barchart.py revision 2180
12115Shsul@eecs.umich.edu# Copyright (c) 2005-2006 The Regents of The University of Michigan
21881Sbinkertn@umich.edu# All rights reserved.
31881Sbinkertn@umich.edu#
41881Sbinkertn@umich.edu# Redistribution and use in source and binary forms, with or without
51881Sbinkertn@umich.edu# modification, are permitted provided that the following conditions are
61881Sbinkertn@umich.edu# met: redistributions of source code must retain the above copyright
71881Sbinkertn@umich.edu# notice, this list of conditions and the following disclaimer;
81881Sbinkertn@umich.edu# redistributions in binary form must reproduce the above copyright
91881Sbinkertn@umich.edu# notice, this list of conditions and the following disclaimer in the
101881Sbinkertn@umich.edu# documentation and/or other materials provided with the distribution;
111881Sbinkertn@umich.edu# neither the name of the copyright holders nor the names of its
121881Sbinkertn@umich.edu# contributors may be used to endorse or promote products derived from
131881Sbinkertn@umich.edu# this software without specific prior written permission.
141881Sbinkertn@umich.edu#
151881Sbinkertn@umich.edu# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
161881Sbinkertn@umich.edu# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
171881Sbinkertn@umich.edu# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
181881Sbinkertn@umich.edu# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
191881Sbinkertn@umich.edu# OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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211881Sbinkertn@umich.edu# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
221881Sbinkertn@umich.edu# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
231881Sbinkertn@umich.edu# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
241881Sbinkertn@umich.edu# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
251881Sbinkertn@umich.edu# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
261881Sbinkertn@umich.edu#
271881Sbinkertn@umich.edu# Authors: Nathan Binkert
281881Sbinkertn@umich.edu#          Lisa Hsu
291881Sbinkertn@umich.edu
301881Sbinkertn@umich.eduimport matplotlib, pylab
312006Sbinkertn@umich.edufrom matplotlib.font_manager import FontProperties
321881Sbinkertn@umich.edufrom matplotlib.numerix import array, arange, reshape, shape, transpose, zeros
331881Sbinkertn@umich.edufrom matplotlib.numerix import Float
342119Shsul@eecs.umich.edufrom matplotlib.ticker import NullLocator
351881Sbinkertn@umich.edu
361881Sbinkertn@umich.edumatplotlib.interactive(False)
371881Sbinkertn@umich.edu
382006Sbinkertn@umich.edufrom chart import ChartOptions
391881Sbinkertn@umich.edu
402006Sbinkertn@umich.educlass BarChart(ChartOptions):
412006Sbinkertn@umich.edu    def __init__(self, default=None, **kwargs):
422006Sbinkertn@umich.edu        super(BarChart, self).__init__(default, **kwargs)
431881Sbinkertn@umich.edu        self.inputdata = None
441881Sbinkertn@umich.edu        self.chartdata = None
452180Sbinkertn@umich.edu        self.inputerr = None
462180Sbinkertn@umich.edu        self.charterr = None
471881Sbinkertn@umich.edu
481881Sbinkertn@umich.edu    def gen_colors(self, count):
491881Sbinkertn@umich.edu        cmap = matplotlib.cm.get_cmap(self.colormap)
501881Sbinkertn@umich.edu        if count == 1:
511881Sbinkertn@umich.edu            return cmap([ 0.5 ])
522179Sbinkertn@umich.edu
532179Sbinkertn@umich.edu        if count < 5:
542179Sbinkertn@umich.edu            return cmap(arange(5) / float(4))[:count]
552179Sbinkertn@umich.edu
562179Sbinkertn@umich.edu        return cmap(arange(count) / float(count - 1))
571881Sbinkertn@umich.edu
581881Sbinkertn@umich.edu    # The input data format does not match the data format that the
591881Sbinkertn@umich.edu    # graph function takes because it is intuitive.  The conversion
601881Sbinkertn@umich.edu    # from input data format to chart data format depends on the
611881Sbinkertn@umich.edu    # dimensionality of the input data.  Check here for the
621881Sbinkertn@umich.edu    # dimensionality and correctness of the input data
631881Sbinkertn@umich.edu    def set_data(self, data):
641881Sbinkertn@umich.edu        if data is None:
651881Sbinkertn@umich.edu            self.inputdata = None
661881Sbinkertn@umich.edu            self.chartdata = None
671881Sbinkertn@umich.edu            return
681881Sbinkertn@umich.edu
691881Sbinkertn@umich.edu        data = array(data)
701881Sbinkertn@umich.edu        dim = len(shape(data))
711881Sbinkertn@umich.edu        if dim not in (1, 2, 3):
721881Sbinkertn@umich.edu            raise AttributeError, "Input data must be a 1, 2, or 3d matrix"
731881Sbinkertn@umich.edu        self.inputdata = data
741881Sbinkertn@umich.edu
751881Sbinkertn@umich.edu        # If the input data is a 1d matrix, then it describes a
761881Sbinkertn@umich.edu        # standard bar chart.
