# Source code for pyqtgraph.graphicsItems.ScatterPlotItem

    import itertools
    import math
    import weakref
    from collections import OrderedDict

    import numpy as np

    from .. import Qt, debug
    from .. import functions as fn
    from .. import getConfigOption
    from ..Point import Point
    from ..Qt import QtCore, QtGui
    from .GraphicsObject import GraphicsObject

    __all__ = ['ScatterPlotItem', 'SpotItem']

    ## Build all symbol paths
    name_list = ['o', 's', 't', 't1', 't2', 't3', 'd', '+', 'x', 'p', 'h', 'star',
                 'arrow_up', 'arrow_right', 'arrow_down', 'arrow_left', 'crosshair']
    Symbols = OrderedDict([(name, QtGui.QPainterPath()) for name in name_list])
    Symbols['o'].addEllipse(QtCore.QRectF(-0.5, -0.5, 1, 1))
    Symbols['s'].addRect(QtCore.QRectF(-0.5, -0.5, 1, 1))

    def makeCrosshair(r=0.5, w=1, h=1):
        path = QtGui.QPainterPath()
        rect = QtCore.QRectF(-r, -r, r * 2, r * 2)
        path.addEllipse(rect)
        path.moveTo(-w, 0)
        path.lineTo(w, 0)
        path.moveTo(0, -h)
        path.lineTo(0, h)
        return path
    Symbols['crosshair'] = makeCrosshair()

    coords = {
        't': [(-0.5, -0.5), (0, 0.5), (0.5, -0.5)],
        't1': [(-0.5, 0.5), (0, -0.5), (0.5, 0.5)],
        't2': [(-0.5, -0.5), (-0.5, 0.5), (0.5, 0)],
        't3': [(0.5, 0.5), (0.5, -0.5), (-0.5, 0)],
        'd': [(0., -0.5), (-0.4, 0.), (0, 0.5), (0.4, 0)],
        '+': [
            (-0.5, -0.1), (-0.5, 0.1), (-0.1, 0.1), (-0.1, 0.5),
            (0.1, 0.5), (0.1, 0.1), (0.5, 0.1), (0.5, -0.1),
            (0.1, -0.1), (0.1, -0.5), (-0.1, -0.5), (-0.1, -0.1)
        ],
        'p': [(0, -0.5), (-0.4755, -0.1545), (-0.2939, 0.4045),
              (0.2939, 0.4045), (0.4755, -0.1545)],
        'h': [(0.433, 0.25), (0., 0.5), (-0.433, 0.25), (-0.433, -0.25),
              (0, -0.5), (0.433, -0.25)],
        'star': [(0, -0.5), (-0.1123, -0.1545), (-0.4755, -0.1545),
                 (-0.1816, 0.059), (-0.2939, 0.4045), (0, 0.1910),
                 (0.2939, 0.4045), (0.1816, 0.059), (0.4755, -0.1545),
                 (0.1123, -0.1545)],
        'arrow_up': [
            (-0.125, 0.125), (0, 0), (0.125, 0.125),
            (0.05, 0.125), (0.05, 0.5), (-0.05, 0.5), (-0.05, 0.125)
        ]
    }
    for k, c in coords.items():
        Symbols[k].moveTo(*c[0])
        for x,y in c[1:]:
            Symbols[k].lineTo(x, y)
        Symbols[k].closeSubpath()
    tr = QtGui.QTransform()
    tr.rotate(45)
    Symbols['x'] = tr.map(Symbols['+'])
    tr.rotate(45)
    Symbols['arrow_right'] = tr.map(Symbols['arrow_up'])
    Symbols['arrow_down'] = tr.map(Symbols['arrow_right'])
    Symbols['arrow_left'] = tr.map(Symbols['arrow_down'])
    _DEFAULT_STYLE = {'symbol': None, 'size': -1, 'pen': None, 'brush': None, 'visible': True}

    def drawSymbol(painter, symbol, size, pen, brush):
        if symbol is None:
            return
        painter.scale(size, size)
        painter.setPen(pen)
        painter.setBrush(brush)
        if isinstance(symbol, str):
            symbol = Symbols[symbol]
        if np.isscalar(symbol):
            symbol = list(Symbols.values())[symbol % len(Symbols)]
        painter.drawPath(symbol)

    def renderSymbol(symbol, size, pen, brush, device=None, dpr=1.0):
        """
        Render a symbol specification to QImage.
        Symbol may be either a QPainterPath or one of the keys in the Symbols dict.
        If *device* is None, a new QPixmap will be returned. Otherwise,
        the symbol will be rendered into the device specified (See QPainter documentation
        for more information).
        """
        ## Render a spot with the given parameters to a pixmap
        penPxWidth = max(math.ceil(pen.widthF()), 1)
        if device is None:
            side = int(math.ceil(dpr*(size+penPxWidth)))
            device = QtGui.QImage(side, side, QtGui.QImage.Format.Format_ARGB32_Premultiplied)
            device.setDevicePixelRatio(dpr)
            device.fill(QtCore.Qt.GlobalColor.transparent)
        p = QtGui.QPainter(device)
        try:
            p.setRenderHint(p.RenderHint.Antialiasing)
            p.translate(device.width()/dpr*0.5, device.height()/dpr*0.5)
            drawSymbol(p, symbol, size, pen, brush)
        finally:
            p.end()
        return device

