"""A collection of tools, tips, and tricks.
2009-07-20 22:36 IJC: Created
2010-10-28 11:53 IJMC: Updated documentation for Sphinx.
2011-06-15 09:34 IJMC: More functions have been added; cleaned documentation.
"""
import pdb
import numpy as np
[docs]def getfigs():
"""Return a list of all open matplotlib figures.
No inputs or options."""
from matplotlib._pylab_helpers import Gcf
figs = [manager.canvas.figure for manager in Gcf.get_all_fig_managers()]
figlist = [fig.number for fig in figs]
return figlist
[docs]def nextfig():
"""Return one greater than the largest-numbered figure currently
open. If no figures are open, return unity.
No inputs or options."""
# 2010-03-01 14:28 IJC: Created
figlist = getfigs()
if len(figlist)==0:
return 1
else:
return max(figlist)+1
return figlist
[docs]def printfigs(filename, figs=None, format=None, pdfmode='texexec', verbose=False, closefigs=False):
"""Print desired figures using designated 'format'. Concatenate PDFs.
:Inputs:
filename -- string. prepended to all open figures
figs -- int or list.
figures to access, then apply savefig to. If None, print
all open figures; if -1, print current figure.
format -- string or list of strings.
if 'pdf', all images are concatenated into one file (use
"pdfs" for individual pdf figure files)
pdfmode -- string;
method of concatenating PDFs. Either 'texexec' or 'gs'
(for GhostScript) or 'tar' to wrap individual
figures in a Tarball.
closefigs -- bool
If True, close each figure after printing it to disk.
:NOTES:
If no explicit path is passed and a subdirectory 'figures'
exists in the current directory, the figures will be printed in
'figures' instead.
:EXAMPLE:
::
from pylab import *
figure(1); plot(arange(10), randn(10), 'ob')
figure(2); plot(arange(15), randn(15), '-xr')
printfigs('testing')
!open testing.pdf
"""
# 2009-07-20 23:10 IJC: Created; inspired by FGD.
# 2009-09-08 13:54 IJC: Made it work with single-figure, non-list input.
# 2010-02-02 11:50 IJC: Now it kills the 'logfile' detritus.
# 2010-10-27 17:05 IJC: New texexec syntax is "result=...", not "result ..."
# 2011-03-01 18:14 IJC: Added capability for multiple formats (in
# a list). Also, figure numbers are not
# catted to the filename when saving a
# single figure.
# 2011-08-29 10:23 IJMC: Now don't try to concatenate single PDF figures.
# 2012-11-01 11:41 IJMC: Slightly changed if-block for 'figs'.
# 2014-05-03 15:04 IJMC: Added 'closefigs' flag.
# 2014-09-02 08:50 IJMC: Added 'tar' PDFMODE
from pylab import savefig, figure, gcf, close
from matplotlib._pylab_helpers import Gcf
import os
import pdb
figlist = getfigs()
if verbose: print "Available figure numbers>>" ,figlist
if figs is None:
figs = figlist
elif figs is -1:
figs = [gcf().number]
else:
if hasattr(figs, '__iter__'):
figs = list(figs)
else:
figs = [figs]
figlist = [val for val in figs if val in figlist]
nfig = len(figlist)
print "Figures to print>>",figlist
if format==None:
format = filename[-3::]
filename = filename[0:len(filename)-4]
if hasattr(format, 'capitalize'):
format = [format]
nformat = 1
elif hasattr(format, '__iter__'):
nformat = len(format)
else:
format = [str(format)]
nformat = 1
if len(figlist)==0:
print "No open figures found; exiting."
return
for thisformat in format:
fnamelist = []
for ii in range(nfig):
if nfig>1:
fname = filename + str(figlist[ii])
else:
fname = filename
if thisformat=='pdf' and nfig>1:
fname = fname + '_temp'
if thisformat=='pdfs':
fname = fname + '.pdf'
else:
fname = fname + '.' + thisformat
figure(figlist[ii])
savefig(fname )
fnamelist.append(fname)
if closefigs and thisformat==format[-1]: # last time at this figure
close(figlist[ii])
if thisformat=='pdf':
if nfig==1:
savefig(fnamelist[0])
else: # we have to concatenate multiple PDF figures:
bigfilename = filename + '.' + thisformat
if os.path.isfile(bigfilename):
os.remove(bigfilename)
if pdfmode=='gs':
execstr = 'gs -q -sPAPERSIZE=letter -dNOPAUSE -dBATCH -sDEVICE=pdfwrite -sOutputFile=' + bigfilename
rmstr = ''
elif pdfmode=='texexec':
execstr = 'texexec --pdfcopy --result=' + bigfilename
rmstr = 'rm %s' % bigfilename.replace('pdf','log')
elif pdfmode[0:3]=='tar':
execstr = 'tar -cvf %s ' % bigfilename.replace('pdf','tar')
fnamelist_local = [os.path.split(fn)[1] for fn in fnamelist]
[os.rename(fn, fn2) for fn,fn2 in zip(fnamelist, fnamelist_local)]
rmstr = 'rm ' + ' '.join(fnamelist_local)
fnamelist = fnamelist_local
for fn in fnamelist:
execstr += ' ' + fn
#pdb.set_trace()
if verbose: print "PDFMODE exec call>>", execstr
os.system(execstr)
#pdb.set_trace()
if len(rmstr)>0:
os.system(rmstr)
for fn in fnamelist:
try:
os.remove(fn)
except:
pass
return
[docs]def plotstyle(i, c=['b', 'g', 'r', 'c', 'm', 'y', 'k'], \
s=['.', 'x', 's', '^', '*', 'o', '+', 'v', 'p', 'D'], \
l=['-', '--', '-.', ':']):
"""Return plot properties to help distinguish many types of plot symbols.
:INPUT:
i -- int.
:OPTIONAL INPUT:
c -- color, or list of colors accepted by pylab.plot
s -- symbol, or list of symbols accepted by pylab.plot
l -- linestyle, or list of linestyles accepted by pylab.plot
:OUTPUT:
tuple of (color, symbol, linestyle)
:REQUIREMENTS: :doc:`numpy`
"""
# 2009-09-10 16:42 IJC: Created
from numpy import tile, array
if not c.__class__==list:
c = list(c)
if not s.__class__==list:
s = list(s)
if not l.__class__==list:
l = list(l)
nc = len(c)
ns = len(s)
nl = len(l)
if not hasattr(i,'__iter__'):
i = array([i])
i = abs(array(i))
nrepc = (max(i)/nc+1.).astype(int)
nreps = (max(i)/ns+1.).astype(int)
nrepl = (max(i)/nl+1.).astype(int)
c = tile(c, nrepc)
s = tile(s, nreps)
l = tile(l, nrepl)
if len(i)==1:
ret = c[i][0], s[i][0], l[i][0]
else:
ret = list(c[i]),list(s[i]),list(l[i])
return ret
def flatten(L, maxdepth=100):
"""Flatten a list.
Stolen from http://mail.python.org/pipermail/tutor/2001-January/002914.html"""
# 2009-09-10 16:54 IJC: Input.
if type(L) != type([]): return [L]
if L == []:
return L
else:
maxdepth -= 1
return flatten(L[0]) + flatten(L[1:], maxdepth=maxdepth)
[docs]def replaceall(seq, obj, rep):
"""Replace all instances of 'obj' with 'rep' in list 'seq'
:INPUT:
seq -- (list) list within which to find-and-replace elements
obj -- target object to replace
rep -- replacement object
:EXAMPLE:
::
import tools
b = [2, ['spam', ['eggs', 5, dict(spam=3)]]]
tools.replaceall(b, 'spam', 'bacon')
print b
:NOTES:
-- Will fail if 'obj' is itself a list.
-- Edits list in-place, so make a copy first if you want to
retain the old version of your list.
-- Has not been tested for extremely deep lists
:SEE ALSO:
:func:`popall`
"""
#2009-09-11 10:22 IJC: Created
n = len(seq)
for ii in range(n):
if seq[ii].__class__==list:
replaceall(seq[ii], obj, rep)
else:
if seq[ii]==obj:
seq[ii]=rep
return
[docs]def popall(seq, obj):
"""Remove all instances of 'obj' from list 'seq'
:INPUT:
seq -- (list) list from which to pop elements
obj -- target object to remove
:EXAMPLE:
::
import tools
b = [3, 'spam', range(5)]
tools.popall(b, 4)
print b
:NOTES:
-- Will fail if 'obj' is itself a list.
-- Edits list in-place, so make a copy first if you want to
retain the old version of your list.
-- Has not been tested for extremely deep lists
:SEE ALSO:
:func:`replaceall`
"""
#2009-09-11 10:22 IJC: Created
n = len(seq)
for ii in range(n):
print ii,seq[ii]
if seq[ii].__class__==list:
popall(seq[ii], obj)
doneYet = False
while not doneYet:
try:
seq.remove(obj)
except:
doneYet = True
return
[docs]def drawRectangle(x,y,width,height,**kw):
"""Draw a rectangle patch on the current, or specified, axes.
:INPUT:
x, y -- lower-left corner of rectangle
width, height -- dimensions of rectangle
:OPTIONAL INPUT:
ax -- Axis to draw upon. if None, defaults to current axes.
dodraw -- if True, call 'draw()' function to immediately re-draw axes.
**kw -- options passable to :func:`matplotlib.patches.Rectangle`
:NOTE: Axes will NOT auto-rescale after this is called.
"""
# 2009-09-17 01:33 IJC: Created
# 2014-03-01 13:51 IJMC: Added 'dodraw' option.
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if kw.has_key('ax'):
ax = kw.pop('ax')
else:
ax = plt.gca()
p = mpatches.Rectangle((x,y), width, height, **kw)
ax.add_patch(p)
if kw.has_key('dodraw') and kw['dodraw']: plt.draw()
return ax, p
[docs]def drawPolygon(xy,**kw):
"""Draw a rectangle patch on the current, or specified, axes.
:INPUT:
xy -- numpy array of coordinates, with shape Nx2.
:OPTIONAL INPUT:
ax -- Axis to draw upon. if None, defaults to current axes.
dodraw -- if True, call 'draw()' function to immediately re-draw axes.
**kw -- options passable to :func:`matplotlib.patches.Polygon`
:SEE ALSO:
:func:`drawRectangle`
:NOTE: Axes will NOT auto-rescale after this is called.
"""
# 2010-12-02 19:58 IJC: Created from drawRectangle
# 2014-03-01 13:51 IJMC: Added 'dodraw' option.
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if kw.has_key('ax'):
ax = kw.pop('ax')
else:
ax = plt.gca()
p = mpatches.Polygon(xy, **kw)
ax.add_patch(p)
if kw.has_key('dodraw') and kw['dodraw']: plt.draw()
return ax, p
[docs]def drawCircle(x,y,radius,**kw):
"""Draw a circular patch on the current, or specified, axes.
:INPUT:
x, y -- center of circle
radius -- radius of circle
:OPTIONAL INPUT:
ax -- Axis to draw upon. if None, defaults to current axes.
dodraw -- if True, call 'draw()' function to immediately re-draw axes.
**kw -- options passable to :func:`matplotlib.patches.Circle`
:NOTE: Axes will NOT auto-rescale after this is called.
"""
# 2011-01-28 16:03 IJC: Created
# 2014-03-01 13:51 IJMC: Added 'dodraw' option.
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if kw.has_key('ax'):
ax = kw.pop('ax')
else:
ax = plt.gca()
p = mpatches.Circle((x,y), radius, **kw)
ax.add_patch(p)
if kw.has_key('dodraw') and kw['dodraw']: plt.draw()
return ax, p
[docs]def drawEllipse(x,y,width, height,**kw):
"""Draw an elliptical patch on the current, or specified, axes.
:INPUT:
x, y -- center of ellipse
width -- width of ellipse
height -- width of ellipse
:OPTIONAL INPUT:
ax -- Axis to draw upon. if None, defaults to current axes.
dodraw -- if True, call 'draw()' function to immediately re-draw axes.
**kw -- options passable to :func:`matplotlib.patches.Ellipse`
(angle, linewidth, fill, ...)
:NOTE: Axes will NOT auto-rescale after this is called.
:SEE_ALSO:
:func:`drawCircle`, :func:`drawRectangle`
"""
# 2011-10-20 11:32 IJMC: Created
# 2014-03-01 13:51 IJMC: Added 'dodraw' option.
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
if kw.has_key('ax'):
ax = kw.pop('ax')
else:
ax = plt.gca()
p = mpatches.Ellipse((x,y), width, height, **kw)
ax.add_patch(p)
if kw.has_key('dodraw') and kw['dodraw']: plt.draw()
return ax, p
[docs]def errxy(x,y,xbins, xmode='mean', ymode='mean', xerr='minmax', yerr='sdom', clean=None, binfactor=None, verbose=False,returnstats=False, timing=False):
"""Bin down datasets in X and Y for errorbar plotting
:INPUTS:
x -- (array) independent variable data
y -- (array) dependent variable data
xbins -- (array) edges of bins, in x-space. Only x-data
between two bin edges will be used. Thus if M bin
edges are entered, (M-1) datapoints will be returned.
If xbins==None, then no binning is done.
:OPTIONAL INPUT:
xmode/ymode -- (str) method to aggregate x/y data into datapoints:
'mean' -- use numpy.mean
'median' -- use numpy.median
'sum' -- use numpy.sum
None -- don't compute; return the empty list []
xerr/yerr -- (str) method to aggregate x/y data into errorbars
'std' -- sample standard deviation (numpy.std)
'sdom' -- standard deviation on the mean; i.e., std/sqrt(N)
'minmax' -- use full range of data in the bin
None -- don't compute; return the empty list []
binfactor -- (int) If not None, average over this many
consecutive values instead of binning explicitly by
time-based bins. Can also be a sequence, telling the
number of values over which to average. E.g.,
binfactor=[10,10,20] will bin over the first 10 points,
the second 10 points, and the next 20 points.
clean -- (dict) keyword options to clean y-data ONLY, via
analysis.removeoutliers, with an additional "nsigma"
keyword. See removeoutliers for more information.
E.g.: clean=dict(nsigma=5,remove='both',niter=1)
:OUTPUTS: a tuple of four arrays to be passed to matplotlib.pyplot.errorbar:
xx -- locations of the aggregated x-datapoint in each bin
yy -- locations of the aggregated y-datapoint in each bin
xerr -- x-errorbars
yerr -- y-errorbars
:EXAMPLE:
::
x = hstack((arange(10), arange(20)+40))
y = randn(len(x))
xbins = [-1,15,70]
xx,yy,xerr,yerr = errxy(x,y,xbins)
plot(x,y, '.b')
errorbar(xx,yy,xerr=xerr,yerr=yerr, fmt='or')
:NOTES:
To just bin down uncleaned data (i.e., no 'error' terms
returned), set clean, xerr, yerr to None. However, when
computing all values (xerr and yerr not None) it is faster
to set clean to some rediculous value, i.e.,
clean=dict(niter=0, nsigma=9e99). This probably means more
optimization could be done.
Be sure you call the errorbar function using the keywords xerr
and yerr, since otherwise the default order of inputs to the
function is (x,y,yerr,xerr).
