def main():
"""
NAME
watsonsV.py
DESCRIPTION
calculates Watson's V statistic from input files
INPUT FORMAT
takes dec/inc as first two columns in two space delimited files
SYNTAX
watsonsV.py [command line options]
OPTIONS
-h prints help message and quits
-f FILE (with optional second)
-f2 FILE (second file)
-ant, flip antipodal directions to opposite direction
in first file if only one file or flip all in second, if two files
-P (don't save or show plot)
-sav save figure and quit silently
-fmt [png,svg,eps,pdf,jpg] format for saved figure
OUTPUT
Watson's V and the Monte Carlo Critical Value Vc.
in plot, V is solid and Vc is dashed.
"""
Flip=0
show,plot=1,0
fmt='svg'
file2=""
if '-h' in sys.argv: # check if help is needed
print main.__doc__
sys.exit() # graceful quit
if '-ant' in sys.argv: Flip=1
if '-sav' in sys.argv: show,plot=0,1 # don't display, but do save plot
if '-fmt' in sys.argv:
ind=sys.argv.index('-fmt')
fmt=sys.argv[ind+1]
if '-P' in sys.argv: show=0 # don't display or save plot
if '-f' in sys.argv:
ind=sys.argv.index('-f')
file1=sys.argv[ind+1]
data=numpy.loadtxt(file1).transpose()
D1=numpy.array([data[0],data[1]]).transpose()
else:
print "-f is required"
print main.__doc__
sys.exit()
if '-f2' in sys.argv:
ind=sys.argv.index('-f2')
file2=sys.argv[ind+1]
data2=numpy.loadtxt(file2).transpose()
D2=numpy.array([data2[0],data2[1]]).transpose()
if Flip==1:
D2,D=pmag.flip(D2) # D2 are now flipped
if len(D2)!=0:
if len(D)!=0:
D2=numpy.concatenate(D,D2) # put all in D2
elif len(D)!=0:
D2=D
else:
print 'length of second file is zero'
sys.exit()
elif Flip==1:D2,D1=pmag.flip(D1) # peel out antipodal directions, put in D2
#
counter,NumSims=0,5000
#
# first calculate the fisher means and cartesian coordinates of each set of Directions
#
pars_1=pmag.fisher_mean(D1)
pars_2=pmag.fisher_mean(D2)
#
# get V statistic for these
#
V=pmag.vfunc(pars_1,pars_2)
#
# do monte carlo simulation of datasets with same kappas, but common mean
#
Vp=[] # set of Vs from simulations
if show==1:print "Doing ",NumSims," simulations"
for k in range(NumSims):
counter+=1
if counter==50:
if show==1:print k+1
counter=0
Dirp=[]
# get a set of N1 fisher distributed vectors with k1, calculate fisher stats
for i in range(pars_1["n"]):
Dirp.append(pmag.fshdev(pars_1["k"]))
pars_p1=pmag.fisher_mean(Dirp)
# get a set of N2 fisher distributed vectors with k2, calculate fisher stats
Dirp=[]
for i in range(pars_2["n"]):
Dirp.append(pmag.fshdev(pars_2["k"]))
pars_p2=pmag.fisher_mean(Dirp)
# get the V for these
Vk=pmag.vfunc(pars_p1,pars_p2)
Vp.append(Vk)
#
# sort the Vs, get Vcrit (95th one)
#
Vp.sort()
k=int(.95*NumSims)
if show==1:
print "Watson's V, Vcrit: "
print ' %10.1f %10.1f'%(V,Vp[k])
if show==1 or plot==1:
CDF={'cdf':1}
pmagplotlib.plot_init(CDF['cdf'],5,5)
pmagplotlib.plotCDF(CDF['cdf'],Vp,"Watson's V",'r',"")
pmagplotlib.plotVs(CDF['cdf'],[V],'g','-')
pmagplotlib.plotVs(CDF['cdf'],[Vp[k]],'b','--')
if plot==0:pmagplotlib.drawFIGS(CDF)
files={}
if file2!="":
files['cdf']='WatsonsV_'+file1+'_'+file2+'.'+fmt
else:
files['cdf']='WatsonsV_'+file1+'.'+fmt
if pmagplotlib.isServer:
black = '#000000'
purple = '#800080'
titles={}
titles['cdf']='Cumulative Distribution'
CDF = pmagplotlib.addBorders(CDF,titles,black,purple)
pmagplotlib.saveP(CDF,files)
elif plot==0:
ans=raw_input(" S[a]ve to save plot, [q]uit without saving: ")
if ans=="a": pmagplotlib.saveP(CDF,files)
if plot==1: # save and quit silently
pmagplotlib.saveP(CDF,files)
def bootstrap_common_mean(Data1,Data2,NumSims=1000):
"""
Conduct a bootstrap test (Tauxe, 2010) for a common mean on two declination,
inclination data sets
This function modifies code from PmagPy for use calculating and plotting
bootstrap statistics. Three plots are generated (one for x, one for y and
one for z). If the 95 percent confidence bounds for each component overlap
each other, the two directions are not significantly different.