771881Sbinkertn@umich.edu        if dim == 1:
781881Sbinkertn@umich.edu            self.chartdata = array([[data]])
791881Sbinkertn@umich.edu
801881Sbinkertn@umich.edu        # If the input data is a 2d matrix, then it describes a bar
811881Sbinkertn@umich.edu        # chart with groups. The matrix being an array of groups of
821881Sbinkertn@umich.edu        # bars.
831881Sbinkertn@umich.edu        if dim == 2:
841881Sbinkertn@umich.edu            self.chartdata = transpose([data], axes=(2,0,1))
851881Sbinkertn@umich.edu
861881Sbinkertn@umich.edu        # If the input data is a 3d matrix, then it describes an array
871881Sbinkertn@umich.edu        # of groups of bars with each bar being an array of stacked
881881Sbinkertn@umich.edu        # values.
891881Sbinkertn@umich.edu        if dim == 3:
901881Sbinkertn@umich.edu            self.chartdata = transpose(data, axes=(1,2,0))
911881Sbinkertn@umich.edu
921881Sbinkertn@umich.edu    def get_data(self):
931881Sbinkertn@umich.edu        return self.inputdata
941881Sbinkertn@umich.edu
951881Sbinkertn@umich.edu    data = property(get_data, set_data)
961881Sbinkertn@umich.edu
972180Sbinkertn@umich.edu    def set_err(self, err):
982180Sbinkertn@umich.edu        if err is None:
992180Sbinkertn@umich.edu            self.inputerr = None
1002180Sbinkertn@umich.edu            self.charterr = None
1012180Sbinkertn@umich.edu            return
1022180Sbinkertn@umich.edu
1032180Sbinkertn@umich.edu        err = array(err)
1042180Sbinkertn@umich.edu        dim = len(shape(err))
1052180Sbinkertn@umich.edu        if dim not in (1, 2, 3):
1062180Sbinkertn@umich.edu            raise AttributeError, "Input err must be a 1, 2, or 3d matrix"
1072180Sbinkertn@umich.edu        self.inputerr = err
1082180Sbinkertn@umich.edu
1092180Sbinkertn@umich.edu        if dim == 1:
1102180Sbinkertn@umich.edu            self.charterr = array([[err]])
1112180Sbinkertn@umich.edu
1122180Sbinkertn@umich.edu        if dim == 2:
1132180Sbinkertn@umich.edu            self.charterr = transpose([err], axes=(2,0,1))
1142180Sbinkertn@umich.edu
1152180Sbinkertn@umich.edu        if dim == 3:
1162180Sbinkertn@umich.edu            self.charterr = transpose(err, axes=(1,2,0))
1172180Sbinkertn@umich.edu
1182180Sbinkertn@umich.edu    def get_err(self):
1192180Sbinkertn@umich.edu        return self.inputerr
1202180Sbinkertn@umich.edu
1212180Sbinkertn@umich.edu    err = property(get_err, set_err)
1222180Sbinkertn@umich.edu
1231881Sbinkertn@umich.edu    # Graph the chart data.
