Source code for pyqtgraph.functions

# -*- coding: utf-8 -*-
"""
functions.py -  Miscellaneous functions with no other home
Copyright 2010  Luke Campagnola
Distributed under MIT/X11 license. See license.txt for more information.
"""

from __future__ import division

import decimal
import re
import struct
import sys
import warnings
import math

import numpy as np
from .util.cupy_helper import getCupy
from .util.numba_helper import getNumbaFunctions

from . import debug, reload
from .Qt import QtGui, QtCore, QT_LIB, QtVersion
from . import Qt
from .metaarray import MetaArray
from collections import OrderedDict

# in order of appearance in this file.
# add new functions to this list only if they are to reside in pg namespace.
__all__ = [
    'siScale', 'siFormat', 'siParse', 'siEval', 'siApply',
    'Color', 'mkColor', 'mkBrush', 'mkPen', 'hsvColor',
    'CIELabColor', 'colorCIELab', 'colorDistance',
    'colorTuple', 'colorStr', 'intColor', 'glColor',
    'makeArrowPath', 'eq',
    'affineSliceCoords', 'affineSlice',
    'interweaveArrays', 'interpolateArray', 'subArray',
    'transformToArray', 'transformCoordinates',
    'solve3DTransform', 'solveBilinearTransform',
    'clip_scalar', 'clip_array', 'rescaleData', 'applyLookupTable',
    'makeRGBA', 'makeARGB',
    # 'try_fastpath_argb', 'ndarray_to_qimage',
    'makeQImage',
    # 'ndarray_from_qimage',
    'imageToArray', 'colorToAlpha',
    'gaussianFilter', 'downsample', 'arrayToQPath',
    # 'ndarray_from_qpolygonf', 'create_qpolygonf', 'arrayToQPolygonF',
    'isocurve', 'traceImage', 'isosurface',
    'invertQTransform',
    'pseudoScatter', 'toposort', 'disconnect', 'SignalBlock']


Colors = {
    'b': QtGui.QColor(0,0,255,255),
    'g': QtGui.QColor(0,255,0,255),
    'r': QtGui.QColor(255,0,0,255),
    'c': QtGui.QColor(0,255,255,255),
    'm': QtGui.QColor(255,0,255,255),
    'y': QtGui.QColor(255,255,0,255),
    'k': QtGui.QColor(0,0,0,255),
    'w': QtGui.QColor(255,255,255,255),
    'd': QtGui.QColor(150,150,150,255),
    'l': QtGui.QColor(200,200,200,255),
    's': QtGui.QColor(100,100,150,255),
}  

SI_PREFIXES = 'yzafpnµm kMGTPEZY'
SI_PREFIXES_ASCII = 'yzafpnum kMGTPEZY'
SI_PREFIX_EXPONENTS = dict([(SI_PREFIXES[i], (i-8)*3) for i in range(len(SI_PREFIXES))])
SI_PREFIX_EXPONENTS['u'] = -6

FLOAT_REGEX = re.compile(r'(?P<number>[+-]?((((\d+(\.\d*)?)|(\d*\.\d+))([eE][+-]?\d+)?)|((?i:nan)|(inf))))\s*((?P<siPrefix>[u' + SI_PREFIXES + r']?)(?P<suffix>\w.*))?$')
INT_REGEX = re.compile(r'(?P<number>[+-]?\d+)\s*(?P<siPrefix>[u' + SI_PREFIXES + r']?)(?P<suffix>.*)$')

    
[docs]def siScale(x, minVal=1e-25, allowUnicode=True): """ Return the recommended scale factor and SI prefix string for x. Example:: siScale(0.0001) # returns (1e6, 'μ') # This indicates that the number 0.0001 is best represented as 0.0001 * 1e6 = 100 μUnits """ if isinstance(x, decimal.Decimal): x = float(x) try: if not math.isfinite(x): return(1, '') except: raise if abs(x) < minVal: m = 0 else: m = int(clip_scalar(math.floor(math.log(abs(x))/math.log(1000)), -9.0, 9.0)) if m == 0: pref = '' elif m < -8 or m > 8: pref = 'e%d' % (m*3) else: if allowUnicode: pref = SI_PREFIXES[m+8] else: pref = SI_PREFIXES_ASCII[m+8] m1 = -3*m p = 10.**m1 return (p, pref)
[docs]def siFormat(x, precision=3, suffix='', space=True, error=None, minVal=1e-25, allowUnicode=True): """ Return the number x formatted in engineering notation with SI prefix. Example:: siFormat(0.0001, suffix='V') # returns "100 μV" """ if space is True: space = ' ' if space is False: space = '' (p, pref) = siScale(x, minVal, allowUnicode) if not (len(pref) > 0 and pref[0] == 'e'): pref = space + pref if error is None: fmt = "%." + str(precision) + "g%s%s" return fmt % (x*p, pref, suffix) else: if allowUnicode: plusminus = space + "±" + space else: plusminus = " +/- " fmt = "%." + str(precision) + "g%s%s%s%s" return fmt % (x*p, pref, suffix, plusminus, siFormat(error, precision=precision, suffix=suffix, space=space, minVal=minVal))
[docs]def siParse(s, regex=FLOAT_REGEX, suffix=None): """Convert a value written in SI notation to a tuple (number, si_prefix, suffix). Example:: siParse('100 µV") # returns ('100', 'µ', 'V') Note that in the above example, the µ symbol is the "micro sign" (UTF-8 0xC2B5), as opposed to the Greek letter mu (UTF-8 0xCEBC). Parameters ---------- s : str The string to parse. regex : re.Pattern, optional Compiled regular expression object for parsing. The default is a general-purpose regex for parsing floating point expressions, potentially containing an SI prefix and a suffix. suffix : str, optional Suffix to check for in ``s``. The default (None) indicates there may or may not be a suffix contained in the string and it is returned if found. An empty string ``""`` is handled differently: if the string contains a suffix, it is discarded. This enables interpreting characters following the numerical value as an SI prefix. """ s = s.strip() if suffix is not None and len(suffix) > 0: if s[-len(suffix):] != suffix: raise ValueError("String '%s' does not have the expected suffix '%s'" % (s, suffix)) s = s[:-len(suffix)] + 'X' # add a fake suffix so the regex still picks up the si prefix # special case: discard any extra characters if suffix is explicitly empty if suffix == "": s += 'X' m = regex.match(s) if m is None: raise ValueError('Cannot parse number "%s"' % s) try: sip = m.group('siPrefix') except IndexError: sip = '' if suffix is None: try: suf = m.group('suffix') except IndexError: suf = '' else: suf = suffix return m.group('number'), '' if sip is None else sip, '' if suf is None else suf
[docs]def siEval(s, typ=float, regex=FLOAT_REGEX, suffix=None): """ Convert a value written in SI notation to its equivalent prefixless value. Example:: siEval("100 μV") # returns 0.0001 """ val, siprefix, suffix = siParse(s, regex, suffix=suffix) v = typ(val) return siApply(v, siprefix)
def siApply(val, siprefix): """ """ n = SI_PREFIX_EXPONENTS[siprefix] if siprefix != '' else 0 if n > 0: return val * 10**n elif n < 0: # this case makes it possible to use Decimal objects here return val / 10**-n else: return val class Color(QtGui.QColor): def __init__(self, *args): QtGui.QColor.__init__(self, mkColor(*args)) def glColor(self): """Return (r,g,b,a) normalized for use in opengl""" return self.getRgbF() def __getitem__(self, ind): return (self.red, self.green, self.blue, self.alpha)[ind]()
[docs]def mkColor(*args): """ Convenience function for constructing QColor from a variety of argument types. Accepted arguments are: ================ ================================================ 'c' one of: r, g, b, c, m, y, k, w R, G, B, [A] integers 0-255 (R, G, B, [A]) tuple of integers 0-255 float greyscale, 0.0-1.0 int see :func:`intColor() <pyqtgraph.intColor>` (int, hues) see :func:`intColor() <pyqtgraph.intColor>` "#RGB" hexadecimal strings prefixed with '#' "#RGBA" previously allowed use without prefix is deprecated and "#RRGGBB" will be removed in 0.13 "#RRGGBBAA" QColor QColor instance; makes a copy. ================ ================================================ """ err = 'Not sure how to make a color from "%s"' % str(args) if len(args) == 1: if isinstance(args[0], str): c = args[0] if len(c) == 1: try: return Colors[c] except KeyError: raise ValueError('No color named "%s"' % c) have_alpha = len(c) in [5, 9] and c[0] == '#' # "#RGBA" and "#RRGGBBAA" if not have_alpha: # try parsing SVG named colors, including "#RGB" and "#RRGGBB". # note that QColor.setNamedColor() treats a 9-char hex string as "#AARRGGBB". qcol = QtGui.QColor() qcol.setNamedColor(c) if qcol.isValid(): return qcol # on failure, fallback to pyqtgraph parsing # this includes the deprecated case of non-#-prefixed hex strings if c[0] == '#': c = c[1:] else: warnings.warn( "Parsing of hex strings that do not start with '#' is" "deprecated and support will be removed in 0.13", DeprecationWarning, stacklevel=2 ) if len(c) == 3: r = int(c[0]*2, 16) g = int(c[1]*2, 16) b = int(c[2]*2, 16) a = 255 elif len(c) == 4: r = int(c[0]*2, 16) g = int(c[1]*2, 16) b = int(c[2]*2, 16) a = int(c[3]*2, 16) elif len(c) == 6: r = int(c[0:2], 16) g = int(c[2:4], 16) b = int(c[4:6], 16) a = 255 elif len(c) == 8: r = int(c[0:2], 16) g = int(c[2:4], 16) b = int(c[4:6], 16) a = int(c[6:8], 16) else: raise ValueError(f"Unknown how to convert string {c} to color") elif isinstance(args[0], QtGui.QColor): return QtGui.QColor(args[0]) elif np.issubdtype(type(args[0]), np.floating): r = g = b = int(args[0] * 255) a = 255 elif hasattr(args[0], '__len__'): if len(args[0]) == 3: r, g, b = args[0] a = 255 elif len(args[0]) == 4: r, g, b, a = args[0] elif len(args[0]) == 2: return intColor(*args[0]) else: raise TypeError(err) elif np.issubdtype(type(args[0]), np.integer): return intColor(args[0]) else: raise TypeError(err) elif len(args) == 3: r, g, b = args a = 255 elif len(args) == 4: r, g, b, a = args else: raise TypeError(err) args = [int(a) if np.isfinite(a) else 0 for a in (r, g, b, a)] return QtGui.QColor(*args)
[docs]def mkBrush(*args, **kwds): """ | Convenience function for constructing Brush. | This function always constructs a solid brush and accepts the same arguments as :func:`mkColor() <pyqtgraph.mkColor>` | Calling mkBrush(None) returns an invisible brush. """ if 'color' in kwds: color = kwds['color'] elif len(args) == 1: arg = args[0] if arg is None: return QtGui.QBrush(QtCore.Qt.BrushStyle.NoBrush) elif isinstance(arg, QtGui.QBrush): return QtGui.QBrush(arg) else: color = arg elif len(args) > 1: color = args return QtGui.QBrush(mkColor(color))
[docs]def mkPen(*args, **kargs): """ Convenience function for constructing QPen. Examples:: mkPen(color) mkPen(color, width=2) mkPen(cosmetic=False, width=4.5, color='r') mkPen({'color': "#FF0", width: 2}) mkPen(None) # (no pen) In these examples, *color* may be replaced with any arguments accepted by :func:`mkColor() <pyqtgraph.mkColor>` """ color = kargs.get('color', None) width = kargs.get('width', 1) style = kargs.get('style', None) dash = kargs.get('dash', None) cosmetic = kargs.get('cosmetic', True) hsv = kargs.get('hsv', None) if len(args) == 1: arg = args[0] if isinstance(arg, dict): return mkPen(**arg) if isinstance(arg, QtGui.QPen): return QtGui.QPen(arg) ## return a copy of this pen elif arg is None: style = QtCore.Qt.PenStyle.NoPen else: color = arg if len(args) > 1: color = args if color is None: color = mkColor('l') if hsv is not None: color = hsvColor(*hsv) else: color = mkColor(color) pen = QtGui.QPen(QtGui.QBrush(color), width) pen.setCosmetic(cosmetic) if style is not None: pen.setStyle(style) if dash is not None: pen.setDashPattern(dash) return pen
[docs]def hsvColor(hue, sat=1.0, val=1.0, alpha=1.0): """Generate a QColor from HSVa values. (all arguments are float 0.0-1.0)""" return QtGui.QColor.fromHsvF(hue, sat, val, alpha)
