def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.handlelen + self.handletextsep if isinstance(handle, Line2D): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) legline.update_from(handle) self._set_artist_props(legline) # after update legline.set_clip_box(None) legline.set_markersize(self.markerscale * legline.get_markersize()) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle( xy=(min(self._xdata), y - 3 / 4 * HEIGHT), width=self.handlelen, height=HEIGHT / 2, ) p.update_from(handle) self._set_artist_props(p) p.set_clip_box(None) ret.append(p) elif isinstance(handle, LineCollection): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.set_clip_box(None) lw = handle.get_linewidth()[0] dashes = handle.get_dashes() color = handle.get_colors()[0] legline.set_color(color) legline.set_linewidth(lw) legline.set_dashes(dashes) ret.append(legline) elif isinstance(handle, RegularPolyCollection): p = Rectangle( xy=(min(self._xdata), y - 3 / 4 * HEIGHT), width=self.handlelen, height=HEIGHT / 2, ) p.set_facecolor(handle._facecolors[0]) if handle._edgecolors != 'None': p.set_edgecolor(handle._edgecolors[0]) self._set_artist_props(p) p.set_clip_box(None) ret.append(p) else: ret.append(None) return ret
def _get_plottable(self): # If log scale is set, only pos data will be returned x, y = self._x, self._y try: logx = self._transform.get_funcx().get_type()==LOG10 except RuntimeError: logx = False # non-separable try: logy = self._transform.get_funcy().get_type()==LOG10 except RuntimeError: logy = False # non-separable if not logx and not logy: return x, y if self._logcache is not None: waslogx, waslogy, xcache, ycache = self._logcache if logx==waslogx and waslogy==logy: return xcache, ycache Nx = len(x) Ny = len(y) if logx: indx = greater(x, 0) else: indx = ones(len(x)) if logy: indy = greater(y, 0) else: indy = ones(len(y)) ind = nonzero(logical_and(indx, indy)) x = take(x, ind) y = take(y, ind) self._logcache = logx, logy, x, y return x, y
def _update_x_y_logcache(self): # check cache need_update = False try: for key, var_id in self._cache_inputs.iteritems(): if (id(getattr(self, key)) != var_id): need_update = True break except: need_update = True if (not need_update): return # update cache for key in self._cache_inputs.keys(): try: self._cache_inputs[key] = id(getattr(self, key)) except: pass # make sure that result values exist and release # previous values self._cached__x = None self._cached__y = None self._cached__segments = None self._cached__logcache = None if (self.is_unitsmgr_set()): unitsmgr = self.get_unitsmgr() x, y = unitsmgr._convert_units((self._x_orig, self._xunits), (self._y_orig, self._yunits)) else: x, y = (self._x_orig, self._y_orig) x = ma.ravel(x) y = ma.ravel(y) if len(x) == 1 and len(y) > 1: x = x * ones(y.shape, Float) if len(y) == 1 and len(x) > 1: y = y * ones(x.shape, Float) if len(x) != len(y): raise RuntimeError('xdata and ydata must be the same length') mx = ma.getmask(x) my = ma.getmask(y) mask = ma.mask_or(mx, my) if mask is not ma.nomask: x = ma.masked_array(x, mask=mask).compressed() y = ma.masked_array(y, mask=mask).compressed() self._cached__segments = unmasked_index_ranges(mask) else: self._cached__segments = None self._cached__x = asarray(x, Float) self._cached__y = asarray(y, Float) self._cached__logcache = None
def _update_x_y_logcache(self): # check cache need_update = False try: for key, var_id in self._cache_inputs.iteritems(): if id(getattr(self, key)) != var_id: need_update = True break except: need_update = True if not need_update: return # update cache for key in self._cache_inputs.keys(): try: self._cache_inputs[key] = id(getattr(self, key)) except: pass # make sure that result values exist and release # previous values self._cached__x = None self._cached__y = None self._cached__segments = None self._cached__logcache = None if self.is_unitsmgr_set(): unitsmgr = self.get_unitsmgr() x, y = unitsmgr._convert_units((self._x_orig, self._xunits), (self._y_orig, self._yunits)) else: x, y = (self._x_orig, self._y_orig) x = ma.ravel(x) y = ma.ravel(y) if len(x) == 1 and len(y) > 1: x = x * ones(y.shape, Float) if len(y) == 1 and len(x) > 1: y = y * ones(x.shape, Float) if len(x) != len(y): raise RuntimeError("xdata and ydata must be the same length") mx = ma.getmask(x) my = ma.getmask(y) mask = ma.mask_or(mx, my) if mask is not ma.nomask: x = ma.masked_array(x, mask=mask).compressed() y = ma.masked_array(y, mask=mask).compressed() self._cached__segments = unmasked_index_ranges(mask) else: self._cached__segments = None self._cached__x = asarray(x, Float) self._cached__y = asarray(y, Float) self._cached__logcache = None
def vec_pad_ones(xs, ys, zs): try: try: vec = nx.array([xs, ys, zs, nx.ones(xs.shape)]) except (AttributeError, TypeError): vec = nx.array([xs, ys, zs, nx.ones((len(xs)))]) except TypeError: vec = nx.array([xs, ys, zs, 1]) return vec