Arguments
----------
Data1 : a list of directional data [dec,inc]
Data2 : a list of directional data [dec,inc]
NumSims : number of bootstrap samples (default is 1000)
"""
counter=0
BDI1=pmag.di_boot(Data1)
BDI2=pmag.di_boot(Data2)
cart1= pmag.dir2cart(BDI1).transpose()
X1,Y1,Z1=cart1[0],cart1[1],cart1[2]
cart2= pmag.dir2cart(BDI2).transpose()
X2,Y2,Z2=cart2[0],cart2[1],cart2[2]
print "Here are the results of the bootstrap test for a common mean:"
fignum = 1
fig = plt.figure(figsize=(9,3))
fig = plt.subplot(1,3,1)
minimum = int(0.025*len(X1))
maximum = int(0.975*len(X1))
X1,y=pmagplotlib.plotCDF(fignum,X1,"X component",'r',"")
bounds1=[X1[minimum],X1[maximum]]
pmagplotlib.plotVs(fignum,bounds1,'r','-')
X2,y=pmagplotlib.plotCDF(fignum,X2,"X component",'b',"")
bounds2=[X2[minimum],X2[maximum]]
pmagplotlib.plotVs(fignum,bounds2,'b','--')
plt.ylim(0,1)
plt.subplot(1,3,2)
Y1,y=pmagplotlib.plotCDF(fignum,Y1,"Y component",'r',"")
bounds1=[Y1[minimum],Y1[maximum]]
pmagplotlib.plotVs(fignum,bounds1,'r','-')
Y2,y=pmagplotlib.plotCDF(fignum,Y2,"Y component",'b',"")
bounds2=[Y2[minimum],Y2[maximum]]
pmagplotlib.plotVs(fignum,bounds2,'b','--')
plt.ylim(0,1)
plt.subplot(1,3,3)
Z1,y=pmagplotlib.plotCDF(fignum,Z1,"Z component",'r',"")
bounds1=[Z1[minimum],Z1[maximum]]
pmagplotlib.plotVs(fignum,bounds1,'r','-')
Z2,y=pmagplotlib.plotCDF(fignum,Z2,"Z component",'b',"")
bounds2=[Z2[minimum],Z2[maximum]]
pmagplotlib.plotVs(fignum,bounds2,'b','--')
plt.ylim(0,1)
plt.tight_layout()
plt.show()
def watson_common_mean(Data1,Data2,NumSims=5000,plot='no'):
"""
Conduct a Watson V test for a common mean on two declination, inclination data sets
This function calculates Watson's V statistic from input files through Monte Carlo
simulation in order to test whether two populations of directional data could have
been drawn from a common mean. The critical angle between the two sample mean
directions and the corresponding McFadden and McElhinny (1990) classification is printed.
Required Arguments
----------
Data1 : a list of directional data [dec,inc]
Data2 : a list of directional data [dec,inc]
Optional Arguments
----------
NumSims : number of Monte Carlo simulations (default is 5000)
plot : the default is no plot ('no'). Putting 'yes' will the plot the CDF from
the Monte Carlo simulations.
"""
pars_1=pmag.fisher_mean(Data1)
pars_2=pmag.fisher_mean(Data2)
cart_1=pmag.dir2cart([pars_1["dec"],pars_1["inc"],pars_1["r"]])
cart_2=pmag.dir2cart([pars_2['dec'],pars_2['inc'],pars_2["r"]])
Sw=pars_1['k']*pars_1['r']+pars_2['k']*pars_2['r'] # k1*r1+k2*r2
xhat_1=pars_1['k']*cart_1[0]+pars_2['k']*cart_2[0] # k1*x1+k2*x2
xhat_2=pars_1['k']*cart_1[1]+pars_2['k']*cart_2[1] # k1*y1+k2*y2
xhat_3=pars_1['k']*cart_1[2]+pars_2['k']*cart_2[2] # k1*z1+k2*z2
Rw=np.sqrt(xhat_1**2+xhat_2**2+xhat_3**2)
V=2*(Sw-Rw)
# keep weighted sum for later when determining the "critical angle"
# let's save it as Sr (notation of McFadden and McElhinny, 1990)
Sr=Sw
# do monte carlo simulation of datasets with same kappas as data,
# but a common mean
counter=0
Vp=[] # set of Vs from simulations
for k in range(NumSims):
# get a set of N1 fisher distributed vectors with k1,
# calculate fisher stats
Dirp=[]
for i in range(pars_1["n"]):
Dirp.append(pmag.fshdev(pars_1["k"]))
pars_p1=pmag.fisher_mean(Dirp)
# get a set of N2 fisher distributed vectors with k2,
# calculate fisher stats
Dirp=[]
for i in range(pars_2["n"]):
Dirp.append(pmag.fshdev(pars_2["k"]))
pars_p2=pmag.fisher_mean(Dirp)
# get the V for these
Vk=pmag.vfunc(pars_p1,pars_p2)
Vp.append(Vk)
# sort the Vs, get Vcrit (95th percentile one)
Vp.sort()
k=int(.95*NumSims)
Vcrit=Vp[k]
# equation 18 of McFadden and McElhinny, 1990 calculates the critical
# value of R (Rwc)
Rwc=Sr-(Vcrit/2)
