Python numpy.transpose() Examples

def similarity_label(self, words, normalization=True):
        """
        you can calculate more than one word at the same time.
        """
        if self.model==None:
            raise Exception('no model.')
        if isinstance(words, string_types):
            words=[words]
        vectors=np.transpose(self.model.wv.__getitem__(words))
        if normalization:
            unit_vector=unitvec(vectors,ax=0) # 这样写比原来那样速度提升一倍
            #unit_vector=np.zeros((len(vectors),len(words)))
            #for i in range(len(words)):
            #    unit_vector[:,i]=matutils.unitvec(vectors[:,i])
            dists=np.dot(self.Label_vec_u, unit_vector)
        else:
            dists=np.dot(self.Label_vec, vectors)
        return dists 

def train_lr_rfeinman(densities_pos, densities_neg, uncerts_pos, uncerts_neg):
    """
    TODO
    :param densities_pos:
    :param densities_neg:
    :param uncerts_pos:
    :param uncerts_neg:
    :return:
    """
    values_neg = np.concatenate(
        (densities_neg.reshape((1, -1)),
         uncerts_neg.reshape((1, -1))),
        axis=0).transpose([1, 0])
    values_pos = np.concatenate(
        (densities_pos.reshape((1, -1)),
         uncerts_pos.reshape((1, -1))),
        axis=0).transpose([1, 0])

    values = np.concatenate((values_neg, values_pos))
    labels = np.concatenate(
        (np.zeros_like(densities_neg), np.ones_like(densities_pos)))

    lr = LogisticRegressionCV(n_jobs=-1).fit(values, labels)

    return values, labels, lr 

def train(self, inputs_list, targets_list):
        inputs = np.array(inputs_list, ndmin=2).T
        targets = np.array(targets_list, ndmin=2).T

        hidden_inputs = np.dot(self.wih, inputs)
        hidden_outputs = self.activation_function(hidden_inputs)

        final_inputs = np.dot(self.who, hidden_outputs)
        final_outputs = self.activation_function(final_inputs)

        output_errors = targets - final_outputs
        hidden_errors = np.dot(self.who.T, output_errors)

        self.who += self.lr * np.dot((output_errors *
                                      final_outputs *
                                      (1.0 - final_outputs)), np.transpose(hidden_outputs))
        self.wih += self.lr * np.dot((hidden_errors *
                                      hidden_outputs *
                                      (1.0 - hidden_outputs)), np.transpose(inputs))
        
        pass

    # query 

def jacobian(self, p, into=None):
        # transpose to be 3 x 2 x n
        p = np.transpose(np.reshape(p, (-1, 3, 2)), (1,2,0))
        # First, get the two legs...
        (dx_ab, dy_ab) = p[1] - p[0]
        (dx_ac, dy_ac) = p[2] - p[0]
        (dx_bc, dy_bc) = p[2] - p[1]
        # now, the area is half the z-value of the cross-product...
        sarea0 = 0.5 * (dx_ab*dy_ac - dx_ac*dy_ab)
        # but we want to abs it
        dsarea0 = np.sign(sarea0)
        z = np.transpose([[-dy_bc,dx_bc], [dy_ac,-dx_ac], [-dy_ab,dx_ab]], (2,0,1))
        z = times(0.5*dsarea0, z)
        m = numel(p)
        n = p.shape[2]
        ii = (np.arange(n) * np.ones([6, n])).T.flatten()
        z = sps.csr_matrix((z.flatten(), (ii, np.arange(len(ii)))), shape=(n, m))
        return safe_into(into, z) 

def from_logeccen(logecc, vmin=0, vmax=90, offset=0.75):
    '''
    from_logeccen(logecc) yields a rescaled linear-space version of the log-eccentricity value (or
      values) logecc.
    from_logeccen(logxy_matrix) rescales all the (x,y) points in the given matrix to have
      linearly-spaced eccentricity values.