    def _mkPen(*args, **kwargs):
        """
        Wrapper for fn.mkPen which avoids creating a new QPen object if passed one as its
        sole argument. This is used to avoid unnecessary cache misses in SymbolAtlas which
        uses the QPen object id in its key.
        """
        if len(args) == 1 and isinstance(args[0], QtGui.QPen):
            return args[0]
        else:
            return fn.mkPen(*args, **kwargs)

    def _mkBrush(*args, **kwargs):
        """
        Wrapper for fn.mkBrush which avoids creating a new QBrush object if passed one as its
        sole argument. This is used to avoid unnecessary cache misses in SymbolAtlas which
        uses the QBrush object id in its key.
        """
        if len(args) == 1 and isinstance(args[0], QtGui.QBrush):
            return args[0]
        else:
            return fn.mkBrush(*args, **kwargs)

    class SymbolAtlas(object):
        """
        Used to efficiently construct a single QPixmap containing all rendered symbols
        for a ScatterPlotItem. This is required for fragment rendering.

        Use example:
            atlas = SymbolAtlas()
            sc1 = atlas[[('o', 5, QPen(..), QBrush(..))]]
            sc2 = atlas[[('t', 10, QPen(..), QBrush(..))]]
            pm = atlas.pixmap

        """
        _idGenerator = itertools.count()

        def __init__(self):
            self._dpr = 1.0
            self.clear()

        def __getitem__(self, styles):
            """
            Given a list of tuples, (symbol, size, pen, brush), return a list of coordinates of
            corresponding symbols within the atlas. Note that these coordinates may change if the atlas is rebuilt.
            """
            keys = self._keys(styles)
            new = {key: style for key, style in zip(keys, styles) if key not in self._coords}

            if new:
                self._extend(new)

            return list(map(self._coords.__getitem__, keys))

        def __len__(self):
            return len(self._coords)

        def devicePixelRatio(self):
            return self._dpr

        def setDevicePixelRatio(self, dpr):
            self._dpr = dpr

        @property
        def pixmap(self):
            if self._pixmap is None:
                self._pixmap = self._createPixmap()
            return self._pixmap

        @property
        def maxWidth(self):
            # return the max logical width
            return self._maxWidth / self._dpr

        def rebuild(self, styles=None):
            profiler = debug.Profiler()  # noqa: profiler prints on GC
            if styles is None:
                data = []
            else:
                keys = set(self._keys(styles))
                data = list(self._itemData(keys))

            self.clear()
            if data:
                self._extendFromData(data)

        def clear(self):
            self._data = np.zeros((0, 0, 4), dtype=np.ubyte)  # numpy array of atlas image
            self._coords = {}
            self._pixmap = None
            self._maxWidth = 0
            self._totalWidth = 0
            self._totalArea = 0
            self._pos = (0, 0)
            self._rowShape = (0, 0)

        def diagnostics(self):
            n = len(self)
            w, h, _ = self._data.shape
            a = self._totalArea
            return dict(count=n,
                        width=w,
                        height=h,
                        area=w * h,
                        area_used=1.0 if n == 0 else a / (w * h),
                        squareness=1.0 if n == 0 else 2 * w * h / (w**2 + h**2))

        def _keys(self, styles):
            def getId(obj):
                try:
                    return obj._id
                except AttributeError:
                    obj._id = next(SymbolAtlas._idGenerator)
                    return obj._id

            return [
                (symbol if isinstance(symbol, (str, int)) else getId(symbol), size, getId(pen), getId(brush))
                for symbol, size, pen, brush in styles
            ]

        def _itemData(self, keys):
            for key in keys:
                y, x, h, w = self._coords[key]
                yield key, self._data[x:x + w, y:y + h]

        def _extend(self, styles):
            profiler = debug.Profiler()

            images = []
            data = []
            for key, style in styles.items():
                img = renderSymbol(*style, dpr=self._dpr)
                arr = fn.ndarray_from_qimage(img)
                images.append(img)  # keep these to delay garbage collection
                data.append((key, arr))

            profiler('render')
            self._extendFromData(data)
            profiler('insert')

        def _extendFromData(self, data):
            self._pack(data)

            # expand array if necessary
            wNew, hNew = self._minDataShape()
            wOld, hOld, _ = self._data.shape
            if (wNew > wOld) or (hNew > hOld):
                arr = np.zeros((wNew, hNew, 4), dtype=np.ubyte)
                arr[:wOld, :hOld] = self._data
                self._data = arr

            # insert data into array
            for key, arr in data:
                y, x, h, w = self._coords[key]
                self._data[x:x+w, y:y+h] = arr

            self._pixmap = None

        def _pack(self, data):
            # pack each item rectangle as efficiently as possible into a larger, expanding, approximate square
            n = len(self)
            wMax = self._maxWidth
            wSum = self._totalWidth
            aSum = self._totalArea
            x, y = self._pos
            wRow, hRow = self._rowShape

            # update packing statistics
            for _, arr in data:
                w, h, _ = arr.shape
                wMax = max(w, wMax)
                wSum += w
                aSum += w * h
            n += len(data)

            # maybe expand row width for squareness and to accommodate largest width
            wRowEst = int(wSum / (n ** 0.5))
            if wRowEst > 2 * wRow:
                wRow = wRowEst
            wRow = max(wMax, wRow)