# Matrices and math taken from "CIELab Color Space" by Gernot Hoffmann # http://docs-hoffmann.de/cielab03022003.pdf MATRIX_XYZ_FROM_RGB = np.array( ( ( 0.4124, 0.3576, 0.1805), ( 0.2126, 0.7152, 0.0722), ( 0.0193, 0.1192, 0.9505) ) ) MATRIX_RGB_FROM_XYZ = np.array( ( ( 3.2410,-1.5374,-0.4985), (-0.9692, 1.8760, 0.0416), ( 0.0556,-0.2040, 1.0570) ) ) VECTOR_XYZn = np.array( ( 0.9505, 1.0000, 1.0891) ) # white reference at illuminant D65
[docs]def CIELabColor(L, a, b, alpha=1.0): """ Generates as QColor from CIE L*a*b* values. Parameters ---------- L: float Lightness value ranging from 0 to 100 a, b: float (green/red) and (blue/yellow) coordinates, typically -127 to +127. alpha: float, optional Opacity, ranging from 0 to 1 Notes ----- The CIE L*a*b* color space parametrizes color in terms of a luminance `L` and the `a` and `b` coordinates that locate the hue in terms of a "green to red" and a "blue to yellow" axis. These coordinates seek to parametrize human color preception in such a way that the Euclidean distance between the coordinates of two colors represents the visual difference between these colors. In particular, the difference ΔE = sqrt( (L1-L2)² + (a1-a2)² + (b1-b2)² ) = 2.3 is considered the smallest "just noticeable difference" between colors. This simple equation represents the CIE76 standard. Later standards CIE94 and CIE2000 refine the difference calculation ΔE, while maintaining the L*a*b* coordinates. Alternative (and arguably more accurate) methods exist to quantify color difference, but the CIELab color space remains a convenient approximation. Under a known illumination, assumed to be white standard illuminant D65 here, a CIELab color induces a response in the human eye that is described by the tristimulus value XYZ. Once this is known, an sRGB color can be calculated to induce the same response. More information and underlying mathematics can be found in e.g. "CIELab Color Space" by Gernot Hoffmann, available at http://docs-hoffmann.de/cielab03022003.pdf . Also see :func:`colorDistance() <pyqtgraph.colorDistance>`. """ # convert to tristimulus XYZ values vec_XYZ = np.full(3, ( L +16)/116 ) # Y1 = (L+16)/116 vec_XYZ[0] += a / 500 # X1 = (L+16)/116 + a/500 vec_XYZ[2] -= b / 200 # Z1 = (L+16)/116 - b/200 for idx, val in enumerate(vec_XYZ): if val > 0.20689: vec_XYZ[idx] = vec_XYZ[idx]**3 else: vec_XYZ[idx] = (vec_XYZ[idx] - 16/116) / 7.787 vec_XYZ = VECTOR_XYZn * vec_XYZ # apply white reference # print(f'XYZ: {vec_XYZ}') # convert XYZ to linear RGB vec_RGB = MATRIX_RGB_FROM_XYZ @ vec_XYZ # gamma-encode linear RGB arr_sRGB = np.zeros(3) for idx, val in enumerate( vec_RGB[:3] ): if val > 0.0031308: # (t) RGB value for linear/exponential transition arr_sRGB[idx] = 1.055 * val**(1/2.4) - 0.055 else: arr_sRGB[idx] = 12.92 * val # (s) arr_sRGB = clip_array( arr_sRGB, 0.0, 1.0 ) # avoid QColor errors return QtGui.QColor.fromRgbF( *arr_sRGB, alpha )
[docs]def colorCIELab(qcol): """ Describes a QColor by an array of CIE L*a*b* values. Also see :func:`CIELabColor() <pyqtgraph.CIELabColor>` . Parameters ---------- qcol: QColor QColor to be converted Returns ------- NumPy array Color coordinates `[L, a, b]`. """ srgb = qcol.getRgbF()[:3] # get sRGB values from QColor # convert gamma-encoded sRGB to linear: vec_RGB = np.zeros(3) for idx, val in enumerate( srgb ): if val > (12.92 * 0.0031308): # coefficients (s) * (t) vec_RGB[idx] = ((val+0.055)/1.055)**2.4 else: vec_RGB[idx] = val / 12.92 # (s) coefficient # converted linear RGB to tristimulus XYZ: vec_XYZ = MATRIX_XYZ_FROM_RGB @ vec_RGB # normalize with white reference and convert to L*a*b* values vec_XYZ1 = vec_XYZ / VECTOR_XYZn for idx, val in enumerate(vec_XYZ1): if val > 0.008856: vec_XYZ1[idx] = vec_XYZ1[idx]**(1/3) else: vec_XYZ1[idx] = 7.787*vec_XYZ1[idx] + 16/116 vec_Lab = np.array([ 116 * vec_XYZ1[1] - 16, # Y1 500 * (vec_XYZ1[0] - vec_XYZ1[1]), # X1 - Y1 200 * (vec_XYZ1[1] - vec_XYZ1[2])] ) # Y1 - Z1 return vec_Lab
[docs]def colorDistance(colors, metric='CIE76'): """ Returns the perceptual distances between a sequence of QColors. See :func:`CIELabColor() <pyqtgraph.CIELabColor>` for more information. Parameters ---------- colors: list of QColor Two or more colors to calculate the distances between. metric: string, optional Metric used to determined the difference. Only 'CIE76' is supported at this time, where a distance of 2.3 is considered a "just noticeable difference". The default may change as more metrics become available. Returns ------- List The `N-1` sequential distances between `N` colors. """ metric = metric.upper() if len(colors) < 1: return np.array([], dtype=np.float) if metric == 'CIE76': dist = [] lab1 = None for col in colors: lab2 = colorCIELab(col) if lab1 is None: #initialize on first element lab1 = lab2 continue dE = math.sqrt( np.sum( (lab1-lab2)**2 ) ) dist.append(dE) lab1 = lab2 return np.array(dist) raise ValueError(f'Metric {metric} is not available.')
[docs]def colorTuple(c): """Return a tuple (R,G,B,A) from a QColor""" return c.getRgb()
[docs]def colorStr(c): """Generate a hex string code from a QColor""" return ('%02x'*4) % colorTuple(c)
[docs]def intColor(index, hues=9, values=1, maxValue=255, minValue=150, maxHue=360, minHue=0, sat=255, alpha=255): """ Creates a QColor from a single index. Useful for stepping through a predefined list of colors. The argument *index* determines which color from the set will be returned. All other arguments determine what the set of predefined colors will be Colors are chosen by cycling across hues while varying the value (brightness). By default, this selects from a list of 9 hues.""" hues = int(hues) values = int(values) ind = int(index) % (hues * values) indh = ind % hues indv = ind // hues if values > 1: v = minValue + indv * ((maxValue-minValue) // (values-1)) else: v = maxValue h = minHue + (indh * (maxHue-minHue)) // hues return QtGui.QColor.fromHsv(h, sat, v, alpha)
[docs]def glColor(*args, **kargs): """ Convert a color to OpenGL color format (r,g,b,a) floats 0.0-1.0 Accepts same arguments as :func:`mkColor <pyqtgraph.mkColor>`. """ c = mkColor(*args, **kargs) return c.getRgbF()
def makeArrowPath(headLen=20, headWidth=None, tipAngle=20, tailLen=20, tailWidth=3, baseAngle=0): """ Construct a path outlining an arrow with the given dimensions. The arrow points in the -x direction with tip positioned at 0,0. If *headWidth* is supplied, it overrides *tipAngle* (in degrees). If *tailLen* is None, no tail will be drawn. """ if headWidth is None: headWidth = headLen * math.tan(math.radians(tipAngle * 0.5)) path = QtGui.QPainterPath() path.moveTo(0,0) path.lineTo(headLen, -headWidth) if tailLen is None: innerY = headLen - headWidth * math.tan(math.radians(baseAngle)) path.lineTo(innerY, 0) else: tailWidth *= 0.5 innerY = headLen - (headWidth-tailWidth) * math.tan(math.radians(baseAngle)) path.lineTo(innerY, -tailWidth) path.lineTo(headLen + tailLen, -tailWidth) path.lineTo(headLen + tailLen, tailWidth) path.lineTo(innerY, tailWidth) path.lineTo(headLen, headWidth) path.lineTo(0,0) return path
[docs]def eq(a, b): """The great missing equivalence function: Guaranteed evaluation to a single bool value. This function has some important differences from the == operator: 1. Returns True if a IS b, even if a==b still evaluates to False. 2. While a is b will catch the case with np.nan values, special handling is done for distinct float('nan') instances using math.isnan. 3. Tests for equivalence using ==, but silently ignores some common exceptions that can occur (AtrtibuteError, ValueError). 4. When comparing arrays, returns False if the array shapes are not the same. 5. When comparing arrays of the same shape, returns True only if all elements are equal (whereas the == operator would return a boolean array). 6. Collections (dict, list, etc.) must have the same type to be considered equal. One consequence is that comparing a dict to an OrderedDict will always return False. """ if a is b: return True # The above catches np.nan, but not float('nan') if isinstance(a, float) and isinstance(b, float): if math.isnan(a) and math.isnan(b): return True # Avoid comparing large arrays against scalars; this is expensive and we know it should return False. aIsArr = isinstance(a, (np.ndarray, MetaArray)) bIsArr = isinstance(b, (np.ndarray, MetaArray)) if (aIsArr or bIsArr) and type(a) != type(b): return False # If both inputs are arrays, we can speeed up comparison if shapes / dtypes don't match # NOTE: arrays of dissimilar type should be considered unequal even if they are numerically # equal because they may behave differently when computed on. if aIsArr and bIsArr and (a.shape != b.shape or a.dtype != b.dtype): return False # Recursively handle common containers if isinstance(a, dict) and isinstance(b, dict): if type(a) != type(b) or len(a) != len(b): return False if set(a.keys()) != set(b.keys()): return False for k, v in a.items(): if not eq(v, b[k]): return False if isinstance(a, OrderedDict) or sys.version_info >= (3, 7): for a_item, b_item in zip(a.items(), b.items()): if not eq(a_item, b_item): return False return True if isinstance(a, (list, tuple)) and isinstance(b, (list, tuple)): if type(a) != type(b) or len(a) != len(b): return False for v1,v2 in zip(a, b): if not eq(v1, v2): return False return True # Test for equivalence. # If the test raises a recognized exception, then return Falase try: try: # Sometimes running catch_warnings(module=np) generates AttributeError ??? catcher = warnings.catch_warnings(module=np) # ignore numpy futurewarning (numpy v. 1.10) catcher.__enter__() except Exception: catcher = None e = a==b except (ValueError, AttributeError): return False except: print('failed to evaluate equivalence for:') print(" a:", str(type(a)), str(a)) print(" b:", str(type(b)), str(b)) raise finally: if catcher is not None: catcher.__exit__(None, None, None) t = type(e) if t is bool: return e elif t is np.bool_: return bool(e) elif isinstance(e, np.ndarray) or (hasattr(e, 'implements') and e.implements('MetaArray')): try: ## disaster: if a is an empty array and b is not, then e.all() is True if a.shape != b.shape: return False except: return False if (hasattr(e, 'implements') and e.implements('MetaArray')): return e.asarray().all() else: return e.all() else: raise TypeError("== operator returned type %s" % str(type(e)))
def affineSliceCoords(shape, origin, vectors, axes): """Return the array of coordinates used to sample data arrays in affineSlice(). """ # sanity check if len(shape) != len(vectors): raise Exception("shape and vectors must have same length.") if len(origin) != len(axes): raise Exception("origin and axes must have same length.") for v in vectors: if len(v) != len(axes): raise Exception("each vector must be same length as axes.") shape = list(map(np.ceil, shape)) ## make sure vectors are arrays if not isinstance(vectors, np.ndarray): vectors = np.array(vectors) if not isinstance(origin, np.ndarray): origin = np.array(origin) origin.shape = (len(axes),) + (1,)*len(shape) ## Build array of sample locations. grid = np.mgrid[tuple([slice(0,x) for x in shape])] ## mesh grid of indexes x = (grid[np.newaxis,...] * vectors.transpose()[(Ellipsis,) + (np.newaxis,)*len(shape)]).sum(axis=1) ## magic x += origin return x