    from_logeccen is the inverse of to_logeccen.
    '''
    if pimms.is_matrix(logecc):
        xy = np.asarray(logecc)
        trq = xy.shape[0] != 2
        xy = np.transpose(xy) if trq else np.asarray(xy)
        r = np.sqrt(np.sum(xy**2, axis=0))
        esc = from_logeccen(r, vmin=vmin, vmax=vmax, offset=offset)
        ecc = zinv(r)
        xy = xy * [ecc,ecc] * [esc,esc]
        return xy.T if trq else xy
    else:
        logecc = np.asarray(logecc)
        (vmin,vmax,offset) = [np.asarray(u) for u in (vmin,vmax,offset)]
        (vmin, vmax) = [np.log(u + offset) for u in (vmin, vmax)]
        logecc = logecc*(vmax - vmin) + vmin
        return np.exp(logecc) - offset 

def __call__(self, x, y=None):
        if y is not None: x = (x,y)
        x = np.asarray(x)
        if len(x.shape) == 1: return self([x])[0]
        x = np.transpose(x) if x.shape[0] == 2 else x
        if not x.flags['WRITEABLE']: x = np.array(x)
        crd = self.coordinates
        sig = self.sigma
        wts = self._weight
        res = np.zeros(x.shape[0])
        for (sh, qd, bi) in zip(self.spatial_hashes, self.bin_query_distances, self.sigma_bins):
            neis = sh.query_ball_point(x, qd)
            res += [
                np.sum(w * np.exp(-0.5 * d2/s**2))
                for (ni,pt) in zip(neis,x)
                for ii in [bi[ni]]
                for (w,s,d2) in [(wts[ii], sig[ii], np.sum((crd[ii] - pt)**2, axis=1))]]
        return res 

def visualize_sampling(self, permutations):
        max_length = len(permutations[0])
        grid = np.zeros([max_length,max_length]) # initialize heatmap grid to 0

        transposed_permutations = np.transpose(permutations)
        for t, cities_t in enumerate(transposed_permutations): # step t, cities chosen at step t
            city_indices, counts = np.unique(cities_t,return_counts=True,axis=0)
            for u,v in zip(city_indices, counts):
                grid[t][u]+=v # update grid with counts from the batch of permutations

        # plot heatmap
        fig = plt.figure()
        rcParams.update({'font.size': 22})
        ax = fig.add_subplot(1,1,1)
        ax.set_aspect('equal')
        plt.imshow(grid, interpolation='nearest', cmap='gray')
        plt.colorbar()
        plt.title('Sampled permutations')
        plt.ylabel('Time t')
        plt.xlabel('City i')
        plt.show() 

def superpose_array(refArray, array, check=False):
    """
    Superpose arrays by calculating the rotation matrix and the
    translations that minimize the root mean square deviation between and
    array of vectors and a reference array.

    :Parameters:
        #. refArray (numpy.ndarray): the NX3 reference array to superpose to.
        #. array (numpy.ndarray): the NX3 array to calculate the
           transformation of.
        #. check (boolean): whether to check arguments before generating
           points.

    :Returns:
        #. superposedArray (numpy.ndarray): the NX3 array to superposed array.
    """
    rotationMatrix, _,_,_ = get_superposition_transformation(refArray=refArray, array=array, check=check)
    return np.dot( rotationMatrix, np.transpose(array).\
                   reshape(1,3,-1)).transpose().reshape(-1,3) 

def measure_cost(repeat, scipy_trans_lhs, scipy_dns_lhs, func_name, *args, **kwargs):
    """Measure time cost of running a function
    """
    mx.nd.waitall()
    args_list = []
    for arg in args:
        args_list.append(arg)
    start = time.time()
    if scipy_trans_lhs:
        args_list[0] = np.transpose(args_list[0]) if scipy_dns_lhs else sp.spmatrix.transpose(args_list[0])
    for _ in range(repeat):
        func_name(*args_list, **kwargs)
    mx.nd.waitall()
    end = time.time()
    diff = end - start
    return diff / repeat 