def _draw_steps(self, renderer, gc, xt, yt): siz=len(xt) if siz<2: return xt2=ones((2*siz,), xt.typecode()) xt2[0:-1:2], xt2[1:-1:2], xt2[-1]=xt, xt[1:], xt[-1] yt2=ones((2*siz,), yt.typecode()) yt2[0:-1:2], yt2[1::2]=yt, yt gc.set_linestyle('solid') gc.set_capstyle('projecting') renderer.draw_lines(gc, xt2, yt2)
def _draw_steps(self, renderer, gc, xt, yt): siz = len(xt) if siz < 2: return xt2 = ones((2 * siz, ), xt.typecode()) xt2[0:-1:2], xt2[1:-1:2], xt2[-1] = xt, xt[1:], xt[-1] yt2 = ones((2 * siz, ), yt.typecode()) yt2[0:-1:2], yt2[1::2] = yt, yt gc.set_linestyle('solid') gc.set_capstyle('projecting') renderer.draw_lines(gc, xt2, yt2)
def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.handlelen + self.handletextsep if isinstance(handle, Line2D): ydata = (y-HEIGHT/2)*ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) legline.update_from(handle) self._set_artist_props(legline) # after update legline.set_clip_box(None) legline.set_markersize(self.markerscale*legline.get_markersize()) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle(xy=(min(self._xdata), y-3/4*HEIGHT), width = self.handlelen, height=HEIGHT/2, ) p.update_from(handle) self._set_artist_props(p) p.set_clip_box(None) ret.append(p) elif isinstance(handle, LineCollection): ydata = (y-HEIGHT/2)*ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.set_clip_box(None) lw = handle.get_linewidth()[0] dashes = handle.get_dashes() color = handle.get_colors()[0] legline.set_color(color) legline.set_linewidth(lw) legline.set_dashes(dashes) ret.append(legline) elif isinstance(handle, RegularPolyCollection): p = Rectangle(xy=(min(self._xdata), y-3/4*HEIGHT), width = self.handlelen, height=HEIGHT/2, ) p.set_facecolor(handle._facecolors[0]) if handle._edgecolors != 'None': p.set_edgecolor(handle._edgecolors[0]) self._set_artist_props(p) p.set_clip_box(None) ret.append(p) else: ret.append(None) return ret
def _draw_steps(self, renderer, gc, xt, yt): siz=len(xt) if siz<2: return xt2=ones((2*siz,), typecode(xt)) xt2[0:-1:2], xt2[1:-1:2], xt2[-1]=xt, xt[1:], xt[-1] yt2=ones((2*siz,), typecode(yt)) yt2[0:-1:2], yt2[1::2]=yt, yt gc.set_linestyle('solid') if self._newstyle: renderer.draw_lines(gc, xt2, yt2, self._transform) else: renderer.draw_lines(gc, xt2, yt2)
def _get_numeric_clipped_data_in_range(self): # if the x or y clip is set, only plot the points in the # clipping region. If log scale is set, only pos data will be # returned try: self._xc, self._yc except AttributeError: x, y = self._x, self._y else: x, y = self._xc, self._yc try: logx = self._transform.get_funcx().get_type() == LOG10 except RuntimeError: logx = False # non-separable try: logy = self._transform.get_funcy().get_type() == LOG10 except RuntimeError: logy = False # non-separable if not logx and not logy: return x, y if self._logcache is not None: waslogx, waslogy, xcache, ycache = self._logcache if logx == waslogx and waslogy == logy: return xcache, ycache Nx = len(x) Ny = len(y) if logx: indx = greater(x, 0) else: indx = ones(len(x)) if logy: indy = greater(y, 0) else: indy = ones(len(y)) ind = nonzero(logical_and(indx, indy)) x = take(x, ind) y = take(y, ind) self._logcache = logx, logy, x, y return x, y
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args)==1: x, y = args[0] else: x, y = args self._x_orig = x self._y_orig = y if (self._xunits and hasattr(x, 'convert_to')): x = x.convert_to(self._xunits).get_value() if (hasattr(x, 'get_value')): x = x.get_value() if (self._yunits and hasattr(y, 'convert_to')): y = y.convert_to(self._yunits).get_value() if (hasattr(y, 'get_value')): y = y.get_value() x = ma.ravel(x) y = ma.ravel(y) if len(x)==1 and len(y)>1: x = x * ones(y.shape, Float) if len(y)==1 and len(x)>1: y = y * ones(x.shape, Float) if len(x) != len(y): raise RuntimeError('xdata and ydata must be the same length') mx = ma.getmask(x) my = ma.getmask(y) mask = ma.mask_or(mx, my) if mask is not ma.nomask: x = ma.masked_array(x, mask=mask).compressed() y = ma.masked_array(y, mask=mask).compressed() self._segments = unmasked_index_ranges(mask) else: self._segments = None self._x = asarray(x, Float) self._y = asarray(y, Float) self._logcache = None
def psd(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0): """ The power spectral density by Welches average periodogram method. The vector x is divided into NFFT length segments. Each segment is detrended by function detrend and windowed by function window. noperlap gives the length of the overlap between segments. The absolute(fft(segment))**2 of each segment are averaged to compute Pxx, with a scaling to correct for power loss due to windowing. Fs is the sampling frequency. -- NFFT must be a power of 2 -- detrend and window are functions, unlike in matlab where they are vectors. -- if length x < NFFT, it will be zero padded to NFFT Returns the tuple Pxx, freqs Refs: Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986) """ if NFFT % 2: raise ValueError, 'NFFT must be a power of 