[docs]def affineSlice(data, shape, origin, vectors, axes, order=1, returnCoords=False, **kargs): """ Take a slice of any orientation through an array. This is useful for extracting sections of multi-dimensional arrays such as MRI images for viewing as 1D or 2D data. The slicing axes are aribtrary; they do not need to be orthogonal to the original data or even to each other. It is possible to use this function to extract arbitrary linear, rectangular, or parallelepiped shapes from within larger datasets. The original data is interpolated onto a new array of coordinates using either interpolateArray if order<2 or scipy.ndimage.map_coordinates otherwise. For a graphical interface to this function, see :func:`ROI.getArrayRegion <pyqtgraph.ROI.getArrayRegion>` ============== ==================================================================================================== **Arguments:** *data* (ndarray) the original dataset *shape* the shape of the slice to take (Note the return value may have more dimensions than len(shape)) *origin* the location in the original dataset that will become the origin of the sliced data. *vectors* list of unit vectors which point in the direction of the slice axes. Each vector must have the same length as *axes*. If the vectors are not unit length, the result will be scaled relative to the original data. If the vectors are not orthogonal, the result will be sheared relative to the original data. *axes* The axes in the original dataset which correspond to the slice *vectors* *order* The order of spline interpolation. Default is 1 (linear). See scipy.ndimage.map_coordinates for more information. *returnCoords* If True, return a tuple (result, coords) where coords is the array of coordinates used to select values from the original dataset. *All extra keyword arguments are passed to scipy.ndimage.map_coordinates.* -------------------------------------------------------------------------------------------------------------------- ============== ==================================================================================================== Note the following must be true: | len(shape) == len(vectors) | len(origin) == len(axes) == len(vectors[i]) Example: start with a 4D fMRI data set, take a diagonal-planar slice out of the last 3 axes * data = array with dims (time, x, y, z) = (100, 40, 40, 40) * The plane to pull out is perpendicular to the vector (x,y,z) = (1,1,1) * The origin of the slice will be at (x,y,z) = (40, 0, 0) * We will slice a 20x20 plane from each timepoint, giving a final shape (100, 20, 20) The call for this example would look like:: affineSlice(data, shape=(20,20), origin=(40,0,0), vectors=((-1, 1, 0), (-1, 0, 1)), axes=(1,2,3)) """ x = affineSliceCoords(shape, origin, vectors, axes) ## transpose data so slice axes come first trAx = list(range(data.ndim)) for ax in axes: trAx.remove(ax) tr1 = tuple(axes) + tuple(trAx) data = data.transpose(tr1) #print "tr1:", tr1 ## dims are now [(slice axes), (other axes)] if order > 1: try: import scipy.ndimage except ImportError: raise ImportError("Interpolating with order > 1 requires the scipy.ndimage module, but it could not be imported.") # iterate manually over unused axes since map_coordinates won't do it for us extraShape = data.shape[len(axes):] output = np.empty(tuple(shape) + extraShape, dtype=data.dtype) for inds in np.ndindex(*extraShape): ind = (Ellipsis,) + inds output[ind] = scipy.ndimage.map_coordinates(data[ind], x, order=order, **kargs) else: # map_coordinates expects the indexes as the first axis, whereas # interpolateArray expects indexes at the last axis. tr = tuple(range(1, x.ndim)) + (0,) output = interpolateArray(data, x.transpose(tr), order=order) tr = list(range(output.ndim)) trb = [] for i in range(min(axes)): ind = tr1.index(i) + (len(shape)-len(axes)) tr.remove(ind) trb.append(ind) tr2 = tuple(trb+tr) ## Untranspose array before returning output = output.transpose(tr2) if returnCoords: return (output, x) else: return output
def interweaveArrays(*args): """ Parameters ---------- args : numpy.ndarray series of 1D numpy arrays of the same length and dtype Returns ------- numpy.ndarray A numpy array with all the input numpy arrays interwoven Examples -------- >>> result = interweaveArrays(numpy.ndarray([0, 2, 4]), numpy.ndarray([1, 3, 5])) >>> result array([0, 1, 2, 3, 4, 5]) """ size = sum(x.size for x in args) result = np.empty((size,), dtype=args[0].dtype) n = len(args) for index, array in enumerate(args): result[index::n] = array return result def interpolateArray(data, x, default=0.0, order=1): """ N-dimensional interpolation similar to scipy.ndimage.map_coordinates. This function returns linearly-interpolated values sampled from a regular grid of data. It differs from `ndimage.map_coordinates` by allowing broadcasting within the input array. ============== =========================================================================================== **Arguments:** *data* Array of any shape containing the values to be interpolated. *x* Array with (shape[-1] <= data.ndim) containing the locations within *data* to interpolate. (note: the axes for this argument are transposed relative to the same argument for `ndimage.map_coordinates`). *default* Value to return for locations in *x* that are outside the bounds of *data*. *order* Order of interpolation: 0=nearest, 1=linear. ============== =========================================================================================== Returns array of shape (x.shape[:-1] + data.shape[x.shape[-1]:]) For example, assume we have the following 2D image data:: >>> data = np.array([[1, 2, 4 ], [10, 20, 40 ], [100, 200, 400]]) To compute a single interpolated point from this data:: >>> x = np.array([(0.5, 0.5)]) >>> interpolateArray(data, x) array([ 8.25]) To compute a 1D list of interpolated locations:: >>> x = np.array([(0.5, 0.5), (1.0, 1.0), (1.0, 2.0), (1.5, 0.0)]) >>> interpolateArray(data, x) array([ 8.25, 20. , 40. , 55. ]) To compute a 2D array of interpolated locations:: >>> x = np.array([[(0.5, 0.5), (1.0, 2.0)], [(1.0, 1.0), (1.5, 0.0)]]) >>> interpolateArray(data, x) array([[ 8.25, 40. ], [ 20. , 55. ]]) ..and so on. The *x* argument may have any shape as long as ```x.shape[-1] <= data.ndim```. In the case that ```x.shape[-1] < data.ndim```, then the remaining axes are simply broadcasted as usual. For example, we can interpolate one location from an entire row of the data:: >>> x = np.array([[0.5]]) >>> interpolateArray(data, x) array([[ 5.5, 11. , 22. ]]) This is useful for interpolating from arrays of colors, vertexes, etc. """ if order not in (0, 1): raise ValueError("interpolateArray requires order=0 or 1 (got %s)" % order) prof = debug.Profiler() nd = data.ndim md = x.shape[-1] if md > nd: raise TypeError("x.shape[-1] must be less than or equal to data.ndim") totalMask = np.ones(x.shape[:-1], dtype=bool) # keep track of out-of-bound indexes if order == 0: xinds = np.round(x).astype(int) # NOTE: for 0.5 this rounds to the nearest *even* number for ax in range(md): mask = (xinds[...,ax] >= 0) & (xinds[...,ax] <= data.shape[ax]-1) xinds[...,ax][~mask] = 0 # keep track of points that need to be set to default totalMask &= mask result = data[tuple([xinds[...,i] for i in range(xinds.shape[-1])])] elif order == 1: # First we generate arrays of indexes that are needed to # extract the data surrounding each point fields = np.mgrid[(slice(0,order+1),) * md] xmin = np.floor(x).astype(int) xmax = xmin + 1 indexes = np.concatenate([xmin[np.newaxis, ...], xmax[np.newaxis, ...]]) fieldInds = [] for ax in range(md): mask = (xmin[...,ax] >= 0) & (x[...,ax] <= data.shape[ax]-1) # keep track of points that need to be set to default totalMask &= mask # ..and keep track of indexes that are out of bounds # (note that when x[...,ax] == data.shape[ax], then xmax[...,ax] will be out # of bounds, but the interpolation will work anyway) mask &= (xmax[...,ax] < data.shape[ax]) axisIndex = indexes[...,ax][fields[ax]] axisIndex[axisIndex < 0] = 0 axisIndex[axisIndex >= data.shape[ax]] = 0 fieldInds.append(axisIndex) prof() # Get data values surrounding each requested point fieldData = data[tuple(fieldInds)] prof() ## Interpolate s = np.empty((md,) + fieldData.shape, dtype=float) dx = x - xmin # reshape fields for arithmetic against dx for ax in range(md): f1 = fields[ax].reshape(fields[ax].shape + (1,)*(dx.ndim-1)) sax = f1 * dx[...,ax] + (1-f1) * (1-dx[...,ax]) sax = sax.reshape(sax.shape + (1,) * (s.ndim-1-sax.ndim)) s[ax] = sax s = np.product(s, axis=0) result = fieldData * s for i in range(md): result = result.sum(axis=0) prof() if totalMask.ndim > 0: result[~totalMask] = default else: if totalMask is False: result[:] = default prof() return result def subArray(data, offset, shape, stride): """ Unpack a sub-array from *data* using the specified offset, shape, and stride. Note that *stride* is specified in array elements, not bytes. For example, we have a 2x3 array packed in a 1D array as follows:: data = [_, _, 00, 01, 02, _, 10, 11, 12, _] Then we can unpack the sub-array with this call:: subArray(data, offset=2, shape=(2, 3), stride=(4, 1)) ..which returns:: [[00, 01, 02], [10, 11, 12]] This function operates only on the first axis of *data*. So changing the input in the example above to have shape (10, 7) would cause the output to have shape (2, 3, 7). """ data = np.ascontiguousarray(data)[offset:] shape = tuple(shape) extraShape = data.shape[1:] strides = list(data.strides[::-1]) itemsize = strides[-1] for s in stride[1::-1]: strides.append(itemsize * s) strides = tuple(strides[::-1]) return np.ndarray(buffer=data, shape=shape+extraShape, strides=strides, dtype=data.dtype)
[docs]def transformToArray(tr): """ Given a QTransform, return a 3x3 numpy array. Given a QMatrix4x4, return a 4x4 numpy array. Example: map an array of x,y coordinates through a transform:: ## coordinates to map are (1,5), (2,6), (3,7), and (4,8) coords = np.array([[1,2,3,4], [5,6,7,8], [1,1,1,1]]) # the extra '1' coordinate is needed for translation to work ## Make an example transform tr = QtGui.QTransform() tr.translate(3,4) tr.scale(2, 0.1) ## convert to array m = pg.transformToArray()[:2] # ignore the perspective portion of the transformation ## map coordinates through transform mapped = np.dot(m, coords) """ #return np.array([[tr.m11(), tr.m12(), tr.m13()],[tr.m21(), tr.m22(), tr.m23()],[tr.m31(), tr.m32(), tr.m33()]]) ## The order of elements given by the method names m11..m33 is misleading-- ## It is most common for x,y translation to occupy the positions 1,3 and 2,3 in ## a transformation matrix. However, with QTransform these values appear at m31 and m32. ## So the correct interpretation is transposed: if isinstance(tr, QtGui.QTransform): return np.array([[tr.m11(), tr.m21(), tr.m31()], [tr.m12(), tr.m22(), tr.m32()], [tr.m13(), tr.m23(), tr.m33()]]) elif isinstance(tr, QtGui.QMatrix4x4): return np.array(tr.copyDataTo()).reshape(4,4) else: raise Exception("Transform argument must be either QTransform or QMatrix4x4.")