Data 'x' are determined to be in a bin with sides (L, R) when
satisfying the condition (x>L) and (x<=R)
:SEE ALSO: matplotlib.pyplot.errorbar, :func:`analysis.removeoutliers`
:REQUIREMENTS: :doc:`numpy`, :doc:`analysis`
"""
# 2009-09-29 20:07 IJC: Created w/mean-median and std-sdom-minmax.
# 2009-12-14 16:01 IJC: xbins can be 'None' for no binning.
# 2009-12-15 10:09 IJC: Added "binfactor" option.
# 2009-12-22 09:56 IJC: "binfactor" can now be a sequence.
# 2009-12-29 01:16 IJC: Fixed a bug with binfactor sequences.
# 2010-04-29 09:59 IJC: Added 'returnstats' feature
# 2010-10-19 16:25 IJC: Added 'sum' option for x-data
# 2011-03-22 12:57 IJC: Added 'none' option for data and errors
# 2012-03-20 16:33 IJMC: Fixed bug; xmode=='none' now works.
# 2012-03-27 14:00 IJMC: Now using np.digitize -- speed boost.
# Rewrote code to optimize (somewhat),
# cleaned up 'import' statements.
# 2012-04-08 15:57 IJMC: New speed boost from adopting
# numpy.histogram-like implementation:
# numpy.searchsorted, etc.
import numpy as np
from analysis import removeoutliers
if timing:
import time
tic = time.time()
def sdom(data):
"""Return standard deviation of the mean."""
return np.std(data)/np.sqrt(data.size)
def getcenter(data, cmode):
"""Get data center based on mode. Helper function."""
if cmode is None:
ret = 0
elif cmode=='mean':
ret = np.mean(data)
elif cmode=='median':
ret = np.median(data)
elif cmode=='sum':
ret = np.sum(data)
return ret
def geterr(data, emode, cmode):
"""Get errorbar. Helper function."""
if emode is None:
ret = []
elif emode=='std':
ret = np.std(data)
elif emode=='sdom':
ret = sdom(data)
elif emode=='minmax':
if len(data)==0:
ret = [np.nan, np.nan]
else:
center = getcenter(data,cmode)
ret = [center-min(data), max(data)-center]
return ret
def cleandata(data, clean, returnstats=False):
"""Clean data using removeoutliers. Helper function."""
init_count = np.array(data).size
if clean==None: # Don't clean at all!
#clean = dict(nsigma=1000, niter=0)
if returnstats:
ret = data, (init_count, init_count)
else:
ret = data
else: # Clean the data somehow ('clean' must be a dict)
if not clean.has_key('nsigma'):
clean.update(dict(nsigma=99999))
data = removeoutliers(data, **clean)
if returnstats:
ret = data, (init_count, np.array(data).size)
else:
ret = data
return ret
if timing:
print "%1.3f sec since starting function; helpers defined" % (time.time() - tic)
####### Begin main function ##########
sorted_index = np.argsort(x)
x = np.array(x, copy=False)[sorted_index]
y = np.array(y, copy=False)[sorted_index]
#x = np.array(x,copy=True).ravel()
#y = np.array(y,copy=True).ravel()
xbins = np.array(xbins,copy=True).ravel()
if xbins[0]==None and binfactor==None:
if returnstats ==False:
ret = x, y, np.ones(x.shape)*np.nan, np.ones(y.shape)*np.nan
else:
ret = x, y, np.ones(x.shape)*np.nan, np.ones(y.shape)*np.nan, (x.size, x.size)
return ret
if binfactor==None: # used passed-in 'xbins'
xbins = np.sort(xbins)
elif hasattr(binfactor,'__iter__'): # use variable-sized bins
binfactor = np.array(binfactor).copy()
sortedx = np.sort(x)
betweens = np.hstack((x.min()-1, 0.5*(sortedx[1::]+sortedx[0:len(x)-1]), x.max()+1))
xbins = []
counter = 0
for ii in range(len(binfactor)):
thisbin = betweens[counter]
xbins.append(thisbin)
counter += binfactor[ii]
xbins.append(x.max() + 1)
else: # bin down by the same factor throughout
binfactor = int(binfactor)
sortedx = np.sort(x)
betweens = np.hstack((x.min()-1, 0.5*(sortedx[1::]+sortedx[0:len(x)-1]), x.max()+1))
xbins = betweens[::binfactor]
if timing:
print "%1.3f sec since starting function; bins defined" % (time.time() - tic)
nbins = len(xbins)-1
arraynan = np.array([np.nan])
exx = []
eyy = []
xx = np.zeros(nbins)
yy = np.zeros(nbins)
yy2 = np.zeros(nbins)
init_count, final_count = y.size, 0
if timing:
setuptime = 0
xdatatime = 0
ydatatime = 0
statstime = 0
#import pylab as py
#xxx = np.sort(x)
if timing: tic1 = time.time()
#inds = np.digitize(x, xbins)
inds2 = [[x.searchsorted(xbins[ii], side='left'), \
x.searchsorted(xbins[ii+1], side='left')] for ii in range(nbins)]
if timing: setuptime += (time.time() - tic1)
#pdb.set_trace()
#bin_means = [data[digitized == i].mean() for i in range(1, len(bins))]
dox = xmode is not None
doy = ymode is not None
doex = xerr is not None
doey = yerr is not None
if clean is None:
if timing: tic3 = time.time()
if dox: exec ('xfunc = np.%s' % xmode) in locals()
if doy: exec ('yfunc = np.%s' % ymode) in locals()
for ii in range(nbins):
#index = inds==(ii+1)
if dox:
#xx[ii] = xfunc(x[index])
xx[ii] = xfunc(x[inds2[ii][0]:inds2[ii][1]])
if doy:
#yy[ii] = yfunc(y[index])
yy[ii] = yfunc(y[inds2[ii][0]:inds2[ii][1]])
if doex:
#exx.append(geterr(x[index], xerr, xmode))
exx.append(geterr(x[inds2[ii][0]:inds2[ii][1]], xerr, xmode))
if doey:
#eyy.append(geterr(y[index], yerr, ymode))
eyy.append(geterr(y[inds2[ii][0]:inds2[ii][1]], yerr, ymode))
if timing: statstime += (time.time() - tic3)
#pdb.set_trace()
else:
for ii in range(nbins):
if timing: tic1 = time.time()
#index = inds==(ii+1)
if timing: setuptime += (time.time() - tic1)
if timing: tic2 = time.time()
xdata = x[inds2[ii][0]:inds2[ii][1]]
if timing: xdatatime += (time.time() - tic2)
if timing: tic25 = time.time()
if ymode is None and yerr is None: # We're free to ignore the y-data:
ydata = arraynan
else: # We have to compute something with the y-data:
if clean is not None:
ydata, retstats = cleandata(y[inds2[ii][0]:inds2[ii][1]], clean, returnstats=True)
if returnstats:
final_count += retstats[1]
else: # We don't have to clean the data
ydata = y[inds2[ii][0]:inds2[ii][1]]
if returnstats:
final_count += ydata.size
if timing: ydatatime += (time.time() - tic25)
if timing: tic3 = time.time()
xx[ii] = getcenter(xdata,xmode)
if timing: tic4 = time.time()
yy[ii] = getcenter(ydata,ymode)
if timing: tic5 = time.time()
exx.append(geterr( xdata,xerr,xmode))
if timing: tic6 = time.time()
eyy.append(geterr( ydata,yerr,ymode))
if timing: tic7 = time.time()
if timing: statstime += (time.time() - tic3)
#exx[ii] = geterr( xdata,xerr,xmode)
#eyy[ii] = geterr( ydata,yerr,ymode)
if timing:
print "%1.3f sec for setting up bins & indices..." % setuptime
print "%1.3f sec for getting x data clean and ready." % xdatatime
print "%1.3f sec for getting y data clean and ready." % ydatatime
#print "%1.3f sec for computing x-data statistics." % (tic4-tic3)
#print "%1.3f sec for computing y-data statistics." % (tic5-tic4)
#print "%1.3f sec for computing x-error statistics." % (tic6-tic5)
#print "%1.3f sec for computing y-error statistics." % (tic7-tic6)
print "%1.3f sec for computing statistics........." % statstime
if timing:
print "%1.3f sec since starting function; uncertainties defined" % (time.time() - tic)
#xx = array(xx)
#yy = array(yy)
exx = np.array(exx).transpose() # b/c 2D if minmax option used
eyy = np.array(eyy).transpose() # b/c 2D if minmax option used
#pdb.set_trace()
if returnstats:
ret= xx,yy,exx,eyy,(init_count, final_count)
else:
ret = xx,yy,exx,eyy
#print 'tools: returnstats, len(ret)>>', returnstats, len(ret)
if timing:
print "%1.3f sec since starting function; returning" % (time.time() - tic)
return ret
[docs]def ploth(*args, **kw):
"""Plot 1D data in a histogram-like format. If x-coordinates are
specified, they refer to the centers of the histogram bars.
Uses same format as matplotlib.pyplot.plot. For example:
::
ploth(x, y) # plot x and y using solid linestyle (default)
ploth(x, y, 'bo') # plot x and y using blue circle markers w/no line
ploth(y) # plot y using x as index array 0..N-1
ploth(y, 'r*--') # ditto, but with red star corners and dashed line
:OPTIONS:
rot90 : bool
If True, data will be plotted histogram-style vertically,
rather than the standard horizontal plotting.
:REQUIREMENTS: :doc:`numpy`, :doc:`analysis`
"""
# 2009-09-17 09:26 IJC: Created
# 2012-09-27 19:19 IJMC: Added 'rot90' keyword
from numpy import arange, concatenate, vstack
from pylab import plot
if len(args)==1:
y=args[0]
ny = len(y)
x = arange(ny)
plotstr = '-'
elif len(args)==2 and args[1].__class__==str:
y=args[0]
ny = len(y)
x = arange(ny)
plotstr = args[1]
elif len(args)==2 and args[1].__class__<>str:
x = args[0]
y=args[1]
ny = len(y)
plotstr = '-'
elif len(args)>=3:
x = args[0]
y=args[1]
ny = len(y)
plotstr = args[1]
if kw.has_key('rot90') and kw['rot90']:
temp = x
x = y
y = temp
ny = len(y)
nx = len(x)
rot90 = kw.pop('rot90')
else:
rot90 = False
x1= 0.5*(x[1::]+x[0:ny-1])
xx = concatenate(([x[0]], vstack((x1,x1)).transpose().ravel(), [x[-1]]))
yy = vstack((y,y)).transpose().ravel()
if rot90:
phandle = plot(xx,yy,plotstr,**kw)
else:
phandle = plot(xx,yy,plotstr,**kw)
return phandle
[docs]def flatten(x, maxdepth=100):
"""flatten(sequence) -> list
Returns a single, flat list which contains all elements retrieved
from the sequence and all recursively contained sub-sequences
(iterables).
:OPTIONAL INPUTS:
maxdepth -- scalar
number of layers deep to dig. Seting to zero causes no flattening to occur.
:Examples:
::
>>> [1, 2, [3,4], (5,6)]
[1, 2, [3, 4], (5, 6)]
>>> flatten([[[1,2,3], (42,None)], [4,5], [6], 7, MyVector(8,9,10)])
[1, 2, 3, 42, None, 4, 5, 6, 7, 8, 9, 10]"""
# 2009-09-26 14:05 IJC: Taken from
# http://kogs-www.informatik.uni-hamburg.de/~meine/python_tricks
# 2011-06-24 15:40 IJMC: Added maxdepth keyword
result = []
for el in x:
#if isinstance(el, (list, tuple)):
if hasattr(el, "__iter__") and not isinstance(el, basestring) and maxdepth>0:
maxdepth -= 1
result.extend(flatten(el, maxdepth=maxdepth))
else:
result.append(el)
return result
[docs]def fconvolve(a, v, oversamp=2):
"""Returns the discrete, linear convolution of 1-D sequences a and v,
using Fast Fourier Transforms. Restrictions are: a and v must
both be real-valued, and len(a)>len(v).
:REQUIREMENTS: :doc:`analysis`, :doc:`numpy`
"""
# 2009-10-29 11:00 IJC: Created
from analysis import pad
from numpy.fft import fft, ifft, fftshift
from numpy import real, array
a = array(a,copy=True).ravel()
v = array(v,copy=True).ravel()
na = len(a)
nv = len(v)
nfft = oversamp*na
a2 = pad(a, 1, nfft)[0,:]
v2 = pad(v, 1, nfft)[0,:]
fa2 = fft(a2)
fv2 = fft(v2)
ret = real(fftshift(ifft(fa2 * fv2)))
return pad(ret, 1, na).ravel()
[docs]def cplim(a1,a2):
"""Copy axis limits from one axes to another.
:INPUTS:
a1, a2 -- either (1) handles to axes objects, or (2) figure
numbers. If figures have subplots, you can refer to a
particular subplot using decimal notation. So, 1.3
would refer to subplot 3 of figure 1.
:REQUIREMENTS: :doc:`matplotlib` (when this is written...)
"""
# 2009-12-08 16:30 IJC: Had the idea...
print "To be written -- and what a great day it will be."
return
[docs]def legc(leg,col='color'):
"""Color legend text to match linecolor.
:Inputs:
'leg' is a legend object.
'col' sets the field of the leg.get_lines() objects to use to find
the color.
You may need to refresh the figure to see the changes."""
# 2009-12-14 09:50 IJC: Created
texts = leg.get_texts()
lines = leg.get_lines()
for label,line in zip(texts,lines):
label.set_color(line.get_color())
return leg
[docs]def keylist(filelist, keys):
"""Create an object based on FITS header keys extracted from a filelist.
:Inputs:
filelist -- sequence of strings representing filenames (for PyFITS)
keys -- sequence of strings representing header keys
#Keys not found in a file will result in the string value
:REQUIREMENTS: :doc:`pyfits`, :doc:`spitzer`
"""
try:
from astropy.io import fits as pyfits
except:
import pyfits
from spitzer import baseObject
# 2010-01-24 15:23 IJC: Created
# 2010-01-26 10:27 IJC: Solved a pernicious little problem: always
# call object creation w/parentheses!
obj = baseObject()
for k in keys:
exec('obj.%s=[]'%k)
for f in filelist:
h = pyfits.getheader(f)
for k in keys:
exec("obj.%s.append(h['%s'])" %(k,k) )
return obj
[docs]def plotc(x,y,z,**kw):
"""Plot x,y data with an evolving z component by changing its
color using a matplotlib colormap 'cm' object.
Will bomb if z elements are non-finite.
:OPTIONS:
map : str
colormap to use for z
zmin, zmax : floats
maximum/minimum values of z for colorscale
sizenotcolor : bool
If True, 'z' specifies marker size not color.
others : various
Any options passable to matplotlib's :func:`plot`
:SEE ALSO:
:func:`contourg`, :func:`matplotlib.colormaps`
:REQUIREMENTS: :doc:`pylab`
"""
# 2010-02-08 16:47 IJC: Created
# 2011-09-07 10:51 IJMC: Added zmin, zmax options. And use
# variable-number of keywords now.
# 2013-10-09 17:16 IJMC: Added sizenotcolor option.
# 2014-10-06 10:50 IJMC: Updated 'see also' note.
from pylab import plot, cm, array
defaults = dict(map='Blues', zmin=None, zmax=None, linestyle='None', marker='o', sizenotcolor=False)
for key in defaults:
if (not kw.has_key(key)):
kw[key] = defaults[key]
map = kw.pop('map')
zmin = kw.pop('zmin')
zmax = kw.pop('zmax')
sizenotcolor = kw.pop('sizenotcolor')
try:
cmap = eval('cm.'+map)
except:
print "Colormap %s not found -- exiting!" % map
return -1
z2 = array(z,copy=True)
if not sizenotcolor:
if zmin is None:
zmin = z2.min()
if zmax is None:
zmax = z2.max()
z3 = (z2-zmin) / (zmax-zmin)
z4 = z3 * cmap.N
z2 = cmap(z4.astype(int))
plotlist = []
print kw
for xx,yy,param in zip(x,y,z2):
if sizenotcolor:
kw['ms'] = param
else:
kw['color'] = param
plotlist.append(plot([xx],[yy],**kw))
return plotlist
[docs]def hist2d(x,y, bins=None):
"""Compute 2-d histogram data for specified bins.