# following equation 19 of McFadden and McElhinny (1990) the critical
# angle is calculated. If the observed angle (also calculated below)
# between the data set means exceeds the critical angle the hypothesis
# of a common mean direction may be rejected at the 95% confidence
# level. The critical angle is simply a different way to present
# Watson's V parameter so it makes sense to use the Watson V parameter
# in comparison with the critical value of V for considering the test
# results. What calculating the critical angle allows for is the
# classification of McFadden and McElhinny (1990) to be made
# for data sets that are consistent with sharing a common mean.
k1=pars_1['k']
k2=pars_2['k']
R1=pars_1['r']
R2=pars_2['r']
critical_angle=np.degrees(np.arccos(((Rwc**2)-((k1*R1)**2)
-((k2*R2)**2))/
(2*k1*R1*k2*R2)))
D1=(pars_1['dec'],pars_1['inc'])
D2=(pars_2['dec'],pars_2['inc'])
angle=pmag.angle(D1,D2)
print "Results of Watson V test: "
print ""
print "Watson's V: " '%.1f' %(V)
print "Critical value of V: " '%.1f' %(Vcrit)
if V<Vcrit:
print '"Pass": Since V is less than Vcrit, the null hypothesis'
print 'that the two populations are drawn from distributions'
print 'that share a common mean direction can not be rejected.'
elif V>Vcrit:
print '"Fail": Since V is greater than Vcrit, the two means can'
print 'be distinguished at the 95% confidence level.'
print ""
print "M&M1990 classification:"
print ""
print "Angle between data set means: " '%.1f'%(angle)
print "Critical angle for M&M1990: " '%.1f'%(critical_angle)
if V>Vcrit:
print ""
elif V<Vcrit:
if critical_angle<5:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'A'"
elif critical_angle<10:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'B'"
elif critical_angle<20:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'C'"
else:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'INDETERMINATE;"
if plot=='yes':
CDF={'cdf':1}
#pmagplotlib.plot_init(CDF['cdf'],5,5)
p1 = pmagplotlib.plotCDF(CDF['cdf'],Vp,"Watson's V",'r',"")
p2 = pmagplotlib.plotVs(CDF['cdf'],[V],'g','-')
p3 = pmagplotlib.plotVs(CDF['cdf'],[Vp[k]],'b','--')
pmagplotlib.drawFIGS(CDF)
def watson_common_mean(Data1, Data2, NumSims=5000, plot='no'):
"""
Conduct a Watson V test for a common mean on two declination, inclination data sets
This function calculates Watson's V statistic from input files through Monte Carlo
simulation in order to test whether two populations of directional data could have
been drawn from a common mean. The critical angle between the two sample mean
directions and the corresponding McFadden and McElhinny (1990) classification is printed.
Required Arguments
----------
Data1 : a list of directional data [dec,inc]
Data2 : a list of directional data [dec,inc]
Optional Arguments
----------
NumSims : number of Monte Carlo simulations (default is 5000)
plot : the default is no plot ('no'). Putting 'yes' will the plot the CDF from
the Monte Carlo simulations.
"""
pars_1 = pmag.fisher_mean(Data1)
pars_2 = pmag.fisher_mean(Data2)
cart_1 = pmag.dir2cart([pars_1["dec"], pars_1["inc"], pars_1["r"]])
cart_2 = pmag.dir2cart([pars_2['dec'], pars_2['inc'], pars_2["r"]])
Sw = pars_1['k'] * pars_1['r'] + pars_2['k'] * pars_2['r'] # k1*r1+k2*r2
xhat_1 = pars_1['k'] * cart_1[0] + pars_2['k'] * cart_2[0] # k1*x1+k2*x2
xhat_2 = pars_1['k'] * cart_1[1] + pars_2['k'] * cart_2[1] # k1*y1+k2*y2
xhat_3 = pars_1['k'] * cart_1[2] + pars_2['k'] * cart_2[2] # k1*z1+k2*z2
Rw = np.sqrt(xhat_1**2 + xhat_2**2 + xhat_3**2)
V = 2 * (Sw - Rw)
# keep weighted sum for later when determining the "critical angle"
# let's save it as Sr (notation of McFadden and McElhinny, 1990)
Sr = Sw
# do monte carlo simulation of datasets with same kappas as data,
# but a common mean
counter = 0
Vp = [] # set of Vs from simulations
for k in range(NumSims):
# get a set of N1 fisher distributed vectors with k1,
# calculate fisher stats
Dirp = []
for i in range(pars_1["n"]):
Dirp.append(pmag.fshdev(pars_1["k"]))
pars_p1 = pmag.fisher_mean(Dirp)
# get a set of N2 fisher distributed vectors with k2,
# calculate fisher stats
Dirp = []
for i in range(pars_2["n"]):
Dirp.append(pmag.fshdev(pars_2["k"]))
pars_p2 = pmag.fisher_mean(Dirp)
# get the V for these
Vk = pmag.vfunc(pars_p1, pars_p2)
Vp.append(Vk)
# sort the Vs, get Vcrit (95th percentile one)
Vp.sort()
k = int(.95 * NumSims)
Vcrit = Vp[k]
# equation 18 of McFadden and McElhinny, 1990 calculates the critical
# value of R (Rwc)
Rwc = Sr - (Vcrit / 2)
