main ###############################

# initialize parameters 

def forward(self, input):
        """During the forward pass, it inhibits all inhibitions below some 
        threshold :math:`?`, typically :math:`0`. In other words, it computes point-wise 
        
        .. math:: y=max(0,x) 
        
        Parameters
        ----------
        x : float32
            The activation (the summed, weighted input of a neuron).
    
        Returns
        -------
        float32
            The output of the rectify function applied to the activation.
        """
        self.last_forward = input
        return np.maximum(0.0, input) 

def forward(self, input):
        """:math:`\\varphi(\\mathbf{x})_j =
        \\frac{e^{\mathbf{x}_j}}{\sum_{k=1}^K e^{\mathbf{x}_k}}`
        where :math:`K` is the total number of neurons in the layer. This
        activation function gets applied row-wise.
        
        Parameters
        ----------
        x : float32
            The activation (the summed, weighted input of a neuron).
    
        Returns
        -------
        float32 where the sum of the row is 1 and each single value is in [0, 1]
            The output of the softmax function applied to the activation.
        """
        assert np.ndim(input) == 2
        self.last_forward = input
        x = input - np.max(input, axis=1, keepdims=True)
        exp_x = np.exp(x)
        s = exp_x / np.sum(exp_x, axis=1, keepdims=True)
        return s 

def main(max_iter):
    # prepare
    npdl.utils.random.set_seed(1234)

    # data
    digits = load_digits()

    X_train = digits.data
    X_train /= np.max(X_train)

    Y_train = digits.target
    n_classes = np.unique(Y_train).size

    # model
    model = npdl.model.Model()
    model.add(npdl.layers.Dense(n_out=500, n_in=64, activation=npdl.activations.ReLU()))
    model.add(npdl.layers.Dense(n_out=n_classes, activation=npdl.activations.Softmax()))
    model.compile(loss=npdl.objectives.SCCE(), optimizer=npdl.optimizers.SGD(lr=0.005))

    # train
    model.fit(X_train, npdl.utils.data.one_hot(Y_train), max_iter=max_iter, validation_split=0.1) 

def _updateMaxTextSize(self, x):
        ## Informs that the maximum tick size orthogonal to the axis has
        ## changed; we use this to decide whether the item needs to be resized
        ## to accomodate.
        if self.orientation in ['left', 'right']:
            mx = max(self.textWidth, x)
            if mx > self.textWidth or mx < self.textWidth-10:
                self.textWidth = mx
                if self.style['autoExpandTextSpace'] is True:
                    self._updateWidth()
                    #return True  ## size has changed
        else:
            mx = max(self.textHeight, x)
            if mx > self.textHeight or mx < self.textHeight-10:
                self.textHeight = mx
                if self.style['autoExpandTextSpace'] is True:
                    self._updateHeight()
                    #return True  ## size has changed 

def _updateHeight(self):
        if not self.isVisible():
            h = 0
        else:
            if self.fixedHeight is None:
                if not self.style['showValues']:
                    h = 0
                elif self.style['autoExpandTextSpace'] is True:
                    h = self.textHeight
                else:
                    h = self.style['tickTextHeight']
                h += self.style['tickTextOffset'][1] if self.style['showValues'] else 0
                h += max(0, self.style['tickLength'])
                if self.label.isVisible():
                    h += self.label.boundingRect().height() * 0.8
            else:
                h = self.fixedHeight
        
        self.setMaximumHeight(h)
        self.setMinimumHeight(h)
        self.picture = None 

def _updateWidth(self):
        if not self.isVisible():
            w = 0
        else:
            if self.fixedWidth is None:
                if not self.style['showValues']:
                    w = 0
                elif self.style['autoExpandTextSpace'] is True:
                    w = self.textWidth
                else:
                    w = self.style['tickTextWidth']
                w += self.style['tickTextOffset'][0] if self.style['showValues'] else 0
                w += max(0, self.style['tickLength'])
                if self.label.isVisible():
                    w += self.label.boundingRect().height() * 0.8  ## bounding rect is usually an overestimate
            else:
                w = self.fixedWidth
        
        self.setMaximumWidth(w)
        self.setMinimumWidth(w)
        self.picture = None