:INPUT:
x
y
:OPTIONAL INPUT:
bins: a two-tuple containing one of the following:
(nx,ny) -- tuple, number of bins in each direction
(xlims, ylims) -- tuple of sequences (x- and y-bin edges)
:OUTPUT:
A 3-tuple consisting of:
xbins -- the centers of the x bins
ybins -- the centers of the y bins
hist -- The 2D histogram array
:SEE ALSO: :func:`numpy.histogram2d`
:REQUIREMENTS: :doc:`numpy`
"""
# 2010-02-25 17:26 IJC: Created from my old Hess Diagram fcn.
# 2010-03-04 13:59 IJC: Fixed a typo -- now actually returns bin centers
from numpy import arange, array, zeros, isfinite, linspace
x = array(x).ravel()
y = array(y).ravel()
x = x[isfinite(x)]
y = y[isfinite(y)]
if bins==None:
bins = [20,20]
if hasattr(bins,'__iter__'):
if len(bins)<2:
print "bins must have len>2"
return -1
else:
print "bins must have len>2"
return -1
# Test X bins
if hasattr(bins[0],'__iter__'): # sequence of limits
nx = len(bins[0])-1
xlims = bins[0]
else:
nx = bins[0]
xlims = linspace(x.min(), x.max(), nx+1)
# Test Y bins
if hasattr(bins[1],'__iter__'): # sequence of limits
ny = len(bins[1])-1
ylims = bins[1]
else:
ny = bins[1]
ylims = linspace(y.min(), y.max(), ny+1)
xcen = zeros(nx,float)
ycen = zeros(ny,float)
hist = zeros((ny,nx),int)
for ii in range(nx):
xindex = (x>xlims[ii]) * (x<xlims[ii+1])
xcen[ii] = 0.5*(xlims[ii]+xlims[ii+1])
for jj in range(ny):
ycen[jj] = 0.5*(ylims[jj]+ylims[jj+1])
yindex = (y>ylims[jj]) * (y<ylims[jj+1])
index = xindex * yindex
hist[jj,ii] = index.sum()
return (xcen, ycen, hist)
[docs]def plotcorrs(params, labs=None, tit=None, xrot=0, yrot=0, cmap=None,figsize=None,plotregion=[.1,.1,.8,.8], n=6, nbins=None, clim=None, docontour=False, contourcolor='k', newfig=True):
""" Plot correlation coefficient matrix in one big, huge, honkin'
figure. Color-code the figure based on the correlation
coefficients between parameters.
:INPUTS:
params -- (M x N array) M instantiations of a set of N parameters.
:OPTIONS:
labs -- (list) labels for each of the N parameters
tit -- (str) title for figure
xrot/yrot -- (float) axis label rotation, in degrees
cmap -- (matplotlib cm) -- colormap for color-coding.
figsize -- (2-list) -- width and height of figure
plotregion -- (4-list) -- (left, bottom, width, height) of plotted region in each figure
n -- (int) -- number of subplots across each figure
nbins : int
Bin the data into this many bins, and show 2D histograms instead of points.
clim : None
Colorscale limits for normalized 2D histograms (where hist.sum() = 1.0)
docontour : bool
Whether to plot contours, or do an 'imshow'
newfig : bool
Whether to generate a new figure, or plot in the current axes.
contourcolor
Color of contour line, if "docontour" is set to a list of confidence intervals.
:REQUIREMENTS: :doc:`pylab`, :doc:`nsdata`
:NOTES:
Based on the concept by Nymyer and Harrington at U. Central Florida
Beware of plotting two many points, and clogging your system!
"""
# 2010-05-27 09:27 IJC: Created
# 2010-08-26 14:49 IJC: Added test for higher-rank dimensional
# 2010-08-27 09:21 IJC: Moved 'tit' title text lower
# 2011-11-03 12:03 IJMC: Added 'nbins' option
# 2012-03-30 09:04 IJMC: Moved axes labels to upper-right, rather than lower-left.
# 2013-08-19 13:17 IJMC: Added 'docontour' option.
# 2013-10-09 14:59 IJMC: Added 'newfig' option.
import pylab as py
import nsdata as ns
import kdestats as kde
n = int(n)
n, m = params.shape
if n>=m:
npts0 = n
nparam = m
else:
npts0 = m
nparam = n
params = params.copy().transpose()
if nbins is not None:
nbins = int(nbins)
hist_bins = [py.linspace(min(params[:,ii]), max(params[:,ii]), nbins+1) for ii in range(nparam)]
hist_cmap = cmap
nind = params.shape[1]
if labs is None:
labs = ['']*nind
if figsize is None:
figsize = [9,9]
nperpage = min(n,nind-1)
nfigs = py.ceil(float(nind-1.)/nperpage).astype(int)
#print "nind, nperpage, nfigs>>",nind, nperpage, nfigs
subx0,suby0, xwid,ywid = plotregion
subdx = xwid/(nperpage) # was nind-1.
subdy = ywid/(nperpage) # was nind-1.
#print "subx0,suby0,subdx,subdy>>",[subx0,suby0,subdx,subdy]
oldaxlinewidth = py.rcParams['axes.linewidth']
if nind>40:
py.rcParams['axes.linewidth'] = 0
figs = []
allsubplots = []
# Iterate over figure columns
for kk2 in range(nfigs):
# Iterate over figure rows
for kk1 in range(nfigs):
if newfig:
f=py.figure(nextfig(),figsize)
else:
f = py.gcf()
subplots = []
jj0 = 0
#Iterate over subplot columns:
for jj in range(nperpage*kk2,min(nperpage*(kk2+1),nind)):
# Set the vertical panel offset:
if kk1==kk2: # a figure on the diagonal
ii0 = jj0+1
elif kk1>kk2: # a figure below the diagonal
ii0 = 1
#Iterate over subplots rows:
for ii in range(max(jj+1,nperpage*kk1+1), min(nperpage*(kk1+1)+1,nind)):
#print '(kk2,kk1,jj,jj0,ii,ii0): (%i,%i,%i,%i,%i,%i)'%(kk2,kk1,jj,jj0,ii,ii0), [subx0+subdx*jj0,suby0+subdy*(nperpage-ii0),subdx,subdy]
s = py.axes([subx0+subdx*jj0,suby0+subdy*(nperpage-ii0),subdx,subdy])
param_doesnt_vary = params[:,jj].std()==0 or params[:,ii].std()==0 or \
(py.np.abs(params[:,jj].std()/py.median(params[:,jj])) < 1e-9) or \
(py.np.abs(params[:,ii].std()/py.median(params[:,ii])) < 1e-9)
if nbins is None or param_doesnt_vary:
py.plot(params[:,jj],params[:,ii],',k')
#pdb.set_trace()
else:
#pdb.set_trace()
thishist = py.histogram2d(params[:,jj], params[:,ii], \
bins=[hist_bins[jj], hist_bins[ii]])
if docontour:
xplot = 0.5*(thishist[1][1:] + thishist[1][0:-1])
yplot = 0.5*(thishist[2][1:] + thishist[2][0:-1])
if hasattr(docontour, '__iter__'):
clev = [kde.confmap(1.0*thishist[0]/npts0, thisDC) for thisDC in docontour]
py.contour(xplot, yplot, 1.0*thishist[0].transpose()/npts0, clev, colors=contourcolor, linewidths=2)
else:
py.contourf(xplot, yplot, 1.0*thishist[0].transpose()/npts0, cmap=hist_cmap)
h_axis = py.xlim() + py.ylim()
else:
ns.imshow(1.0*thishist[0].transpose()/npts0, x=thishist[1], y=thishist[2], cmap=hist_cmap)
h_axis = py.xlim() + py.ylim()[::-1]
#pdb.set_trace()
py.axis(h_axis)
if clim is None:
py.clim([0., thishist[0].ravel().max()*1.0/npts0])
else:
py.clim(clim)
if jj0>0: #
s.set_yticklabels('');
else:
#py.ylabel(labs[ii], rotation=yrot)
pass
if newfig: s.set_yticks(s.get_yticks()[1:-1]);
if ii0 == (jj0+1):
s.get_xaxis().set_label_position('top')
py.xlabel(labs[jj])
s.get_yaxis().set_label_position('right')
py.ylabel(labs[ii])#, rotation='horizontal')
s.get_yaxis().get_label().set_rotation(90)
if ii0<(nperpage-1) and ii<(nind-1):
s.set_xticklabels('');
else:
#py.xlabel(labs[jj],rotation=xrot)
s.get_xaxis().set_major_formatter(py.FormatStrFormatter('%01.2f'));
if newfig: s.set_xticks(s.get_xticks()[1:-1]);
if nperpage>10:
s.set_xticklabels('');
s.set_yticklabels('');
if nperpage>50:
s.set_xticks([])
s.set_yticks([])
else:
[obj.set_rotation(90.) for obj in s.get_xticklabels()] ;
if cmap is not None:
s.set_axis_bgcolor(cmap(.3+.7*abs(py.corrcoef(params[:,jj],params[:,ii])[0,1])))
#py.title('(kk2,kk1,jj,jj0,ii,ii0): (%i,%i,%i,%i,%i,%i)'%(kk2,kk1,jj,jj0,ii,ii0))
if nbins is not None and (not param_doesnt_vary):
py.axis(h_axis)
subplots.append(s)
ii0 += 1
jj0+=1
figs.append(f)
allsubplots.append(subplots)
if tit is not None:
f.text(.5,.9,tit,fontsize=24,horizontalalignment='center')
py.draw()
py.rcParams['axes.linewidth'] = oldaxlinewidth
for ff,ss in zip(figs,allsubplots):
if len(ss)==0:
py.close(ff)
return figs, allsubplots
[docs]def pparams(params, npts=None, figsize=[15,10],newfig=True, labs=None):
"""Take a set of parameters and plot them. Assume that the larger
of the array's two dimensions is N (the number of instantiations)
and the smaller is M (the number of parameters).
If npts is not None, then pick only every (N/npts)th point.
if newfig is False, plot into the current figure.
:REQUIREMENTS: :doc:`numpy`, :doc:`pylab`
"""
# 2012-02-17 09:45 IJMC: Added labs option
from numpy import sqrt
from pylab import figure, plot, subplot, xticks, gcf, title
n, m = params.shape
if n>=m:
npts0 = n
nparam = m
else:
npts0 = m
nparam = n
params = params.copy().transpose()
ndown = sqrt(nparam).astype(int)
nacross = int(1.0*nparam/ndown)
if ndown*nacross<nparam:
nacross +=1
if npts is None:
npts = npts0
sampling = max(int(npts0/npts), 1)
if newfig==True:
fig = figure(nextfig(), figsize)
else:
fig = gcf()
for ii in range(nparam):
subplot(ndown,nacross, ii+1)
plot(params[::sampling,ii]); xticks([])
if labs is not None:
title(labs[ii])
return fig
[docs]def hparams(params, nbins=10, figsize=[15,10], normed=False,newfig=True, labs=None, cumulative=False, minorticks=True, plotconf=.683, plotmid=True, color=None):
"""Take a set of parameters and histogram them. Assume that the larger
of the array's two dimensions is N (the number of instantiations)
and the smaller is M (the number of parameters).
:Options:
nbins sets the number of bins
normed sets the histogram normalization
if newfig is False, plot into the current figure.
labs is a list of string labels
cumulative plots normalized cumulative distribution function
minorticks displays minor tick marks
plotconf displays confidence levels at the desired (fractional)
threshold. E.g., plotconf=0.683 displays the one-sigma
confidence limits. Set to 'None' for no confidence levels.
plotmid plots nothing (if False), the median (if True), or the
specified values (if a sequence). Defaults to median if
plotconf is True.
color sets the plotting color.
:Requirements: :doc:`numpy`, :doc:`pylab`
"""
# 2010-11-30 12:11 IJC: Now xticks are rotated 90 degrees.
# 2012-01-22 16:35 IJMC: Added 'labs' option
# 2012-03-26 13:09 IJMC: Added 'cumulative' and 'minorticks' options
# 2012-05-10 16:30 IJMC: Added plotconf and plotmid options.
# 2013-03-11 08:45 IJMC: Added color option.
# 2014-07-12 17:29 IJMC: Changed defaults to show conf. & median.
from numpy import sqrt
from pylab import figure, gcf, subplot, draw
from analysis import dumbconf
n, m = params.shape
if n>=m:
npts0 = n
nparam = m
else:
npts0 = m
nparam = n
params = params.copy().transpose()
if cumulative:
normed=True
if (plotmid is True) or ((plotconf is not None) and (not hasattr(plotmid, '__iter__'))):
plotmid = np.median(params, axis=0)
ndown = sqrt(nparam).astype(int)
nacross = int(1.0*nparam/ndown)
if ndown*nacross<nparam:
nacross +=1
if newfig==True:
fig = figure(nextfig(), figsize)
else:
fig = gcf()
histoptions = dict(histtype='step', cumulative=cumulative, normed=normed)
if color is not None:
histoptions['color'] = color
for ii in range(nparam):
sax = subplot(ndown,nacross, ii+1)
sax.hist(params[:,ii],nbins, **histoptions)
if cumulative:
sax.set_ylim([0,1])
else:
sax.set_ylim([0, sax.get_ylim()[1]])
sax.set_yticklabels([])
if minorticks:
sax. minorticks_on()
[tick.set_rotation(90.) for tick in sax.get_xaxis().get_ticklabels()]
if labs is not None:
sax.text(.05, .9, labs[ii], verticalalignment='top', horizontalalignment='left', transform=sax.transAxes)
if plotmid is not False:
sax.plot([plotmid[ii]]*2, sax.get_ylim(), '-k')
if plotconf is not None:
x0 = plotmid[ii]
xup = -x0 + dumbconf(params[:,ii], (1.-plotconf)/2., mid=x0, type='lower')[0]
xdn = x0 - dumbconf(params[:,ii], (1.-plotconf)/2., mid=x0, type='upper')[0]
if xup==0 or xdn==0:
ndigit = 1
else:
ndigit = np.abs(int(np.floor(min(np.log10(np.abs(xup)), np.log10(np.abs(xdn)))) - 1))
precstr = '%' + ('1.%i' % ndigit) + 'e'
sax.plot([x0-xdn]*2, sax.get_ylim(), '--k')
sax.plot([x0+xup]*2, sax.get_ylim(), '--k')
sax.set_ylabel((precstr + '\n(+' + precstr + ' / -' + precstr + ')\n') % (x0, xup, xdn), horizontalalignment='center')
draw()
return fig
[docs]def getparams(params, chisq=None, conf=[.683]):
"""Find confidence levels and optimal parameters.
If chisq is None:
Take the median of each parameter, and compute the upper and
lower confidence limits using the parameter distributions and
this model.