[docs]def transformCoordinates(tr, coords, transpose=False): """ Map a set of 2D or 3D coordinates through a QTransform or QMatrix4x4. The shape of coords must be (2,...) or (3,...) The mapping will _ignore_ any perspective transformations. For coordinate arrays with ndim=2, this is basically equivalent to matrix multiplication. Most arrays, however, prefer to put the coordinate axis at the end (eg. shape=(...,3)). To allow this, use transpose=True. """ if transpose: ## move last axis to beginning. This transposition will be reversed before returning the mapped coordinates. coords = coords.transpose((coords.ndim-1,) + tuple(range(0,coords.ndim-1))) nd = coords.shape[0] if isinstance(tr, np.ndarray): m = tr else: m = transformToArray(tr) m = m[:m.shape[0]-1] # remove perspective ## If coords are 3D and tr is 2D, assume no change for Z axis if m.shape == (2,3) and nd == 3: m2 = np.zeros((3,4)) m2[:2, :2] = m[:2,:2] m2[:2, 3] = m[:2,2] m2[2,2] = 1 m = m2 ## if coords are 2D and tr is 3D, ignore Z axis if m.shape == (3,4) and nd == 2: m2 = np.empty((2,3)) m2[:,:2] = m[:2,:2] m2[:,2] = m[:2,3] m = m2 ## reshape tr and coords to prepare for multiplication m = m.reshape(m.shape + (1,)*(coords.ndim-1)) coords = coords[np.newaxis, ...] # separate scale/rotate and translation translate = m[:,-1] m = m[:, :-1] ## map coordinates and return mapped = (m*coords).sum(axis=1) ## apply scale/rotate mapped += translate if transpose: ## move first axis to end. mapped = mapped.transpose(tuple(range(1,mapped.ndim)) + (0,)) return mapped
[docs]def solve3DTransform(points1, points2): """ Find a 3D transformation matrix that maps points1 onto points2. Points must be specified as either lists of 4 Vectors or (4, 3) arrays. """ import numpy.linalg pts = [] for inp in (points1, points2): if isinstance(inp, np.ndarray): A = np.empty((4,4), dtype=float) A[:,:3] = inp[:,:3] A[:,3] = 1.0 else: A = np.array([[inp[i].x(), inp[i].y(), inp[i].z(), 1] for i in range(4)]) pts.append(A) ## solve 3 sets of linear equations to determine transformation matrix elements matrix = np.zeros((4,4)) for i in range(3): ## solve Ax = B; x is one row of the desired transformation matrix matrix[i] = numpy.linalg.solve(pts[0], pts[1][:,i]) return matrix
[docs]def solveBilinearTransform(points1, points2): """ Find a bilinear transformation matrix (2x4) that maps points1 onto points2. Points must be specified as a list of 4 Vector, Point, QPointF, etc. To use this matrix to map a point [x,y]:: mapped = np.dot(matrix, [x*y, x, y, 1]) """ import numpy.linalg ## A is 4 rows (points) x 4 columns (xy, x, y, 1) ## B is 4 rows (points) x 2 columns (x, y) A = np.array([[points1[i].x()*points1[i].y(), points1[i].x(), points1[i].y(), 1] for i in range(4)]) B = np.array([[points2[i].x(), points2[i].y()] for i in range(4)]) ## solve 2 sets of linear equations to determine transformation matrix elements matrix = np.zeros((2,4)) for i in range(2): matrix[i] = numpy.linalg.solve(A, B[:,i]) ## solve Ax = B; x is one row of the desired transformation matrix return matrix
def clip_scalar(val, vmin, vmax): """ convenience function to avoid using np.clip for scalar values """ return vmin if val < vmin else vmax if val > vmax else val def clip_array(arr, vmin, vmax, out=None): # replacement for np.clip due to regression in # performance since numpy 1.17 # https://github.com/numpy/numpy/issues/14281 if vmin is None and vmax is None: # let np.clip handle the error return np.clip(arr, vmin, vmax, out=out) if vmin is None: return np.core.umath.minimum(arr, vmax, out=out) elif vmax is None: return np.core.umath.maximum(arr, vmin, out=out) elif sys.platform == 'win32': # Windows umath.clip is slower than umath.maximum(umath.minimum) if out is None: out = np.empty_like(arr) out = np.core.umath.minimum(arr, vmax, out=out) return np.core.umath.maximum(out, vmin, out=out) else: return np.core.umath.clip(arr, vmin, vmax, out=out) def _rescaleData_nditer(data_in, scale, offset, work_dtype, out_dtype, clip): """Refer to documentation for rescaleData()""" data_out = np.empty_like(data_in, dtype=out_dtype) # integer clip operations are faster than float clip operations # so test to see if we can perform integer clipping fits_int32 = False if data_in.dtype.kind in 'ui' and out_dtype.kind in 'ui': # estimate whether data range after rescale will fit within an int32. # this means that the input dtype should be an 8-bit or 16-bit integer type. # casting to an int32 will lose the fractional part, therefore the # output dtype must be an integer kind. lim_in = np.iinfo(data_in.dtype) # convert numpy scalar to python scalar to avoid overflow warnings lo = offset.item(0) if isinstance(offset, np.number) else offset dst_bounds = scale * (lim_in.min - lo), scale * (lim_in.max - lo) if dst_bounds[1] < dst_bounds[0]: dst_bounds = dst_bounds[1], dst_bounds[0] lim32 = np.iinfo(np.int32) fits_int32 = lim32.min < dst_bounds[0] and dst_bounds[1] < lim32.max it = np.nditer([data_in, data_out], flags=['external_loop', 'buffered'], op_flags=[['readonly'], ['writeonly', 'no_broadcast']], op_dtypes=[None, work_dtype], casting='unsafe', buffersize=32768) with it: for x, y in it: y[...] = x y -= offset y *= scale # Clip before converting dtype to avoid overflow if clip is not None: if fits_int32: # converts to int32, clips back to float32 np.core.umath.clip(y.astype(np.int32), clip[0], clip[1], out=y) else: clip_array(y, clip[0], clip[1], out=y) return data_out
[docs]def rescaleData(data, scale, offset, dtype=None, clip=None): """Return data rescaled and optionally cast to a new dtype. The scaling operation is:: data => (data-offset) * scale """ if dtype is None: out_dtype = data.dtype else: out_dtype = np.dtype(dtype) if out_dtype.kind in 'ui': lim = np.iinfo(out_dtype) if clip is None: # don't let rescale cause integer overflow clip = lim.min, lim.max clip = max(clip[0], lim.min), min(clip[1], lim.max) # make clip limits integer-valued (no need to cast to int) # this improves performance, especially on Windows clip = [math.trunc(x) for x in clip] if np.can_cast(data, np.float32): work_dtype = np.float32 else: work_dtype = np.float64 cp = getCupy() if cp and cp.get_array_module(data) == cp: # Cupy does not support nditer # https://github.com/cupy/cupy/issues/5021 data_out = data.astype(work_dtype, copy=True) data_out -= offset data_out *= scale # Clip before converting dtype to avoid overflow if clip is not None: clip_array(data_out, clip[0], clip[1], out=data_out) # don't copy if no change in dtype return data_out.astype(out_dtype, copy=False) numba_fn = getNumbaFunctions() if numba_fn and clip is not None: # if we got here by makeARGB(), clip will not be None at this point return numba_fn.rescaleData(data, scale, offset, out_dtype, clip) return _rescaleData_nditer(data, scale, offset, work_dtype, out_dtype, clip)
[docs]def applyLookupTable(data, lut): """ Uses values in *data* as indexes to select values from *lut*. The returned data has shape data.shape + lut.shape[1:] Note: color gradient lookup tables can be generated using GradientWidget. Parameters ---------- data : ndarray lut : ndarray Either cupy or numpy arrays are accepted, though this function has only consistently behaved correctly on windows with cuda toolkit version >= 11.1. """ if data.dtype.kind not in ('i', 'u'): data = data.astype(int) cp = getCupy() if cp and cp.get_array_module(data) == cp: # cupy.take only supports "wrap" mode return cp.take(lut, cp.clip(data, 0, lut.shape[0] - 1), axis=0) else: return np.take(lut, data, axis=0, mode='clip')
def makeRGBA(*args, **kwds): """Equivalent to makeARGB(..., useRGBA=True)""" kwds['useRGBA'] = True return makeARGB(*args, **kwds)
[docs]def makeARGB(data, lut=None, levels=None, scale=None, useRGBA=False, output=None): """ Convert an array of values into an ARGB array suitable for building QImages, OpenGL textures, etc. Returns the ARGB array (unsigned byte) and a boolean indicating whether there is alpha channel data. This is a two stage process: 1) Rescale the data based on the values in the *levels* argument (min, max). 2) Determine the final output by passing the rescaled values through a lookup table. Both stages are optional. ============== ================================================================================== **Arguments:** data numpy array of int/float types. If levels List [min, max]; optionally rescale data before converting through the lookup table. The data is rescaled such that min->0 and max->*scale*:: rescaled = (clip(data, min, max) - min) * (*scale* / (max - min)) It is also possible to use a 2D (N,2) array of values for levels. In this case, it is assumed that each pair of min,max values in the levels array should be applied to a different subset of the input data (for example, the input data may already have RGB values and the levels are used to independently scale each channel). The use of this feature requires that levels.shape[0] == data.shape[-1]. scale The maximum value to which data will be rescaled before being passed through the lookup table (or returned if there is no lookup table). By default this will be set to the length of the lookup table, or 255 if no lookup table is provided. lut Optional lookup table (array with dtype=ubyte). Values in data will be converted to color by indexing directly from lut. The output data shape will be input.shape + lut.shape[1:]. Lookup tables can be built using ColorMap or GradientWidget. useRGBA If True, the data is returned in RGBA order (useful for building OpenGL textures). The default is False, which returns in ARGB order for use with QImage (Note that 'ARGB' is a term used by the Qt documentation; the *actual* order is BGRA). ============== ================================================================================== """ cp = getCupy() xp = cp.get_array_module(data) if cp else np profile = debug.Profiler() if data.ndim not in (2, 3): raise TypeError("data must be 2D or 3D") if data.ndim == 3 and data.shape[2] > 4: raise TypeError("data.shape[2] must be <= 4") if lut is not None and not isinstance(lut, xp.ndarray): lut = xp.array(lut) if levels is None: # automatically decide levels based on data dtype if data.dtype.kind == 'u': levels = xp.array([0, 2**(data.itemsize*8)-1]) elif data.dtype.kind == 'i': s = 2**(data.itemsize*8 - 1) levels = xp.array([-s, s-1]) elif data.dtype.kind == 'b': levels = xp.array([0,1]) else: raise Exception('levels argument is required for float input types') if not isinstance(levels, xp.ndarray): levels = xp.array(levels) levels = levels.astype(xp.float64) if levels.ndim == 1: if levels.shape[0] != 2: raise Exception('levels argument must have length 2') elif levels.ndim == 2: if lut is not None and lut.ndim > 1: raise Exception('Cannot make ARGB data when both levels and lut have ndim > 2') if levels.shape != (data.shape[-1], 2): raise Exception('levels must have shape (data.shape[-1], 2)') else: raise Exception("levels argument must be 1D or 2D (got shape=%s)." % repr(levels.shape)) profile('check inputs') # Decide on maximum scaled value if scale is None: if lut is not None: scale = lut.shape[0] else: scale = 255. # Decide on the dtype we want after scaling if lut is None: dtype = xp.ubyte else: dtype = xp.min_scalar_type(lut.shape[0]-1) # awkward, but fastest numpy native nan evaluation nanMask = None if data.dtype.kind == 'f' and xp.isnan(data.min()): nanMask = xp.isnan(data) if data.ndim > 2: nanMask = xp.any(nanMask, axis=-1) # Apply levels if given if levels is not None: if isinstance(levels, xp.ndarray) and levels.ndim == 2: # we are going to rescale each channel independently if levels.shape[0] != data.shape[-1]: raise Exception("When rescaling multi-channel data, there must be the same number of levels as channels (data.shape[-1] == levels.shape[0])") newData = xp.empty(data.shape, dtype=int) for i in range(data.shape[-1]): minVal, maxVal = levels[i] if minVal == maxVal: maxVal = xp.nextafter(maxVal, 2*maxVal) rng = maxVal-minVal rng = 1 if rng == 0 else rng newData[...,i] = rescaleData(data[...,i], scale / rng, minVal, dtype=dtype) data = newData else: # Apply level scaling unless it would have no effect on the data minVal, maxVal = levels if minVal != 0 or maxVal != scale: if minVal == maxVal: maxVal = xp.nextafter(maxVal, 2*maxVal) rng = maxVal-minVal rng = 1 if rng == 0 else rng data = rescaleData(data, scale/rng, minVal, dtype=dtype) profile('apply levels') # apply LUT if given if lut is not None: data = applyLookupTable(data, lut) else: if data.dtype != xp.ubyte: data = xp.clip(data, 0, 255).astype(xp.ubyte) profile('apply lut') # this will be the final image array if output is None: imgData = xp.empty(data.shape[:2]+(4,), dtype=xp.ubyte) else: imgData = output profile('allocate') # decide channel order if useRGBA: dst_order = [0, 1, 2, 3] # R,G,B,A elif sys.byteorder == 'little': dst_order = [2, 1, 0, 3] # B,G,R,A (ARGB32 little endian) else: dst_order = [1, 2, 3, 0] # A,R,G,B (ARGB32 big endian) # copy data into image array fastpath = try_fastpath_argb(xp, data, imgData, useRGBA) if fastpath: pass elif data.ndim == 2: # This is tempting: # imgData[..., :3] = data[..., xp.newaxis] # ..but it turns out this is faster: for i in range(3): imgData[..., dst_order[i]] = data elif data.shape[2] == 1: for i in range(3): imgData[..., dst_order[i]] = data[..., 0] else: for i in range(0, data.shape[2]): imgData[..., dst_order[i]] = data[..., i] profile('reorder channels') # add opaque alpha channel if needed if data.ndim == 3 and data.shape[2] == 4: alpha = True else: alpha = False if not fastpath: # fastpath has already filled it in imgData[..., dst_order[3]] = 255 # apply nan mask through alpha channel if nanMask is not None: alpha = True # Workaround for https://github.com/cupy/cupy/issues/4693 if xp == cp: imgData[nanMask, :, dst_order[3]] = 0 else: imgData[nanMask, dst_order[3]] = 0 profile('alpha channel') return imgData, alpha