2' # zero pad x up to NFFT if it is shorter than NFFT if len(x)<NFFT: n = len(x) x = resize(x, (NFFT,)) x[n:] = 0 # for real x, ignore the negative frequencies if x.typecode()==Complex: numFreqs = NFFT else: numFreqs = NFFT//2+1 windowVals = window(ones((NFFT,),x.typecode())) step = NFFT-noverlap ind = range(0,len(x)-NFFT+1,step) n = len(ind) Pxx = zeros((numFreqs,n), Float) # do the ffts of the slices for i in range(n): thisX = x[ind[i]:ind[i]+NFFT] thisX = windowVals*detrend(thisX) fx = absolute(fft(thisX))**2 Pxx[:,i] = divide(fx[:numFreqs], norm(windowVals)**2) # Scale the spectrum by the norm of the window to compensate for # windowing loss; see Bendat & Piersol Sec 11.5.2 if n>1: Pxx = mean(Pxx,1) freqs = Fs/NFFT*arange(numFreqs) Pxx.shape = len(freqs), return Pxx, freqs
def _update_positions(self, renderer): # called from renderer to allow more precise estimates of # widths and heights with get_window_extent def get_tbounds(text): #get text bounds in axes coords bbox = text.get_window_extent(renderer) bboxa = inverse_transform_bbox(self._transform, bbox) return bboxa.get_bounds() hpos = [] for t, tabove in zip(self.texts[1:], self.texts[:-1]): x,y = t.get_position() l,b,w,h = get_tbounds(tabove) hpos.append( (b,h) ) t.set_position( (x, b-0.1*h) ) # now do the same for last line l,b,w,h = get_tbounds(self.texts[-1]) hpos.append( (b,h) ) for handle, tup in zip(self.handles, hpos): y,h = tup if isinstance(handle, Line2D): ydata = y*ones(self._xdata.shape, Float) handle.set_ydata(ydata+h/2) elif isinstance(handle, Rectangle): handle.set_y(y+1/4*h) handle.set_height(h/2) # Set the data for the legend patch bbox = self._get_handle_text_bbox(renderer).deepcopy() bbox.scale(1 + self.pad, 1 + self.pad) l,b,w,h = bbox.get_bounds() self.legendPatch.set_bounds(l,b,w,h) BEST, UR, UL, LL, LR, R, CL, CR, LC, UC, C = range(11) ox, oy = 0, 0 # center if iterable(self._loc) and len(self._loc)==2: xo = self.legendPatch.get_x() yo = self.legendPatch.get_y() x, y = self._loc ox = x-xo oy = y-yo self._offset(ox, oy) else: if self._loc in (UL, LL, CL): # left ox = self.axespad - l if self._loc in (BEST, UR, LR, R, CR): # right ox = 1 - (l + w + self.axespad) if self._loc in (BEST, UR, UL, UC): # upper oy = 1 - (b + h + self.axespad) if self._loc in (LL, LR, LC): # lower oy = self.axespad - b if self._loc in (LC, UC, C): # center x ox = (0.5-w/2)-l if self._loc in (CL, CR, C): # center y oy = (0.5-h/2)-b self._offset(ox, oy)
def _init(self): self._lut = ones((self.N + 3, 4), Float) self._lut[:-3, 0] = makeMappingArray(self.N, self._segmentdata['red']) self._lut[:-3, 1] = makeMappingArray(self.N, self._segmentdata['green']) self._lut[:-3, 2] = makeMappingArray(self.N, self._segmentdata['blue']) self._isinit = True self._set_extremes()
def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.HANDLELEN + self.HANDLETEXTSEP if isinstance(handle, Line2D): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.copy_properties(handle) legline.set_markersize(0.6 * legline.get_markersize()) legline.set_data_clipping(False) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle( xy=(min(self._xdata), y - 3 / 4 * HEIGHT), width=self.HANDLELEN, height=HEIGHT / 2, ) self._set_artist_props(p) p.copy_properties(handle) ret.append(p) else: ret.append(None) return ret
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args)==1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape)>1: self._x = ravel(self._x) if len(self._y.shape)>1: self._y = ravel(self._y) if len(self._y)==1 and len(self._x)>1: self._y = self._y*ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError('xdata and ydata must be the same length') if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.HANDLELEN + self.HANDLETEXTSEP if isinstance(handle, Line2D): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.copy_properties(handle) legline.set_markersize(0.6 * legline.get_markersize()) legline.set_data_clipping(False) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle(xy=(min(self._xdata), y - 3 / 4 * HEIGHT), width=self.HANDLELEN, height=HEIGHT / 2) self._set_artist_props(p) p.copy_properties(handle) ret.append(p) else: ret.append(None) return ret
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args) == 1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape) > 1: self._x = ravel(self._x) if len(self._y.shape) > 1: self._y = ravel(self._y) if len(self._y) == 1 and len(self._x) > 1: self._y = self._y * ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError('xdata and ydata must be the same length') if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args) == 1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._x_orig = x self._y_orig = y x = ma.ravel(x) y = ma.ravel(y) if len(x) == 1 and len(y) > 1: x = x * ones(y.shape, Float) if len(y) == 1 and len(x) > 1: y = y * ones(x.shape, Float) if len(x) != len(y): raise RuntimeError("xdata and ydata must be the same length") mx = ma.getmask(x) my = ma.getmask(y) mask = ma.mask_or(mx, my) if mask is not None: x = ma.masked_array(x, mask=mask).compressed() y = ma.masked_array(y, mask=mask).compressed() self._segments = unmasked_index_ranges(mask) else: self._segments = None self._x = asarray(x, Float) self._y = asarray(y, Float) if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args) == 1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._x_orig = x self._y_orig = y x = ma.ravel(x) y = ma.ravel(y) if len(x) == 1 and len(y) > 1: x = x * ones(y.shape, Float) if len(y) == 1 and len(x) > 1: y = y * ones(x.shape, Float) if len(x) != len(y): raise RuntimeError('xdata and ydata must be the same length') mx = ma.getmask(x) my = ma.getmask(y) mask = ma.mask_or(mx, my) if mask is not None: x = ma.masked_array(x, mask=mask).compressed() y = ma.masked_array(y, mask=mask).compressed() self._segments = unmasked_index_ranges(mask) else: self._segments = None self._x = asarray(x, Float) self._y = asarray(y, Float) if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args) == 1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._masked_x = None self._masked_y = None mx = ma.getmask(x) my = ma.getmask(y) if mx is not None: mx = ravel(mx) self._masked_x = x if my is not None: my = ravel(my) self._masked_y = y mask = ma.mask_or(mx, my) if mask is not None: x = ma.masked_array(ma.ravel(x), mask=mask).compressed() y = ma.masked_array(ma.ravel(y), mask=mask).compressed() self._segments = unmasked_index_ranges(mask) else: self._segments = None self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape) > 1: self._x = ravel(self._x) if len(self._y.shape) > 1: self._y = ravel(self._y) # What is the rationale for the following two lines? # And why is there not a similar pair with _x and _y reversed? if len(self._y) == 1 and len(self._x) > 1: self._y = self._y * ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError("xdata and ydata must be the same length") if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def set_data(self, *args): """ Set the x and y data ACCEPTS: (array xdata, array ydata) """ if len(args) == 1: x, y = args[0] else: x, y = args try: del self._xc, self._yc except AttributeError: pass self._masked_x = None self._masked_y = None mx = ma.getmask(x) my = ma.getmask(y) if mx is not None: mx = ravel(mx) self._masked_x = x if my is not None: my = ravel(my) self._masked_y = y mask = ma.mask_or(mx, my) if mask is not None: x = ma.masked_array(ma.ravel(x), mask=mask).compressed() y = ma.masked_array(ma.ravel(y), mask=mask).compressed() self._segments = unmasked_index_ranges(mask) else: self._segments = None self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape) > 1: self._x = ravel(self._x) if len(self._y.shape) > 1: self._y = ravel(self._y) # What is the rationale for the following two lines? # And why is there not a similar pair with _x and _y reversed? if len(self._y) == 1 and len(self._x) > 1: self._y = self._y * ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError('xdata and ydata must be the same length') if self._useDataClipping: self._xsorted = self._is_sorted(self._x) self._logcache = None
def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.handlelen + self.handletextsep if isinstance(handle, Line2D): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.copy_properties(handle) legline.set_markersize(0.6 * legline.get_markersize()) legline.set_data_clipping(False) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle( xy=(min(self._xdata), y - 3 / 4 * HEIGHT), width=self.handlelen, height=HEIGHT / 2, ) p.copy_properties(handle) self._set_artist_props(p) ret.append(p) elif isinstance(handle, LineCollection): ydata = (y - HEIGHT / 2) * ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) lw = handle.get_linewidths()[0] color = handle.get_colors()[0] legline.set_color(color) legline.set_linewidth(lw) ret.append(legline) else: ret.append(None) return ret
def _get_handles(self, handles, texts): HEIGHT = self._approx_text_height() ret = [] # the returned legend lines for handle, label in zip(handles, texts): x, y = label.get_position() x -= self.handlelen + self.handletextsep if isinstance(handle, Line2D): ydata = (y-HEIGHT/2)*ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) legline.copy_properties(handle) legline.set_markersize(self.markerscale*legline.get_markersize()) legline.set_data_clipping(False) ret.append(legline) elif isinstance(handle, Patch): p = Rectangle(xy=(min(self._xdata), y-3/4*HEIGHT), width = self.handlelen, height=HEIGHT/2, ) p.copy_properties(handle) self._set_artist_props(p) ret.append(p) elif isinstance(handle, LineCollection): ydata = (y-HEIGHT/2)*ones(self._xdata.shape, Float) legline = Line2D(self._xdata, ydata) self._set_artist_props(legline) lw = handle.get_linewidths()[0] color = handle.get_colors()[0] legline.set_color(color) legline.set_linewidth(lw) ret.append(legline) else: ret.append(None) return ret