Else:
Take a set of fit parameters and associated chi-squared values.
Take as the optimum model that model with the MEDIAN chi-squared
value. Compute upper and lower confidence limits using the
parameter distributions and this optimum model.
:INPUTS:
params : N-D numpy array
model parameters
chisq : 1-D numpy array
chi-squared values.
conf : sequence or float
confidence levels to report
:OUTPUTS:
:SEE ALSO:
:func:`analysis.dumbconf`
:REQUIREMENTS: :doc:`numpy`
"""
# 2010-07-20 11:37 IJC: Created
# 2010-10-28 12:01 IJC: Updated documentation
from numpy import sqrt, median, array, ceil,sort,nonzero,floor
if len(params.shape)==1:
params = params.reshape(len(params),1)
n, m = params.shape
if chisq is None:
if m>n:
params = array(params,copy=True).transpose()
nmod = params.shape[0]
else:
nmod = len(chisq)
if n==nmod:
pass
else:
params = array(params,copy=True).transpose()
# Don't allow an even number of parameter sets
if nmod/2==nmod/2.:
params = array(params,copy=True)[1::]#[0:nmod-1,:]
if chisq is None:
pass
else:
chisq = array(chisq,copy=True)[1::]#[0:nmod-1]
nmod -= 1
nparam = params.shape[1]
ret = []
if chisq is None:
medmodel = median(params,0)
else:
medmodel = params[chisq==median(chisq),:].ravel()
for ii in range(nparam):
thisret = [medmodel[ii]]
for thisconf in conf:
thisconf = abs(thisconf)
sorted_param = sort(params[:,ii])
mid_index = nonzero(sorted_param==medmodel[ii])[0].mean()
n_offset = nmod*thisconf/2.
upper_index = ceil(min(mid_index+n_offset,nmod-1)).astype(int)
lower_index = floor(max(mid_index-n_offset,0)).astype(int)
upper = sorted_param[upper_index]-medmodel[ii]
lower = sorted_param[lower_index]-medmodel[ii]
thisret += [upper, lower]
ret.append(thisret)
return ret
[docs]def combinations(input_list):
"""Return all possible combinations of the elements in an input
sequence. The last returned element will be the empty list.
E.g., combinations([0,1]) returns [[0, 1], [0], [1], []]
Taken from the internet:
http://desk.stinkpot.org:8080/tricks/index.php/2008/04/get-all-possible-combinations-of-a-lists-elements-in-python/
:Requirements: :doc:`copy`
"""
# 2010-10-09 17:06 IJC: Created from internet
import copy
swap_list_list = [[]]
for swap in input_list:
temp_lists = []
for list_stub in swap_list_list:
this_list = copy.copy(list_stub)
this_list.append(swap)
temp_lists.append(this_list)
temp_lists.append(list_stub)
swap_list_list = temp_lists
return swap_list_list
[docs]def pcmodelxcorr(pcaout, data, model, npcs=6, nblock=1000, xl=50, modstr='model', titstr=''):
"""Plot cross-correlations between projection of principal components
onto data and a model.
:INPUTS:
pcaout -- output from pcsa.pca, but its only important component
is that pcaout[2] is an array of PC eigenvectors; the
strongest vector would be pcaout[2][:,-1], etc.
data -- numpy array. Should be shape N x M -- N observations of M
variables, arranged in L blocks, and should have been
mean-subtracted prior to PCA (i.e., data -= data.mean(0))
model -- numpy array. Should be shape M.
npcs -- int. Number of principal components to cross-correlate
with.
nblock -- int. NUmber of channels to use at a time in
correlations. Must be an integral divisor of
data.shape[1]
xl -- int. +/- X-limits to display in plots.
:Requirements: :doc:`pylab`, :doc:`numpy`, :doc:`pcsa`
Usage is pretty specific to echelle-data
"""
# 2010-10-15 11:10 IJC: Created
import pylab as py
from numpy import abs
from pcsa import pca_project
import pdb
ps = [pca_project(pcaout[2][:,-ii], data-data.mean(0))[0] \
for ii in range(1,npcs+1)]
nobs, ndat = data.shape
nord = ndat/nblock
figs = []
maxlag = nblock/2
lags = py.arange(-maxlag+1, maxlag)
for ii in range(npcs):
figs.append(py.figure())
x_mod = [py.xcorr(pcp-pcp.mean(), mod-mod.mean(), maxlags=maxlag-1)[1] \
for pcp, mod in zip(ps[ii].reshape(nord,nblock), \
model.reshape(nord, nblock))]
py.close()
pdb.set_trace()
xc_gmean = abs(py.array(x_mod).prod(0))**(1./nord)
xc_amean = py.array(x_mod).mean(0)
py.figure()
py.subplot(211)
py.semilogy(lags, xc_gmean)
py.ylabel('geometric mean' )
py.xlabel('lags')
py.xlim([-50,50])
py.ylim([xc_gmean[abs(lags)<xl].min(), xc_gmean.max()])
py.title(titstr + '\n' + modstr + ' and PC #%i' % ii)
py.subplot(212)
py.plot(lags, xc_amean)
py.ylabel('arithmetic mean' )
py.xlabel('lags')
py.xlim([-xl,xl])
return figs
[docs]def dcf(t, x, y, zerolag=True, nbin=11, binwidth=None, bins=None, prebin=None, reterr=False):
"""Compute the Discrete Correlation Function for unevenly sampled data.
If your data are evenly sampled, just use :func:`numpy.correlate`!
:INPUTS:
t -- (1D sequence) - time sampling of input data.
x, y -- (1D sequences) - input data.
Note that t, x, y should all have the same lengths!
:OPTIONAL INPUT:
zerolag -- (bool) - whether to compute DCF for zero-lag datapoints.
nbin -- (int) - number of computed correlation/lag values to average over
binwidth -- (float) - width of bins to average over, in units
of t. If set, this overrides nbin.
bins -- (sequence) - edges of bins to use in averaging DCF
values. If set, this overrides both nbin
and binwidth.
prebin -- (scalar) - factor by which to bin down initial data
and lag pairs. This translates into a
speed boost of about this same factor.
reterr -- bool - False or True
:RETURNS:
meanlags -- average lag in each averaged bin
rdcf -- DCF value in each averaged bin
rdcf_err -- uncertainty in the DCF value for each averaged bin
:SEE ALSO: :func:`numpy.correlate`
:REQUIREMENTS: :doc:`analysis`, :doc:`numpy`
"""
# 2010-11-12 IJC: Created
# 2010-11-17 09:25 IJC: Added 'bins' option
# 2011-03-22 13:54 IJC: Added 'prebin' option
# 2012-03-21 13:25 IJMC: Switched "import *" to "import array, " ... etc.
# 2014-12-19 08:21 IJMC: Added 'reterr' option
import analysis as an
#from numpy import array, meshgrid, nonzero, arange, argsort, isfinite
import pdb
t = np.array(t)
x = np.array(x, copy=True)
y = np.array(y, copy=True)
nx, ny = x.size, y.size
npts = max(nx, ny)
x -= x.mean()
y -= y.mean()
xx, yy = np.meshgrid(x, y)
sx = x.std()
sy = y.std()
# Generate data-pair indices:
if zerolag:
pairs1, pairs2 = np.nonzero(np.ones((npts, npts), bool))
else:
xind, yind = np.meshgrid(np.arange(npts), np.arange(npts))
pairs1, pairs2 = np.nonzero(xind<>yind)
del xind
del yind
# Compute lags:
tt, tt2 = np.meshgrid(t, t)
lags = (tt-tt2)[pairs1, pairs2]
del tt
del tt2
uij = (xx * yy)[pairs1, pairs2] / (sx * sy)
del xx
del yy
tind = np.argsort(lags)
lags = lags[tind]
uij = uij[tind]
del tind
#pdb.set_trace()
# The regular "DCF" uncertainty is just the standard deviation of the mean:
#if bins is not None:
# meanlags, rdcf, meanlags_width, rdcf_err = \
# errxy(lags, uij, bins, xerr='minmax', yerr='sdom')
#elif binwidth is None:
# meanlags, rdcf, meanlags_width, rdcf_err = \
# errxy(lags, uij, None, xerr='minmax', yerr='sdom', binfactor=nbin)
#else:
# bins = arange(lags.min(), lags.max() + binwidth, binwidth)
# meanlags, rdcf, meanlags_width, rdcf_err = \
# errxy(lags, uij, bins, xerr='minmax', yerr='sdom')
if prebin>1:
lags = an.binarray(lags, 2)
uij = an.binarray(uij, 2)
if reterr:
yerr = 'sdom'
else:
yerr = None
if bins is not None:
meanlags, rdcf, meanlags_width, rdcf_err = \
errxy(lags, uij, bins, xerr=None, yerr=yerr)
elif binwidth is None:
meanlags, rdcf, meanlags_width, rdcf_err = \
errxy(lags, uij, None, xerr=None, yerr=yerr, binfactor=nbin)
else:
bins = np.arange(lags.min(), lags.max() + binwidth, binwidth)
meanlags, rdcf, meanlags_width, rdcf_err = \
errxy(lags, uij, bins, xerr=None, yerr=yerr)
finite_ind = np.isfinite(meanlags) * np.isfinite(rdcf)
if reterr:
finite_ind *= np.isfinite(rdcf_err)
meanlags = meanlags[finite_ind]
rdcf = rdcf[finite_ind]
if reterr:
rdcf_err = rdcf_err[finite_ind]
return meanlags, rdcf, rdcf_err
[docs]def getfilelist(path='.', includes=[], excludes=[]):
"""Return a list of filenames meeting certain criteria.
:INPUTS:
path -- (str) path to directory to be scanned
includes -- (list of strs) -- all strings in this list must be
present in a filename to be returned
excludes -- (list of strs) -- any string in this list will
prevent a filename from being returned
"""
# 2011-01-30 22:20 IJC: Created
import os
f = os.popen('ls %s/' % path)
filenames = [os.path.split(line)[1].strip() for line in f.readlines()]
f.close()
filtered_filenames = []
if len(includes)>0:
for fn in filenames:
string_found = True
for incstr in includes:
if fn.find(incstr)==-1:
string_found = False
if string_found:
filtered_filenames.append(fn)
if len(excludes)>0:
returned_filenames = []
for fn in filtered_filenames:
file_excluded = False
for excstr in excludes:
if fn.find(excstr)>-1:
file_excluded = True
if not file_excluded:
returned_filenames.append(fn)
else:
returned_filenames = filtered_filenames
return returned_filenames
[docs]def loadpickle(filename,mode='both'):
"""Load a pickle from a given filename. If it can't be loaded by
pickle, return -1 -- otherwise return the pickled object.
mode : str
'dill', 'pickle', or 'both' to try both
E.g.,
data = tools.loadpickle(filename)"""
# 2011-02-10 15:45 IJC: Created
# 2014-08-29 19:25 IJMC: First, try dill:
# 2014-12-31 17:03 IJMC: Added 'dill' vs 'pickle' option
if mode=='both':
import dill
import pickle
elif mode=='dill':
try:
import dill as pickle
except:
import pickle
elif mode=='pickle':
import pickle
good = True
try:
f = open(filename, 'r')
except:
print "Could not open file: %s" % filename
good = False
if good:
try:
ret = pickle.load(f)
except:
good = False
if mode=='both':
try:
ret = dill.load(f)
good = True
except:
print "Mode 'both' failed to load file:"
good = False
if not good:
print "Could not load pickle from %s" % filename
try:
f.close()
except:
print "Could not close file %s" % filename
good = False
if good:
pass
else:
ret = -1
return ret
[docs]def savepickle(obj, filename):
"""Save a pickle to a given filename. If it can't be saved by
pickle, return -1 -- otherwise return the file object.
To save multiple objects in one file, use (e.g.) a dict:
tools.savepickle(dict(a=[1,2], b='eggs'), filename)
"""
# 2011-05-21 11:22 IJMC: Created from loadpickle.
# 2011-05-28 09:36 IJMC: Added dict example
# 2014-08-27 12:47 IJMC: By default, try to use Dill:
try:
import dill as pickle
except:
import pickle
good = True
try:
f = open(filename, 'wb')
except:
print "Could not open file: %s : for writing." % filename
good = False
if good:
try:
ret = pickle.dump(obj, f)
except:
print "Could not write object to pickle file: %s" % filename
good = False
try:
f.close()
except:
print "Could not close pickle file %s" % filename
good = False
if good:
pass
else:
f = -1
return f
[docs]def dict2obj(dic):
"""Take an input Dict, and turn it into an object with fields
corresponding to the dict's keys.
:SEE_ALSO:
:func:obj2dict`
"""
# 2011-02-17 09:41 IJC: Created
from spitzer import baseObject
ret = baseObject()
if not isinstance(dic, dict):
print "Input was not a Python dict! Exiting."
else:
for key in dic.keys():
exec('ret.%s = dic["%s"]' % (key, key))
return ret
[docs]def obj2dict(object, ignore=('_',), verbose=False):
"""Convert an object into a dict. Ignore functions & methods, and
any attributes starting with the 'ignore' keys.
:SEE_ALSO:
:func:`dict2obj`
"""
# 2014-08-29 19:34 IJMC: Created.
import inspect
ret = dict()
for attribute in dir(object):
for ign in ignore:
if attribute.find(ign)==0:
parseIt = False
if verbose:
print "Ignoring attribute '%s' in input object." % attribute
else:
parseIt = True
if parseIt:
val = getattr(object, attribute)
if not inspect.isroutine(val):
ret[attribute] = val
elif verbose:
print "Attribute '%s' in input object is a routine; ignoring it.." % attribute
return ret
#def loadspectrum(filename, lambdascale=1., limits=None, skiprows=None, lamdacol=0, datacol=1 ):
# """Load a spectrum from a FITS or ASCII file, and return the
# wavelength and data in two vectors.#
#
# :INPUTS:
#
# filename (str) -- filename to load. If extension is "FITS"
# load using pyfits, otherwise try to load as
# an ASCII file.
#
# lambdacol (int) -- column number
[docs]def find_peaks(vec, sep=0, thresh=None):
"""
Find all large values in input vector that are separated by at least
'wid' pixels.
:INPUTS:
vec (sequence) -- 1D vector
sep (scalar) -- minimum separation of returned peaks
thresh (scalar) -- ignore all peaks lower than this value.
:EXAMPLE:
import pylab as py
import tools
x = py.linspace(0, 10, 100) # Generate fake time index
y = py.sin(6.28*x/10.) + py.sin(6.28*x/2.) # Generate fake data
peakvals, peaklocs = tools.find_peaks(y, sep=10) # Find the peaks
py.plot(x, y, '-', x[peaklocs], peakvals, 'or') # Plot them
:RETURNS:
peakvals, peakindices
"""
# 2011-03-22 14:54 IJC: Created
# 2012-08-09 22:51 IJMC: Added thresh option.
import numpy as np
from pylab import find
import pdb
if thresh is None:
thresh = -np.inf
vec = np.array(vec)
npix = len(vec)
sep = np.floor(sep).astype(int)
available_index = np.ones(npix, bool)
peakvals = np.zeros(npix, float)
peakindices = np.zeros(npix, float)
npks = 0
inds = np.arange(npix, dtype=int)
while available_index.any():
#pdb.set_trace()
this_peak = vec[available_index].max()
this_location = inds[available_index][vec[inds[available_index]] == vec[inds[available_index]].max()][0]
available_index[max(0, this_location - sep):min(npix, this_location + sep)+1] = False
if this_peak >= thresh:
peakvals[npks] = this_peak
peakindices[npks] = this_location
npks += 1
peakvals = peakvals[0:npks]
peakindices = peakindices[0:npks].astype(int)
return peakvals, peakindices
[docs]def addobj(obj1, obj2, exclude='TBD'):
"""Combine fields in two objects with the same attributes. A
handy function!