def decode_topk(self, sess, latest_tokens, enc_top_states, dec_init_states):
    """Return the topK results and new decoder states."""
    feed = {
        self._enc_top_states: enc_top_states,
        self._dec_in_state:
            np.squeeze(np.array(dec_init_states)),
        self._abstracts:
            np.transpose(np.array([latest_tokens])),
        self._abstract_lens: np.ones([len(dec_init_states)], np.int32)}

    results = sess.run(
        [self._topk_ids, self._topk_log_probs, self._dec_out_state],
        feed_dict=feed)

    ids, probs, states = results[0], results[1], results[2]
    new_states = [s for s in states]
    return ids, probs, new_states 

def _write_map_files(b_in, b_out, transform):
  cats = get_categories()

  env = utils.Foo(padding=10, resolution=5, num_point_threshold=2,
                  valid_min=-10, valid_max=200, n_samples_per_face=200)
  robot = utils.Foo(radius=15, base=10, height=140, sensor_height=120,
                    camera_elevation_degree=-15)
  
  building_loader = factory.get_dataset('sbpd')
  for flip in [False, True]:
    b = nav_env.Building(b_out, robot, env, flip=flip,
                         building_loader=building_loader)
    logging.info("building_in: %s, building_out: %s, transform: %d", b_in,
                 b_out, transform)
    maps = _get_semantic_maps(b_in, transform, b.map, flip, cats)
    maps = np.transpose(np.array(maps), axes=[1,2,0])

    #  Load file from the cache.
    file_name = '{:s}_{:d}_{:d}_{:d}_{:d}_{:d}_{:d}.pkl'
    file_name = file_name.format(b.building_name, b.map.size[0], b.map.size[1],
                                 b.map.origin[0], b.map.origin[1],
                                 b.map.resolution, flip)
    out_file = os.path.join(DATA_DIR, 'processing', 'class-maps', file_name)
    logging.info('Writing semantic maps to %s.', out_file)
    save_variables(out_file, [maps, cats], ['maps', 'cats'], overwrite=True) 

def intersection(boxes1, boxes2):
  """Compute pairwise intersection areas between boxes.

  Args:
    boxes1: a numpy array with shape [N, 4] holding N boxes
    boxes2: a numpy array with shape [M, 4] holding M boxes

  Returns:
    a numpy array with shape [N*M] representing pairwise intersection area
  """
  [y_min1, x_min1, y_max1, x_max1] = np.split(boxes1, 4, axis=1)
  [y_min2, x_min2, y_max2, x_max2] = np.split(boxes2, 4, axis=1)

  all_pairs_min_ymax = np.minimum(y_max1, np.transpose(y_max2))
  all_pairs_max_ymin = np.maximum(y_min1, np.transpose(y_min2))
  intersect_heights = np.maximum(
      np.zeros(all_pairs_max_ymin.shape),
      all_pairs_min_ymax - all_pairs_max_ymin)
  all_pairs_min_xmax = np.minimum(x_max1, np.transpose(x_max2))
  all_pairs_max_xmin = np.maximum(x_min1, np.transpose(x_min2))
  intersect_widths = np.maximum(
      np.zeros(all_pairs_max_xmin.shape),
      all_pairs_min_xmax - all_pairs_max_xmin)
  return intersect_heights * intersect_widths 

def collectdata(self,):
        print 'Start Collect Data...'

        train_x_path = os.path.join(self.input_dir, 'unlabeled_X.bin')

        train_xf = open(train_x_path, 'rb')
        train_x = np.fromfile(train_xf, dtype=np.uint8)
        train_x = np.reshape(train_x, (-1, 3, 96, 96))
        train_x = np.transpose(train_x, (0, 3, 2, 1))

        idx = 0
        for i in xrange(train_x.shape[0]):
            if not self.skipimg:
                transform_and_save(img_arr=train_x[i], output_filename=os.path.join(self.unlabeldir, str(idx) + '.jpg'))
            self.trainpairlist[os.path.join('images', 'unlabeled', str(idx) + '.jpg')] = 'labels/11.txt'
            idx += 1

        print 'Finished Collect Data...' 