1241881Sbinkertn@umich.edu    # Input is a 3d matrix that describes a plot that has multiple
1251881Sbinkertn@umich.edu    # groups, multiple bars in each group, and multiple values stacked
1261881Sbinkertn@umich.edu    # in each bar.  The underlying bar() function expects a sequence of
1271881Sbinkertn@umich.edu    # bars in the same stack location and same group location, so the
1281881Sbinkertn@umich.edu    # organization of the matrix is that the inner most sequence
1291881Sbinkertn@umich.edu    # represents one of these bar groups, then those are grouped
1301881Sbinkertn@umich.edu    # together to make one full stack of bars in each group, and then
1311881Sbinkertn@umich.edu    # the outer most layer describes the groups.  Here is an example
1321881Sbinkertn@umich.edu    # data set and how it gets plotted as a result.
1331881Sbinkertn@umich.edu    #
1341881Sbinkertn@umich.edu    # e.g. data = [[[10,11,12], [13,14,15],  [16,17,18], [19,20,21]],
1351881Sbinkertn@umich.edu    #              [[22,23,24], [25,26,27],  [28,29,30], [31,32,33]]]
1361881Sbinkertn@umich.edu    #
1371881Sbinkertn@umich.edu    # will plot like this:
1381881Sbinkertn@umich.edu    #
1391881Sbinkertn@umich.edu    #    19 31    20 32    21 33
1401881Sbinkertn@umich.edu    #    16 28    17 29    18 30
1411881Sbinkertn@umich.edu    #    13 25    14 26    15 27
1421881Sbinkertn@umich.edu    #    10 22    11 23    12 24
1431881Sbinkertn@umich.edu    #
1441881Sbinkertn@umich.edu    # Because this arrangement is rather conterintuitive, the rearrange
1451881Sbinkertn@umich.edu    # function takes various matricies and arranges them to fit this
1461881Sbinkertn@umich.edu    # profile.
1471881Sbinkertn@umich.edu    #
1481881Sbinkertn@umich.edu    # This code deals with one of the dimensions in the matrix being
1491881Sbinkertn@umich.edu    # one wide.
1501881Sbinkertn@umich.edu    #
1511881Sbinkertn@umich.edu    def graph(self):
1521881Sbinkertn@umich.edu        if self.chartdata is None:
1531881Sbinkertn@umich.edu            raise AttributeError, "Data not set for bar chart!"
1541881Sbinkertn@umich.edu
1551881Sbinkertn@umich.edu        dim = len(shape(self.inputdata))
1561881Sbinkertn@umich.edu        cshape = shape(self.chartdata)
1572180Sbinkertn@umich.edu        if self.charterr is not None and shape(self.charterr) != cshape:
1582180Sbinkertn@umich.edu            raise AttributeError, 'Dimensions of error and data do not match'
1592180Sbinkertn@umich.edu
1601881Sbinkertn@umich.edu        if dim == 1:
1611881Sbinkertn@umich.edu            colors = self.gen_colors(cshape[2])
1621881Sbinkertn@umich.edu            colors = [ [ colors ] * cshape[1] ] * cshape[0]
1631881Sbinkertn@umich.edu
1641881Sbinkertn@umich.edu        if dim == 2:
1651881Sbinkertn@umich.edu            colors = self.gen_colors(cshape[0])
1661881Sbinkertn@umich.edu            colors = [ [ [ c ] * cshape[2] ] * cshape[1] for c in colors ]
1671881Sbinkertn@umich.edu
1681881Sbinkertn@umich.edu        if dim == 3:
1691881Sbinkertn@umich.edu            colors = self.gen_colors(cshape[1])
1701881Sbinkertn@umich.edu            colors = [ [ [ c ] * cshape[2] for c in colors ] ] * cshape[0]
1711881Sbinkertn@umich.edu
1721881Sbinkertn@umich.edu        colors = array(colors)
1731881Sbinkertn@umich.edu
1742115Shsul@eecs.umich.edu        self.figure = pylab.figure(figsize=self.chart_size)