def try_fastpath_argb(xp, ain, aout, useRGBA): # we only optimize for certain cases # return False if we did not handle it can_handle = xp is np and ain.dtype == xp.ubyte and ain.flags['C_CONTIGUOUS'] if not can_handle: return False nrows, ncols = ain.shape[:2] nchans = 1 if ain.ndim == 2 else ain.shape[2] Format = QtGui.QImage.Format if nchans == 1: in_fmt = Format.Format_Grayscale8 elif nchans == 3: in_fmt = Format.Format_RGB888 else: in_fmt = Format.Format_RGBA8888 if useRGBA: out_fmt = Format.Format_RGBA8888 else: out_fmt = Format.Format_ARGB32 if in_fmt == out_fmt: aout[:] = ain return True npixels_chunk = 512*1024 batch = int(npixels_chunk / ncols / nchans) batch = max(1, batch) row_beg = 0 while row_beg < nrows: row_end = min(row_beg + batch, nrows) ain_view = ain[row_beg:row_end, ...] aout_view = aout[row_beg:row_end, ...] qimg = QtGui.QImage(ain_view, ncols, ain_view.shape[0], ain.strides[0], in_fmt) qimg = qimg.convertToFormat(out_fmt) aout_view[:] = imageToArray(qimg, copy=False, transpose=False) row_beg = row_end return True def ndarray_to_qimage(arr, fmt): """ Low level function to encapsulate QImage creation differences between bindings. "arr" is assumed to be C-contiguous. """ # C++ QImage has two kind of constructors # - QImage(const uchar*, ...) # - QImage(uchar*, ...) # If the const constructor is used, subsequently calling any non-const method # will trigger the COW mechanism, i.e. a copy is made under the hood. if QT_LIB.startswith('PyQt'): # PyQt5 -> non-const # PyQt6 >= 6.0.1 -> non-const img_ptr = int(Qt.sip.voidptr(arr)) # or arr.ctypes.data else: # bindings that support ndarray # PyQt5 -> const # PyQt6 >= 6.0.1 -> const # PySide2 -> non-const # PySide6 -> non-const img_ptr = arr h, w = arr.shape[:2] bytesPerLine = arr.strides[0] qimg = QtGui.QImage(img_ptr, w, h, bytesPerLine, fmt) qimg.data = arr return qimg
[docs]def makeQImage(imgData, alpha=None, copy=True, transpose=True): """ Turn an ARGB array into QImage. By default, the data is copied; changes to the array will not be reflected in the image. The image will be given a 'data' attribute pointing to the array which shares its data to prevent python freeing that memory while the image is in use. ============== =================================================================== **Arguments:** imgData Array of data to convert. Must have shape (height, width), (height, width, 3), or (height, width, 4). If transpose is True, then the first two axes are swapped. The array dtype must be ubyte. For 2D arrays, the value is interpreted as greyscale. For 3D arrays, the order of values in the 3rd axis must be (b, g, r, a). alpha If the input array is 3D and *alpha* is True, the QImage returned will have format ARGB32. If False, the format will be RGB32. By default, _alpha_ is True if array.shape[2] == 4. copy If True, the data is copied before converting to QImage. If False, the new QImage points directly to the data in the array. Note that the array must be contiguous for this to work (see numpy.ascontiguousarray). transpose If True (the default), the array x/y axes are transposed before creating the image. Note that Qt expects the axes to be in (height, width) order whereas pyqtgraph usually prefers the opposite. ============== =================================================================== """ ## create QImage from buffer profile = debug.Profiler() copied = False if imgData.ndim == 2: imgFormat = QtGui.QImage.Format.Format_Grayscale8 elif imgData.ndim == 3: # If we didn't explicitly specify alpha, check the array shape. if alpha is None: alpha = (imgData.shape[2] == 4) if imgData.shape[2] == 3: # need to make alpha channel (even if alpha==False; QImage requires 32 bpp) if copy is True: d2 = np.empty(imgData.shape[:2] + (4,), dtype=imgData.dtype) d2[:,:,:3] = imgData d2[:,:,3] = 255 imgData = d2 copied = True else: raise Exception('Array has only 3 channels; cannot make QImage without copying.') profile("add alpha channel") if alpha: imgFormat = QtGui.QImage.Format.Format_ARGB32 else: imgFormat = QtGui.QImage.Format.Format_RGB32 else: raise TypeError("Image array must have ndim = 2 or 3.") if transpose: imgData = imgData.transpose((1, 0, 2)) # QImage expects row-major order if not imgData.flags['C_CONTIGUOUS']: if copy is False: extra = ' (try setting transpose=False)' if transpose else '' raise Exception('Array is not contiguous; cannot make QImage without copying.'+extra) imgData = np.ascontiguousarray(imgData) copied = True profile("ascontiguousarray") if copy is True and copied is False: imgData = imgData.copy() profile("copy") return ndarray_to_qimage(imgData, imgFormat)
def ndarray_from_qimage(qimg): img_ptr = qimg.bits() if img_ptr is None: raise ValueError("Null QImage not supported") h, w = qimg.height(), qimg.width() bpl = qimg.bytesPerLine() depth = qimg.depth() logical_bpl = w * depth // 8 if QT_LIB.startswith('PyQt'): # sizeInBytes() was introduced in Qt 5.10 # however PyQt5 5.12 will fail with: # "TypeError: QImage.sizeInBytes() is a private method" # note that sizeInBytes() works fine with: # PyQt5 5.15, PySide2 5.12, PySide2 5.15 img_ptr.setsize(h * bpl) memory = np.frombuffer(img_ptr, dtype=np.ubyte).reshape((h, bpl)) memory = memory[:, :logical_bpl] if depth in (8, 24, 32): dtype = np.uint8 nchan = depth // 8 elif depth in (16, 64): dtype = np.uint16 nchan = depth // 16 else: raise ValueError("Unsupported Image Type") shape = h, w if nchan != 1: shape = shape + (nchan,) arr = memory.view(dtype).reshape(shape) return arr
[docs]def imageToArray(img, copy=False, transpose=True): """ Convert a QImage into numpy array. The image must have format RGB32, ARGB32, or ARGB32_Premultiplied. By default, the image is not copied; changes made to the array will appear in the QImage as well (beware: if the QImage is collected before the array, there may be trouble). The array will have shape (width, height, (b,g,r,a)). """ arr = ndarray_from_qimage(img) fmt = img.format() if fmt == img.Format.Format_RGB32: arr[...,3] = 255 if copy: arr = arr.copy() if transpose: return arr.transpose((1,0,2)) else: return arr
def colorToAlpha(data, color): """ Given an RGBA image in *data*, convert *color* to be transparent. *data* must be an array (w, h, 3 or 4) of ubyte values and *color* must be an array (3) of ubyte values. This is particularly useful for use with images that have a black or white background. Algorithm is taken from Gimp's color-to-alpha function in plug-ins/common/colortoalpha.c Credit: /* * Color To Alpha plug-in v1.0 by Seth Burgess, sjburges@gimp.org 1999/05/14 * with algorithm by clahey */ """ data = data.astype(float) if data.shape[-1] == 3: ## add alpha channel if needed d2 = np.empty(data.shape[:2]+(4,), dtype=data.dtype) d2[...,:3] = data d2[...,3] = 255 data = d2 color = color.astype(float) alpha = np.zeros(data.shape[:2]+(3,), dtype=float) output = data.copy() for i in [0,1,2]: d = data[...,i] c = color[i] mask = d > c alpha[...,i][mask] = (d[mask] - c) / (255. - c) imask = d < c alpha[...,i][imask] = (c - d[imask]) / c output[...,3] = alpha.max(axis=2) * 255. mask = output[...,3] >= 1.0 ## avoid zero division while processing alpha channel correction = 255. / output[...,3][mask] ## increase value to compensate for decreased alpha for i in [0,1,2]: output[...,i][mask] = ((output[...,i][mask]-color[i]) * correction) + color[i] output[...,3][mask] *= data[...,3][mask] / 255. ## combine computed and previous alpha values #raise Exception() return np.clip(output, 0, 255).astype(np.ubyte) def gaussianFilter(data, sigma): """ Drop-in replacement for scipy.ndimage.gaussian_filter. (note: results are only approximately equal to the output of gaussian_filter) """ cp = getCupy() xp = cp.get_array_module(data) if cp else np if xp.isscalar(sigma): sigma = (sigma,) * data.ndim baseline = data.mean() filtered = data - baseline for ax in range(data.ndim): s = sigma[ax] if s == 0: continue # generate 1D gaussian kernel ksize = int(s * 6) x = xp.arange(-ksize, ksize) kernel = xp.exp(-x**2 / (2*s**2)) kshape = [1,] * data.ndim kshape[ax] = len(kernel) kernel = kernel.reshape(kshape) # convolve as product of FFTs shape = data.shape[ax] + ksize scale = 1.0 / (abs(s) * (2*xp.pi)**0.5) filtered = scale * xp.fft.irfft(xp.fft.rfft(filtered, shape, axis=ax) * xp.fft.rfft(kernel, shape, axis=ax), axis=ax) # clip off extra data sl = [slice(None)] * data.ndim sl[ax] = slice(filtered.shape[ax]-data.shape[ax],None,None) filtered = filtered[tuple(sl)] return filtered + baseline def downsample(data, n, axis=0, xvals='subsample'): """Downsample by averaging points together across axis. If multiple axes are specified, runs once per axis. If a metaArray is given, then the axis values can be either subsampled or downsampled to match. """ ma = None if (hasattr(data, 'implements') and data.implements('MetaArray')): ma = data data = data.view(np.ndarray) if hasattr(axis, '__len__'): if not hasattr(n, '__len__'): n = [n]*len(axis) for i in range(len(axis)): data = downsample(data, n[i], axis[i]) return data if n <= 1: return data nPts = int(data.shape[axis] / n) s = list(data.shape) s[axis] = nPts s.insert(axis+1, n) sl = [slice(None)] * data.ndim sl[axis] = slice(0, nPts*n) d1 = data[tuple(sl)] #print d1.shape, s d1.shape = tuple(s) d2 = d1.mean(axis+1) if ma is None: return d2 else: info = ma.infoCopy() if 'values' in info[axis]: if xvals == 'subsample': info[axis]['values'] = info[axis]['values'][::n][:nPts] elif xvals == 'downsample': info[axis]['values'] = downsample(info[axis]['values'], n) return MetaArray(d2, info=info) def _compute_backfill_indices(isfinite): # the presence of inf/nans result in an empty QPainterPath being generated # this behavior started in Qt 5.12.3 and was introduced in this commit # https://github.com/qt/qtbase/commit/c04bd30de072793faee5166cff866a4c4e0a9dd7 # We therefore replace non-finite values # credit: Divakar https://stackoverflow.com/a/41191127/643629 mask = ~isfinite idx = np.arange(len(isfinite)) idx[mask] = -1 np.maximum.accumulate(idx, out=idx) first = np.searchsorted(idx, 0) if first < len(isfinite): # Replace all non-finite entries from beginning of arr with the first finite one idx[:first] = first return idx else: return None def _arrayToQPath_all(x, y, finiteCheck): n = x.shape[0] if n == 0: return QtGui.QPainterPath() backfill_idx = None if finiteCheck: isfinite = np.isfinite(x) & np.isfinite(y) if not np.all(isfinite): backfill_idx = _compute_backfill_indices(isfinite) chunksize = 10000 numchunks = (n + chunksize - 1) // chunksize minchunks = 3 if numchunks < minchunks: # too few chunks, batching would be a pessimization poly = create_qpolygonf(n) arr = ndarray_from_qpolygonf(poly) if backfill_idx is None: arr[:, 0] = x arr[:, 1] = y else: arr[:, 0] = x[backfill_idx] arr[:, 1] = y[backfill_idx] path = QtGui.QPainterPath() if hasattr(path, 'reserve'): # Qt 5.13 path.reserve(n) path.addPolygon(poly) return path # at this point, we have numchunks >= minchunks path = QtGui.QPainterPath() if hasattr(path, 'reserve'): # Qt 5.13 path.reserve(n) subpoly = QtGui.QPolygonF() subpath = None for idx in range(numchunks): sl = slice(idx*chunksize, min((idx+1)*chunksize, n)) currsize = sl.stop - sl.start if currsize != subpoly.size(): if hasattr(subpoly, 'resize'): subpoly.resize(currsize) else: subpoly.fill(QtCore.QPointF(), currsize) subarr = ndarray_from_qpolygonf(subpoly) if backfill_idx is None: subarr[:, 0] = x[sl] subarr[:, 1] = y[sl] else: bfv = backfill_idx[sl] # view subarr[:, 0] = x[bfv] subarr[:, 1] = y[bfv] if subpath is None: subpath = QtGui.QPainterPath() subpath.addPolygon(subpoly) path.connectPath(subpath) if hasattr(subpath, 'clear'): # Qt 5.13 subpath.clear() else: subpath = None return path def _arrayToQPath_finite(x, y, isfinite=None): n = x.shape[0] if n == 0: return QtGui.QPainterPath() if isfinite is None: isfinite = np.isfinite(x) & np.isfinite(y) path = QtGui.QPainterPath() if hasattr(path, 'reserve'): # Qt 5.13 path.reserve(n) sidx = np.nonzero(~isfinite)[0] + 1 # note: the chunks are views xchunks = np.split(x, sidx) ychunks = np.split(y, sidx) chunks = list(zip(xchunks, ychunks)) # create a single polygon able to hold the largest chunk maxlen = max(len(chunk) for chunk in xchunks) subpoly = create_qpolygonf(maxlen) subarr = ndarray_from_qpolygonf(subpoly) # resize and fill do not change the capacity if hasattr(subpoly, 'resize'): subpoly_resize = subpoly.resize else: # PyQt will be less efficient subpoly_resize = lambda n, v=QtCore.QPointF() : subpoly.fill(v, n) # notes: # - we backfill the non-finite in order to get the same image as the # old codepath on the CI. somehow P1--P2 gets rendered differently # from P1--P2--P2 # - we do not generate MoveTo(s) that are not followed by a LineTo, # thus the QPainterPath can be different from the old codepath's # all chunks except the last chunk have a trailing non-finite for xchunk, ychunk in chunks[:-1]: lc = len(xchunk) if lc <= 1: # len 1 means we have a string of non-finite continue subpoly_resize(lc) subarr[:lc, 0] = xchunk subarr[:lc, 1] = ychunk subarr[lc-1] = subarr[lc-2] # fill non-finite with its neighbour path.addPolygon(subpoly) # handle last chunk, which is either all-finite or empty for xchunk, ychunk in chunks[-1:]: lc = len(xchunk) if lc <= 1: # can't draw a line with just 1 point continue subpoly_resize(lc) subarr[:lc, 0] = xchunk subarr[:lc, 1] = ychunk path.addPolygon(subpoly) return path