:INPUTS:
obj1, obj2 : objects of the same kind
:RETURNS:
obj12 : new object, with fields of 1 and 2 combined.
OR
-1, if the objects have absolutely no attributes in common.
:NOTES:
Methods/attributes beginning with an underscore (_) are not combined.
"""
# 2011-05-25 10:11 IJMC: Created
# 2011-06-01 15:15 IJMC: Fixed a bug in concatenate(common_dim)
import copy
import numpy
# Helper function:
def combine_atts(a1, a2):
"""Combine two objects, as best you can!
If they are of different classes, then return None.
If they are non-iterable, combined them in a 2-tuple."""
combined = False
if a1.__class__ <> a2.__class__:
ret = None
combined = True
if ((not hasattr(a1, '__iter__')) or isinstance(a1, list) or isinstance(a1, str)) \
and (not combined):
try:
ret = a1 + a2
except:
ret = (a1, a2)
combined = True
if isinstance(a1, numpy.ndarray) and (not combined):
sh1, sh2 = a1.shape, a2.shape
if sh1 == sh2: # Exactly same dimensions; I don't know
# which dimension to combine along, so
# just create a new one.
ret = numpy.array([a1, a2])
combined = True
elif len(sh1) <> len(sh2): # Wholly different shapes;
# can't combine.
ret = (a1, a2)
combined = True
elif len(set(sh1).difference(sh2)) > 1: # Too many disparate dimensions.
ret = (a1, a2)
combined = True
else: # There must be exactly 1 non-common dimension.
if len(sh1)==0 or len(sh1)==1: # Scalar (0D) or Vector (1D):
ret = numpy.concatenate((a1.ravel(), a2.ravel()))
combined = True
else: # Array (>1 D)
common_dim = (numpy.arange(len(sh1)) * \
(True - (numpy.array(sh1) == set(sh1).intersection(sh2).pop()))).sum()
ret = numpy.concatenate((a1, a2), common_dim)
#if common_dim==0:
# ret = numpy.hstack((a1, a2))
# combined = True
#elif common_dim==1:
# ret = numpy.vstack((a1, a2))
# combined = True
combined = True
if not combined:
ret = (a1, a2)
return ret
try:
newobj = copy.deepcopy(obj1)
except:
try:
newobj = copy.deepcopy(obj2)
except:
print "copy.deepcopy() failed... could not copy either input object"
return -1
# Get all attributes:
att1all = dir(obj1)
att2all = dir(obj2)
# Exclude everything beginning with an underscore:
att1 = []
att2 = []
for att in att1all:
if att[0] == '_':
pass
else:
att1.append(att)
for att in att2all:
if att[0] == '_':
pass
else:
att2.append(att)
# Get attributes common to both objects:
common_atts = set(att1).intersection(att2)
abandoned_atts = (set(att1).union(att2)).difference(common_atts)
if len(common_atts)==0:
return -1
# Remove all non-common attributes:
for att in abandoned_atts:
if hasattr(newobj, att):
setattr(newobj, att, None)
# Combine all common attributes:
for att in common_atts:
if (not hasattr(newobj, att)) or (not hasattr(obj1, att)) or \
(not hasattr(obj2, att)): # Test for coding mistakes:
print "Couldn't find attribute '%s'; something went wrong!" % att
else:
setattr(newobj, att, combine_atts(getattr(obj1, att), getattr(obj2, att)))
return newobj
[docs]def multifunc(params, func1, func2, npar1, npar2=None, args1=(), args2=()):
"""Multiply two functions together.
:EXAMPLE:
::
import numpy as np
multifunc([.785, .785], np.cos, np.sin, 1) # returns cos(pi/4) * sin(pi/4) ~ 0.5
:EXAMPLE:
::
import pylab as py
import tools
x = 2*py.pi * py.linspace(-5, 5, 500)
y = tools.multifunc([x/8., x], np.sin, np.sin, 1).ravel()
py.plot(x, y)
"""
# 2011-06-03 11:26 IJC: Created
# 2012-06-10 16:08 IJMC: Now reflects preferred use of multifunc_general.
print "Multifunc() is deprecated; use multifunc_general() instead."
# Set the parameters for each function:
if npar2 is None:
npar2 = len(params) - npar1
return multifunc_general(params, (func1, func2), (npar1, npar2), (args1, args2))
[docs]def multifunc_general(params, funcs, npar=None, args=None):
"""Multiply results of several functions together.
:INPUTS:
params : sequence
Concatenated sequence of parameters (first arguments) for each
of the functions in 'funcs'.
funcs : function or tuple
Single function, or a tuple of several functions to call.
npar : tuple
If more than one function is used, npar must be a tuple
specifying the number of parameters passes to each function
(as its first input). E.g., if npar = (2, 3) then the result
will be: funcs[0](params[0:2]) * funcs[1](params[2:5])
args : tuple
If more than one function is used, args must be a tuple
specifying the additional arguments to be passed to each
function. E.g.: funcs[0](params[0:2], *args[0])
:EXAMPLE:
::
import numpy as np
multifunc_general([.785, .785], (np.cos, np.sin), (1, 1)) # returns cos(pi/4) * sin(pi/4) ~ 0.5
:EXAMPLE:
::
import pylab as py
import tools
x = 2*py.pi * py.linspace(-10, 10, 500)
y = tools.multifunc_general([x/8., x], (np.sin, np.sin), (1, 1)).ravel()
py.plot(x, y)
"""
# 2012-06-10 15:54 IJMC: Created; modified from multifunc
if not hasattr(funcs, '__iter__'):
ret = funcs(params, *args)
else:
ret = 1.
nfunc = len(funcs)
if npar is None:
print "Multiple functions input; npar ought not to be None!"
return -1
if args is None:
args = ((),) * nfunc
i0 = 0
for ii in range(nfunc):
these_params = params[i0:i0+npar[ii]]
i0 += npar[ii]
ret *= funcs[ii](these_params, *args[ii])
return ret
[docs]def sumfunc_general(params, funcs, npar=None, args=None):
"""Add results of several functions together.
:INPUTS:
params : sequence
Concatenated sequence of parameters (first arguments) for each
of the functions in 'funcs'.
funcs : function or tuple
Single function, or a tuple of several functions to call.
npar : tuple
If more than one function is used, npar must be a tuple
specifying the number of parameters passes to each function
(as its first input). E.g., if npar = (2, 3) then the result
will be: funcs[0](params[0:2]) * funcs[1](params[2:5])
args : tuple
If more than one function is used, args must be a tuple
specifying the additional arguments to be passed to each
function. E.g.: funcs[0](params[0:2], *args[0])
:EXAMPLE:
::
import numpy as np
sumfunc_general([.785, .785], (np.cos, np.sin), (1, 1))
:EXAMPLE:
::
import pylab as py
import tools
x = 2*py.pi * py.linspace(-10, 10, 500)
y = tools.sumfunc_general([x/8., x], (np.sin, np.sin), (1, 1)).ravel()
py.plot(x, y)
"""
# 2012-06-10 15:54 IJMC: Created; modified from multifunc_general
# 2014-08-03 18:07 IJMC: Fixed a little bug: ret had been
# initialized to unity, but should be zero.
if not hasattr(funcs, '__iter__'):
ret = funcs(params, *args)
else:
ret = 0.
nfunc = len(funcs)
if npar is None:
print "Multiple functions input; npar ought not to be None!"
return -1
if args is None:
args = ((),) * nfunc
i0 = 0
for ii in range(nfunc):
these_params = params[i0:i0+npar[ii]]
i0 += npar[ii]
ret += funcs[ii](these_params, *args[ii])
return ret
[docs]def sumfunc(params, func1, func2, npar1, npar2=None, args1=(), args2=()):
"""Add two functions together.
:EXAMPLE:
::
import numpy as np
sumfunc([.785, .785], np.cos, np.sin, 1) # returns cos(pi/4) + sin(pi/4) ~ XXX
:EXAMPLE:
::
import pylab as py
import tools
x = 2*py.pi * py.linspace(-5, 5, 500)
y = tools.sumfunc([x/8., x], np.sin, np.sin, 1).ravel()
py.plot(x, y)
"""
# 2011-10-27 11:50 IJMC: Created from multifunc
# Set the parameters for each function:
if npar2 is None:
npar2 = len(params) - npar1
params1 = params[0:npar1]
params2 = params[npar1:(npar1 + npar2)]
return func1(params1, *args1) + func2(params2, *args2)
[docs]def imrot(*varargin):
"""
Rotate a SQUARE image by theta (in radians)
:SYNTAX:
res = imrot (img, theta)
:NOTES:
This is VERY SLOW and only uses nearest-neighbor interpolation.
Image must be square; size remains the same
"""
# 2011-06-08 15:48 IJMC: Adapted to Python, but without interp2.
# 2006/11/30 IJC: Added interpolation option
# Written by Joseph Green at the Jet Propulsion Laboratory
from analysis import pad
from pylab import array, arange, meshgrid, cos, sin, isnan, dot, sqrt, find, np, dot, vstack
import pdb
nargin = len(varargin)
if nargin==1:
return varargin[0]
elif nargin==2:
img = varargin[0]
theta = varargin[1]
interpMethod = 'nn'
else:
img = varargin[0]
theta = varargin[1]
interpMethod = varargin[2];
npix = max(img.shape);
img = pad(img,npix);
xs = arange(-npix/2, npix/2) + 0.
x, y = meshgrid(xs,xs)
M = array([[cos(theta), sin(theta)], [-sin(theta), cos(theta)]])
xr=x.copy()
yr=y.copy()
xxr, yyr = dot(M, vstack((x.ravel(), y.ravel())))
#pdb.set_trace()
res = 0*img
xlim = xs.min(), xs.max()
for m in range(npix):
for n in range(npix):
if xr[m,n] < xlim[0] or xr[m,n] > xlim[1] or \
yr[m,n] < xlim[0] or yr[m,n] > xlim[1]:
res[m,n] = 0.
else:
distances = sqrt((x - xr[m,n])**2 + (y - yr[m,n])**2).ravel()
#distances = np.abs((x - xr[m,n]) + 1j*(y - yr[m,n]))
mindist = distances.min()
#locations = find(distances==mindist)
if mindist==0:
res[m,n] = (img.ravel()[distances==mindist]) #.mean()
else:
res[m,n] = 0.
return res
[docs]def readPSplotdata(filename,
xlims=None, ylims=None,
spacedelimiter=' ', pairdelimiter=','):
"""Read in a raw PostScript plot datafile and output Numpy arrays.
:INPUTS:
filename : str
filename of the data file.
xlims : tuple
(lowest x value of any data point, highest x value of any data point)
ylims : tuple
(lowest y value of any data point, highest y value of any data point)
spacedelimiter : str
delimiter between data pairs; by default a space (" ")
pairdelimiter : str
delimiter within data pairs; by default a comma (",")
:FILE_FORMAT:
The datafile should have the format:
"m x0,y0 dx1,dy1 dx2,dy2 ..."
:OUTPUTS:
(x, y) -- tuple of 1D arrays
"""
# 2011-08-24 09:20 IJMC: Created
# 2014-08-05 13:12 IJMC: Updated with optional axis-limit inputs;
# contributed by Corey Reed (cjreed@uci.edu).
from numpy import array
# Read file:
f = open(filename, 'r')
rawdata = f.readlines()
f.close()
# Check for validity
# Get datapoints
datavals = []
for line in rawdata:
datavals = datavals + line.split(spacedelimiter)
#
foundinit = False
for dataval in datavals:
if dataval.find(pairdelimiter)>-1:
xval, yval = map(float, dataval.split(pairdelimiter))
if not foundinit: # starting point
foundinit = True
x, y = [xval], [yval]
else: # differential
x.append(x[-1] + xval)
y.append(y[-1] + yval)
# calibrate
if ( (xlims!=None) and (ylims!=None) ):
xmin,xmax = min(x), max(x)
ymin,ymax = min(y), max(y)
xscale = (xlims[1] - xlims[0]) / (xmax-xmin)
yscale = (ylims[1] - ylims[0]) / (ymax-ymin)
xoff = xlims[0] - (xmin*xscale)
yoff = ylims[0] - (ymin*yscale)
x[:] = [(i*xscale)+xoff for i in x]
y[:] = [(i*yscale)+yoff for i in y]
return array(x), array(y)
[docs]def bnu(T, lam):
"""Planck function in frequency.
:INPUTS:
T : scalar or array
temperature in Kelvin
lam : scalar or array
wavelength in microns [but intensity will be per Hz]
Value returned is in cgs units: erg/s/cm^2/Hz/sr
"""
# 2011-11-04 10:47 IJMC: Added to Tools
# 2013-02-19 19:42 IJMC: Updated to use precise value of c.
from numpy import exp
c = 29979245800. # cm/s
nu = c/(lam/1e4)
h = 6.626068e-27 # cgs units
k = 1.3806503e-16 # cgs units
expo = h*nu/(k*T)
nuoverc = 1./ (lam/1e4)
return ((2*h*nuoverc**2 * nu)) / (exp(expo)-1)
[docs]def blam(T, lam):
"""Planck function in wavelength.
:INPUTS:
T : scalar or array
temperature in Kelvin
lam : scalar or array
wavelength in microns
Value returned is in (nearly) cgs units: erg/s/cm^2/micron/sr
"""
# 2012-06-12 19:56 IJMC: Created.
# 2013-02-19 19:42 IJMC: Updated to use precise value of c.
c = 29979245800. # cm/s
nu = c/(lam/1e4) # Hz
# Take advantage of the fact that (lam F_lam) = (nu F_nu):
return bnu(T, lam) * (nu / lam)
[docs]def planet2temp(rprs, fpfs, teff, lam=24., gamma=0.8, ntrials=10000):
"""Convert planet/star size and flux contrasts to brightness temperatures.
:INPUTS:
rprs : 2-tuple, either
[0] : (value, dist) where dist is the sampled posterior
distribution of planet/star radius ratio (e.g., from
MCMC output). OR:
[1] : (value, uncertainty)
fpfs : 2-tuple, either
[0] : (value, dist) where dist is the sampled posterior
distribution of planet/star flux ratio (e.g., from
MCMC output). OR:
[1] : (value, uncertainty)
teff : 2-tuple, either
[0] : (value, dist) where dist is the sampled posterior
distribution of stellar effective temperatures (e.g., from
MCMC output). OR:
[1] : (value, uncertainty)
lam : float
wavelength of observations, in microns
gamma : float
factor to account for the fact that a star's infrared flux is
lower than predicted by a blackbody of a given effective
temperature. Set to 0.8 for 24 microns.
ntrials : int
Number of times to resample distributions.