            # set coordinates by packing along rows
            # sort by rectangle height first to improve packing density
            for key, arr in sorted(data, key=lambda data: data[1].shape[1]):
                w, h, _ = arr.shape
                if x + w > wRow:
                    # move up a row
                    x = 0
                    y += hRow
                    hRow = h
                hRow = max(h, hRow)
                self._coords[key] = (y, x, h, w)
                x += w

            self._maxWidth = wMax
            self._totalWidth = wSum
            self._totalArea = aSum
            self._pos = (x, y)
            self._rowShape = (wRow, hRow)

        def _minDataShape(self):
            x, y = self._pos
            w, h = self._rowShape
            return int(w), int(y + h)

        def _createPixmap(self):
            profiler = debug.Profiler()  # noqa: profiler prints on GC
            if self._data.size == 0:
                pm = QtGui.QPixmap(0, 0)
            else:
                img = fn.ndarray_to_qimage(self._data,
                    QtGui.QImage.Format.Format_ARGB32_Premultiplied)
                pm = QtGui.QPixmap(img)
            return pm

    class ScatterPlotItem(GraphicsObject):
        """
        Displays a set of x/y points. Instances of this class are created
        automatically as part of PlotDataItem; these rarely need to be instantiated
        directly.

        The size, shape, pen, and fill brush may be set for each point individually
        or for all points.

        ============================  ===============================================
        **Signals:**
        sigPlotChanged(self)          Emitted when the data being plotted has changed
        sigClicked(self, points, ev)  Emitted when points are clicked. Sends a list
                                      of all the points under the mouse pointer.
        sigHovered(self, points, ev)  Emitted when the item is hovered. Sends a list
                                      of all the points under the mouse pointer.
        ============================  ===============================================

        """
        #sigPointClicked = QtCore.Signal(object, object)
        sigClicked = QtCore.Signal(object, object, object)
        sigHovered = QtCore.Signal(object, object, object)
        sigPlotChanged = QtCore.Signal(object)

        def __init__(self, *args, **kargs):
            """
            Accepts the same arguments as setData()
            """
            profiler = debug.Profiler()
            GraphicsObject.__init__(self)

            self.picture = None   # QPicture used for rendering when pxmode==False
            self.fragmentAtlas = SymbolAtlas()

            dtype = [
                ('x', float),
                ('y', float),
                ('size', float),
                ('symbol', object),
                ('pen', object),
                ('brush', object),
                ('visible', bool),
                ('data', object),
                ('hovered', bool),
                ('item', object),
                ('sourceRect', [
                    ('x', int),
                    ('y', int),
                    ('w', int),
                    ('h', int)
                ])
            ]

            self.data = np.empty(0, dtype=dtype)
            self.bounds = [None, None]  ## caches data bounds
            self._maxSpotWidth = 0      ## maximum size of the scale-variant portion of all spots
            self._maxSpotPxWidth = 0    ## maximum size of the scale-invariant portion of all spots
            self._pixmapFragments = Qt.internals.PrimitiveArray(QtGui.QPainter.PixmapFragment, 10)
            self.opts = {
                'pxMode': True,
                'useCache': True,  ## If useCache is False, symbols are re-drawn on every paint.
                'antialias': getConfigOption('antialias'),
                'compositionMode': None,
                'name': None,
                'symbol': 'o',
                'size': 7,
                'pen': fn.mkPen(getConfigOption('foreground')),
                'brush': fn.mkBrush(100, 100, 150),
                'hoverable': False,
                'tip': 'x: {x:.3g}\ny: {y:.3g}\ndata={data}'.format,
            }
            self.opts.update(
                {'hover' + opt.title(): _DEFAULT_STYLE[opt] for opt in ['symbol', 'size', 'pen', 'brush']}
            )
            profiler()
            self.setData(*args, **kargs)
            profiler('setData')

            #self.setCacheMode(self.DeviceCoordinateCache)

            # track when the tooltip is cleared so we only clear it once
            # this allows another item in the VB to set the tooltip
            self._toolTipCleared = True

        def setData(self, *args, **kargs):
            """
            **Ordered Arguments:**

            * If there is only one unnamed argument, it will be interpreted like the 'spots' argument.
            * If there are two unnamed arguments, they will be interpreted as sequences of x and y values.

            ====================== ===============================================================================================
            **Keyword Arguments:**
            *spots*                Optional list of dicts. Each dict specifies parameters for a single spot:
                                   {'pos': (x,y), 'size', 'pen', 'brush', 'symbol'}. This is just an alternate method
                                   of passing in data for the corresponding arguments.
            *x*,*y*                1D arrays of x,y values.
            *pos*                  2D structure of x,y pairs (such as Nx2 array or list of tuples)
            *pxMode*               If True, spots are always the same size regardless of scaling, and size is given in px.
                                   Otherwise, size is in scene coordinates and the spots scale with the view. To ensure
                                   effective caching, QPen and QBrush objects should be reused as much as possible.
                                   Default is True
            *symbol*               can be one (or a list) of symbols. For a list of supported symbols, see
                                   :func:`~ScatterPlotItem.setSymbol`. QPainterPath is also supported to specify custom symbol
                                   shapes. To properly obey the position and size, custom symbols should be centered at (0,0) and
                                   width and height of 1.0. Note that it is also possible to 'install' custom shapes by setting
                                   ScatterPlotItem.Symbols[key] = shape.
            *pen*                  The pen (or list of pens) to use for drawing spot outlines.
            *brush*                The brush (or list of brushes) to use for filling spots.
            *size*                 The size (or list of sizes) of spots. If *pxMode* is True, this value is in pixels. Otherwise,
                                   it is in the item's local coordinate system.
            *data*                 a list of python objects used to uniquely identify each spot.
            *hoverable*            If True, sigHovered is emitted with a list of hovered points, a tool tip is shown containing
                                   information about them, and an optional separate style for them is used. Default is False.
            *tip*                  A string-valued function of a spot's (x, y, data) values. Set to None to prevent a tool tip
                                   from being shown.
            *hoverSymbol*          A single symbol to use for hovered spots. Set to None to keep symbol unchanged. Default is None.
            *hoverSize*            A single size to use for hovered spots. Set to -1 to keep size unchanged. Default is -1.
            *hoverPen*             A single pen to use for hovered spots. Set to None to keep pen unchanged. Default is None.
            *hoverBrush*           A single brush to use for hovered spots. Set to None to keep brush unchanged. Default is None.
            *useCache*             (bool) By default, generated point graphics items are cached to
                                   improve performance. Setting this to False can improve image quality
                                   in certain situations.
            *antialias*            Whether to draw symbols with antialiasing. Note that if pxMode is True, symbols are
                                   always rendered with antialiasing (since the rendered symbols can be cached, this
                                   incurs very little performance cost)
            *compositionMode*      If specified, this sets the composition mode used when drawing the
                                   scatter plot (see QPainter::CompositionMode in the Qt documentation).
            *name*                 The name of this item. Names are used for automatically
                                   generating LegendItem entries and by some exporters.
            ====================== ===============================================================================================
            """
            oldData = self.data  ## this causes cached pixmaps to be preserved while new data is registered.
            self.clear()  ## clear out all old data
            self.addPoints(*args, **kargs)