[docs]def arrayToQPath(x, y, connect='all', finiteCheck=True): """ Convert an array of x,y coordinates to QPainterPath as efficiently as possible. The *connect* argument may be 'all', indicating that each point should be connected to the next; 'pairs', indicating that each pair of points should be connected, or an array of int32 values (0 or 1) indicating connections. Parameters ---------- x : (N,) ndarray x-values to be plotted y : (N,) ndarray y-values to be plotted, must be same length as `x` connect : {'all', 'pairs', 'finite', (N,) ndarray}, optional Argument detailing how to connect the points in the path. `all` will have sequential points being connected. `pairs` generates lines between every other point. `finite` only connects points that are finite. If an ndarray is passed, containing int32 values of 0 or 1, only values with 1 will connect to the previous point. Def finiteCheck : bool, default Ture When false, the check for finite values will be skipped, which can improve performance. If finite values are present in `x` or `y`, an empty QPainterPath will be generated. Returns ------- QPainterPath QPainterPath object to be drawn Raises ------ ValueError Raised when the connect argument has an invalid value placed within. Notes ----- A QPainterPath is generated through one of two ways. When the connect parameter is 'all', a QPolygonF object is created, and ``QPainterPath.addPolygon()`` is called. For other connect parameters a ``QDataStream`` object is created and the QDataStream >> QPainterPath operator is used to pass the data. The memory format is as follows numVerts(i4) 0(i4) x(f8) y(f8) <-- 0 means this vertex does not connect 1(i4) x(f8) y(f8) <-- 1 means this vertex connects to the previous vertex ... cStart(i4) fillRule(i4) see: https://github.com/qt/qtbase/blob/dev/src/gui/painting/qpainterpath.cpp All values are big endian--pack using struct.pack('>d') or struct.pack('>i') This binary format may change in future versions of Qt """ n = x.shape[0] if n == 0: return QtGui.QPainterPath() connect_array = None if isinstance(connect, np.ndarray): # make connect argument contain only str type connect_array, connect = connect, 'array' isfinite = None if connect == 'finite': if not finiteCheck: # if user specified to skip finite check, then we skip the heuristic return _arrayToQPath_finite(x, y) # otherwise use a heuristic # if non-finite aren't that many, then use_qpolyponf isfinite = np.isfinite(x) & np.isfinite(y) nonfinite_cnt = n - np.sum(isfinite) all_isfinite = nonfinite_cnt == 0 if all_isfinite: # delegate to connect='all' connect = 'all' finiteCheck = False elif nonfinite_cnt / n < 2 / 100: return _arrayToQPath_finite(x, y, isfinite) else: # delegate to connect=ndarray # finiteCheck=True, all_isfinite=False connect = 'array' connect_array = isfinite if connect == 'all': return _arrayToQPath_all(x, y, finiteCheck) backstore = QtCore.QByteArray() backstore.resize(4 + n*20 + 8) # contents uninitialized backstore.replace(0, 4, struct.pack('>i', n)) # cStart, fillRule (Qt.FillRule.OddEvenFill) backstore.replace(4+n*20, 8, struct.pack('>ii', 0, 0)) arr = np.frombuffer(backstore, dtype=[('c', '>i4'), ('x', '>f8'), ('y', '>f8')], count=n, offset=4) backfill_idx = None if finiteCheck: if isfinite is None: isfinite = np.isfinite(x) & np.isfinite(y) all_isfinite = np.all(isfinite) if not all_isfinite: backfill_idx = _compute_backfill_indices(isfinite) if backfill_idx is None: arr['x'] = x arr['y'] = y else: arr['x'] = x[backfill_idx] arr['y'] = y[backfill_idx] # decide which points are connected by lines if connect == 'pairs': arr['c'][0::2] = 0 arr['c'][1::2] = 1 # connect every 2nd point to every 1st one elif connect == 'array': # Let's call a point with either x or y being nan is an invalid point. # A point will anyway not connect to an invalid point regardless of the # 'c' value of the invalid point. Therefore, we should set 'c' to 0 for # the next point of an invalid point. arr['c'][:1] = 0 # the first vertex has no previous vertex to connect arr['c'][1:] = connect_array[:-1] else: raise ValueError('connect argument must be "all", "pairs", "finite", or array') path = QtGui.QPainterPath() if hasattr(path, 'reserve'): # Qt 5.13 path.reserve(n) ds = QtCore.QDataStream(backstore) ds >> path return path
def ndarray_from_qpolygonf(polyline): nbytes = 2 * len(polyline) * 8 if QT_LIB.startswith('PyQt'): buffer = polyline.data() if buffer is None: buffer = Qt.sip.voidptr(0) buffer.setsize(nbytes) else: ptr = polyline.data() if ptr is None: ptr = 0 buffer = Qt.shiboken.VoidPtr(ptr, nbytes, True) memory = np.frombuffer(buffer, np.double).reshape((-1, 2)) return memory def create_qpolygonf(size): polyline = QtGui.QPolygonF() if QT_LIB.startswith('PyQt'): polyline.fill(QtCore.QPointF(), size) else: polyline.resize(size) return polyline def arrayToQPolygonF(x, y): """ Utility function to convert two 1D-NumPy arrays representing curve data (X-axis, Y-axis data) into a single open polygon (QtGui.PolygonF) object. Thanks to PythonQwt for making this code available License/copyright: MIT License © Pierre Raybaut 2020. Parameters ---------- x : np.array x-axis coordinates for data to be plotted, must have have ndim of 1 y : np.array y-axis coordinates for data to be plotted, must have ndim of 1 and be the same length as x Returns ------- QPolygonF Open QPolygonF object that represents the path looking to be plotted Raises ------ ValueError When xdata or ydata does not meet the required criteria """ if not ( x.size == y.size == x.shape[0] == y.shape[0] ): raise ValueError("Arguments must be 1D and the same size") size = x.size polyline = create_qpolygonf(size) memory = ndarray_from_qpolygonf(polyline) memory[:, 0] = x memory[:, 1] = y return polyline #def isosurface(data, level): #""" #Generate isosurface from volumetric data using marching tetrahedra algorithm. #See Paul Bourke, "Polygonising a Scalar Field Using Tetrahedrons" (http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/) #*data* 3D numpy array of scalar values #*level* The level at which to generate an isosurface #""" #facets = [] ### mark everything below the isosurface level #mask = data < level #### make eight sub-fields #fields = np.empty((2,2,2), dtype=object) #slices = [slice(0,-1), slice(1,None)] #for i in [0,1]: #for j in [0,1]: #for k in [0,1]: #fields[i,j,k] = mask[slices[i], slices[j], slices[k]] ### split each cell into 6 tetrahedra ### these all have the same 'orienation'; points 1,2,3 circle ### clockwise around point 0 #tetrahedra = [ #[(0,1,0), (1,1,1), (0,1,1), (1,0,1)], #[(0,1,0), (0,1,1), (0,0,1), (1,0,1)], #[(0,1,0), (0,0,1), (0,0,0), (1,0,1)], #[(0,1,0), (0,0,0), (1,0,0), (1,0,1)], #[(0,1,0), (1,0,0), (1,1,0), (1,0,1)], #[(0,1,0), (1,1,0), (1,1,1), (1,0,1)] #] ### each tetrahedron will be assigned an index ### which determines how to generate its facets. ### this structure is: ### facets[index][facet1, facet2, ...] ### where each facet is triangular and its points are each ### interpolated between two points on the tetrahedron ### facet = [(p1a, p1b), (p2a, p2b), (p3a, p3b)] ### facet points always circle clockwise if you are looking ### at them from below the isosurface. #indexFacets = [ #[], ## all above #[[(0,1), (0,2), (0,3)]], # 0 below #[[(1,0), (1,3), (1,2)]], # 1 below #[[(0,2), (1,3), (1,2)], [(0,2), (0,3), (1,3)]], # 0,1 below #[[(2,0), (2,1), (2,3)]], # 2 below #[[(0,3), (1,2), (2,3)], [(0,3), (0,1), (1,2)]], # 0,2 below #[[(1,0), (2,3), (2,0)], [(1,0), (1,3), (2,3)]], # 1,2 below #[[(3,0), (3,1), (3,2)]], # 3 above #[[(3,0), (3,2), (3,1)]], # 3 below #[[(1,0), (2,0), (2,3)], [(1,0), (2,3), (1,3)]], # 0,3 below #[[(0,3), (2,3), (1,2)], [(0,3), (1,2), (0,1)]], # 1,3 below #[[(2,0), (2,3), (2,1)]], # 0,1,3 below #[[(0,2), (1,2), (1,3)], [(0,2), (1,3), (0,3)]], # 2,3 below #[[(1,0), (1,2), (1,3)]], # 0,2,3 below #[[(0,1), (0,3), (0,2)]], # 1,2,3 below #[] ## all below #] #for tet in tetrahedra: ### get the 4 fields for this tetrahedron #tetFields = [fields[c] for c in tet] ### generate an index for each grid cell #index = tetFields[0] + tetFields[1]*2 + tetFields[2]*4 + tetFields[3]*8 ### add facets #for i in range(index.shape[0]): # data x-axis #for j in range(index.shape[1]): # data y-axis #for k in range(index.shape[2]): # data z-axis #for f in indexFacets[index[i,j,k]]: # faces to generate for this tet #pts = [] #for l in [0,1,2]: # points in this face #p1 = tet[f[l][0]] # tet corner 1 #p2 = tet[f[l][1]] # tet corner 2 #pts.append([(p1[x]+p2[x])*0.5+[i,j,k][x]+0.5 for x in [0,1,2]]) ## interpolate between tet corners #facets.append(pts) #return facets
[docs]def isocurve(data, level, connected=False, extendToEdge=False, path=False): """ Generate isocurve from 2D data using marching squares algorithm. ============== ========================================================= **Arguments:** data 2D numpy array of scalar values level The level at which to generate an isosurface connected If False, return a single long list of point pairs If True, return multiple long lists of connected point locations. (This is slower but better for drawing continuous lines) extendToEdge If True, extend the curves to reach the exact edges of the data. path if True, return a QPainterPath rather than a list of vertex coordinates. This forces connected=True. ============== ========================================================= This function is SLOW; plenty of room for optimization here. """ if path is True: connected = True if extendToEdge: d2 = np.empty((data.shape[0]+2, data.shape[1]+2), dtype=data.dtype) d2[1:-1, 1:-1] = data d2[0, 1:-1] = data[0] d2[-1, 1:-1] = data[-1] d2[1:-1, 0] = data[:, 0] d2[1:-1, -1] = data[:, -1] d2[0,0] = d2[0,1] d2[0,-1] = d2[1,-1] d2[-1,0] = d2[-1,1] d2[-1,-1] = d2[-1,-2] data = d2 sideTable = [ [], [0,1], [1,2], [0,2], [0,3], [1,3], [0,1,2,3], [2,3], [2,3], [0,1,2,3], [1,3], [0,3], [0,2], [1,2], [0,1], [] ] edgeKey=[ [(0,1), (0,0)], [(0,0), (1,0)], [(1,0), (1,1)], [(1,1), (0,1)] ] lines = [] ## mark everything below the isosurface level mask = data < level ### make four sub-fields and compute indexes for grid cells index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte) fields = np.empty((2,2), dtype=object) slices = [slice(0,-1), slice(1,None)] for i in [0,1]: for j in [0,1]: fields[i,j] = mask[slices[i], slices[j]] #vertIndex = i - 2*j*i + 3*j + 4*k ## this is just to match Bourk's vertex numbering scheme vertIndex = i+2*j #print i,j,k," : ", fields[i,j,k], 2**vertIndex np.add(index, fields[i,j] * 2**vertIndex, out=index, casting='unsafe') #print index #print index ## add lines for i in range(index.shape[0]): # data x-axis for j in range(index.shape[1]): # data y-axis sides = sideTable[index[i,j]] for l in range(0, len(sides), 2): ## faces for this grid cell edges = sides[l:l+2] pts = [] for m in [0,1]: # points in this face p1 = edgeKey[edges[m]][0] # p1, p2 are points at either side of an edge p2 = edgeKey[edges[m]][1] v1 = data[i+p1[0], j+p1[1]] # v1 and v2 are the values at p1 and p2 v2 = data[i+p2[0], j+p2[1]] f = (level-v1) / (v2-v1) fi = 1.0 - f p = ( ## interpolate between corners p1[0]*fi + p2[0]*f + i + 0.5, p1[1]*fi + p2[1]*f + j + 0.5 ) if extendToEdge: ## check bounds p = ( min(data.shape[0]-2, max(0, p[0]-1)), min(data.shape[1]-2, max(0, p[1]-1)), ) if connected: gridKey = i + (1 if edges[m]==2 else 0), j + (1 if edges[m]==3 else 0), edges[m]%2 pts.append((p, gridKey)) ## give the actual position and a key identifying the grid location (for connecting segments) else: pts.append(p) lines.append(pts) if not connected: return lines ## turn disjoint list of segments into continuous lines #lines = [[2,5], [5,4], [3,4], [1,3], [6,7], [7,8], [8,6], [11,12], [12,15], [11,13], [13,14]] #lines = [[(float(a), a), (float(b), b)] for a,b in lines] points = {} ## maps each point to its connections for a,b in lines: if a[1] not in points: points[a[1]] = [] points[a[1]].append([a,b]) if b[1] not in points: points[b[1]] = [] points[b[1]].append([b,a]) ## rearrange into chains for k in list(points.keys()): try: chains = points[k] except KeyError: ## already used this point elsewhere continue #print "===========", k for chain in chains: #print " chain:", chain x = None while True: if x == chain[-1][1]: break ## nothing left to do on this chain x = chain[-1][1] if x == k: break ## chain has looped; we're done and can ignore the opposite chain y = chain[-2][1] connects = points[x] for conn in connects[:]: if conn[1][1] != y: #print " ext:", conn chain.extend(conn[1:]) #print " del:", x del points[x] if chain[0][1] == chain[-1][1]: # looped chain; no need to continue the other direction chains.pop() break ## extract point locations lines = [] for chain in points.values(): if len(chain) == 2: chain = chain[1][1:][::-1] + chain[0] # join together ends of chain else: chain = chain[0] lines.append([p[0] for p in chain]) if not path: return lines ## a list of pairs of points path = QtGui.QPainterPath() for line in lines: path.moveTo(*line[0]) for p in line[1:]: path.lineTo(*p) return path