def pre_processing(obs, cuda):
    mean = np.array([0.485, 0.456, 0.406]).reshape([1, 1, 3])
    std = np.array([0.229, 0.224, 0.225]).reshape([1, 1, 3])
    obs = obs / 255
    obs = (obs - mean) / std
    obs = np.transpose(obs, (2, 0, 1))
    obs = np.expand_dims(obs, 0)
    obs = np.array(obs)
    if cuda:
        torch_device = torch.device('cuda:0')
    else:
        torch_device = torch.device('cpu')
    obs_tensor = torch.tensor(obs, dtype=torch.float32, device=torch_device, requires_grad=True)
    return obs_tensor

# generate the entire images 

def resample(imgs, spacing, new_spacing,order=2):
    if len(imgs.shape)==3:
        new_shape = np.round(imgs.shape * spacing / new_spacing)
        true_spacing = spacing * imgs.shape / new_shape
        resize_factor = new_shape / imgs.shape
        imgs = zoom(imgs, resize_factor, mode = 'nearest',order=order)
        return imgs, true_spacing
    elif len(imgs.shape)==4:
        n = imgs.shape[-1]
        newimg = []
        for i in range(n):
            slice = imgs[:,:,:,i]
            newslice,true_spacing = resample(slice,spacing,new_spacing)
            newimg.append(newslice)
        newimg=np.transpose(np.array(newimg),[1,2,3,0])
        return newimg,true_spacing
    else:
        raise ValueError('wrong shape') 

def intersection(boxes1, boxes2):
  """Compute pairwise intersection areas between boxes.

  Args:
    boxes1: a numpy array with shape [N, 4] holding N boxes
    boxes2: a numpy array with shape [M, 4] holding M boxes

  Returns:
    a numpy array with shape [N*M] representing pairwise intersection area
  """
  [y_min1, x_min1, y_max1, x_max1] = np.split(boxes1, 4, axis=1)
  [y_min2, x_min2, y_max2, x_max2] = np.split(boxes2, 4, axis=1)

  all_pairs_min_ymax = np.minimum(y_max1, np.transpose(y_max2))
  all_pairs_max_ymin = np.maximum(y_min1, np.transpose(y_min2))
  intersect_heights = np.maximum(
      np.zeros(all_pairs_max_ymin.shape),
      all_pairs_min_ymax - all_pairs_max_ymin)
  all_pairs_min_xmax = np.minimum(x_max1, np.transpose(x_max2))
  all_pairs_max_xmin = np.maximum(x_min1, np.transpose(x_min2))
  intersect_widths = np.maximum(
      np.zeros(all_pairs_max_xmin.shape),
      all_pairs_min_xmax - all_pairs_max_xmin)
  return intersect_heights * intersect_widths 

def load_batch_norm(idx, variables, weights, assign_ops, offset):
  """Loads kernel, gamma, beta, mean, variance for Batch Normalization"""
  kernel = variables[idx]
  gamma, beta, mean, variance = variables[idx + 1:idx + 5]
  batch_norm_vars = [beta, gamma, mean, variance]

  for var in batch_norm_vars:
    shape = var.shape.as_list()
    num_params = np.prod(shape)
    var_weights = weights[offset:offset + num_params].reshape(shape)
    offset += num_params
    assign_ops.append(tf.assign(var, var_weights))

  shape = kernel.shape.as_list()
  num_params = np.prod(shape)
  var_weights = weights[offset:offset + num_params].reshape((shape[3], shape[2], shape[0], shape[1]))
  var_weights = np.transpose(var_weights, (2, 3, 1, 0))
  offset += num_params
  assign_ops.append(tf.assign(kernel, var_weights))
  return assign_ops, offset 

def lid_term(logits, batch_size=100):
    """Calculate LID loss term for a minibatch of logits

    :param logits: 
    :return: 
    """
    # y_pred = tf.nn.softmax(logits)
    y_pred = logits

    # calculate pairwise distance
    r = tf.reduce_sum(y_pred * y_pred, 1)
    # turn r into column vector
    r1 = tf.reshape(r, [-1, 1])
    D = r1 - 2 * tf.matmul(y_pred, tf.transpose(y_pred)) + tf.transpose(r1) + \
        tf.ones([batch_size, batch_size])