        def addPoints(self, *args, **kargs):
            """
            Add new points to the scatter plot.
            Arguments are the same as setData()
            """

            ## deal with non-keyword arguments
            if len(args) == 1:
                kargs['spots'] = args[0]
            elif len(args) == 2:
                kargs['x'] = args[0]
                kargs['y'] = args[1]
            elif len(args) > 2:
                raise Exception('Only accepts up to two non-keyword arguments.')

            ## convert 'pos' argument to 'x' and 'y'
            if 'pos' in kargs:
                pos = kargs['pos']
                if isinstance(pos, np.ndarray):
                    kargs['x'] = pos[:,0]
                    kargs['y'] = pos[:,1]
                else:
                    x = []
                    y = []
                    for p in pos:
                        if isinstance(p, QtCore.QPointF):
                            x.append(p.x())
                            y.append(p.y())
                        else:
                            x.append(p[0])
                            y.append(p[1])
                    kargs['x'] = x
                    kargs['y'] = y

            ## determine how many spots we have
            if 'spots' in kargs:
                numPts = len(kargs['spots'])
            elif 'y' in kargs and kargs['y'] is not None:
                numPts = len(kargs['y'])
            else:
                kargs['x'] = []
                kargs['y'] = []
                numPts = 0

            ## Clear current SpotItems since the data references they contain will no longer be current
            self.data['item'][...] = None

            ## Extend record array
            oldData = self.data
            self.data = np.empty(len(oldData)+numPts, dtype=self.data.dtype)
            ## note that np.empty initializes object fields to None and string fields to ''

            self.data[:len(oldData)] = oldData
            #for i in range(len(oldData)):
                #oldData[i]['item']._data = self.data[i]  ## Make sure items have proper reference to new array

            newData = self.data[len(oldData):]
            newData['size'] = -1  ## indicates to use default size
            newData['visible'] = True

            if 'spots' in kargs:
                spots = kargs['spots']
                for i in range(len(spots)):
                    spot = spots[i]
                    for k in spot:
                        if k == 'pos':
                            pos = spot[k]
                            if isinstance(pos, QtCore.QPointF):
                                x,y = pos.x(), pos.y()
                            else:
                                x,y = pos[0], pos[1]
                            newData[i]['x'] = x
                            newData[i]['y'] = y
                        elif k == 'pen':
                            newData[i][k] = _mkPen(spot[k])
                        elif k == 'brush':
                            newData[i][k] = _mkBrush(spot[k])
                        elif k in ['x', 'y', 'size', 'symbol', 'data']:
                            newData[i][k] = spot[k]
                        else:
                            raise Exception("Unknown spot parameter: %s" % k)
            elif 'y' in kargs:
                newData['x'] = kargs['x']
                newData['y'] = kargs['y']

            if 'name' in kargs:
                self.opts['name'] = kargs['name']
            if 'pxMode' in kargs:
                self.setPxMode(kargs['pxMode'])
            if 'antialias' in kargs:
                self.opts['antialias'] = kargs['antialias']
            if 'hoverable' in kargs:
                self.opts['hoverable'] = bool(kargs['hoverable'])
            if 'tip' in kargs:
                self.opts['tip'] = kargs['tip']
            if 'useCache' in kargs:
                self.opts['useCache'] = kargs['useCache']