# following equation 19 of McFadden and McElhinny (1990) the critical
# angle is calculated. If the observed angle (also calculated below)
# between the data set means exceeds the critical angle the hypothesis
# of a common mean direction may be rejected at the 95% confidence
# level. The critical angle is simply a different way to present
# Watson's V parameter so it makes sense to use the Watson V parameter
# in comparison with the critical value of V for considering the test
# results. What calculating the critical angle allows for is the
# classification of McFadden and McElhinny (1990) to be made
# for data sets that are consistent with sharing a common mean.
k1 = pars_1['k']
k2 = pars_2['k']
R1 = pars_1['r']
R2 = pars_2['r']
critical_angle = np.degrees(
np.arccos(((Rwc**2) - ((k1 * R1)**2) - ((k2 * R2)**2)) /
(2 * k1 * R1 * k2 * R2)))
D1 = (pars_1['dec'], pars_1['inc'])
D2 = (pars_2['dec'], pars_2['inc'])
angle = pmag.angle(D1, D2)
print "Results of Watson V test: "
print ""
print "Watson's V: " '%.1f' % (V)
print "Critical value of V: " '%.1f' % (Vcrit)
if V < Vcrit:
print '"Pass": Since V is less than Vcrit, the null hypothesis'
print 'that the two populations are drawn from distributions'
print 'that share a common mean direction can not be rejected.'
elif V > Vcrit:
print '"Fail": Since V is greater than Vcrit, the two means can'
print 'be distinguished at the 95% confidence level.'
print ""
print "M&M1990 classification:"
print ""
print "Angle between data set means: " '%.1f' % (angle)
print "Critical angle for M&M1990: " '%.1f' % (critical_angle)
if V > Vcrit:
print ""
elif V < Vcrit:
if critical_angle < 5:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'A'"
elif critical_angle < 10:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'B'"
elif critical_angle < 20:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'C'"
else:
print "The McFadden and McElhinny (1990) classification for"
print "this test is: 'INDETERMINATE;"
if plot == 'yes':
CDF = {'cdf': 1}
#pmagplotlib.plot_init(CDF['cdf'],5,5)
p1 = pmagplotlib.plotCDF(CDF['cdf'], Vp, "Watson's V", 'r', "")
p2 = pmagplotlib.plotVs(CDF['cdf'], [V], 'g', '-')
p3 = pmagplotlib.plotVs(CDF['cdf'], [Vp[k]], 'b', '--')
pmagplotlib.drawFIGS(CDF)
def main():
"""
NAME
revtest_MM1990.py
DESCRIPTION
calculates Watson's V statistic from input files through Monte Carlo simulation in order to test whether normal and reversed populations could have been drawn from a common mean (equivalent to watsonV.py). Also provides the critical angle between the two sample mean directions and the corresponding McFadden and McElhinny (1990) classification.
INPUT FORMAT
takes dec/inc as first two columns in two space delimited files (one file for normal directions, one file for reversed directions).
SYNTAX
revtest_MM1990.py [command line options]
OPTIONS
-h prints help message and quits
-f FILE
-f2 FILE
-P (don't plot the Watson V cdf)
OUTPUT
Watson's V between the two populations and the Monte Carlo Critical Value Vc.
M&M1990 angle, critical angle and classification
Plot of Watson's V CDF from Monte Carlo simulation (red line), V is solid and Vc is dashed.
"""
D1, D2 = [], []
plot = 1
Flip = 1
if "-h" in sys.argv: # check if help is needed
print main.__doc__
sys.exit() # graceful quit
if "-P" in sys.argv:
plot = 0
if "-f" in sys.argv:
ind = sys.argv.index("-f")
file1 = sys.argv[ind + 1]
f1 = open(file1, "rU")
for line in f1.readlines():
rec = line.split()
Dec, Inc = float(rec[0]), float(rec[1])
D1.append([Dec, Inc, 1.0])
f1.close()
if "-f2" in sys.argv:
ind = sys.argv.index("-f2")
file2 = sys.argv[ind + 1]
f2 = open(file2, "rU")
print "be patient, your computer is doing 5000 simulations..."
for line in f2.readlines():
rec = line.split()
Dec, Inc = float(rec[0]), float(rec[1])
D2.append([Dec, Inc, 1.0])
f2.close()
# take the antipode for the directions in file 2
D2_flip = []
for rec in D2:
d, i = (rec[0] - 180.0) % 360.0, -rec[1]
D2_flip.append([d, i, 1.0])
pars_1 = pmag.fisher_mean(D1)
pars_2 = pmag.fisher_mean(D2_flip)
cart_1 = pmag.dir2cart([pars_1["dec"], pars_1["inc"], pars_1["r"]])
cart_2 = pmag.dir2cart([pars_2["dec"], pars_2["inc"], pars_2["r"]])
Sw = pars_1["k"] * pars_1["r"] + pars_2["k"] * pars_2["r"] # k1*r1+k2*r2
xhat_1 = pars_1["k"] * cart_1[0] + pars_2["k"] * cart_2[0] # k1*x1+k2*x2
xhat_2 = pars_1["k"] * cart_1[1] + pars_2["k"] * cart_2[1] # k1*y1+k2*y2
xhat_3 = pars_1["k"] * cart_1[2] + pars_2["k"] * cart_2[2] # k1*z1+k2*z2
Rw = numpy.sqrt(xhat_1 ** 2 + xhat_2 ** 2 + xhat_3 ** 2)
V = 2 * (Sw - Rw)
#
# keep weighted sum for later when determining the "critical angle" let's save it as Sr (notation of McFadden and McElhinny, 1990)
#
Sr = Sw
#
# do monte carlo simulation of datasets with same kappas, but common mean
#
counter, NumSims = 0, 5000
Vp = [] # set of Vs from simulations
for k in range(NumSims):
#
# get a set of N1 fisher distributed vectors with k1, calculate fisher stats
#
Dirp = []
for i in range(pars_1["n"]):
Dirp.append(pmag.fshdev(pars_1["k"]))
pars_p1 = pmag.fisher_mean(Dirp)
#
# get a set of N2 fisher distributed vectors with k2, calculate fisher stats
#
Dirp = []
for i in range(pars_2["n"]):
Dirp.append(pmag.fshdev(pars_2["k"]))
pars_p2 = pmag.fisher_mean(Dirp)
#
# get the V for these
#
Vk = pmag.vfunc(pars_p1, pars_p2)
Vp.append(Vk)
#
# sort the Vs, get Vcrit (95th percentile one)
#
Vp.sort()
k = int(0.95 * NumSims)
Vcrit = Vp[k]
#
# equation 18 of McFadden and McElhinny, 1990 calculates the critical value of R (Rwc)
#
Rwc = Sr - (Vcrit / 2)