:REQUIREMENTS:
:doc:`scipy.optimize`, :doc:`numpy`
"""
# 2011-11-04 11:27 IJMC: Created
from numpy import random
from scipy import optimize, array
def err_temp_bb(temp, bnu_t, lam):
return bnu_t - bnu(temp, lam)
if not hasattr(rprs, '__iter__'):
rprs = (rprs, 0)
if not hasattr(fpfs, '__iter__'):
fpfs = (fpfs, 0)
if not hasattr(teff, '__iter__'):
teff = (teff, 0)
# Create resampled distributions:
npts_r = len(rprs)
npts_f = len(fpfs)
npts_t = len(teff)
resample_r = hasattr(rprs[1], '__iter__')
resample_f = hasattr(fpfs[1], '__iter__')
resample_t = hasattr(teff[1], '__iter__')
rprs_0 = rprs[0]
fpfs_0 = fpfs[0]
teff_0 = teff[0]
if not resample_r:
rprs = random.normal(rprs[0], rprs[1], ntrials)
else:
rprs = array(rprs[1], copy=False)[random.uniform(0, len(rprs[1]), ntrials).astype(int)]
if not resample_f:
fpfs = random.normal(fpfs[0], fpfs[1], ntrials)
else:
fpfs = array(fpfs[1], copy=False)[random.uniform(0, len(fpfs[1]), ntrials).astype(int)]
if not resample_t:
teff = random.normal(teff[0], teff[1], ntrials)
else:
teff = array(teff[1], copy=False)[random.uniform(0, len(teff[1]), ntrials).astype(int)]
planet_flux = fpfs * bnu(teff*gamma, lam) / (rprs**2)
planet_flux_0 = fpfs_0 * bnu(teff_0*gamma, lam) / (rprs_0**2)
planet_temps = array([optimize.fsolve(err_temp_bb, 1000, \
args=(thisflux, lam)) \
for thisflux in planet_flux]).ravel()
planet_temp_0 = optimize.fsolve(err_temp_bb, 1000, \
args=(planet_flux_0, lam))
return (planet_temp_0, planet_temps)
[docs]def erf_approx(z, N):
"""Weideman 1994's approximate complex error function.
:INPUTS:
z : real or complex float
N : number of terms to use.
:NOTES:
returns w(z) = exp(-z**2) erfc(-1j*z)
"""
# 2011-11-14 17:01 IJMC: Created
import numpy as np
M = 2 * N
M2 = 2*M # number of sampling points
k = np.arange(-M+1, M).reshape(M2 - 1, 1)
L = np.sqrt(N / np.sqrt(2))
theta = k * np.pi/M
t = L * np.tan(theta/2)
# Function to be transformed:
f = np.exp(-t**2) * (L**2 + t**2)
f = np.concatenate(([0], f))
[docs]def ee_psf(psf, energy=0.8, center=None):
"""%% Determine the diameter in pixels for a given Encircled Energy
%
% [d, ee] = ee_psf(psf, energy)
% [d, ee] = ee_psf(psf, energy, center);
%
% INPUTS: psf - array representing a point spread function
% energy- encircled energy percentage (default = 0.8).
% Can also be a vector of values, in which case the
% outputs 'd' and 'encircledenergy' are also vectors.
% OPTIONAL INPUT:
% center- [x y] coordinates of the center of the psf. If not
% passed, defaults to the coordinates of the maximum-
% valued point of the psf array.
%
% OUTPUTS: d - diameter of circle enclosing 'energy' [pix] at the
% corresponding desired encircled energy value
% ee - encircled energy at computed 'd' at the
% corresponding desired encircled energy value
%function [d, encircledenergy] = ee_psf(psf, energy, center)
"""
# 2012-01-06 15:48 IJMC: Converted from Matlab to Python;
# originally written at JPL.
from analysis import pad
import numpy as np
psf = np.array(psf, copy=False)
npix = max(psf.shape)
psf = pad(psf,npix);
if center is None:
xc, yc = np.nonzero(psf==psf.ravel().max())
center = [yc, xc];
if energy is None:
energy = np.array([0.8])
elif not hasattr(energy, '__iter__'):
energy = np.array([energy])
else:
energy = np.array(energy, copy=False)
encircledenergy = np.zeros(len(energy)) # initialize encircled energy array
d = np.zeros(len(energy)) # initialize diameter-pixel array
xc, yc = center[0:2]
ee = 0
eeold = -1
xs = np.arange(npix) - xc
ys = np.arange(npix) - yc
[x,y] = np.meshgrid(xs, ys)
r = np.abs(x + 1j*y)
energy_tot = psf.sum()
for inc_energy in range(len(energy)):
rad = 0
ee = 0
dfactor = 4 # these two lines determine how it searches
dpix = dfactor**np.floor(np.log(npix)/np.log(dfactor) - 1)
while (ee <> eeold):
while (ee < energy[inc_energy]) and (ee<>eeold):
rad = rad+dpix
emasked = (r < rad)*psf
eeold = ee
ee = emasked.sum()/energy_tot
#disp(['Inner: Rad=' num2str(rad) ' ,Encircled energy = ' num2str(ee)])
rad = rad - dpix
dpix = dpix/dfactor
rad = rad + dpix
emasked = (r < rad)*psf
eeold = ee
ee = emasked.sum()/energy_tot
#disp(['Outer: Rad=' num2str(rad) ', encircled energy = ' num2str(ee)])
d[inc_energy] = 2*rad
encircledenergy[inc_energy] = ee
return d, encircledenergy
[docs]def extinct_cardelli(lam_um, RV=3.1, warn=True):
"""Compute the Cardelli et al. 1989 A_lam/A_V extinction (reddening).
:INTPUTS:
lam_um : float or Numpy array
wavelength desired, in microns
RV : float
R_V extinction parameter
warn : bool
If True, print a warning if wavelength is outside the valid range.
:OUTPUTS:
extinct : float or Numpy array
extinction -- A_lambda/A_V
:NOTES:
This is only valid for wavelengths in the range 0.3 - 3.3 microns!
"""
# 2012-02-24 23:06 IJMC: Created
from numpy import array
if not hasattr(lam_um, '__iter__'):
lam_um = array([lam_um], copy=True)
else:
lam_um = array(lam_um, copy=True)
#lam_um = 1./lam_um
ind0 = lam_um < (1./1.1) # visible
ind1 = lam_um >= (1./1.1) # near-infrared
ind2 = (lam_um < 0.25) + (lam_um > 3.5)
extinct = 0*lam_um
if warn and ind2.any():
print "Wavelengths found outside valid range (0.3-3 microns). Results are suspect."
x = 1./lam_um
if ind0.any():
y = x[ind0] - 1.82
extinct[ind0] += 1.
a = [0.17699, -0.50447, -0.02427, 0.72085, 0.01979, -0.77530, 0.32999]
b = [1.41338, 2.28305, 1.07233, -5.38434, -0.62251, 5.30260, -2.09002]
ypow = y.copy()
for ii in range(7):
extinct[ind0] += (a[ii] + b[ii] / RV) * ypow
ypow *= y
if ind1.any():
extinct[ind1] = x[ind1]**1.61 * (0.574 - 0.527 / RV)
return extinct
[docs]def shift_image(im, dx=0, dy=0, buffer=0):
"""Shift a 2D image by the specified number of integer pixels.
:INPUTS:
im : 2D Numpy array
numpy array of desired size
dx : int
number of pixels to shift in x direction
dy : int
number of pixels to shift in y direction
buffer : scalar
Default value for unfilled pixels
"""
# 2012-02-25 02:46 IJMC: Created
from numpy import array, abs
im = array(im, copy=False)
nx, ny = im.shape
newim = 0*im + buffer
if abs(dx)<nx and abs(dy)<ny:
xnew1 = max(0, dx)
xnew2 = min(nx, nx+dx)
xorg1 = max(0, -dx)
xorg2 = min(nx, nx-dx)
ynew1 = max(0, dy)
ynew2 = min(ny, ny+dy)
yorg1 = max(0, -dy)
yorg2 = min(ny, ny-dy)
newim[xnew1:xnew2,ynew1:ynew2] = im[xorg1:xorg2,yorg1:yorg2]
return newim
[docs]def resamp(frame, resamp, retcoords=False):
"""Resample a 2D array by a given factor, using bilinear interpolation.
:INPUTS:
frame : 2D Numpy Array
data array to be resampled
resamp : positive scalar
resampling factor (typically an integer greater than 1)
retcoords: bool
If True, return tuple (frame2, x2, y2)
:NOTES:
Result needs to be scaled by (1/resamp^2) to conserve flux
"""
# 2012-02-25 07:21 IJMC: Created
# 2012-02-26 14:19 IJMC: Added retcoords option
from numpy import array, arange
from scipy import interpolate
# Parse inputs:
resamp = float(resamp)
frame = array(frame, copy=False)
nx0, ny0 = frame.shape
nx = ((nx0 - 1)*resamp + 1.) # Avoid resampling at pixel locations
ny = ((ny0 - 1)*resamp + 1.) # outside the original boundaries.
xx0 = range(nx0)
yy0 = range(ny0)
x1,y1 = arange(nx)/resamp, arange(ny)/resamp
rectspline = interpolate.fitpack2.RectBivariateSpline(xx0, yy0, frame, kx=1, ky=1, s=0)
frame2 = rectspline(x1, y1)#/resamp/resamp
if retcoords:
ret = frame2, x1, y1
else:
ret = frame2
return ret
[docs]def plotlikelihood_2d(L, x=None, y=None, conf=[0.683], figsize=[8, 6], contourargs=dict(colors='k'), posteriorargs=dict(color='k'), limitargs=dict(color='k', linestyle=':'), xlabel=None, ylabel=None, buffers=[.1, .1, .1, .1]):
"""Plot contours and histograms for 2D likelihood array.
:INPUTS:
L : 2d Numpy array
Likelihood values, not necessarily normalized. (Remember that
L = exp[-chi^2 / 2.] )
x : sequence
Values along the first dimension of L. Thus len(x) must equal
L.size[0]
y : sequence
Values along the second dimension of L. Thus len(x) must equal
L.size[1]
figsize : 2-sequence
Size of figure to be created, in inches.
conf : scalar or sequence
Confidence intervals to plot
contourargs : dict
Keyword arguments to be passed to matplotlib.contour
posteriorargs : dict
Keyword arguments to be passed to matplotlib.plot for
posterior distributions
limitargs : dict
Keyword arguments to be passed to matplotlib.plot for
1D confidence limits
xlabel : str
ylabel : str
buffers : 4-sequence
fractional buffer width around edges: [left, right, bottom, top]
"""
# 2012-06-19 11:47 IJMC: Created
from kdestats import confmap
import pylab as py
if not hasattr(conf, '__iter__'):
conf = [conf]
nconf = len(conf)
# Define array indices:
nx, ny = L.shape
x0 = np.arange(nx)
y0 = np.arange(ny)
# Define axis values:
if x is None:
x = x0.copy()
if y is None:
y = y0.copy()
# Define axis labels:
if xlabel is None:
xlabel = ''
if ylabel is None:
ylabel = ''
# Define marginalized posterior probability distributions:
yppd = L.sum(0)
xppd = L.sum(1)
# Define confidence levels:
conflevels = confmap(L, conf)
xconf = [[np.interp(val, np.cumsum(xppd/xppd.sum()), x) for val in [(1.-cl)/2., 1. - (1.-cl)/2.]] for cl in conf]
yconf = [[np.interp(val, np.cumsum(yppd/yppd.sum()), y) for val in [(1.-cl)/2., 1. - (1.-cl)/2.]] for cl in conf]
# Prepare for plotting:
lbuffer, rbuffer, bbuffer, tbuffer = buffers
eff_width = 1. - lbuffer - rbuffer
eff_height = 1. - tbuffer - bbuffer
contour_frac = 0.6
# Begin plotting:
py.figure(nextfig(), figsize)
cax = py.subplot(2, 2, 3, position=[lbuffer, bbuffer, eff_width*contour_frac, eff_height*contour_frac])
py.contour(x, y, L.transpose(), conflevels, **contourargs)
py.minorticks_on()
py.xlabel(xlabel)
py.ylabel(ylabel)
axlim = py.axis()
for limits in yconf:
py.plot(axlim[0:2], [limits[0]]*2, **limitargs)
py.plot(axlim[0:2], [limits[1]]*2, **limitargs)
for limits in xconf:
py.plot([limits[0]]*2, axlim[2:4], **limitargs)
py.plot([limits[1]]*2, axlim[2:4], **limitargs)
hax = py.subplot(2, 2, 1, position=[lbuffer, bbuffer + eff_height*contour_frac + 1e-5, eff_width*contour_frac, eff_height*(1. - contour_frac)])
hax.plot(x, xppd, **posteriorargs)
x_ylim = py.ylim()
for limits in xconf:
py.plot([limits[0]]*2, x_ylim, **limitargs)
py.plot([limits[1]]*2, x_ylim, **limitargs)
py.ylim(x_ylim)
py.xlim(axlim[0:2])
yt = py.yticks()[0]
py.xticks(py.xticks()[0], [])
py.yticks(yt[yt>0], [])
py.ylim(x_ylim)
py.xlim(axlim[0:2])
py.minorticks_on()
hay = py.subplot(2, 2, 4, position=[lbuffer + eff_width*contour_frac + 1e-5, bbuffer, eff_width*(1. - contour_frac), eff_height*contour_frac])
hay.plot(yppd, y, **posteriorargs)
y_xlim = py.xlim()
for limits in yconf:
py.plot(y_xlim, [limits[0]]*2, **limitargs)
py.plot(y_xlim, [limits[1]]*2, **limitargs)
py.ylim(axlim[2::])
py.xlim(y_xlim)
xt = py.xticks()[0]
py.xticks(xt[xt>0], [])
py.yticks(py.yticks()[0], [])
py.xlim(y_xlim)
py.ylim(axlim[2::])
py.minorticks_on()
return cax, hax, hay
[docs]def areaOverlappingCircles(r1, r2, d):
"""Return overlapping area of two circles. From Wolfram Mathworld.
r1, r2 are the radii of the circles.
d is the distance between their centers.
"""
# 2012-07-30 15:40 IJMC: Created, from Wolfram Mathworld
if r1> r2:
temp = r1
r1 = r2
r2 = temp
r1s = r1*r1
r2s = r2*r2
if not hasattr(d, '__iter__'):
d = np.array([d])
else:
d = np.array(d, copy=False)
valid_index = (d < (r1+r2)) * (d > (r2-r1))
fulloverlap_index = d <= (r2-r1)
ds = d[valid_index]**2
area = np.zeros(d.shape)
area[fulloverlap_index] = np.pi*r1s
area[valid_index] = \
r1s * np.arccos((ds + r1s - r2s) / (2*d[valid_index]*r1)) + \
r2s * np.arccos((ds + r2s - r1s) / (2*d[valid_index]*r2)) - \
0.5 * np.sqrt((-d[valid_index]+r1+r2)*(d[valid_index]+r1-r2)*(d[valid_index]-r1+r2)*(d[valid_index]+r1+r2))
return area
[docs]def findRectangles(a, minsepy=None, minsepx=None, edgepad=10):
"""Find corner coordinates of approximate rectangle shapes in an array.