def vander(x, N=None): """ X = vander(x,N=None) The Vandermonde matrix of vector x. The i-th column of X is the the i-th power of x. N is the maximum power to compute; if N is None it defaults to len(x). """ if N is None: N = len(x) X = ones((len(x), N), typecode(x)) for i in range(N - 1): X[:, i] = x**(N - i - 1) return X
def vander(x,N=None): """ X = vander(x,N=None) The Vandermonde matrix of vector x. The i-th column of X is the the i-th power of x. N is the maximum power to compute; if N is None it defaults to len(x). """ if N is None: N=len(x) X = ones( (len(x),N), x.typecode()) for i in range(N-1): X[:,i] = x**(N-i-1) return X
def specgram(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=128): """ Compute a spectrogram of data in x. Data are split into NFFT length segements and the PSD of each section is computed. The windowing function window is applied to each segment, and the amount of overlap of each segment is specified with noverlap See pdf for more info. The returned times are the midpoints of the intervals over which the ffts are calculated """ x = asarray(x) assert (NFFT > noverlap) if log(NFFT) / log(2) != int(log(NFFT) / log(2)): raise ValueError, 'NFFT must be a power of 2' # zero pad x up to NFFT if it is shorter than NFFT if len(x) < NFFT: n = len(x) x = resize(x, (NFFT, )) x[n:] = 0 # for real x, ignore the negative frequencies if typecode(x) == Complex: numFreqs = NFFT else: numFreqs = NFFT // 2 + 1 windowVals = window(ones((NFFT, ), typecode(x))) step = NFFT - noverlap ind = arange(0, len(x) - NFFT + 1, step) n = len(ind) Pxx = zeros((numFreqs, n), Float) # do the ffts of the slices for i in range(n): thisX = x[ind[i]:ind[i] + NFFT] thisX = windowVals * detrend(thisX) fx = absolute(fft(thisX))**2 # Scale the spectrum by the norm of the window to compensate for # windowing loss; see Bendat & Piersol Sec 11.5.2 Pxx[:, i] = divide(fx[:numFreqs], norm(windowVals)**2) t = 1 / Fs * (ind + NFFT / 2) freqs = Fs / NFFT * arange(numFreqs) return Pxx, freqs, t
def get_vector(self): """optimise points for projection""" si = 0 ei = 0 segis = [] points = [] for p in self._verts: points.extend(p) ei = si + len(p) segis.append((si, ei)) si = ei xs, ys, zs = zip(*points) ones = nx.ones(len(xs)) self.vec = nx.array([xs, ys, zs, ones]) self.segis = segis
def get_vector(self): """optimise points for projection""" si = 0 ei = 0 segis = [] points = [] for p in self._verts: points.extend(p) ei = si+len(p) segis.append((si,ei)) si = ei xs,ys,zs = zip(*points) ones = nx.ones(len(xs)) self.vec = nx.array([xs,ys,zs,ones]) self.segis = segis
def specgram(x, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=128): """ Compute a spectrogram of data in x. Data are split into NFFT length segements and the PSD of each section is computed. The windowing function window is applied to each segment, and the amount of overlap of each segment is specified with noverlap See pdf for more info. The returned times are the midpoints of the intervals over which the ffts are calculated """ assert(NFFT>noverlap) if log(NFFT)/log(2) != int(log(NFFT)/log(2)): raise ValueError, 'NFFT must be a power of 2' # zero pad x up to NFFT if it is shorter than NFFT if len(x)<NFFT: n = len(x) x = resize(x, (NFFT,)) x[n:] = 0 # for real x, ignore the negative frequencies if x.typecode()==Complex: numFreqs = NFFT else: numFreqs = NFFT//2+1 windowVals = window(ones((NFFT,),x.typecode())) step = NFFT-noverlap ind = arange(0,len(x)-NFFT+1,step) n = len(ind) Pxx = zeros((numFreqs,n), Float) # do the ffts of the slices for i in range(n): thisX = x[ind[i]:ind[i]+NFFT] thisX = windowVals*detrend(thisX) fx = absolute(fft(thisX))**2 # Scale the spectrum by the norm of the window to compensate for # windowing loss; see Bendat & Piersol Sec 11.5.2 Pxx[:,i] = divide(fx[:numFreqs], norm(windowVals)**2) t = 1/Fs*(ind+NFFT/2) freqs = Fs/NFFT*arange(numFreqs) return Pxx, freqs, t
def styles_example(epsoutfile): mystyles = ['.', '-', '-"', '_ ', '6_1 ', '- . '] count = len(mystyles) x1 = 0.8*arange(2) g = pyxgraph(xlimits=(-0.1, 1.1), xticks=(0, 1, 1), ylimits=(-1, count), yticks=(0, count-1, 1), ylabel='linestyles', key=None, width=8) for i in xrange(count): y = ones(2)+i-1 g.pyxplot((x1, y), style="l", lw=1, color=0, lt=mystyles[i]) g.pyxlabel((0.85, i), '\\tt{'+repr(mystyles[i]).replace('_','\\_')+'}', style=[pyx.text.halign.left], graphcoords=True) g.pyxsave(epsoutfile)
def styles_example(epsoutfile): x1 = 0.25*arange(2) x2 = x1+0.5-0.125 x3 = x1+1.0-0.25 g = pyxgraph(xlimits=(-0.1, 1.1), xticks=(0, 1, 1), ylimits=(-1, 12), yticks=(0, 11, 1), ylabel='linestyles', key=None, width=8) for i in xrange(12): y = ones(2)+i-1 g.pyxplot((x1, y), style="l", lw=1, color=0, lt=i) g.pyxplot((x2, y), style="l", lw=3, color=0, lt=i) g.pyxplot((x3, y), style="l", lw=1, color=0, lt=i, dl=4) g.pyxlabel( (0.125,1.05), "lw=1", [pyx.text.halign.center]) g.pyxlabel( (0.5,1.05), "lw=3", [pyx.text.halign.center]) g.pyxlabel( (0.875,1.05), "lw=1, dl=4", [pyx.text.halign.center]) g.pyxsave(epsoutfile)