    # find the k nearest neighbor
    D1 = -tf.sqrt(D)
    D2, _ = tf.nn.top_k(D1, k=21, sorted=True)
    D3 = -D2[:, 1:]

    m = tf.transpose(tf.multiply(tf.transpose(D3), 1.0 / D3[:, -1]))
    v_log = tf.reduce_sum(tf.log(m + 1e-9), axis=1)  # to avoid nan
    lids = -20 / v_log

    ## batch normalize lids
    # lids = tf.nn.l2_normalize(lids, dim=0, epsilon=1e-12)

    return lids 

def lid_adv_term(clean_logits, adv_logits, batch_size=100):
    """Calculate LID loss term for a minibatch of advs logits

    :param logits: clean logits
    :param A_logits: adversarial logits
    :return: 
    """
    # y_pred = tf.nn.softmax(logits)
    c_pred = tf.reshape(clean_logits, (batch_size, -1))
    a_pred = tf.reshape(adv_logits, (batch_size, -1))

    # calculate pairwise distance
    r = tf.reduce_sum(c_pred * a_pred, 1)
    # turn r into column vector
    r1 = tf.reshape(r, [-1, 1])
    D = r1 - 2 * tf.matmul(c_pred, tf.transpose(a_pred)) + tf.transpose(r1) + \
        tf.ones([batch_size, batch_size])

    # find the k nearest neighbor
    D1 = -tf.sqrt(D)
    D2, _ = tf.nn.top_k(D1, k=21, sorted=True)
    D3 = -D2[:, 1:]

    m = tf.transpose(tf.multiply(tf.transpose(D3), 1.0 / D3[:, -1]))
    v_log = tf.reduce_sum(tf.log(m + 1e-9), axis=1)  # to avoid nan
    lids = -20 / v_log

    ## batch normalize lids
    lids = tf.nn.l2_normalize(lids, dim=0, epsilon=1e-12)

    return lids 

def make_image(img, mean=(0,0,0), std=(1,1,1)):
    for i in range(0, 3):
        img[i] = img[i] * std[i] + mean[i]    # unnormalize
    npimg = img.numpy()
    return np.transpose(npimg, (1, 2, 0)) 

def end(self, success=True):
        from neuropythy import path_trace
        # we've finished; clean up and make the line
        if success:
            if len(self.xs) < 1: raise ValueError('Drawn line has no points')
            pts = np.transpose([self.xs, self.ys])
            # remove us from the trace meta-data if we're in it
            rd = self.trace.meta_data.get('roi_drawer')
            if rd is self: self.trace.meta_data = self.trace.meta_data.discard('roi_drawer')
            self.trace.persist()
        else: self.trace = None
        if self.line:
            for conn in self.connections:
                self.line.figure.canvas.mpl_disconnect(conn)
        # redraw the final version:
        if self.closed:
            self.xs.append(self.xs[0])
            self.ys.append(self.ys[0])
            self.line.set_data(self.xs, self.ys)
            self.line.figure.canvas.draw()
        matplotlib.pyplot.close(self.line.figure)
        # clear everything
        self.connection = None
        self.line = None
        self.xs = None
        self.ys = None 

def lh_white_indices(lh_white_mask):
        '''
        sub.lh_white_indices is a frozenset of the indices of the white voxels in the given
        subject's lh, represented as 3-tuples.
        '''
        if lh_white_mask is None: return None
        if is_image(lh_white_mask): lh_white_mask = lh_white_mask.dataobj
        idcs = np.transpose(np.where(lh_white_mask))
        return frozenset([tuple(row) for row in idcs]) 

def rh_white_indices(rh_white_mask):
        '''
        sub.rh_white_indices is a frozenset of the indices of the white voxels in the given
        subject's rh, represented as 3-tuples.
        '''
        if rh_white_mask is None: return None
        if is_image(rh_white_mask): rh_white_mask = rh_white_mask.dataobj
        idcs = np.transpose(np.where(rh_white_mask))
        return frozenset([tuple(row) for row in idcs]) 

def unaddress(self, data, surface=0.5):
        '''
        cortex.unaddress(address) yields the (3 x n) coordinate matrix of the given addresses (or,
          if address is singular, the 3D vector) in the given cortex. If the address is a 2D instead
          of a 3D address, then the mid-gray position is returned by default.