#
# following equation 19 of McFadden and McElhinny (1990) the critical angle is calculated.
#
k1 = pars_1["k"]
k2 = pars_2["k"]
R1 = pars_1["r"]
R2 = pars_2["r"]
critical_angle = numpy.degrees(
numpy.arccos(((Rwc ** 2) - ((k1 * R1) ** 2) - ((k2 * R2) ** 2)) / (2 * k1 * R1 * k2 * R2))
)
D1_mean = (pars_1["dec"], pars_1["inc"])
D2_mean = (pars_2["dec"], pars_2["inc"])
angle = pmag.angle(D1_mean, D2_mean)
#
# print the results of the test
#
print ""
print "Results of Watson V test: "
print ""
print "Watson's V: " "%.1f" % (V)
print "Critical value of V: " "%.1f" % (Vcrit)
if V < Vcrit:
print '"Pass": Since V is less than Vcrit, the null hypothesis that the two populations are drawn from distributions that share a common mean direction (antipodal to one another) cannot be rejected.'
elif V > Vcrit:
print '"Fail": Since V is greater than Vcrit, the two means can be distinguished at the 95% confidence level.'
print ""
print "M&M1990 classification:"
print ""
print "Angle between data set means: " "%.1f" % (angle)
print "Critical angle of M&M1990: " "%.1f" % (critical_angle)
if V > Vcrit:
print ""
elif V < Vcrit:
if critical_angle < 5:
print "The McFadden and McElhinny (1990) classification for this test is: 'A'"
elif critical_angle < 10:
print "The McFadden and McElhinny (1990) classification for this test is: 'B'"
elif critical_angle < 20:
print "The McFadden and McElhinny (1990) classification for this test is: 'C'"
else:
print "The McFadden and McElhinny (1990) classification for this test is: 'INDETERMINATE;"
if plot == 1:
CDF = {"cdf": 1}
pmagplotlib.plot_init(CDF["cdf"], 5, 5)
p1 = pmagplotlib.plotCDF(CDF["cdf"], Vp, "Watson's V", "r", "")
p2 = pmagplotlib.plotVs(CDF["cdf"], [V], "g", "-")
p3 = pmagplotlib.plotVs(CDF["cdf"], [Vp[k]], "b", "--")
pmagplotlib.drawFIGS(CDF)
files, fmt = {}, "svg"
if file2 != "":
files["cdf"] = "WatsonsV_" + file1 + "_" + file2 + "." + fmt
else:
files["cdf"] = "WatsonsV_" + file1 + "." + fmt
if pmagplotlib.isServer:
black = "#000000"
purple = "#800080"
titles = {}
titles["cdf"] = "Cumulative Distribution"
CDF = pmagplotlib.addBorders(CDF, titles, black, purple)
pmagplotlib.saveP(CDF, files)
else:
ans = raw_input(" S[a]ve to save plot, [q]uit without saving: ")
if ans == "a":
pmagplotlib.saveP(CDF, files)
def bootstrap_common_mean(Data1, Data2, NumSims=1000):
"""
Conduct a bootstrap test (Tauxe, 2010) for a common mean on two declination,
inclination data sets
This function modifies code from PmagPy for use calculating and plotting
bootstrap statistics. Three plots are generated (one for x, one for y and
one for z). If the 95 percent confidence bounds for each component overlap
each other, the two directions are not significantly different.