def set_data(self, x, y): try: del self._xc, self._yc except AttributeError: pass self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape)>1: self._x = ravel(self._x) if len(self._y.shape)>1: self._y = ravel(self._y) if len(self._y)==1 and len(self._x)>1: self._y = self._y*ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError('xdata and ydata must be the same length') if self._useDataClipping: self._xsorted = self._is_sorted(self._x)
def set_data(self, x, y): try: del self._xc, self._yc except AttributeError: pass self._x = asarray(x, Float) self._y = asarray(y, Float) if len(self._x.shape) > 1: self._x = ravel(self._x) if len(self._y.shape) > 1: self._y = ravel(self._y) if len(self._y) == 1 and len(self._x) > 1: self._y = self._y * ones(self._x.shape, Float) if len(self._x) != len(self._y): raise RuntimeError('xdata and ydata must be the same length') if self._useDataClipping: self._xsorted = self._is_sorted(self._x)
def _initialize_reg_tri(self, z, badmask): ''' Initialize two arrays used by the low-level contour algorithm. This is temporary code; most of the reg initialization should be done in c. For each masked point, we need to mark as missing the four regions with that point as a corner. ''' imax, jmax = shape(z) nreg = jmax * (imax + 1) + 1 reg = ones((1, nreg), typecode='i') reg[0, :jmax + 1] = 0 reg[0, -jmax:] = 0 for j in range(0, nreg, jmax): reg[0, j] = 0 if badmask is not None: for i in range(imax): for j in range(jmax): if badmask[i, j]: ii = i * jmax + j if ii < nreg: reg[0, ii] = 0 ii += 1 if ii < nreg: reg[0, ii] = 0 ii += jmax if ii < nreg: reg[0, ii] = 0 ii -= 1 if ii < nreg: reg[0, ii] = 0 triangle = zeros((imax, jmax), typecode='s') return reg, triangle
def _initialize_reg_tri(self, z, badmask): ''' Initialize two arrays used by the low-level contour algorithm. This is temporary code; most of the reg initialization should be done in c. For each masked point, we need to mark as missing the four regions with that point as a corner. ''' imax, jmax = shape(z) nreg = jmax*(imax+1)+1 reg = ones((1, nreg), typecode = 'i') reg[0,:jmax+1]=0 reg[0,-jmax:]=0 for j in range(0, nreg, jmax): reg[0,j]=0 if badmask is not None: for i in range(imax): for j in range(jmax): if badmask[i,j]: ii = i*jmax+j if ii < nreg: reg[0,ii] = 0 ii += 1 if ii < nreg: reg[0,ii] = 0 ii += jmax if ii < nreg: reg[0,ii] = 0 ii -= 1 if ii < nreg: reg[0,ii] = 0 triangle = zeros((imax,jmax), typecode='s') return reg, triangle
def csd(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0): """ The cross spectral density Pxy by Welches average periodogram method. The vectors x and y are divided into NFFT length segments. Each segment is detrended by function detrend and windowed by function window. noverlap gives the length of the overlap between segments. The product of the direct FFTs of x and y are averaged over each segment to compute Pxy, with a scaling to correct for power loss due to windowing. Fs is the sampling frequency. NFFT must be a power of 2 Returns the tuple Pxy, freqs Refs: Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986) """ if NFFT % 2: raise ValueError, 'NFFT must be a power of 2' # zero pad x and y up to NFFT if they are shorter than NFFT if len(x) < NFFT: n = len(x) x = resize(x, (NFFT, )) x[n:] = 0 if len(y) < NFFT: n = len(y) y = resize(y, (NFFT, )) y[n:] = 0 # for real x, ignore the negative frequencies if typecode(x) == Complex: numFreqs = NFFT else: numFreqs = NFFT // 2 + 1 windowVals = window(ones((NFFT, ), typecode(x))) step = NFFT - noverlap ind = range(0, len(x) - NFFT + 1, step) n = len(ind) Pxy = zeros((numFreqs, n), Complex) # do the ffts of the slices for i in range(n): thisX = x[ind[i]:ind[i] + NFFT] thisX = windowVals * detrend(thisX) thisY = y[ind[i]:ind[i] + NFFT] thisY = windowVals * detrend(thisY) fx = fft(thisX) fy = fft(thisY) Pxy[:, i] = conjugate(fx[:numFreqs]) * fy[:numFreqs] # Scale the spectrum by the norm of the window to compensate for # windowing loss; see Bendat & Piersol Sec 11.5.2 if n > 1: Pxy = mean(Pxy, 1) Pxy = divide(Pxy, norm(windowVals)**2) freqs = Fs / NFFT * arange(numFreqs) Pxy.shape = len(freqs), return Pxy, freqs