:INPUTS:
a : 2D Numpy array
minsep : scalar
Minimum separation from one upper or left-hand border to the
next. (cf. :func:`find_peaks`)
edgepad : int
Pad the array with this many zeros on all sides (to find
rectangles abutting array edges)
"""
# 2012-08-09 23:51 IJMC: Created
# 2012-08-17 14:53 IJMC: Added 'edgepad' option.
# 2012-10-21 22:46 IJMC: Fixed 'x_borders' when edgepad is called.
from scipy.signal import medfilt2d
from analysis import pad
dtype = a.dtype
if dtype not in (np.float32, np.float64):
a = a.astype(np.float32)
#sm = medfilt2d(a, 5)
sm = pad(medfilt2d(a, 5), a.shape[0]+edgepad*2, a.shape[1]+edgepad*2)
smlox = np.hstack((np.diff(sm, axis=1), np.zeros((sm.shape[0],1))))
smloy = np.vstack((np.diff(sm, axis=0), np.zeros(sm.shape[0])))
boxcar = np.ones(5)/5.
smloys = np.convolve(smloy.sum(1), boxcar, 'same')
smloxs = np.convolve(smlox.sum(0), boxcar, 'same')
y_lowers = np.sort(find_peaks(smloys, minsepy, thresh=10)[1]) - edgepad
y_uppers = np.sort(find_peaks(-smloys, minsepy, thresh=10)[1]) - edgepad
nreg = y_uppers.size
corners = np.zeros((nreg, 4), dtype=int)
corners[:,2] = y_lowers + 1
corners[:,3] = y_uppers + 1
for ii in range(nreg):
subreg = smlox[y_lowers[ii]:y_uppers[ii]]
xedges = np.abs(np.convolve(subreg.sum(0), boxcar, 'same'))
x_borders = np.sort(find_peaks(xedges, minsepx)[1][0:2])
corners[ii,0:2] = x_borders - edgepad+1
return corners
[docs]def scrapeints(string):
"""Extract a series of integers from a string. Slow but robust.
readints('[124, 56|abcdsfad4589.2]')
will return:
[124, 56, 4589, 2]
"""
# 2012-08-28 16:19 IJMC: Created
numbers = []
nchar = len(string)
thisnumber = ''
for n, char in enumerate(string):
try:
val = int(char)
anumber = True
except:
anumber = False
if anumber:
thisnumber = thisnumber + char
else: #if (not anumber) or n==(nchar-1):
if len(thisnumber)>0:
numbers.append(int(thisnumber))
thisnumber = ''
return numbers
[docs]def array_or_filename(input, kw_getdata=dict(), kw_array=dict(), noneoutput=None):
"""If input is a Numpy array, return it. If it is of type str,
use Pyfits to read in the file and return it. Keyword options are
available for the calls to pyfits.getdata and numpy.array. If
input is None, return noneoutput."""
# 2012-09-03 11:43 IJMC: Created
from pyfits import getdata
if input is None:
output = noneoutput
else:
if isinstance(input, str):
output = getdata(input, **kw_getdata)
else:
output = np.array(input, **kw_array)
return output
[docs]def roundparams(value, error, seconderror=None, extraplaces=1):
"""Round a value and its associated error(s) to 2 decimal places.
:INPUTS:
value, error : scalars
:OUTPUTS:
value, error
:EXAMPLE:
::
import tools
tools.roundparams(1.23456, .09876)
:SEE_ALSO:
:func:`roundvals`
"""
# 2012-09-27 17:47 IJMC: Created
if seconderror is not None:
pow = np.abs(np.floor(np.log10(0.5*(np.abs(error)+np.abs(seconderror)))))
else:
pow = np.abs(np.floor(np.log10(np.abs(error))))
value = np.round(value, decimals=pow+extraplaces)
val1 = np.round(error, decimals=pow+extraplaces)
ret = value, val1
fstrp = '%+'+ ('1.%i' % (pow+1)) + 'f'
fstrm = '%+'+ ('1.%i' % (pow+1)) + 'f'
if seconderror is not None:
val2 = np.round(seconderror, decimals=pow+1)
ret = ret + (val2,)
fstr = '$%s^{%s}_{%s}$' % (fstrp,fstrp,fstrm)
retstr = fstr % (value, val1, val2)
else:
fstr = '$%s \\pm %s$' % (fstrp,fstrp)
retstr = fstr % (value, val1)
return retstr
[docs]def sample_2dcdf(cdf, x, y, nsamp=1, verbose=False):
"""Sample a 2D Probability Distribution Function (2d-histogram)
:INPUTS:
CDF : 2D NumPy array
Two-dimensional (N x M) probability distribution function
(histogram) from which you wish to draw samples. This need not
be in any particular normalized form -- the only condition is
that the value in each cell is proportional to the probability
of that cell.
x : 1D NumPy array
N+1 Values indexing the cells of the CDF (one per row), evenly spaced
y : 1D NumPy array
M+1 Values indexing the cells of the CDF (one per column), evenly spaced
nsamp : int
Number of samples to be drawn.
:NOTES:
Note that this approach uses simple, dumb nearest-neighbor
interpolation when drawing candidate samples. Exceedingly
granular CDFs may suffer.
Note that this code isn't optimized; try it with small samples
before you use it on large ones!
"""
# 2012-09-30 21:44 IJMC: Created
# Initialize:
cdf = np.array(cdf, copy=False)
x = np.array(x, copy=False)
y = np.array(y, copy=False)
ret1 = np.zeros(nsamp, dtype=y.dtype)
ret2 = np.zeros(nsamp, dtype=x.dtype)
xcenters = 0.5 * (x[1:] + x[0:-1])
ycenters = 0.5 * (y[1:] + y[0:-1])
#NOrmalize:
prob = 1.0 * cdf / cdf.max()
success_estimate = 1.0 * prob.sum() / prob.size
n_maxsamp = int(2*nsamp/success_estimate)
if verbose:
print "Success estimate is %1.3e" % success_estimate
print "Will need to draw approximately %i samples to generate desired number (%i)." % (n_maxsamp, nsamp)
# Generate initial random samples to draw from:
sampx = np.random.uniform(low=x.min(), high=x.max(), size=n_maxsamp)
sampy = np.random.uniform(low=y.min(), high=y.max(), size=n_maxsamp)
accept_prob = np.random.uniform(size=n_maxsamp)
nsampled = 0
ii = 0
while nsampled < nsamp:
# Locate the candidate sample in the CDF array:
ind_x = (np.abs(xcenters-sampx[ii])==np.abs(xcenters-sampx[ii]).min())#.nonzero()
ind_y = (np.abs(ycenters-sampy[ii])==np.abs(ycenters-sampy[ii]).min())#.nonzero()
# Accept or reject the candidate sample:
if prob[ind_x, ind_y] > accept_prob[ii]:
ret1[nsampled] = sampx[ii]
ret2[nsampled] = sampy[ii]
nsampled += 1
ii += 1
# If we ran out of random samples, draw more:
if ii >= n_maxsamp:
sampx = np.random.uniform(low=x.min(), high=x.max(), size=n_maxsamp)
sampy = np.random.uniform(low=y.min(), high=y.max(), size=n_maxsamp)
accept_prob = np.random.uniform(size=n_maxsamp)
ii = 0
return ret1, ret2
[docs]def sample_1dcdf(pdf, x, nsamp=1, verbose=False, absnorm=False):
"""Sample a 1D Posterior Distribution Function (1d-histogram)
:INPUTS:
PDF : 1D NumPy array
Distribution function (histogram) from which you wish to draw
samples. This need not be in any particular normalized form --
the only condition is that the value in each cell is
proportional to the probability of that cell.
x : 1D NumPy array
N Values indexing the cells of the CDF (one per row)
nsamp : int
Number of samples to be drawn.
absnorm : bool
If True, normalize pdf so that it integrates to 1.0
"""
# 2012-10-28 13:13 IJMC: Created.
# 2012-11-20 16:18 IJMC: Fixed a small bug.
# Initialize:
argind = np.argsort(x)
x = np.array(x, copy=False)[argind]
pdf = np.array(pdf, copy=False)[argind]
ret = np.zeros(nsamp, dtype=x.dtype)
#NOrmalize:
#if absnorm:
prob = 1.0 * pdf / pdf.max()
#else:
# prob = pdf
success_estimate = 1.0 * prob.sum() / prob.size
n_maxsamp = int(2*nsamp/success_estimate)
if verbose:
print "Success estimate is %1.3e" % success_estimate
print "Will need to draw approximately %i samples to generate desired number (%i)." % (n_maxsamp, nsamp)
# Generate initial random samples to draw from:
nsampled = 0
ii = 0
while nsampled < nsamp:
sampx = np.random.uniform(low=x.min(), high=x.max(), size=n_maxsamp)
accept_prob = np.interp(sampx, x, prob, left=0.0, right=0.0)
accept_ind = np.random.uniform(low=0., high=1., size=n_maxsamp) < accept_prob
n_accepted = accept_ind.sum()
ind0 = nsampled
ind1 = min(nsampled+n_accepted, nsamp)
ret[ind0:ind1] = sampx[accept_ind][0:ind1-ind0]
nsampled += n_accepted
#pdb.set_trace()
#if verbose:
# print "%i sampled accepted" % n_accepted
# print nsampled, n_accepted, nsamp
return ret
[docs]def textfig(textlist, **kw):
"""Generate a figure from a list of strings.
:INPUTS:
textlist : list
List of text strings, one per entry.
:OPTIONS:
any options valid for passing to matplotlib.text
Also: the dict 'figoptions' will be passed to figure()
:RETURNS:
(fig, ax) -- handles to Figure and Axes that were created
"""
# 2013-03-10 13:27 IJMC: Created
# 2014-08-14 17:41 IJMC: Changed font family to 'monospace',
# because 'Courier' led to bugs when saving
# PDF figures.
# 2014-10-24 00:10 IJMC: Added 'fig' and 'ax' options.
import pylab as py
# Handle input options:
defaults = dict(horizontalalignment='left', fontsize=9, family='monospace', weight='bold', fig=None, ax=None)
if kw.has_key('figoptions'):
figoptions = kw.pop('figoptions')
else:
figoptions = dict()
if kw.has_key('axoptions'):
axoptions = kw.pop('axoptions')
else:
axoptions = dict(position=[.02, .02, .96, .9])
for key in defaults.keys():
if not kw.has_key(key):
kw[key] = defaults[key]
# Generate figure and axis:
fig = kw.pop('fig')
if fig is None:
fig = py.figure(nextfig(), **figoptions)
ax = kw.pop('ax')
if ax is None:
ax = py.axes(**axoptions)
nlines = len(textlist)
vertpos = py.linspace(.95, .05, nlines)
py.xticks([])
py.yticks([])
# Plot the text:
for line, pos in zip(textlist, vertpos):
py.text(.05, pos, line, transform=ax.transAxes, **kw)
return fig, ax
[docs]def roundvals(input, ndigit=2, strout=True):
"""Round all input values to the smallest number of digits used.
:INPUTS:
input : scalar, or 1D list or array
values to be rounded
ndigit : int
Number of significant digits to be retained
strout : bool
Return text strings? If not, return a 1D NumPy array.
:EXAMPLE:
::
import tools
tools.roundvals([235, -4, 0.045380])
:SEE_ALSO:
:func:`roundparams`
"""
# 2013-03-11 08:29 IJMC: Created
# 2013-04-20 09:35 IJMC: Now, don't be thrown off by zero values.
# 2014-06-21 14:59 IJMC: Fixed problem with all-NaN inputs.
if not hasattr(input, '__iter__'):
input = [input]
scalarInput = True
else:
scalarInput = False
input = np.array(input, copy=False)
#np.abs(input).min()
if np.isfinite(input).any():
ndig = np.abs(np.floor(np.log10(np.abs(input[np.abs(input)>0])).min()).astype(int)) + (ndigit-1)
else:
ndig = 1
if strout:
precstr = '%' + ('1.%i' % ndig) + 'f'
ret = [precstr % val for val in input]
else:
ret = np.round(input, ndig)
if scalarInput:
ret = ret[0]
return ret
[docs]def gelman_rubin(chains, verbose=False):
"""Compute the Gelman-Rubin convergence metric for MCMC chains.
:INPUTS:
chains : 2D NumPy array
A stack of all MCMC chains to be compared, created with
something like :func:`numpy.vstack`. The chains must all be
the same length, and they must have more links than the total
number of chains.
OR
chains : 3D NumPy array
N chains of L links for P parameters (e.g., the 'chain'
attribute of an emcee.sampler object), of shape NxLxP.
:OUTPUTS:
R metric. If this is 'close to 1.0,' then your chains have
converged to the same distribution. The definition of 'close'
could be 1.2, 1.1, 1.01... it's up to you!
:REFERENCE:
Eq. 20 of Gelman & Rubin 1992, Statistical Sciences, Vol. 7, p. 457
http://www.star.le.ac.uk/~sav2/idl/rhat.pro
"""
# 2014-01-23 11:14 IJMC: Created by copying from the IDL code
# located at
# http://www.star.le.ac.uk/~sav2/idl/rhat.pro
#---------------------------------------------------------
#Main routine
chains = np.array(chains, copy=False)
if 0 in chains.shape:
print "Input array cannot have any dimensions of size zero! Returning 9e99."
return np.array([9e99])
if chains.ndim==2:
if (chains.shape[0] > chains.shape[1]):
dimension = 0
else:
dimension = 1
nn = chains.shape[dimension]
#mean value of each chain
mean_j = chains.mean(axis=dimension)
#variance within each chain
var_j = chains.var(axis=dimension)
#now compute B and W from Gelman & Rubin
B = nn*mean_j.var()
W = var_j.mean()
#compute Gelman-Rubin R^2
R2 = ( W*(nn-1)/nn + B/nn ) / W
R = np.array([np.sqrt(R2)])
if verbose:
print '-- Mean of each chain: j=0,1,2,...'
print mean_j
print '-- Variance of each chain: j=0,1,2,...'
print var_j
print '-- B/N, W, R^2, R, N'
print (B/nn),W,R2,R,nn
elif chains.ndim==3:
nn = chains.shape[1]
mean_j = chains.mean(axis=1)
var_j = chains.var(axis=1)
B = nn * mean_j.var(axis=0)
W = var_j.mean(axis=0)
R2 = ( W*(nn-1)/nn + B/nn ) / W
R = np.sqrt(R2)
else:
print "Must input a 2D or 3D array! Returning 9e99."
R = np.array([9e99])
return R
[docs]def get_emcee_start(bestparams, variations, nwalkers, maxchisq, args, homein=True, retchisq=False, depth=np.inf):
"""Get starting positions for EmCee walkers.
:INPUTS:
bestparams : sequence (1D NumPy array)
Optimal parameters for your fitting function (length N)
variations : 1D or 2D NumPy array
If 1D, this should be length N and new trial positions will be
generated using numpy.random.normal(bestparams,
variations). Thus all values should be greater than zero!