            ## Set any extra parameters provided in keyword arguments
            for k in ['pen', 'brush', 'symbol', 'size']:
                if k in kargs:
                    setMethod = getattr(self, 'set' + k[0].upper() + k[1:])
                    setMethod(kargs[k], update=False, dataSet=newData, mask=kargs.get('mask', None))
                kh = 'hover' + k.title()
                if kh in kargs:
                    vh = kargs[kh]
                    if k == 'pen':
                        vh = _mkPen(vh)
                    elif k == 'brush':
                        vh = _mkBrush(vh)
                    self.opts[kh] = vh
            if 'data' in kargs:
                self.setPointData(kargs['data'], dataSet=newData)

            self.prepareGeometryChange()
            self.informViewBoundsChanged()
            self.bounds = [None, None]
            self.invalidate()
            self.updateSpots(newData)
            self.sigPlotChanged.emit(self)

        def invalidate(self):
            ## clear any cached drawing state
            self.picture = None
            self.update()

        def getData(self):
            return self.data['x'], self.data['y']

        def implements(self, interface=None):
            ints = ['plotData']
            if interface is None:
                return ints
            return interface in ints

        def name(self):
            return self.opts.get('name', None)

        def setPen(self, *args, **kargs):
            """Set the pen(s) used to draw the outline around each spot.
            If a list or array is provided, then the pen for each spot will be set separately.
            Otherwise, the arguments are passed to pg.mkPen and used as the default pen for
            all spots which do not have a pen explicitly set."""
            update = kargs.pop('update', True)
            dataSet = kargs.pop('dataSet', self.data)

            if len(args) == 1 and (isinstance(args[0], np.ndarray) or isinstance(args[0], list)):
                pens = args[0]
                if 'mask' in kargs and kargs['mask'] is not None:
                    pens = pens[kargs['mask']]
                if len(pens) != len(dataSet):
                    raise Exception("Number of pens does not match number of points (%d != %d)" % (len(pens), len(dataSet)))
                dataSet['pen'] = list(map(_mkPen, pens))
            else:
                self.opts['pen'] = _mkPen(*args, **kargs)

            dataSet['sourceRect'] = 0
            if update:
                self.updateSpots(dataSet)

        def setBrush(self, *args, **kargs):
            """Set the brush(es) used to fill the interior of each spot.
            If a list or array is provided, then the brush for each spot will be set separately.
            Otherwise, the arguments are passed to pg.mkBrush and used as the default brush for
            all spots which do not have a brush explicitly set."""
            update = kargs.pop('update', True)
            dataSet = kargs.pop('dataSet', self.data)

            if len(args) == 1 and (isinstance(args[0], np.ndarray) or isinstance(args[0], list)):
                brushes = args[0]
                if 'mask' in kargs and kargs['mask'] is not None:
                    brushes = brushes[kargs['mask']]
                if len(brushes) != len(dataSet):
                    raise Exception("Number of brushes does not match number of points (%d != %d)" % (len(brushes), len(dataSet)))
                dataSet['brush'] = list(map(_mkBrush, brushes))
            else:
                self.opts['brush'] = _mkBrush(*args, **kargs)

            dataSet['sourceRect'] = 0
            if update:
                self.updateSpots(dataSet)

        def setSymbol(self, symbol, update=True, dataSet=None, mask=None):
            """Set the symbol(s) used to draw each spot.
            If a list or array is provided, then the symbol for each spot will be set separately.
            Otherwise, the argument will be used as the default symbol for
            all spots which do not have a symbol explicitly set.

            **Supported symbols:**

            * 'o'  circle (default)
            * 's'  square
            * 't'  triangle
            * 'd'  diamond
            * '+'  plus
            * 't1' triangle pointing upwards
            * 't2'  triangle pointing right side
            * 't3'  triangle pointing left side
            * 'p'  pentagon
            * 'h'  hexagon
            * 'star'
            * 'x'  cross
            * 'arrow_up'
            * 'arrow_right'
            * 'arrow_down'
            * 'arrow_left'
            * 'crosshair'
            * any QPainterPath to specify custom symbol shapes.

            """
            if dataSet is None:
                dataSet = self.data

            if isinstance(symbol, np.ndarray) or isinstance(symbol, list):
                symbols = symbol
                if mask is not None:
                    symbols = symbols[mask]
                if len(symbols) != len(dataSet):
                    raise Exception("Number of symbols does not match number of points (%d != %d)" % (len(symbols), len(dataSet)))
                dataSet['symbol'] = symbols
            else:
                self.opts['symbol'] = symbol
                self._spotPixmap = None

            dataSet['sourceRect'] = 0
            if update:
                self.updateSpots(dataSet)

        def setSize(self, size, update=True, dataSet=None, mask=None):
            """Set the size(s) used to draw each spot.
            If a list or array is provided, then the size for each spot will be set separately.
            Otherwise, the argument will be used as the default size for
            all spots which do not have a size explicitly set."""
            if dataSet is None:
                dataSet = self.data

            if isinstance(size, np.ndarray) or isinstance(size, list):
                sizes = size
                if mask is not None:
                    sizes = sizes[mask]
                if len(sizes) != len(dataSet):
                    raise Exception("Number of sizes does not match number of points (%d != %d)" % (len(sizes), len(dataSet)))
                dataSet['size'] = sizes
            else:
                self.opts['size'] = size
                self._spotPixmap = None

            dataSet['sourceRect'] = 0
            if update:
                self.updateSpots(dataSet)

        def setPointsVisible(self, visible, update=True, dataSet=None, mask=None):
            """Set whether or not each spot is visible.
            If a list or array is provided, then the visibility for each spot will be set separately.
            Otherwise, the argument will be used for all spots."""
            if dataSet is None:
                dataSet = self.data

            if isinstance(visible, np.ndarray) or isinstance(visible, list):
                visibilities = visible
                if mask is not None:
                    visibilities = visibilities[mask]
                if len(visibilities) != len(dataSet):
                    raise Exception("Number of visibilities does not match number of points (%d != %d)" % (len(visibilities), len(dataSet)))
                dataSet['visible'] = visibilities
            else:
                dataSet['visible'] = visible

            dataSet['sourceRect'] = 0
            if update:
                self.updateSpots(dataSet)

        def setPointData(self, data, dataSet=None, mask=None):
            if dataSet is None:
                dataSet = self.data

            if isinstance(data, np.ndarray) or isinstance(data, list):
                if mask is not None:
                    data = data[mask]
                if len(data) != len(dataSet):
                    raise Exception("Length of meta data does not match number of points (%d != %d)" % (len(data), len(dataSet)))