1752115Shsul@eecs.umich.edu
1762115Shsul@eecs.umich.edu        outer_axes = None
1772115Shsul@eecs.umich.edu        inner_axes = None
1782119Shsul@eecs.umich.edu        if self.xsubticks is not None:
1792119Shsul@eecs.umich.edu            color = self.figure.get_facecolor()
1802119Shsul@eecs.umich.edu            self.metaaxes = self.figure.add_axes(self.figure_size, axisbg=color, frameon=False)
1812119Shsul@eecs.umich.edu            for tick in self.metaaxes.xaxis.majorTicks:
1822119Shsul@eecs.umich.edu                tick.tick1On = False
1832119Shsul@eecs.umich.edu                tick.tick2On = False
1842115Shsul@eecs.umich.edu            self.metaaxes.set_yticklabels([])
1852115Shsul@eecs.umich.edu            self.metaaxes.set_yticks([])
1862115Shsul@eecs.umich.edu            size = [0] * 4
1872115Shsul@eecs.umich.edu            size[0] = self.figure_size[0]
1882160Shsul@eecs.umich.edu            size[1] = self.figure_size[1] + .12
1892115Shsul@eecs.umich.edu            size[2] = self.figure_size[2]
1902160Shsul@eecs.umich.edu            size[3] = self.figure_size[3] - .12
1912115Shsul@eecs.umich.edu            self.axes = self.figure.add_axes(size)
1922115Shsul@eecs.umich.edu            outer_axes = self.metaaxes
1932115Shsul@eecs.umich.edu            inner_axes = self.axes
1942115Shsul@eecs.umich.edu        else:
1952115Shsul@eecs.umich.edu            self.axes = self.figure.add_axes(self.figure_size)
1962115Shsul@eecs.umich.edu            outer_axes = self.axes
1972115Shsul@eecs.umich.edu            inner_axes = self.axes
1982115Shsul@eecs.umich.edu
1991881Sbinkertn@umich.edu        bars_in_group = len(self.chartdata)
2002160Shsul@eecs.umich.edu
2012160Shsul@eecs.umich.edu        width = 1.0 / ( bars_in_group + 1)
2022160Shsul@eecs.umich.edu        center = width / 2
2031881Sbinkertn@umich.edu
2041881Sbinkertn@umich.edu        bars = []
2051881Sbinkertn@umich.edu        for i,stackdata in enumerate(self.chartdata):
2062006Sbinkertn@umich.edu            bottom = array([0.0] * len(stackdata[0]), Float)
2071881Sbinkertn@umich.edu            stack = []
2081881Sbinkertn@umich.edu            for j,bardata in enumerate(stackdata):
2091881Sbinkertn@umich.edu                bardata = array(bardata)
2101881Sbinkertn@umich.edu                ind = arange(len(bardata)) + i * width + center
2112180Sbinkertn@umich.edu                yerr = None
2122180Sbinkertn@umich.edu                if self.charterr is not None:
2132180Sbinkertn@umich.edu                    yerr = self.charterr[i][j]
2141881Sbinkertn@umich.edu                bar = self.axes.bar(ind, bardata, width, bottom=bottom,
2152180Sbinkertn@umich.edu                                    color=colors[i][j], yerr=yerr)
2162160Shsul@eecs.umich.edu                if self.xsubticks is not None:
2172115Shsul@eecs.umich.edu                    self.metaaxes.bar(ind, [0] * len(bardata), width)
2181881Sbinkertn@umich.edu                stack.append(bar)
2191881Sbinkertn@umich.edu                bottom += bardata
2201881Sbinkertn@umich.edu            bars.append(stack)
2211881Sbinkertn@umich.edu
2221881Sbinkertn@umich.edu        if self.xlabel is not None:
2232115Shsul@eecs.umich.edu            outer_axes.set_xlabel(self.xlabel)
2241881Sbinkertn@umich.edu
2251881Sbinkertn@umich.edu        if self.ylabel is not None:
2262115Shsul@eecs.umich.edu            inner_axes.set_ylabel(self.ylabel)