Arguments
----------
Data1 : a list of directional data [dec,inc]
Data2 : a list of directional data [dec,inc]
NumSims : number of bootstrap samples (default is 1000)
"""
counter = 0
BDI1 = pmag.di_boot(Data1)
BDI2 = pmag.di_boot(Data2)
cart1 = pmag.dir2cart(BDI1).transpose()
X1, Y1, Z1 = cart1[0], cart1[1], cart1[2]
cart2 = pmag.dir2cart(BDI2).transpose()
X2, Y2, Z2 = cart2[0], cart2[1], cart2[2]
print "Here are the results of the bootstrap test for a common mean:"
fignum = 1
fig = plt.figure(figsize=(9, 3))
fig = plt.subplot(1, 3, 1)
minimum = int(0.025 * len(X1))
maximum = int(0.975 * len(X1))
X1, y = pmagplotlib.plotCDF(fignum, X1, "X component", 'r', "")
bounds1 = [X1[minimum], X1[maximum]]
pmagplotlib.plotVs(fignum, bounds1, 'r', '-')
X2, y = pmagplotlib.plotCDF(fignum, X2, "X component", 'b', "")
bounds2 = [X2[minimum], X2[maximum]]
pmagplotlib.plotVs(fignum, bounds2, 'b', '--')
plt.ylim(0, 1)
plt.subplot(1, 3, 2)
Y1, y = pmagplotlib.plotCDF(fignum, Y1, "Y component", 'r', "")
bounds1 = [Y1[minimum], Y1[maximum]]
pmagplotlib.plotVs(fignum, bounds1, 'r', '-')
Y2, y = pmagplotlib.plotCDF(fignum, Y2, "Y component", 'b', "")
bounds2 = [Y2[minimum], Y2[maximum]]
pmagplotlib.plotVs(fignum, bounds2, 'b', '--')
plt.ylim(0, 1)
plt.subplot(1, 3, 3)
Z1, y = pmagplotlib.plotCDF(fignum, Z1, "Z component", 'r', "")
bounds1 = [Z1[minimum], Z1[maximum]]
pmagplotlib.plotVs(fignum, bounds1, 'r', '-')
Z2, y = pmagplotlib.plotCDF(fignum, Z2, "Z component", 'b', "")
bounds2 = [Z2[minimum], Z2[maximum]]
pmagplotlib.plotVs(fignum, bounds2, 'b', '--')
plt.ylim(0, 1)
plt.tight_layout()
plt.show()
def main():
"""
NAME
find_EI.py
DESCRIPTION
Applies series of assumed flattening factor and "unsquishes" inclinations assuming tangent function.
Finds flattening factor that gives elongation/inclination pair consistent with TK03.
Finds bootstrap confidence bounds
SYNTAX
find_EI.py [command line options]
OPTIONS
-h prints help message and quits
-i allows interactive input of file name
-f FILE specify input file name
-nb N specify number of bootstraps - the more the better, but slower!, default is 1000
-fmt [svg,png,eps,pdf..] change plot format, default is svg
INPUT
dec/inc pairs, delimited with space or tabs
OUTPUT
four plots: 1) equal area plot of original directions
2) Elongation/inclination pairs as a function of f, data plus 25 bootstrap samples
3) Cumulative distribution of bootstrapped optimal inclinations plus uncertainties.
Estimate from original data set plotted as solid line
4) Orientation of principle direction through unflattening
NOTE: If distribution does not have a solution, plot labeled: Pathological. Some bootstrap samples may have
valid solutions and those are plotted in the CDFs and E/I plot.
"""
fmt,nb='svg',1000
if '-i' in sys.argv:
file=raw_input("Enter file name for processing: ")
elif '-f' in sys.argv:
ind=sys.argv.index('-f')
file=sys.argv[ind+1]
else:
print main.__doc__
sys.exit()
if '-nb' in sys.argv:
ind=sys.argv.index('-nb')
nb=int(sys.argv[ind+1])
if '-fmt' in sys.argv:
ind=sys.argv.index('-fmt')
fmt=sys.argv[ind+1]
data=numpy.loadtxt(file)
upper,lower=int(round(.975*nb)),int(round(.025*nb))
E,I=[],[]
PLTS={'eq':1,'ei':2,'cdf':3,'v2':4}
pmagplotlib.plot_init(PLTS['eq'],6,6)
pmagplotlib.plot_init(PLTS['ei'],5,5)
pmagplotlib.plot_init(PLTS['cdf'],5,5)
pmagplotlib.plot_init(PLTS['v2'],5,5)
pmagplotlib.plotEQ(PLTS['eq'],data,'Data')
pmagplotlib.drawFIGS(PLTS)
ppars=pmag.doprinc(data)
Io=ppars['inc']
n=ppars["N"]
Es,Is,Fs,V2s=find_f(data)
Inc,Elong=Is[-1],Es[-1]
pmagplotlib.plotEI(PLTS['ei'],Es,Is,Fs[-1])
pmagplotlib.plotV2s(PLTS['v2'],V2s,Is,Fs[-1])
b=0
print "Bootstrapping.... be patient"
while b<nb:
bdata=pmag.pseudo(data)
Es,Is,Fs,V2s=find_f(bdata)
if b<25:
pmagplotlib.plotEI(PLTS['ei'],Es,Is,Fs[-1])
if Es[-1]!=0:
ppars=pmag.doprinc(bdata)
I.append(abs(Is[-1]))
E.append(Es[-1])
b+=1
if b%25==0:print b,' out of ',nb
I.sort()
E.sort()
Eexp=[]
for i in I:
Eexp.append(EI(i))
if Inc==0:
title= 'Pathological Distribution: '+'[%7.1f, %7.1f]' %(I[lower],I[upper])
else:
title= '%7.1f [%7.1f, %7.1f]' %( Inc, I[lower],I[upper])
pmagplotlib.plotEI(PLTS['ei'],Eexp,I,1)
pmagplotlib.plotCDF(PLTS['cdf'],I,'Inclinations','r',title)
pmagplotlib.plotVs(PLTS['cdf'],[I[lower],I[upper]],'b','--')
pmagplotlib.plotVs(PLTS['cdf'],[Inc],'g','-')
pmagplotlib.plotVs(PLTS['cdf'],[Io],'k','-')
pmagplotlib.drawFIGS(PLTS)
print "Io Inc I_lower, I_upper, Elon, E_lower, E_upper"
print '%7.1f %s %7.1f _ %7.1f ^ %7.1f: %6.4f _ %6.4f ^ %6.4f' %(Io, " => ", Inc, I[lower],I[upper], Elong, E[lower],E[upper])
ans= raw_input("S[a]ve plots - <return> to quit: ")
if ans!='a':
print "\n Good bye\n"
sys.exit()
files={}
files['eq']='findEI_eq.'+fmt
files['ei']='findEI_ei.'+fmt
files['cdf']='findEI_cdf.'+fmt
files['v2']='findEI_v2.'+fmt
pmagplotlib.saveP(PLTS,files)
def main():
"""
NAME
watsonsV.py
DESCRIPTION
calculates Watson's V statistic from input files
INPUT FORMAT
takes dec/inc as first two columns in two space delimited files
SYNTAX
watsonsV.py [command line options]
OPTIONS
-h prints help message and quits
-f FILE (with optional second)
-f2 FILE (second file)
-ant, flip antipodal directions in FILE to opposite direction
-P (don't plot)
OUTPUT
Watson's V and the Monte Carlo Critical Value Vc.