            ## Bug: If data is a numpy record array, then items from that array must be copied to dataSet one at a time.
            ## (otherwise they are converted to tuples and thus lose their field names.
            if isinstance(data, np.ndarray) and (data.dtype.fields is not None)and len(data.dtype.fields) > 1:
                for i, rec in enumerate(data):
                    dataSet['data'][i] = rec
            else:
                dataSet['data'] = data

        def setPxMode(self, mode):
            if self.opts['pxMode'] == mode:
                return

            self.opts['pxMode'] = mode
            self.invalidate()

        def updateSpots(self, dataSet=None):
            profiler = debug.Profiler()  # noqa: profiler prints on GC
            if dataSet is None:
                dataSet = self.data

            invalidate = False
            if self.opts['pxMode'] and self.opts['useCache']:
                mask = dataSet['sourceRect']['w'] == 0
                if np.any(mask):
                    invalidate = True
                    coords = self.fragmentAtlas[
                        list(zip(*self._style(['symbol', 'size', 'pen', 'brush'], data=dataSet, idx=mask)))
                    ]
                    dataSet['sourceRect'][mask] = coords

                self._maybeRebuildAtlas()
            else:
                invalidate = True

            self._updateMaxSpotSizes(data=dataSet)

            if invalidate:
                self.invalidate()

        def _maybeRebuildAtlas(self, threshold=4, minlen=1000):
            n = len(self.fragmentAtlas)
            if (n > minlen) and (n > threshold * len(self.data)):
                self.fragmentAtlas.rebuild(
                    list(zip(*self._style(['symbol', 'size', 'pen', 'brush'])))
                )
                self.data['sourceRect'] = 0
                self.updateSpots()

        def _style(self, opts, data=None, idx=None, scale=None):
            if data is None:
                data = self.data

            if idx is None:
                idx = np.s_[:]

            for opt in opts:
                col = data[opt][idx]
                if col.base is not None:
                    col = col.copy()

                if self.opts['hoverable']:
                    val = self.opts['hover' + opt.title()]
                    if val != _DEFAULT_STYLE[opt]:
                        col[data['hovered'][idx]] = val

                col[np.equal(col, _DEFAULT_STYLE[opt])] = self.opts[opt]

                if opt == 'size' and scale is not None:
                    col *= scale

                yield col

        def _updateMaxSpotSizes(self, **kwargs):
            if self.opts['pxMode'] and self.opts['useCache']:
                w, pw = 0, self.fragmentAtlas.maxWidth
            else:
                w, pw = max(itertools.chain([(self._maxSpotWidth, self._maxSpotPxWidth)],
                                  self._measureSpotSizes(**kwargs)))
            self._maxSpotWidth = w
            self._maxSpotPxWidth = pw
            self.bounds = [None, None]

        def _measureSpotSizes(self, **kwargs):
            """Generate pairs (width, pxWidth) for spots in data"""
            styles = zip(*self._style(['size', 'pen'], **kwargs))

            if self.opts['pxMode']:
                for size, pen in styles:
                    yield 0, size + pen.widthF()
            else:
                for size, pen in styles:
                    if pen.isCosmetic():
                        yield size, pen.widthF()
                    else:
                        yield size + pen.widthF(), 0

        def clear(self):
            """Remove all spots from the scatter plot"""
            #self.clearItems()
            self._maxSpotWidth = 0
            self._maxSpotPxWidth = 0
            self.data = np.empty(0, dtype=self.data.dtype)
            self.bounds = [None, None]
            self.invalidate()

        def dataBounds(self, ax, frac=1.0, orthoRange=None):
            if frac >= 1.0 and orthoRange is None and self.bounds[ax] is not None:
                return self.bounds[ax]

            #self.prepareGeometryChange()
            if self.data is None or len(self.data) == 0:
                return (None, None)

            if ax == 0:
                d = self.data['x']
                d2 = self.data['y']
            elif ax == 1:
                d = self.data['y']
                d2 = self.data['x']
            else:
                raise ValueError("Invalid axis value")

            if orthoRange is not None:
                mask = (d2 >= orthoRange[0]) * (d2 <= orthoRange[1])
                d = d[mask]

                if d.size == 0:
                    return (None, None)

            if frac >= 1.0:
                self.bounds[ax] = (np.nanmin(d) - self._maxSpotWidth*0.7072, np.nanmax(d) + self._maxSpotWidth*0.7072)
                return self.bounds[ax]
            elif frac <= 0.0:
                raise Exception("Value for parameter 'frac' must be > 0. (got %s)" % str(frac))
            else:
                mask = np.isfinite(d)
                d = d[mask]
                return np.percentile(d, [50 * (1 - frac), 50 * (1 + frac)])

        def pixelPadding(self):
            return self._maxSpotPxWidth*0.7072

        def boundingRect(self):
            (xmn, xmx) = self.dataBounds(ax=0)
            (ymn, ymx) = self.dataBounds(ax=1)
            if xmn is None or xmx is None:
                xmn = 0
                xmx = 0
            if ymn is None or ymx is None:
                ymn = 0
                ymx = 0

            px = py = 0.0
            pxPad = self.pixelPadding()
            if pxPad > 0:
                # determine length of pixel in local x, y directions
                px, py = self.pixelVectors()
                try:
                    px = 0 if px is None else px.length()
                except OverflowError:
                    px = 0
                try:
                    py = 0 if py is None else py.length()
                except OverflowError:
                    py = 0