def cohere_pairs(X, ij, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0, preferSpeedOverMemory=True, progressCallback=donothing_callback, returnPxx=False): """ Cxy, Phase, freqs = cohere_pairs( X, ij, ...) Compute the coherence for all pairs in ij. X is a numSamples,numCols Numeric array. ij is a list of tuples (i,j). Each tuple is a pair of indexes into the columns of X for which you want to compute coherence. For example, if X has 64 columns, and you want to compute all nonredundant pairs, define ij as ij = [] for i in range(64): for j in range(i+1,64): ij.append( (i,j) ) The other function arguments, except for 'preferSpeedOverMemory' (see below), are explained in the help string of 'psd'. Return value is a tuple (Cxy, Phase, freqs). Cxy -- a dictionary of (i,j) tuples -> coherence vector for that pair. Ie, Cxy[(i,j) = cohere(X[:,i], X[:,j]). Number of dictionary keys is len(ij) Phase -- a dictionary of phases of the cross spectral density at each frequency for each pair. keys are (i,j). freqs -- a vector of frequencies, equal in length to either the coherence or phase vectors for any i,j key. Eg, to make a coherence Bode plot: subplot(211) plot( freqs, Cxy[(12,19)]) subplot(212) plot( freqs, Phase[(12,19)]) For a large number of pairs, cohere_pairs can be much more efficient than just calling cohere for each pair, because it caches most of the intensive computations. If N is the number of pairs, this function is O(N) for most of the heavy lifting, whereas calling cohere for each pair is O(N^2). However, because of the caching, it is also more memory intensive, making 2 additional complex arrays with approximately the same number of elements as X. The parameter 'preferSpeedOverMemory', if false, limits the caching by only making one, rather than two, complex cache arrays. This is useful if memory becomes critical. Even when preferSpeedOverMemory is false, cohere_pairs will still give significant performace gains over calling cohere for each pair, and will use subtantially less memory than if preferSpeedOverMemory is true. In my tests with a 43000,64 array over all nonredundant pairs, preferSpeedOverMemory=1 delivered a 33% performace boost on a 1.7GHZ Athlon with 512MB RAM compared with preferSpeedOverMemory=0. But both solutions were more than 10x faster than naievly crunching all possible pairs through cohere. See test/cohere_pairs_test.py in the src tree for an example script that shows that this cohere_pairs and cohere give the same results for a given pair. """ numRows, numCols = X.shape # zero pad if X is too short if numRows < NFFT: tmp = X X = zeros((NFFT, numCols), typecode(X)) X[:numRows, :] = tmp del tmp numRows, numCols = X.shape # get all the columns of X that we are interested in by checking # the ij tuples seen = {} for i, j in ij: seen[i] = 1 seen[j] = 1 allColumns = seen.keys() Ncols = len(allColumns) del seen # for real X, ignore the negative frequencies if typecode(X) == Complex: numFreqs = NFFT else: numFreqs = NFFT // 2 + 1 # cache the FFT of every windowed, detrended NFFT length segement # of every channel. If preferSpeedOverMemory, cache the conjugate # as well windowVals = window(ones((NFFT, ), typecode(X))) ind = range(0, numRows - NFFT + 1, NFFT - noverlap) numSlices = len(ind) FFTSlices = {} FFTConjSlices = {} Pxx = {} slices = range(numSlices) normVal = norm(windowVals)**2 for iCol in allColumns: progressCallback(i / Ncols, 'Cacheing FFTs') Slices = zeros((numSlices, numFreqs), Complex) for iSlice in slices: thisSlice = X[ind[iSlice]:ind[iSlice] + NFFT, iCol] thisSlice = windowVals * detrend(thisSlice) Slices[iSlice, :] = fft(thisSlice)[:numFreqs] FFTSlices[iCol] = Slices if preferSpeedOverMemory: FFTConjSlices[iCol] = conjugate(Slices) Pxx[iCol] = divide(mean(absolute(Slices)**2), normVal) del Slices, ind, windowVals # compute the coherences and phases for all pairs using the # cached FFTs Cxy = {} Phase = {} count = 0 N = len(ij) for i, j in ij: count += 1 if count % 10 == 0: progressCallback(count / N, 'Computing coherences') if preferSpeedOverMemory: Pxy = FFTSlices[i] * FFTConjSlices[j] else: Pxy = FFTSlices[i] * conjugate(FFTSlices[j]) if numSlices > 1: Pxy = mean(Pxy) Pxy = divide(Pxy, normVal) Cxy[(i, j)] = divide(absolute(Pxy)**2, Pxx[i] * Pxx[j]) Phase[(i, j)] = arctan2(Pxy.imag, Pxy.real) freqs = Fs / NFFT * arange(numFreqs) if returnPxx: return Cxy, Phase, freqs, Pxx else: return Cxy, Phase, freqs
def cohere_pairs( X, ij, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0, preferSpeedOverMemory=True, progressCallback=donothing_callback, returnPxx=False): """ Cxy, Phase, freqs = cohere_pairs( X, ij, ...) Compute the coherence for all pairs in ij. X is a numSamples,numCols Numeric array. ij is a list of tuples (i,j). Each tuple is a pair of indexes into the columns of X for which you want to compute coherence. For example, if X has 64 columns, and you want to compute all nonredundant pairs, define ij as ij = [] for i in range(64): for j in range(i+1,64): ij.append( (i,j) ) The other function arguments, except for 'preferSpeedOverMemory' (see below), are explained in the help string of 'psd'. Return value is a tuple (Cxy, Phase, freqs). Cxy -- a dictionary of (i,j) tuples -> coherence vector for that pair. Ie, Cxy[(i,j) = cohere(X[:,i], X[:,j]). Number of dictionary keys is len(ij) Phase -- a dictionary of phases of the cross spectral density at each frequency for each pair. keys are (i,j). freqs -- a vector of frequencies, equal in length to either the coherence or phase vectors for any i,j key. Eg, to make a coherence Bode plot: subplot(211) plot( freqs, Cxy[(12,19)]) subplot(212) plot( freqs, Phase[(12,19)]) For a large number of pairs, cohere_pairs can be much more efficient than just calling cohere for each pair, because it caches most of the intensive computations. If N is the number of pairs, this function is O(N) for most of the heavy lifting, whereas calling cohere for each pair is O(N^2). However, because of the caching, it is also more memory intensive, making 2 additional complex arrays with approximately the same number of elements as X. The parameter 'preferSpeedOverMemory', if false, limits the caching by only making one, rather than two, complex cache arrays. This is useful if memory becomes critical. Even when preferSpeedOverMemory is false, cohere_pairs will still give significant performace gains over calling cohere for each pair, and will use subtantially less memory than if preferSpeedOverMemory is true. In my tests with a 43000,64 array over all nonredundant pairs, preferSpeedOverMemory=1 delivered a 33% performace boost on a 1.7GHZ Athlon with 512MB RAM compared with preferSpeedOverMemory=0. But both solutions were more than 10x faster than naievly crunching all possible pairs through cohere. See test/cohere_pairs_test.py in the src tree for an example script that shows that this cohere_pairs and cohere give the same results for a given pair. """ numRows, numCols = X.shape # zero pad if X is too short if numRows < NFFT: tmp = X X = zeros( (NFFT, numCols), X.typecode()) X[:numRows,:] = tmp del tmp numRows, numCols = X.shape # get all the columns of X that we are interested in by checking # the ij tuples seen = {} for i,j in ij: seen[i]=1; seen[j] = 1 allColumns = seen.keys() Ncols = len(allColumns) del seen # for real X, ignore the negative frequencies if X.typecode()==Complex: numFreqs = NFFT else: numFreqs = NFFT//2+1 # cache the FFT of every windowed, detrended NFFT length segement # of every channel. If preferSpeedOverMemory, cache the conjugate # as well windowVals = window(ones((NFFT,), X.typecode())) ind = range(0, numRows-NFFT+1, NFFT-noverlap) numSlices = len(ind) FFTSlices = {} FFTConjSlices = {} Pxx = {} slices = range(numSlices) normVal = norm(windowVals)**2 for iCol in allColumns: progressCallback(i/Ncols, 'Cacheing FFTs') Slices = zeros( (numSlices,numFreqs), Complex) for iSlice in slices: thisSlice = X[ind[iSlice]:ind[iSlice]+NFFT, iCol] thisSlice = windowVals*detrend(thisSlice) Slices[iSlice,:] = fft(thisSlice)[:numFreqs] FFTSlices[iCol] = Slices if preferSpeedOverMemory: FFTConjSlices[iCol] = conjugate(Slices) Pxx[iCol] = divide(mean(absolute(Slices)**2), normVal) del Slices, ind, windowVals # compute the coherences and phases for all pairs using the # cached FFTs Cxy = {} Phase = {} count = 0 N = len(ij) for i,j in ij: count +=1 if count%10==0: progressCallback(count/N, 'Computing coherences') if preferSpeedOverMemory: Pxy = FFTSlices[i] * FFTConjSlices[j] else: Pxy = FFTSlices[i] * conjugate(FFTSlices[j]) if numSlices>1: Pxy = mean(Pxy) Pxy = divide(Pxy, normVal) Cxy[(i,j)] = divide(absolute(Pxy)**2, Pxx[i]*Pxx[j]) Phase[(i,j)] = arctan2(Pxy.imag, Pxy.real) freqs = Fs/NFFT*arange(numFreqs) if returnPxx: return Cxy, Phase, freqs, Pxx else: return Cxy, Phase, freqs
def csd(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning, noverlap=0): """ The cross spectral density Pxy by Welches average periodogram method. The vectors x and y are divided into NFFT length segments. Each segment is detrended by function detrend and windowed by function window. noverlap gives the length of the overlap between segments. The product of the direct FFTs of x and y are averaged over each segment to compute Pxy, with a scaling to correct for power loss due to windowing. Fs is the sampling frequency. NFFT must be a power of 2 Returns the tuple Pxy, freqs Refs: Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John Wiley & Sons (1986) """ if NFFT % 2: raise ValueError, 'NFFT must be a power of 2' # zero pad x and y up to NFFT if they are shorter than NFFT if len(x)<NFFT: n = len(x) x = resize(x, (NFFT,)) x[n:] = 0 if len(y)<NFFT: n = len(y) y = resize(y, (NFFT,)) y[n:] = 0 # for real x, ignore the negative frequencies if x.typecode()==Complex: numFreqs = NFFT else: numFreqs = NFFT//2+1 windowVals = window(ones((NFFT,),x.typecode())) step = NFFT-noverlap ind = range(0,len(x)-NFFT+1,step) n = len(ind) Pxy = zeros((numFreqs,n), Complex) # do the ffts of the slices for i in range(n): thisX = x[ind[i]:ind[i]+NFFT] thisX = windowVals*detrend(thisX) thisY = y[ind[i]:ind[i]+NFFT] thisY = windowVals*detrend(thisY) fx = fft(thisX) fy = fft(thisY) Pxy[:,i] = conjugate(fx[:numFreqs])*fy[:numFreqs] # Scale the spectrum by the norm of the window to compensate for # windowing loss; see Bendat & Piersol Sec 11.5.2 if n>1: Pxy = mean(Pxy,1) Pxy = divide(Pxy, norm(windowVals)**2) freqs = Fs/NFFT*arange(numFreqs) Pxy.shape = len(freqs), return Pxy, freqs