        The following options may be given:
          * surface (default: 0.5) specifies the surface to use for 2D addresses; this should be
            either 'white', 'pial', 'midgray', or a real number in the range [0,1] where 0 is the
            white surface and 1 is the pial surface.
        '''
        (faces, coords) = address_data(data, 3, surface=surface)
        (bc, ds) = (coords[:2], coords[2])
        faces = self.tess.index(faces)
        (wx, px) = (self.white_surface.coordinates, self.pial_surface.coordinates)
        if all(len(np.shape(x)) > 1 for x in (faces, coords)):
            (wtx, ptx) = [
                np.transpose([sx[:,ff] if ff[0] >= 0 else null for ff in faces.T], (2,1,0))
                for null in [np.full((3, wx.shape[0]), np.nan)]
                for sx   in (wx, px)]
        elif faces == -1:
            return np.full(selfx.shape[0], np.nan)
        else:
            (wtx, ptx) = [sx[:,faces].T for sx in (wx, px)]
        (wu, pu) = [geo.barycentric_to_cartesian(tx, bc) for tx in (wtx, ptx)]
        return wu*ds + pu*(1 - ds) 

def line_segment_intersection_2D(p12arg, p34arg, atol=1e-8):
    '''
    line_segment_intersection((a, b), (c, d)) yields the intersection point between the line
    passing through points a and b and the line segment that passes from point c to point d. If
    there is no intersection point, then (numpy.nan, numpy.nan) is returned.
    '''
    (p1,p2) = p12arg
    (p3,p4) = p34arg
    pi = np.asarray(line_intersection_2D(p12arg, p34arg, atol=atol))
    p3 = np.asarray(p3)
    u34 = p4 - p3
    cfn = lambda px,iis: (px if iis is None or len(px.shape) == 1 or px.shape[1] == len(iis) else
                          px[:,iis])
    dfn = lambda a,b:     a[0]*b[0] + a[1]*b[1]
    sfn = lambda a,b:     ((a-b)                 if len(a.shape) == len(b.shape) else
                           (np.transpose([a])-b) if len(a.shape) <  len(b.shape) else
                           (a - np.transpose([b])))
    fn  = lambda px,iis:  (1 - ((dfn(cfn(u34,iis), sfn(         px, cfn(p3,iis))) > 0) *
                                (dfn(cfn(u34,iis), sfn(cfn(p4,iis),          px)) > 0)))
    if len(pi.shape) == 1:
        if not np.isfinite(pi[0]): return (np.nan, np.nan)
        bad = fn(pi, None)
        return (np.nan, np.nan) if bad else pi
    else:
        nonpar = np.where(np.isfinite(pi[0]))[0]
        bad = fn(cfn(pi, nonpar), nonpar)
        (xi,yi) = pi
        bad = nonpar[np.where(bad)[0]]
        xi[bad] = np.nan
        yi[bad] = np.nan
        return (xi,yi) 

def triangle_normal(a,b,c):
    '''
    triangle_normal(a, b, c) yields the normal vector of the triangle whose vertices are given by
      the points a, b, and c. If the points are 2D points, then 3D normal vectors are still yielded,
      that are always (0,0,1) or (0,0,-1). This function auto-threads over matrices, in which case
      they must be in equivalent orientations, and the result is returned in whatever orientation
      they are given in. In some cases, the intended orientation of the matrices is ambiguous (e.g.,
      if a, b, and c are 2 x 3 matrices), in which case the matrix is always assumed to be given in
      (dims x vertices) orientation.
    '''
    (a,b,c) = [np.asarray(x) for x in (a,b,c)]
    if len(a.shape) == 1 and len(b.shape) == 1 and len(c.shape) == 1:
        return triangle_normal(*[np.transpose([x]) for x in (a,b,c)])[:,0]
    (a,b,c) = [np.transpose([x]) if len(x.shape) == 1 else x for x in (a,b,c)]
    # find a required number of dimensions, if possible
    if a.shape[0] in (2,3):
        dims = a.shape[0]
        tx = True
    else:
        dims = a.shape[1]
        (a,b,c) = [x.T for x in (a,b,c)]
        tx = False
    n = (a.shape[1] if a.shape[1] != 1 else b.shape[1] if b.shape[1] != 1 else
         c.shape[1] if c.shape[1] != 1 else 1)
    if dims == 2:
        (a,b,c) = [np.vstack((x, np.zeros((1,n)))) for x in (a,b,c)]
    ab = normalize(b - a)
    ac = normalize(c - a)
    res = np.cross(ab, ac, axisa=0, axisb=0)
    return res.T if tx else res 