2271881Sbinkertn@umich.edu
2281881Sbinkertn@umich.edu        if self.yticks is not None:
2291881Sbinkertn@umich.edu            ymin, ymax = self.axes.get_ylim()
2301881Sbinkertn@umich.edu            nticks = float(len(self.yticks))
2311881Sbinkertn@umich.edu            ticks = arange(nticks) / (nticks - 1) * (ymax - ymin)  + ymin
2322115Shsul@eecs.umich.edu            inner_axes.set_yticks(ticks)
2332115Shsul@eecs.umich.edu            inner_axes.set_yticklabels(self.yticks)
2342006Sbinkertn@umich.edu        elif self.ylim is not None:
2352115Shsul@eecs.umich.edu            self.inner_axes.set_ylim(self.ylim)
2361881Sbinkertn@umich.edu
2371881Sbinkertn@umich.edu        if self.xticks is not None:
2382115Shsul@eecs.umich.edu            outer_axes.set_xticks(arange(cshape[2]) + .5)
2392115Shsul@eecs.umich.edu            outer_axes.set_xticklabels(self.xticks)
2402119Shsul@eecs.umich.edu
2412115Shsul@eecs.umich.edu        if self.xsubticks is not None:
2422115Shsul@eecs.umich.edu            inner_axes.set_xticks(arange((cshape[0] + 1)*cshape[2])*width + 2*center)
2432115Shsul@eecs.umich.edu            self.xsubticks.append('')
2442160Shsul@eecs.umich.edu            inner_axes.set_xticklabels(self.xsubticks * cshape[2], fontsize=7, rotation=90)
2452119Shsul@eecs.umich.edu
2461881Sbinkertn@umich.edu        if self.legend is not None:
2471881Sbinkertn@umich.edu            if dim == 1:
2481881Sbinkertn@umich.edu                lbars = bars[0][0]
2491881Sbinkertn@umich.edu            if dim == 2:
2501881Sbinkertn@umich.edu                lbars = [ bars[i][0][0] for i in xrange(len(bars))]
2511881Sbinkertn@umich.edu            if dim == 3:
2521881Sbinkertn@umich.edu                number = len(bars[0])
2531881Sbinkertn@umich.edu                lbars = [ bars[0][number - j - 1][0] for j in xrange(number)]
2541881Sbinkertn@umich.edu
2552180Sbinkertn@umich.edu            if self.fig_legend:
2562180Sbinkertn@umich.edu                self.figure.legend(lbars, self.legend, self.legend_loc,
2572180Sbinkertn@umich.edu                                   prop=FontProperties(size=self.legend_size))
2582180Sbinkertn@umich.edu            else:
2592180Sbinkertn@umich.edu                self.axes.legend(lbars, self.legend, self.legend_loc,
2602180Sbinkertn@umich.edu                                 prop=FontProperties(size=self.legend_size))
2611881Sbinkertn@umich.edu
2621881Sbinkertn@umich.edu        if self.title is not None:
2631881Sbinkertn@umich.edu            self.axes.set_title(self.title)
2641881Sbinkertn@umich.edu
2651881Sbinkertn@umich.edu    def savefig(self, name):
2661881Sbinkertn@umich.edu        self.figure.savefig(name)
2671881Sbinkertn@umich.edu
2682006Sbinkertn@umich.edu    def savecsv(self, name):
2692006Sbinkertn@umich.edu        f = file(name, 'w')
2702006Sbinkertn@umich.edu        data = array(self.inputdata)
2712006Sbinkertn@umich.edu        dim = len(data.shape)
2722006Sbinkertn@umich.edu
2732006Sbinkertn@umich.edu        if dim == 1:
2742006Sbinkertn@umich.edu            #if self.xlabel:
2752006Sbinkertn@umich.edu            #    f.write(', '.join(list(self.xlabel)) + '\n')
2762006Sbinkertn@umich.edu            f.write(', '.join([ '%f' % val for val in data]) + '\n')
2772006Sbinkertn@umich.edu        if dim == 2:
2782006Sbinkertn@umich.edu            #if self.xlabel:
2792006Sbinkertn@umich.edu            #    f.write(', '.join([''] + list(self.xlabel)) + '\n')
2802006Sbinkertn@umich.edu            for i,row in enumerate(data):
2812006Sbinkertn@umich.edu                ylabel = []
2822006Sbinkertn@umich.edu                #if self.ylabel:
2832006Sbinkertn@umich.edu                #    ylabel = [ self.ylabel[i] ]
2842006Sbinkertn@umich.edu                f.write(', '.join(ylabel + [ '%f' % val for val in row]) + '\n')
2852006Sbinkertn@umich.edu        if dim == 3:
2862006Sbinkertn@umich.edu            f.write("don't do 3D csv files\n")
2872006Sbinkertn@umich.edu            pass
2882006Sbinkertn@umich.edu
2892006Sbinkertn@umich.edu        f.close()
2902006Sbinkertn@umich.edu
2911881Sbinkertn@umich.eduif __name__ == '__main__':
2922006Sbinkertn@umich.edu    from random import randrange
2931881Sbinkertn@umich.edu    import random, sys
2941881Sbinkertn@umich.edu
2951881Sbinkertn@umich.edu    dim = 3
2961881Sbinkertn@umich.edu    number = 5
2971881Sbinkertn@umich.edu
2981881Sbinkertn@umich.edu    args = sys.argv[1:]
2991881Sbinkertn@umich.edu    if len(args) > 3:
3001881Sbinkertn@umich.edu        sys.exit("invalid number of arguments")
3011881Sbinkertn@umich.edu    elif len(args) > 0:
3021881Sbinkertn@umich.edu        myshape = [ int(x) for x in args ]
3031881Sbinkertn@umich.edu    else:
3041881Sbinkertn@umich.edu        myshape = [ 3, 4, 8 ]
3051881Sbinkertn@umich.edu
3061881Sbinkertn@umich.edu    # generate a data matrix of the given shape
3071881Sbinkertn@umich.edu    size = reduce(lambda x,y: x*y, myshape)
3081881Sbinkertn@umich.edu    #data = [ random.randrange(size - i) + 10 for i in xrange(size) ]
3091881Sbinkertn@umich.edu    data = [ float(i)/100.0 for i in xrange(size) ]
3101881Sbinkertn@umich.edu    data = reshape(data, myshape)
3111881Sbinkertn@umich.edu
3121881Sbinkertn@umich.edu    # setup some test bar charts
3131881Sbinkertn@umich.edu    if True:
3141881Sbinkertn@umich.edu        chart1 = BarChart()
3151881Sbinkertn@umich.edu        chart1.data = data
3161881Sbinkertn@umich.edu
3171881Sbinkertn@umich.edu        chart1.xlabel = 'Benchmark'
3181881Sbinkertn@umich.edu        chart1.ylabel = 'Bandwidth (GBps)'
3191881Sbinkertn@umich.edu        chart1.legend = [ 'x%d' % x for x in xrange(myshape[-1]) ]
3201881Sbinkertn@umich.edu        chart1.xticks = [ 'xtick%d' % x for x in xrange(myshape[0]) ]
3211881Sbinkertn@umich.edu        chart1.title = 'this is the title'
3222119Shsul@eecs.umich.edu        if len(myshape) > 2:
3232117Shsul@eecs.umich.edu            chart1.xsubticks = [ '%d' % x for x in xrange(myshape[1]) ]
3241881Sbinkertn@umich.edu        chart1.graph()
3252006Sbinkertn@umich.edu        chart1.savefig('/tmp/test1.png')
3262006Sbinkertn@umich.edu        chart1.savefig('/tmp/test1.ps')
3272006Sbinkertn@umich.edu        chart1.savefig('/tmp/test1.eps')
3282006Sbinkertn@umich.edu        chart1.savecsv('/tmp/test1.csv')
3291881Sbinkertn@umich.edu
3301881Sbinkertn@umich.edu    if False:
3311881Sbinkertn@umich.edu        chart2 = BarChart()
3321881Sbinkertn@umich.edu        chart2.data = data
3331881Sbinkertn@umich.edu        chart2.colormap = 'gray'
3341881Sbinkertn@umich.edu        chart2.graph()
3352006Sbinkertn@umich.edu        chart2.savefig('/tmp/test2.png')
3362006Sbinkertn@umich.edu        chart2.savefig('/tmp/test2.ps')
3371881Sbinkertn@umich.edu
3382160Shsul@eecs.umich.edu#    pylab.show()
339