in plot, V is solid and Vc is dashed.
"""
D1,D2=[],[]
Flip=0
plot=1
if '-h' in sys.argv: # check if help is needed
print main.__doc__
sys.exit() # graceful quit
if '-ant' in sys.argv: Flip=1
if '-P' in sys.argv: plot=0
if '-f' in sys.argv:
ind=sys.argv.index('-f')
file1=sys.argv[ind+1]
f=open(file1,'rU')
for line in f.readlines():
rec=line.split()
Dec,Inc=float(rec[0]),float(rec[1])
D1.append([Dec,Inc,1.])
f.close()
if '-f2' in sys.argv:
ind=sys.argv.index('-f2')
file2=sys.argv[ind+1]
f=open(file2,'rU')
for line in f.readlines():
if '\t' in line:
rec=line.split('\t') # split each line on space to get records
else:
rec=line.split() # split each line on space to get records
Dec,Inc=float(rec[0]),float(rec[1])
if Flip==0:
D2.append([Dec,Inc,1.])
else:
D1.append([Dec,Inc,1.])
f.close()
if Flip==1:
D1,D2=pmag.flip(D1)
#
counter,NumSims=0,5000
#
# first calculate the fisher means and cartesian coordinates of each set of Directions
#
pars_1=pmag.fisher_mean(D1)
pars_2=pmag.fisher_mean(D2)
#
# get V statistic for these
#
V=pmag.vfunc(pars_1,pars_2)
#
# do monte carlo simulation of datasets with same kappas, but common mean
#
Vp=[] # set of Vs from simulations
if plot==1:print "Doing ",NumSims," simulations"
for k in range(NumSims):
counter+=1
if counter==50:
if plot==1:print k+1
counter=0
Dirp=[]
# get a set of N1 fisher distributed vectors with k1, calculate fisher stats
for i in range(pars_1["n"]):
Dirp.append(pmag.fshdev(pars_1["k"]))
pars_p1=pmag.fisher_mean(Dirp)
# get a set of N2 fisher distributed vectors with k2, calculate fisher stats
Dirp=[]
for i in range(pars_2["n"]):
Dirp.append(pmag.fshdev(pars_2["k"]))
pars_p2=pmag.fisher_mean(Dirp)
# get the V for these
Vk=pmag.vfunc(pars_p1,pars_p2)
Vp.append(Vk)
#
# sort the Vs, get Vcrit (95th one)
#
Vp.sort()
k=int(.95*NumSims)
print "Watson's V, Vcrit: "
print ' %10.1f %10.1f'%(V,Vp[k])
if plot==1:
CDF={'cdf':1}
pmagplotlib.plot_init(CDF['cdf'],5,5)
pmagplotlib.plotCDF(CDF['cdf'],Vp,"Watson's V",'r',"")
pmagplotlib.plotVs(CDF['cdf'],[V],'g','-')
pmagplotlib.plotVs(CDF['cdf'],[Vp[k]],'b','--')
pmagplotlib.drawFIGS(CDF)
files,fmt={},'svg'
if file2!="":
files['cdf']='WatsonsV_'+file1+'_'+file2+'.'+fmt
else:
files['cdf']='WatsonsV_'+file1+'.'+fmt
if pmagplotlib.isServer:
black = '#000000'
purple = '#800080'
titles={}
titles['cdf']='Cumulative Distribution'
CDF = pmagplotlib.addBorders(CDF,titles,black,purple)
pmagplotlib.saveP(CDF,files)
else:
ans=raw_input(" S[a]ve to save plot, [q]uit without saving: ")
if ans=="a": pmagplotlib.saveP(CDF,files)
def main():
"""
NAME
find_EI.py
DESCRIPTION
Applies assumed flattening factor and "unsquishes" inclinations assuming tangent function.