def traceImage(image, values, smooth=0.5): """ Convert an image to a set of QPainterPath curves. One curve will be generated for each item in *values*; each curve outlines the area of the image that is closer to its value than to any others. If image is RGB or RGBA, then the shape of values should be (nvals, 3/4) The parameter *smooth* is expressed in pixels. """ if values.ndim == 2: values = values.T values = values[np.newaxis, np.newaxis, ...].astype(float) image = image[..., np.newaxis].astype(float) diff = np.abs(image-values) if values.ndim == 4: diff = diff.sum(axis=2) labels = np.argmin(diff, axis=2) paths = [] for i in range(diff.shape[-1]): d = (labels==i).astype(float) d = gaussianFilter(d, (smooth, smooth)) lines = isocurve(d, 0.5, connected=True, extendToEdge=True) path = QtGui.QPainterPath() for line in lines: path.moveTo(*line[0]) for p in line[1:]: path.lineTo(*p) paths.append(path) return paths IsosurfaceDataCache = None
[docs]def isosurface(data, level): """ Generate isosurface from volumetric data using marching cubes algorithm. See Paul Bourke, "Polygonising a Scalar Field" (http://paulbourke.net/geometry/polygonise/) *data* 3D numpy array of scalar values. Must be contiguous. *level* The level at which to generate an isosurface Returns an array of vertex coordinates (Nv, 3) and an array of per-face vertex indexes (Nf, 3) """ ## For improvement, see: ## ## Efficient implementation of Marching Cubes' cases with topological guarantees. ## Thomas Lewiner, Helio Lopes, Antonio Wilson Vieira and Geovan Tavares. ## Journal of Graphics Tools 8(2): pp. 1-15 (december 2003) ## Precompute lookup tables on the first run global IsosurfaceDataCache if IsosurfaceDataCache is None: ## map from grid cell index to edge index. ## grid cell index tells us which corners are below the isosurface, ## edge index tells us which edges are cut by the isosurface. ## (Data stolen from Bourk; see above.) edgeTable = np.array([ 0x0 , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00, 0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90, 0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c, 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30, 0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0, 0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60, 0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc, 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0, 0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c, 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950, 0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc , 0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0, 0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc, 0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0, 0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c, 0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650, 0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460, 0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac, 0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0, 0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230, 0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c, 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190, 0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c, 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0 ], dtype=np.uint16) ## Table of triangles to use for filling each grid cell. ## Each set of three integers tells us which three edges to ## draw a triangle between. ## (Data stolen from Bourk; see above.) triTable = [ [], [0, 8, 3], [0, 1, 9], [1, 8, 3, 9, 8, 1], [1, 2, 10], [0, 8, 3, 1, 2, 10], [9, 2, 10, 0, 2, 9], [2, 8, 3, 2, 10, 8, 10, 9, 8], [3, 11, 2], [0, 11, 2, 8, 11, 0], [1, 9, 0, 2, 3, 11], [1, 11, 2, 1, 9, 11, 9, 8, 11], [3, 10, 1, 11, 10, 3], [0, 10, 1, 0, 8, 10, 8, 11, 10], [3, 9, 0, 3, 11, 9, 11, 10, 9], [9, 8, 10, 10, 8, 11], [4, 7, 8], [4, 3, 0, 7, 3, 4], [0, 1, 9, 8, 4, 7], [4, 1, 9, 4, 7, 1, 7, 3, 1], [1, 2, 10, 8, 4, 7], [3, 4, 7, 3, 0, 4, 1, 2, 10], [9, 2, 10, 9, 0, 2, 8, 4, 7], [2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4], [8, 4, 7, 3, 11, 2], [11, 4, 7, 11, 2, 4, 2, 0, 4], [9, 0, 1, 8, 4, 7, 2, 3, 11], [4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1], [3, 10, 1, 3, 11, 10, 7, 8, 4], [1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4], [4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3], [4, 7, 11, 4, 11, 9, 9, 11, 10], [9, 5, 4], [9, 5, 4, 0, 8, 3], [0, 5, 4, 1, 5, 0], [8, 5, 4, 8, 3, 5, 3, 1, 5], [1, 2, 10, 9, 5, 4], [3, 0, 8, 1, 2, 10, 4, 9, 5], [5, 2, 10, 5, 4, 2, 4, 0, 2], [2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8], [9, 5, 4, 2, 3, 11], [0, 11, 2, 0, 8, 11, 4, 9, 5], [0, 5, 4, 0, 1, 5, 2, 3, 11], [2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5], [10, 3, 11, 10, 1, 3, 9, 5, 4], [4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10], [5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3], [5, 4, 8, 5, 8, 10, 10, 8, 11], [9, 7, 8, 5, 7, 9], [9, 3, 0, 9, 5, 3, 5, 7, 3], [0, 7, 8, 0, 1, 7, 1, 5, 7], [1, 5, 3, 3, 5, 7], [9, 7, 8, 9, 5, 7, 10, 1, 2], [10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3], [8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2], [2, 10, 5, 2, 5, 3, 3, 5, 7], [7, 9, 5, 7, 8, 9, 3, 11, 2], [9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11], [2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7], [11, 2, 1, 11, 1, 7, 7, 1, 5], [9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11], [5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0], [11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0], [11, 10, 5, 7, 11, 5], [10, 6, 5], [0, 8, 3, 5, 10, 6], [9, 0, 1, 5, 10, 6], [1, 8, 3, 1, 9, 8, 5, 10, 6], [1, 6, 5, 2, 6, 1], [1, 6, 5, 1, 2, 6, 3, 0, 8], [9, 6, 5, 9, 0, 6, 0, 2, 6], [5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8], [2, 3, 11, 10, 6, 5], [11, 0, 8, 11, 2, 0, 10, 6, 5], [0, 1, 9, 2, 3, 11, 5, 10, 6], [5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11], [6, 3, 11, 6, 5, 3, 5, 1, 3], [0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6], [3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9], [6, 5, 9, 6, 9, 11, 11, 9, 8], [5, 10, 6, 4, 7, 8], [4, 3, 0, 4, 7, 3, 6, 5, 10], [1, 9, 0, 5, 10, 6, 8, 4, 7], [10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4], [6, 1, 2, 6, 5, 1, 4, 7, 8], [1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7], [8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6], [7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9], [3, 11, 2, 7, 8, 4, 10, 6, 5], [5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11], [0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6], [9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6], [8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6], [5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11], [0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7], [6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9], [10, 4, 9, 6, 4, 10], [4, 10, 6, 4, 9, 10, 0, 8, 3], [10, 0, 1, 10, 6, 0, 6, 4, 0], [8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10], [1, 4, 9, 1, 2, 4, 2, 6, 4], [3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4], [0, 2, 4, 4, 2, 6], [8, 3, 2, 8, 2, 4, 4, 2, 6], [10, 4, 9, 10, 6, 4, 11, 2, 3], [0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6], [3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10], [6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1], [9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3], [8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1], [3, 11, 6, 3, 6, 0, 0, 6, 4], [6, 4, 8, 11, 6, 8], [7, 10, 6, 7, 8, 10, 8, 9, 10], [0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10], [10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0], [10, 6, 7, 10, 7, 1, 1, 7, 3], [1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7], [2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9], [7, 8, 0, 7, 0, 6, 6, 0, 2], [7, 3, 2, 6, 7, 2], [2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7], [2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7], [1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11], [11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1], [8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6], [0, 9, 1, 11, 6, 7], [7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0], [7, 11, 6], [7, 6, 11], [3, 0, 8, 11, 7, 6], [0, 1, 9, 11, 7, 6], [8, 1, 9, 8, 3, 1, 11, 7, 6], [10, 1, 2, 6, 11, 7], [1, 2, 10, 3, 0, 8, 6, 11, 7], [2, 9, 0, 2, 10, 9, 6, 11, 7], [6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8], [7, 2, 3, 6, 2, 7], [7, 0, 8, 7, 6, 0, 6, 2, 0], [2, 7, 6, 2, 3, 7, 0, 1, 9], [1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6], [10, 7, 6, 10, 1, 7, 1, 3, 7], [10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8], [0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7], [7, 6, 10, 7, 10, 8, 8, 10, 9], [6, 8, 4, 11, 8, 6], [3, 6, 11, 3, 0, 6, 0, 4, 6], [8, 6, 11, 8, 4, 6, 9, 0, 1], [9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6], [6, 8, 4, 6, 11, 8, 2, 10, 1], [1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6], [4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9], [10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3], [8, 2, 3, 8, 4, 2, 4, 6, 2], [0, 4, 2, 4, 6, 2], [1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8], [1, 9, 4, 1, 4, 2, 2, 4, 6], [8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1], [10, 1, 0, 10, 0, 6, 6, 0, 4], [4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3], [10, 9, 4, 6, 10, 4], [4, 9, 5, 7, 6, 11], [0, 8, 3, 4, 9, 5, 11, 7, 6], [5, 0, 1, 5, 4, 0, 7, 6, 11], [11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5], [9, 5, 4, 10, 1, 2, 7, 6, 11], [6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5], [7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2], [3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6], [7, 2, 3, 7, 6, 2, 5, 4, 9], [9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7], [3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0], [6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8], [9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7], [1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4], [4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10], [7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10], [6, 9, 5, 6, 11, 9, 11, 8, 9], [3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5], [0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11], [6, 11, 3, 6, 3, 5, 5, 3, 1], [1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6], [0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10], [11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5], [6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3], [5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2], [9, 5, 6, 9, 6, 0, 0, 6, 2], [1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8], [1, 5, 6, 2, 1, 6], [1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6], [10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0], [0, 3, 8, 5, 6, 10], [10, 5, 6], [11, 5, 10, 7, 5, 11], [11, 5, 10, 11, 7, 5, 8, 3, 0], [5, 11, 7, 5, 10, 11, 1, 9, 0], [10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1], [11, 1, 2, 11, 7, 1, 7, 5, 1], [0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11], [9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7], [7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2], [2, 