                # return bounds expanded by pixel size
                px *= pxPad
                py *= pxPad
            return QtCore.QRectF(xmn-px, ymn-py, (2*px)+xmx-xmn, (2*py)+ymx-ymn)

        def viewTransformChanged(self):
            self.prepareGeometryChange()
            GraphicsObject.viewTransformChanged(self)
            self.bounds = [None, None]

        def setExportMode(self, *args, **kwds):
            GraphicsObject.setExportMode(self, *args, **kwds)
            self.invalidate()

        @debug.warnOnException  ## raising an exception here causes crash
        def paint(self, p, option, widget):
            profiler = debug.Profiler()
            cmode = self.opts.get('compositionMode', None)
            if cmode is not None:
                p.setCompositionMode(cmode)
            #p.setPen(fn.mkPen('r'))
            #p.drawRect(self.boundingRect())

            if self._exportOpts is not False:
                aa = self._exportOpts.get('antialias', True)
                scale = self._exportOpts.get('resolutionScale', 1.0)  ## exporting to image; pixel resolution may have changed
            else:
                aa = self.opts['antialias']
                scale = 1.0

            if self.opts['pxMode'] is True:
                # Cull points that are outside view
                viewMask = self._maskAt(self.viewRect())

                # Map points using painter's world transform so they are drawn with pixel-valued sizes
                pts = np.vstack([self.data['x'], self.data['y']])
                pts = fn.transformCoordinates(p.transform(), pts)
                pts = fn.clip_array(pts, -2 ** 30, 2 ** 30)  # prevent Qt segmentation fault.
                p.resetTransform()

                if self.opts['useCache'] and self._exportOpts is False:
                    # Draw symbols from pre-rendered atlas

                    dpr = self.fragmentAtlas.devicePixelRatio()
                    if widget is not None and (dpr_new := widget.devicePixelRatioF()) != dpr:
                        # force a re-render if dpr changed
                        dpr = dpr_new
                        self.fragmentAtlas.setDevicePixelRatio(dpr)
                        self.fragmentAtlas.clear()
                        self.data['sourceRect'] = 0
                        self.updateSpots()

                    # x, y is the center of the target rect
                    xy = pts[:, viewMask].T
                    sr = self.data['sourceRect'][viewMask]

                    self._pixmapFragments.resize(sr.size)
                    frags = self._pixmapFragments.ndarray()
                    frags[:, 0:2] = xy
                    frags[:, 2:6] = np.frombuffer(sr, dtype=int).reshape((-1, 4)) # sx, sy, sw, sh
                    frags[:, 6:10] = [1/dpr, 1/dpr, 0.0, 1.0]   # scaleX, scaleY, rotation, opacity

                    profiler('prep')
                    drawargs = self._pixmapFragments.drawargs()
                    p.drawPixmapFragments(*drawargs, self.fragmentAtlas.pixmap)
                    profiler('draw')
                else:
                    # render each symbol individually
                    p.setRenderHint(p.RenderHint.Antialiasing, aa)

                    for pt, style in zip(
                            pts[:, viewMask].T,
                            zip(*(self._style(['symbol', 'size', 'pen', 'brush'], idx=viewMask, scale=scale)))
                    ):
                        p.resetTransform()
                        p.translate(*pt)
                        drawSymbol(p, *style)
            else:
                if self.picture is None:
                    self.picture = QtGui.QPicture()
                    p2 = QtGui.QPainter(self.picture)

                    for x, y, style in zip(
                            self.data['x'],
                            self.data['y'],
                            zip(*self._style(['symbol', 'size', 'pen', 'brush'], scale=scale))
                    ):
                        p2.resetTransform()
                        p2.translate(x, y)
                        drawSymbol(p2, *style)
                    p2.end()

                p.setRenderHint(p.RenderHint.Antialiasing, aa)
                self.picture.play(p)

        def points(self):
            m = np.equal(self.data['item'], None)
            for i in np.argwhere(m)[:, 0]:
                rec = self.data[i]
                if rec['item'] is None:
                    rec['item'] = SpotItem(rec, self, i)
            return self.data['item']

        def pointsAt(self, pos):
            return self.points()[self._maskAt(pos)][::-1]

        def _maskAt(self, obj):
            """
            Return a boolean mask indicating all points that overlap obj, a QPointF or QRectF.
            """
            if isinstance(obj, QtCore.QPointF):
                l = r = obj.x()
                t = b = obj.y()
            elif isinstance(obj, QtCore.QRectF):
                l = obj.left()
                r = obj.right()
                t = obj.top()
                b = obj.bottom()
            else:
                raise TypeError

            if self.opts['pxMode'] and self.opts['useCache']:
                w = self.data['sourceRect']['w']
                h = self.data['sourceRect']['h']
            else:
                s, = self._style(['size'])
                w = h = s

            w = w / 2
            h = h / 2

            if self.opts['pxMode']:
                # determine length of pixel in local x, y directions
                px, py = self.pixelVectors()
                try:
                    px = 0 if px is None else px.length()
                except OverflowError:
                    px = 0
                try:
                    py = 0 if py is None else py.length()
                except OverflowError:
                    py = 0
                w *= px
                h *= py