def value(self, p):
        # transpose to be 3 x 2 x n
        p = np.transpose(np.reshape(p, (-1, 3, 2)), (1,2,0))
        # First, get the two legs...
        (dx_ab, dy_ab) = p[1] - p[0]
        (dx_ac, dy_ac) = p[2] - p[0]
        (dx_bc, dx_bc) = p[2] - p[1]
        # now, the area is half the z-value of the cross-product...
        sarea = 0.5 * (dx_ab*dy_ac - dx_ac*dy_ab)
        return sarea 

def jacobian(self, p, into=None):
        p = np.transpose(np.reshape(p, (-1, 3, 2)), (1,2,0))
        (dx_ab, dy_ab) = p[1] - p[0]
        (dx_ac, dy_ac) = p[2] - p[0]
        (dx_bc, dy_bc) = p[2] - p[1]
        z = 0.5 * np.transpose([[-dy_bc,dx_bc], [dy_ac,-dx_ac], [-dy_ab,dx_ab]], (2,0,1))
        m = numel(p)
        n = p.shape[2]
        ii = (np.arange(n) * np.ones([6, n])).T.flatten()
        z = sps.csr_matrix((z.flatten(), (ii, np.arange(len(ii)))), shape=(n, m))
        return safe_into(into, z) 

def value(self, p):
        # transpose to be 3 x 2 x n
        p = np.transpose(np.reshape(p, (-1, 3, 2)), (1,2,0))
        # First, get the two legs...
        (dx_ab, dy_ab) = p[1] - p[0]
        (dx_ac, dy_ac) = p[2] - p[0]
        (dx_bc, dy_bc) = p[2] - p[1]
        # now, the area is half the z-value of the cross-product...
        sarea0 = 0.5 * (dx_ab*dy_ac - dx_ac*dy_ab)
        # but we want to abs it
        return np.abs(sarea0) 

def angle_to_cortex(self, theta, rho):
        'See help(neuropythy.registration.RetinotopyModel.angle_to_cortex).'
        #TODO: This should be made to work correctly with visual area boundaries: this could be done
        # by, for each area (e.g., V2) looking at its boundaries (with V1 and V3) and flipping the
        # adjacent triangles so that there is complete coverage of each hemifield, guaranteed.
        if not pimms.is_vector(theta): return self.angle_to_cortex([theta], [rho])[0]
        theta = np.asarray(theta)
        rho = np.asarray(rho)
        zs = np.asarray(
            rho * np.exp([np.complex(z) for z in 1j * ((90.0 - theta)/180.0*np.pi)]),
            dtype=np.complex)
        coords = np.asarray([zs.real, zs.imag]).T
        if coords.shape[0] == 0: return np.zeros((0, len(self.visual_meshes), 2))
        # we step through each area in the forward model and return the appropriate values
        tx = self.transform
        res = np.transpose(
            [self.visual_meshes[area].interpolate(coords, 'cortical_coordinates', method='linear')
             for area in sorted(self.visual_meshes.keys())],
            (1,0,2))
        if tx is not None:
            res = np.asarray(
                [np.dot(tx, np.vstack((area_xy.T, np.ones(len(area_xy)))))[0:2].T
                 for area_xy in res])
        return res