If 2D, this should be size (N x N) and we treat it like a
covariance matrix; new trial positions will be generated using
numpy.random.multivariate_normal(bestparams, variations).
nwalkers : int
Number of positions to be chosen.
maxchisq : int
Maximum "chi-squared" value for a test position to be
accepted. In fact, these values are computed with
:func:`phasecurves.errfunc` as errfunc(test_position, *args)
and so various priors, penalty factors, etc. can also be
passed in as keywords.
args : tuple
Arguments to be passed to :func:`phasecurves.errfunc` for
computing 'chi-squared' values.
homein : bool
If True, "home-in" on improved fitting solutions. In the
unlikely event that a randomly computed test position returns
a better chi-squared than your specified best parameters,
reset the calculation to start from the new, improved set of
parameters.
retchisq : bool
If True, return the tuple (positions, chisq_at_positions)
:BAD_EXAMPLE:
::
pos0 = tools.get_emcee_start(whitelight_bestfit[0], np.abs(whitelight_bestfit[0])/1000., nwalkers, 10*nobs, mcargs)
"""
# 2013-05-01 11:18 IJMC: Created
# 2014-07-24 11:07 IJMC: Fixed typo in warning message.
#get_emcee_start(bestparams, variations, nwalkers, maxchisq, args):
from phasecurves import errfunc
best_chisq = errfunc(bestparams, *args)
if best_chisq >= maxchisq:
print "Specified parameter 'maxchisq' is smaller than the chi-squared value for the specified best parameters. Try increasing maxchisq."
return -1
npar = len(bestparams)
if variations.ndim==2:
usecovar = True
else:
usecovar = False
pos0 = np.zeros((nwalkers, npar), dtype=float)
chisq = np.zeros(nwalkers, dtype=float)
npos = 0
while npos < nwalkers:
if usecovar:
testpos = np.random.multivariate_normal(bestparams, variations)
else:
testpos = np.random.normal(bestparams, variations)
testchi = errfunc(testpos, *args)
if np.isfinite(testchi) and (testchi < best_chisq) and homein and depth>0:
return get_emcee_start(testpos, variations, nwalkers, maxchisq, args, homein=homein, retchisq=retchisq, depth=depth-1)
elif testchi < maxchisq:
pos0[npos] = testpos
chisq[npos] = testchi
npos += 1
if retchisq:
ret = pos0, chisq
else:
ret = pos0
return ret
[docs]def findFrac(validValues, thisValue, retinds=False):
"""
Helper tool for simply linear interpolation.
:INPUTS:
validValues : sequence
List of valid values
thisValue : scalar
Value of interest.
:OUTPUTS:
(TwoClosestValues, relativeFractions)
"""
# 2013-08-12 09:48 IJMC: Created
validValues = np.array(validValues, copy=False)
if thisValue<=validValues.min():
ret = ([validValues.min()], [1.0])
elif thisValue>=validValues.max():
ret = ([validValues.max()], [1.0])
else:
dif = np.abs(validValues - thisValue)
inds = np.argsort(dif)[0:2]
val1, val2 = validValues[inds]
c1 = np.abs(1.0*(val2-thisValue)/(val2-val1))
c2 = np.abs(1.0*(val1-thisValue)/(val2-val1))
ret = ([val1, val2], [c1, c2])
if retinds:
inds = [np.nonzero(validValues==val)[0][0] for val in ret[0]]
ret = (inds, ret[1])
return ret
[docs]def feps_interpol(x, y, a, linear=True):
"""
Wrapper script for NumPy interpolation. Culls duplicate values and
puts x into a monotonically increasing grid.
:INPUTS:
x : NumPy array
1D sequence of values defining the grid coordinates at which
the input values 'y' are defined.
y : NumPy array
1D sequence of values.
a : NumPy array
Values of 'x' at which to interpolate from the values of 'y'.
:EXAMPLE:
::
import numpy as np
x = np.linspace(-3,3,61)
v = np.sin(x)
u = np.array([-2.50, -2.25, -1.85, -1.55, -1.20, -0.85, -0.50, -0.10, \
0, 0.75, 0.85, 1.05, 1.45, 1.85, 2.00, 2.25, 2.75 ])
b = feps_interpol(x,v,u)
:NOTES:
Converted from IDL code from J. Bouwman. Documentation was:
;(SH Feb 26 1999)
;We need to make the grid mononic therefore spline needs to do
;some cleaning before execution
"""
# 2013-12-01 23:47 IJMC: Translated from IDL.
u, idx = np.unique(x, return_index=True)
xt = x[idx]
yt = y[idx]
idx2 = np.argsort(xt)
xt = xt[idx2]
yt = yt[idx2]
idx3 = np.argsort(a)
at = a[idx3]
if linear is not True:
print "nonlinear mode not implemented!"
else:
bt = np.interp(at, xt, yt)
return bt
[docs]class modelGrid:
"""Model Grid object.
"""
def __init__(self):
names = ['MIX_LEN', 'Y', 'Z', 'Zeff', '_Fe_H_', '_a_Fe_', 'ages_Gyr', 'isochrones', 'nages', 'nmags', 'photometricSystem', 'filename']
for name in names:
setattr(self, name, None)
return
[docs]class isochrone:
"""Model Isochrone object.
"""
def __init__(self):
return
[docs]def readDartmouthIsochrones(filename, mode='2012', comment='#'):
"""
Read ASCII-format Dartmouth Isochrone files into Python.
:INPUTS:
filename : str
Filename to load, e.g. 'fehm05afep0.UBVRIJHKsKp'
mode : str
Which type of models to load. For now, '2012' is the only
valid input.
comment : str
Which character(s) indicate(s) a comment, rather than
tabular/numeric data.
:OUTPUT:
A Pythonic object with fields derived from the input file. It
will have fields named 'Y', 'Z', 'Zeff', 'ages_Gyr',
'isochrones', 'photometricSystem', etc.
The 'isochrones' field is a list of isochrones, one at each age
step. It will have fields whose names correspond to photometric
bandpasses (see the example below), as well as standard fields
such as 'LogG', 'LogTeff', 'LogL_Lo', 'M_Mo', etc.
:NOTES:
You can download the models at the DSEP website:
http://stellar.dartmouth.edu/~models/
:REQUIREMENTS:
As written, requires NumPy. (But could be easily rewritten to
avoid this, if necessary).
:EXAMPLE:
::
# Reproduce Fig. 4 of Dotter et al. (2008):
import tools
import pylab as py
filename = 'fehp00afep0.UBVRIJHKsKp'
models = tools.readDartmouthIsochrones(filename, mode='2012')
age2plot = 4 # Plot 4 Gyr track
age_index = (models.ages_Gyr==age2plot).nonzero()[0]
this_isochrone = models.isochrones[age_index]
py.figure()
ax1=py.subplot(121)
py.plot(this_isochrone.LogTeff, this_isochrone.LogL_Lo)
py.xlabel('log T_eff')
py.ylabel('log L/L_sun')
py.axis([3.9, 3.4, -3, 4])
leg = legend(['DSEP'], 3)
ax2=py.subplot(122)
py.plot(this_isochrone.V - this_isochrone.I, this_isochrone.V)
py.xlabel('V - I')
py.ylabel('M_V')
py.axis([0.25, 4, 14, -2])
[ax.minorticks_on() for ax in [ax1, ax2]]
"""
# 2014-08-06 17:31 IJMC: Created
def iscomment(input):
return input.strip()[0]=='#'
def scrapeval(line, thiskey, endflag=' '):
thisind = line.find(thiskey)
endind = line.find(endflag, thisind)
return line[thisind+len(thiskey):endind]
def cleanName(input, bad='/-[]()', good='_'):
iter = 0
nchar = len(input)
inputOK = False
for badChar in bad:
input = input.replace(badChar, good)
return input
f = open(filename, 'r')
rawtext = f.readlines()
f.close()
nlines = len(rawtext)
iter = 0
ret = modelGrid()
ret.isochrones = []
ret.filename = filename
niso = 0
if mode=='2012':
# First parse the header:
while iscomment(rawtext[iter]) and not ('AGE' in rawtext[iter] and 'EEPS' in rawtext[iter]):
if 'NUMBER OF AGES' in rawtext[iter]:
ret.nages = int(scrapeval(rawtext[iter], 'AGES=', 'MAGS'))
ret.nmags = int(scrapeval(rawtext[iter], 'MAGS=', '\n'))
ret.ages_Gyr = np.zeros(ret.nages, dtype=float)
elif 'MIX-LEN' in rawtext[iter]:
param_names = rawtext[iter].strip('#').split()
iter += 1
param_vals = map(float, rawtext[iter].strip('#').split())
for name, val in zip(param_names, param_vals):
setattr(ret, cleanName(name), val)
elif 'PHOTOMETRIC SYSTEM' in rawtext[iter]:
ret.photometricSystem = scrapeval(rawtext[iter], '**PHOTOMETRIC SYSTEM**:', '\n')
iter += 1
while iter<nlines:
if ('AGE' in rawtext[iter] and 'EEPS' in rawtext[iter]):
# Then parse the table of data, beginning with the "AGE" line
iso = isochrone()
iso.age_Gyr = float(scrapeval(rawtext[iter], 'AGE=', 'EEPS'))
iso.EEPS = int(scrapeval(rawtext[iter], 'EEPS=', '\n'))
iter += 1
columnNames = map(cleanName, rawtext[iter].strip('#').split())
for name in columnNames: setattr(iso, name, np.zeros(iso.EEPS, dtype=float))
subIter = 0
ret.ages_Gyr[niso] = iso.age_Gyr
niso += 1
elif len(rawtext[iter].strip())>0:
columnValues = map(float, rawtext[iter].split())
for name, value in zip(columnNames, columnValues):
getattr(iso, name)[subIter] = value
subIter += 1
if subIter==iso.EEPS: ret.isochrones.append(iso)
iter += 1
else:
print "I don't know how to handle mode '%s' -- failing with '-1' flag." % mode
ret = -1
return ret
[docs]def addTwoMags(mag1, mag2):
"""Return the total (astronomical) magnitude of two combined sources.
:INPUTS:
mag1, mag2 : scalars or NumPy arrays.
magnitudes of the two sources.
:RETURNS:
-2.5 * np.log10(10**(-0.4*mag1) + 10**(-0.4*mag2))
"""
# 2014-08-10 15:52 IJMC: Created.
return -2.5 * np.log10(10**(-0.4*mag1) + 10**(-0.4*mag2))
[docs]def invChisq(dof, conf=0.683):
"""Compute the delta-chi^2 corresponding to the given parameters.
:INPUTS:
dof : int, dof > 1
Number of degrees of freedom (or "interesting parameters")
conf : float, 0 <= conf <= 1
Confidence level. See below for some common choices.
:RETURNS:
Desired delta-Chi-squared value.
:EXAMPLE:
::
# Reproduce Table 1 of Avni (1976)
import tools
dofs = [1, 2, 3, 4]
confs = [0.68, 0.90, 0.99]
for conf in confs:
for dof in dofs:
print ("%5.2f " % tools.invChisq(dof, conf=conf)),
print " "
:NOTES:
Some typical values for a Normal (Gaussian) distribution:
========= ================
type confidence level
========= ================
one-sigma 0.6826895
2 sigma 0.9544997
3 sigma 0.9973002
4 sigma 0.9999366
5 sigma 0.9999994
========= ================
"""
# 2014-08-11 20:23 IJMC: Created
# 2014-10-23 22:26 IJMC: New starting guess for fsolve.
from scipy.optimize import fsolve
from scipy.stats import chisqprob
if conf==0:
return 0
else:
def minFunc(dchi): return chisqprob(dchi, dof) - (1.-conf)
out = fsolve(minFunc, dof)
try:
ret = out[0]
except:
ret = out
return ret
[docs]def resampleIsochrone(iso, x, xName='M_Mo', fields='*all*'):
"""Resample parameters of an isochrone-type object.
:INPUTS:
iso : object
Isochrone sub-field object of a stellar model-grid object, of
the type returned by :func:`readDartmouthIsochrones`.
x : 1D NumPy array
The new values to use for interpolation or resampling.
xName : string
The name of the field in 'isochrone.'
fields : string
Which fields to resample. If '*all*', all sub-fields of
'isochrone' with the same size as getattr(isochrone, xName)
will be resampled.
:NOTES:
We use numpy.interp() for the resampling; if 'x' is not an
always-increasing array then interp() may have
problems. Similarly, interp() offers no extrapolation beyond the
original limits of iso.xName.
"""
# 2014-08-12 14:14 IJMC: Created.
if fields =='*all*':
fields = dir(iso)
newIso = isochrone()
xOld = getattr(iso, xName)
for field in dir(iso):
thisField = getattr(iso,field)
if field==xName:
setattr(newIso, field, x)
elif (field in fields) and hasattr(thisField, '__iter__') and len(thisField)==len(xOld):
setattr(newIso, field, np.interp(x, xOld, thisField))
#spline = interpolate.UnivariateSpline(xOld, thisField, k=1, s=0.)
#setattr(newIso, field, spline(x))
else:
setattr(newIso, field, thisField)
return newIso
[docs]def obj2FITS(input):
"""Try to convert any generic object into a multi-extension FITS
file. We examine each attribute of the object: if a string or
scalar, we addit to the Primary HDU header. If a sequence of
numbers, we add it as an extension with the appropriate name.
It probably wouldn't work for heirarchical objects whose
attributes are themselves complicated objects; probably also won't
work for complex-valued arrays.
"""
# 2014-08-15 22:26 IJMC: Created.
# Copied straight from the PyFits source code:
# FSC commentary card string which must contain printable ASCII characters.
# Note: \Z matches the end of the string without allowing newlines
import re
badchars = r'[ -~]*'+'\n'+'\Z'
_ascii_text_re = re.compile(r'[ -~]*\Z')
try:
from astropy.io import fits as pyfits
except:
import pyfits
fields = dir(input)
hdu1 = pyfits.PrimaryHDU([0])
hdu1.header['OBJ2FITS'] = 'Input object converted to FITS file.'
hdus = [hdu1]
for field in fields:
#pdb.set_trace()
val = getattr(input, field)
try:
junk = float(val)
valIsScalar = not isinstance(val, np.ndarray)
except:
valIsScalar = False
if valIsScalar:
hdu1.header[field] = val
else:
# Copied straight from the PyFits source code:
try:
text_value = val.decode('ascii')
except:
validString = False
else:
# Check against the printable characters regexp as well
for badchar in badchars:
text_value = text_value.replace(badchar, '')
m = _ascii_text_re.match(text_value)
validString = m is not None
if validString:
hdu1.header[field] = text_value
else:
try:
junk = np.array(val) + 0
valIsNumericalArray = True
hdus.append(pyfits.ImageHDU(val, name=field))
hdu1.header[field] = 'Extension %i' % (len(hdus)-1)
except:
valIsNumericalArray = False
hdu1.header[field] = 'Could not extract field from input object.'
return pyfits.HDUList(hdus)
def cardUndefined(headercard):
try:
from astropy.io import fits as pyfits
except:
import pyfits
return (headercard is pyfits.card.UNDEFINED) or \
(headercard is pyfits.card.Undefined)
[docs]def contourg(*args, **kw):
"""Plot filled contours of irregularly-spaced data.
:USAGE:
First three inputs must use syntax 'contour(X,Y,Z)'.
Can set "nbinx=50" or "nbiny=50" for number of bins.
Otherwise, syntax is the same as for matplotlib's 'contourf'.
:EXAMPLE:
::
import tools
import numpy as np
:SEE_ALSO:
:func:`plotc`
"""
# 2014-10-06 10:42 IJMC: Created
from pylab import contourf
from scipy.interpolate import griddata
if 'nbinx' in kw.keys():
nbinx = kw.pop('nbinx')
else:
nbinx = 50
if 'nbiny' in kw.keys():
nbiny = kw.pop('nbiny')
else:
nbiny = 50
x0, y0, z0 = args[0:3]
finite = np.isfinite(x0) * np.isfinite(y0) * np.isfinite(z0)
x1 = x0[finite]
y1 = y0[finite]
z1 = z0[finite]
x = np.linspace(x1.min(), x1.max(), nbinx)
y = np.linspace(y1.min(), y1.max(), nbiny)
z = griddata((x1, y1), z1, (x[None,:], y[:,None]), method='linear')
cargs = (x, y, z) + args[3:]
return contourf(*cargs, **kw)