            return (self.data['visible']
                    & (self.data['x'] + w > l)
                    & (self.data['x'] - w < r)
                    & (self.data['y'] + h > t)
                    & (self.data['y'] - h < b))

        def mouseClickEvent(self, ev):
            if ev.button() == QtCore.Qt.MouseButton.LeftButton:
                pts = self.pointsAt(ev.pos())
                if len(pts) > 0:
                    self.ptsClicked = pts
                    ev.accept()
                    self.sigClicked.emit(self, self.ptsClicked, ev)
                else:
                    #print "no spots"
                    ev.ignore()
            else:
                ev.ignore()

        def hoverEvent(self, ev):
            if self.opts['hoverable']:
                old = self.data['hovered']

                if ev.exit:
                    new = np.zeros_like(self.data['hovered'])
                else:
                    new = self._maskAt(ev.pos())

                if self._hasHoverStyle():
                    self.data['sourceRect'][old ^ new] = 0
                    self.data['hovered'] = new
                    self.updateSpots()

                points = self.points()[new][::-1]

                # Show information about hovered points in a tool tip
                vb = self.getViewBox()
                if vb is not None and self.opts['tip'] is not None:
                    if len(points) > 0:
                        cutoff = 3
                        tip = [self.opts['tip'](x=pt.pos().x(), y=pt.pos().y(), data=pt.data())
                               for pt in points[:cutoff]]
                        if len(points) > cutoff:
                            tip.append('({} others...)'.format(len(points) - cutoff))
                        vb.setToolTip('\n\n'.join(tip))
                        self._toolTipCleared = False
                    elif not self._toolTipCleared:
                        vb.setToolTip("")
                        self._toolTipCleared = True

                self.sigHovered.emit(self, points, ev)

        def _hasHoverStyle(self):
            return any(self.opts['hover' + opt.title()] != _DEFAULT_STYLE[opt]
                       for opt in ['symbol', 'size', 'pen', 'brush'])

    class SpotItem(object):
        """
        Class referring to individual spots in a scatter plot.
        These can be retrieved by calling ScatterPlotItem.points() or
        by connecting to the ScatterPlotItem's click signals.
        """

        def __init__(self, data, plot, index):
            self._data = data
            self._index = index
            # SpotItems are kept in plot.data["items"] numpy object array which
            # does not support cyclic garbage collection (numpy issue 6581).
            # Keeping a strong ref to plot here would leak the cycle
            self.__plot_ref = weakref.ref(plot)

        @property
        def _plot(self):
            return self.__plot_ref()

        def data(self):
            """Return the user data associated with this spot."""
            return self._data['data']

        def index(self):
            """Return the index of this point as given in the scatter plot data."""
            return self._index

        def size(self):
            """Return the size of this spot.
            If the spot has no explicit size set, then return the ScatterPlotItem's default size instead."""
            if self._data['size'] == -1:
                return self._plot.opts['size']
            else:
                return self._data['size']

        def pos(self):
            return Point(self._data['x'], self._data['y'])

        def viewPos(self):
            return self._plot.mapToView(self.pos())

        def setSize(self, size):
            """Set the size of this spot.
            If the size is set to -1, then the ScatterPlotItem's default size
            will be used instead."""
            self._data['size'] = size
            self.updateItem()

        def symbol(self):
            """Return the symbol of this spot.
            If the spot has no explicit symbol set, then return the ScatterPlotItem's default symbol instead.
            """
            symbol = self._data['symbol']
            if symbol is None:
                symbol = self._plot.opts['symbol']
            try:
                n = int(symbol)
                symbol = list(Symbols.keys())[n % len(Symbols)]
            except:
                pass
            return symbol

        def setSymbol(self, symbol):
            """Set the symbol for this spot.
            If the symbol is set to '', then the ScatterPlotItem's default symbol will be used instead."""
            self._data['symbol'] = symbol
            self.updateItem()

        def pen(self):
            pen = self._data['pen']
            if pen is None:
                pen = self._plot.opts['pen']
            return fn.mkPen(pen)

        def setPen(self, *args, **kargs):
            """Set the outline pen for this spot"""
            self._data['pen'] = _mkPen(*args, **kargs)
            self.updateItem()

        def resetPen(self):
            """Remove the pen set for this spot; the scatter plot's default pen will be used instead."""
            self._data['pen'] = None  ## Note this is NOT the same as calling setPen(None)
            self.updateItem()

        def brush(self):
            brush = self._data['brush']
            if brush is None:
                brush = self._plot.opts['brush']
            return fn.mkBrush(brush)

        def setBrush(self, *args, **kargs):
            """Set the fill brush for this spot"""
            self._data['brush'] = _mkBrush(*args, **kargs)
            self.updateItem()

        def resetBrush(self):
            """Remove the brush set for this spot; the scatter plot's default brush will be used instead."""
            self._data['brush'] = None  ## Note this is NOT the same as calling setBrush(None)
            self.updateItem()

        def isVisible(self):
            return self._data['visible']

        def setVisible(self, visible):
            """Set whether or not this spot is visible."""
            self._data['visible'] = visible
            self.updateItem()

        def setData(self, data):
            """Set the user-data associated with this spot"""
            self._data['data'] = data

        def updateItem(self):
            self._data['sourceRect'] = (0, 0, 0, 0)  # numpy <=1.13.1 won't let us set this with a single zero
            self._plot.updateSpots(self._data.reshape(1))