5, 10, 2, 3, 5, 3, 7, 5], [8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5], [9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2], [9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2], [1, 3, 5, 3, 7, 5], [0, 8, 7, 0, 7, 1, 1, 7, 5], [9, 0, 3, 9, 3, 5, 5, 3, 7], [9, 8, 7, 5, 9, 7], [5, 8, 4, 5, 10, 8, 10, 11, 8], [5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0], [0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5], [10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4], [2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8], [0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11], [0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5], [9, 4, 5, 2, 11, 3], [2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4], [5, 10, 2, 5, 2, 4, 4, 2, 0], [3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9], [5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2], [8, 4, 5, 8, 5, 3, 3, 5, 1], [0, 4, 5, 1, 0, 5], [8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5], [9, 4, 5], [4, 11, 7, 4, 9, 11, 9, 10, 11], [0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11], [1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11], [3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4], [4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2], [9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3], [11, 7, 4, 11, 4, 2, 2, 4, 0], [11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4], [2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9], [9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7], [3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10], [1, 10, 2, 8, 7, 4], [4, 9, 1, 4, 1, 7, 7, 1, 3], [4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1], [4, 0, 3, 7, 4, 3], [4, 8, 7], [9, 10, 8, 10, 11, 8], [3, 0, 9, 3, 9, 11, 11, 9, 10], [0, 1, 10, 0, 10, 8, 8, 10, 11], [3, 1, 10, 11, 3, 10], [1, 2, 11, 1, 11, 9, 9, 11, 8], [3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9], [0, 2, 11, 8, 0, 11], [3, 2, 11], [2, 3, 8, 2, 8, 10, 10, 8, 9], [9, 10, 2, 0, 9, 2], [2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8], [1, 10, 2], [1, 3, 8, 9, 1, 8], [0, 9, 1], [0, 3, 8], [] ] edgeShifts = np.array([ ## maps edge ID (0-11) to (x,y,z) cell offset and edge ID (0-2) [0, 0, 0, 0], [1, 0, 0, 1], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 1, 1], [0, 1, 1, 0], [0, 0, 1, 1], [0, 0, 0, 2], [1, 0, 0, 2], [1, 1, 0, 2], [0, 1, 0, 2], #[9, 9, 9, 9] ## fake ], dtype=np.uint16) # don't use ubyte here! This value gets added to cell index later; will need the extra precision. nTableFaces = np.array([len(f)/3 for f in triTable], dtype=np.ubyte) faceShiftTables = [None] for i in range(1,6): ## compute lookup table of index: vertexes mapping faceTableI = np.zeros((len(triTable), i*3), dtype=np.ubyte) faceTableInds = np.argwhere(nTableFaces == i) faceTableI[faceTableInds[:,0]] = np.array([triTable[j[0]] for j in faceTableInds]) faceTableI = faceTableI.reshape((len(triTable), i, 3)) faceShiftTables.append(edgeShifts[faceTableI]) ## Let's try something different: #faceTable = np.empty((256, 5, 3, 4), dtype=np.ubyte) # (grid cell index, faces, vertexes, edge lookup) #for i,f in enumerate(triTable): #f = np.array(f + [12] * (15-len(f))).reshape(5,3) #faceTable[i] = edgeShifts[f] IsosurfaceDataCache = (faceShiftTables, edgeShifts, edgeTable, nTableFaces) else: faceShiftTables, edgeShifts, edgeTable, nTableFaces = IsosurfaceDataCache # We use strides below, which means we need contiguous array input. # Ideally we can fix this just by removing the dependency on strides. if not data.flags['C_CONTIGUOUS']: raise TypeError("isosurface input data must be c-contiguous.") ## mark everything below the isosurface level mask = data < level ### make eight sub-fields and compute indexes for grid cells index = np.zeros([x-1 for x in data.shape], dtype=np.ubyte) fields = np.empty((2,2,2), dtype=object) slices = [slice(0,-1), slice(1,None)] for i in [0,1]: for j in [0,1]: for k in [0,1]: fields[i,j,k] = mask[slices[i], slices[j], slices[k]] vertIndex = i - 2*j*i + 3*j + 4*k ## this is just to match Bourk's vertex numbering scheme np.add(index, fields[i,j,k] * 2**vertIndex, out=index, casting='unsafe') ### Generate table of edges that have been cut cutEdges = np.zeros([x+1 for x in index.shape]+[3], dtype=np.uint32) edges = edgeTable[index] for i, shift in enumerate(edgeShifts[:12]): slices = [slice(shift[j],cutEdges.shape[j]+(shift[j]-1)) for j in range(3)] cutEdges[slices[0], slices[1], slices[2], shift[3]] += edges & 2**i ## for each cut edge, interpolate to see where exactly the edge is cut and generate vertex positions m = cutEdges > 0 vertexInds = np.argwhere(m) ## argwhere is slow! vertexes = vertexInds[:,:3].astype(np.float32) dataFlat = data.reshape(data.shape[0]*data.shape[1]*data.shape[2]) ## re-use the cutEdges array as a lookup table for vertex IDs cutEdges[vertexInds[:,0], vertexInds[:,1], vertexInds[:,2], vertexInds[:,3]] = np.arange(vertexInds.shape[0]) for i in [0,1,2]: vim = vertexInds[:,3] == i vi = vertexInds[vim, :3] viFlat = (vi * (np.array(data.strides[:3]) // data.itemsize)[np.newaxis,:]).sum(axis=1) v1 = dataFlat[viFlat] v2 = dataFlat[viFlat + data.strides[i]//data.itemsize] vertexes[vim,i] += (level-v1) / (v2-v1) ### compute the set of vertex indexes for each face. ## This works, but runs a bit slower. #cells = np.argwhere((index != 0) & (index != 255)) ## all cells with at least one face #cellInds = index[cells[:,0], cells[:,1], cells[:,2]] #verts = faceTable[cellInds] #mask = verts[...,0,0] != 9 #verts[...,:3] += cells[:,np.newaxis,np.newaxis,:] ## we now have indexes into cutEdges #verts = verts[mask] #faces = cutEdges[verts[...,0], verts[...,1], verts[...,2], verts[...,3]] ## and these are the vertex indexes we want. ## To allow this to be vectorized efficiently, we count the number of faces in each ## grid cell and handle each group of cells with the same number together. ## determine how many faces to assign to each grid cell nFaces = nTableFaces[index] totFaces = nFaces.sum() faces = np.empty((totFaces, 3), dtype=np.uint32) ptr = 0 #import debug #p = debug.Profiler() ## this helps speed up an indexing operation later on cs = np.array(cutEdges.strides)//cutEdges.itemsize cutEdges = cutEdges.flatten() ## this, strangely, does not seem to help. #ins = np.array(index.strides)/index.itemsize #index = index.flatten() for i in range(1,6): ### expensive: #profiler() cells = np.argwhere(nFaces == i) ## all cells which require i faces (argwhere is expensive) #profiler() if cells.shape[0] == 0: continue cellInds = index[cells[:,0], cells[:,1], cells[:,2]] ## index values of cells to process for this round #profiler() ### expensive: verts = faceShiftTables[i][cellInds] #profiler() np.add(verts[...,:3], cells[:,np.newaxis,np.newaxis,:], out=verts[...,:3], casting='unsafe') ## we now have indexes into cutEdges verts = verts.reshape((verts.shape[0]*i,)+verts.shape[2:]) #profiler() ### expensive: verts = (verts * cs[np.newaxis, np.newaxis, :]).sum(axis=2) vertInds = cutEdges[verts] #profiler() nv = vertInds.shape[0] #profiler() faces[ptr:ptr+nv] = vertInds #.reshape((nv, 3)) #profiler() ptr += nv return vertexes, faces
def _pinv_fallback(tr): arr = np.array([tr.m11(), tr.m12(), tr.m13(), tr.m21(), tr.m22(), tr.m23(), tr.m31(), tr.m32(), tr.m33()]) arr.shape = (3, 3) pinv = np.linalg.pinv(arr) return QtGui.QTransform(*pinv.ravel().tolist()) def invertQTransform(tr): """Return a QTransform that is the inverse of *tr*. A pseudo-inverse is returned if tr is not invertible. Note that this function is preferred over QTransform.inverted() due to bugs in that method. (specifically, Qt has floating-point precision issues when determining whether a matrix is invertible) """ try: det = tr.determinant() detr = 1.0 / det # let singular matrices raise ZeroDivisionError inv = tr.adjoint() inv *= detr return inv except ZeroDivisionError: return _pinv_fallback(tr)
[docs]def pseudoScatter(data, spacing=None, shuffle=True, bidir=False, method='exact'): """Return an array of position values needed to make beeswarm or column scatter plots. Used for examining the distribution of values in an array. Given an array of x-values, construct an array of y-values such that an x,y scatter-plot will not have overlapping points (it will look similar to a histogram). """ if method == 'exact': return _pseudoScatterExact(data, spacing=spacing, shuffle=shuffle, bidir=bidir) elif method == 'histogram': return _pseudoScatterHistogram(data, spacing=spacing, shuffle=shuffle, bidir=bidir)
def _pseudoScatterHistogram(data, spacing=None, shuffle=True, bidir=False): """Works by binning points into a histogram and spreading them out to fill the bin. Faster method, but can produce blocky results. """ inds = np.arange(len(data)) if shuffle: np.random.shuffle(inds) data = data[inds] if spacing is None: spacing = 2.*np.std(data)/len(data)**0.5 yvals = np.empty(len(data)) dmin = data.min() dmax = data.max() nbins = int((dmax-dmin) / spacing) + 1 bins = np.linspace(dmin, dmax, nbins) dx = bins[1] - bins[0] dbins = ((data - bins[0]) / dx).astype(int) binCounts = {} for i,j in enumerate(dbins): c = binCounts.get(j, -1) + 1 binCounts[j] = c yvals[i] = c if bidir is True: for i in range(nbins): yvals[dbins==i] -= binCounts.get(i, 0) * 0.5 return yvals[np.argsort(inds)] ## un-shuffle values before returning def _pseudoScatterExact(data, spacing=None, shuffle=True, bidir=False): """Works by stacking points up one at a time, searching for the lowest position available at each point. This method produces nice, smooth results but can be prohibitively slow for large datasets. """ inds = np.arange(len(data)) if shuffle: np.random.shuffle(inds) data = data[inds] if spacing is None: spacing = 2.*np.std(data)/len(data)**0.5 s2 = spacing**2 yvals = np.empty(len(data)) if len(data) == 0: return yvals yvals[0] = 0 for i in range(1,len(data)): x = data[i] # current x value to be placed x0 = data[:i] # all x values already placed y0 = yvals[:i] # all y values already placed y = 0 dx = (x0-x)**2 # x-distance to each previous point xmask = dx < s2 # exclude anything too far away if xmask.sum() > 0: if bidir: dirs = [-1, 1] else: dirs = [1] yopts = [] for direction in dirs: y = 0 dx2 = dx[xmask] dy = (s2 - dx2)**0.5 limits = np.empty((2,len(dy))) # ranges of y-values to exclude limits[0] = y0[xmask] - dy limits[1] = y0[xmask] + dy while True: # ignore anything below this y-value if direction > 0: mask = limits[1] >= y else: mask = limits[0] <= y limits2 = limits[:,mask] # are we inside an excluded region? mask = (limits2[0] < y) & (limits2[1] > y) if mask.sum() == 0: break if direction > 0: y = limits2[:,mask].max() else: y = limits2[:,mask].min() yopts.append(y) if bidir: y = yopts[0] if -yopts[0] < yopts[1] else yopts[1] else: y = yopts[0] yvals[i] = y return yvals[np.argsort(inds)] ## un-shuffle values before returning def toposort(deps, nodes=None, seen=None, stack=None, depth=0): """Topological sort. Arguments are: deps dictionary describing dependencies where a:[b,c] means "a depends on b and c" nodes optional, specifies list of starting nodes (these should be the nodes which are not depended on by any other nodes). Other candidate starting nodes will be ignored. Example:: # Sort the following graph: # # B ──┬─────> C <── D # │ │ # E <─┴─> A <─┘ # deps = {'a': ['b', 'c'], 'c': ['b', 'd'], 'e': ['b']} toposort(deps) => ['b', 'd', 'c', 'a', 'e'] """ # fill in empty dep lists deps = deps.copy() for k,v in list(deps.items()): for k in v: if k not in deps: deps[k] = [] if nodes is None: ## run through deps to find nodes that are not depended upon rem = set() for dep in deps.values(): rem |= set(dep) nodes = set(deps.keys()) - rem if seen is None: seen = set() stack = [] sorted = [] for n in nodes: if n in stack: raise Exception("Cyclic dependency detected", stack + [n]) if n in seen: continue seen.add(n) sorted.extend( toposort(deps, deps[n], seen, stack+[n], depth=depth+1)) sorted.append(n) return sorted def disconnect(signal, slot): """Disconnect a Qt signal from a slot. This method augments Qt's Signal.disconnect(): * Return bool indicating whether disconnection was successful, rather than raising an exception * Attempt to disconnect prior versions of the slot when using pg.reload """ while True: try: signal.disconnect(slot) return True except (TypeError, RuntimeError): slot = reload.getPreviousVersion(slot) if slot is None: return False class SignalBlock(object): """Class used to temporarily block a Qt signal connection:: with SignalBlock(signal, slot): # do something that emits a signal; it will # not be delivered to slot """ def __init__(self, signal, slot): self.signal = signal self.slot = slot def __enter__(self): self.reconnect = disconnect(self.signal, self.slot) return self def __exit__(self, *args): if self.reconnect: self.signal.connect(self.slot)