Finds flattening factor that gives elongation/inclination pair consistent with TK03.
Finds bootstrap confidence bounds
SYNTAX
find_EI.py [-h][-i] [-f FILE]
INPUT
dec/inc pairs
OUTPUT
three plots: 1) equal area plot of original directions
2) Elongation/inclination pairs as a function of f, data plus 25 bootstrap samples
3) Cumulative distribution of bootstrapped optimal inclinations plus uncertainties.
Estimate from original data set plotted as solid line
"""
if '-i' in sys.argv:
file=raw_input("Enter file name for processing: ")
f=open(file,'rU')
elif '-f' in sys.argv:
ind=sys.argv.index('-f')
file=sys.argv[ind+1]
f=open(file,'rU')
else:
print main.__doc__
sys.exit()
rseed,nb,data=10,5000,[]
upper,lower=int(round(.975*nb)),int(round(.025*nb))
E,I=[],[]
PLTS={'eq':1,'ei':2,'cdf':3,'v2':4}
pmagplotlib.plot_init(PLTS['eq'],6,6)
pmagplotlib.plot_init(PLTS['ei'],5,5)
pmagplotlib.plot_init(PLTS['cdf'],5,5)
pmagplotlib.plot_init(PLTS['v2'],5,5)
random.seed(rseed)
for line in f.readlines():
rec=line.split()
dec=float(rec[0])
inc=float(rec[1])
rec=[dec,inc,1.]
data.append(rec)
pmagplotlib.plotEQ(PLTS['eq'],data,'Data')
ppars=pmag.doprinc(data)
Io=ppars['inc']
n=ppars["N"]
Es,Is,Fs,V2s=find_f(data)
Inc,Elong=Is[-1],Es[-1]
pmagplotlib.plotEI(PLTS['ei'],Es,Is,Fs[-1])
pmagplotlib.plotV2s(PLTS['v2'],V2s,Is,Fs[-1])
b=0
print "Bootstrapping.... be patient"
while b<nb:
bdata=[]
for j in range(n):
boot=random.randint(0,n-1)
random.jumpahead(rseed)
bdata.append(data[boot])
Es,Is,Fs,V2s=find_f(bdata)
if b<25:
pmagplotlib.plotEI(PLTS['ei'],Es,Is,Fs[-1])
if Es[-1]!=0:
ppars=pmag.doprinc(bdata)
I.append(abs(Is[-1]))
E.append(Es[-1])
b+=1
if b%25==0:print b,' out of ',nb
I.sort()
E.sort()
Eexp=[]
for i in I:
Eexp.append(EI(i))
title= '%7.1f [%7.1f, %7.1f]' %( Inc, I[lower],I[upper])
pmagplotlib.plotEI(PLTS['ei'],Eexp,I,1)
pmagplotlib.plotCDF(PLTS['cdf'],I,'Inclinations','r',title)
pmagplotlib.plotVs(PLTS['cdf'],[I[lower],I[upper]],'b','--')
pmagplotlib.plotVs(PLTS['cdf'],[Inc],'g','-')
pmagplotlib.plotVs(PLTS['cdf'],[Io],'k','-')
print "Io Inc I_lower, I_upper, Elon, E_lower, E_upper"
print '%7.1f %s %7.1f _ %7.1f ^ %7.1f: %6.4f _ %6.4f ^ %6.4f' %(Io, " => ", Inc, I[lower],I[upper], Elong, E[lower],E[upper])
try:
raw_input("Return to save plots - <return> to quit: ")
except EOFError:
print "\n Good bye\n"
sys.exit()
files={}
files['eq']='findEI_eq.svg'
files['ei']='findEI_ei.svg'
files['cdf']='findEI_cdf.svg'
files['v2']='findEI_v2.svg'
pmagplotlib.saveP(PLTS,files)
def common_dir_MM90(dir1,dir2,NumSims=5000,plot='no'):
dir1['r']=get_R(dir1)
dir2['r']=get_R(dir2)
#largely based on iWatsonV routine of Swanson-Hyell in IPMag
cart_1=pmag.dir2cart([dir1["dec"],dir1["inc"],dir1["r"]])
cart_2=pmag.dir2cart([dir2['dec'],dir2['inc'],dir2["r"]])
Sw=dir1['k']*dir1['r']+dir2['k']*dir2['r'] # k1*r1+k2*r2
xhat_1=dir1['k']*cart_1[0]+dir2['k']*cart_2[0] # k1*x1+k2*x2
xhat_2=dir1['k']*cart_1[1]+dir2['k']*cart_2[1] # k1*y1+k2*y2
xhat_3=dir1['k']*cart_1[2]+dir2['k']*cart_2[2] # k1*z1+k2*z2
Rw=np.sqrt(xhat_1**2+xhat_2**2+xhat_3**2)
V=2*(Sw-Rw)
# keep weighted sum for later when determining the "critical angle"
# let's save it as Sr (notation of McFadden and McElhinny, 1990)
Sr=Sw
# do monte carlo simulation of datasets with same kappas as data,
# but a common mean
counter=0
Vp=[] # set of Vs from simulations
for k in range(NumSims):
# get a set of N1 fisher distributed vectors with k1,
# calculate fisher stats
Dirp=[]
for i in range(int(dir1["n"])):
Dirp.append(pmag.fshdev(dir1["k"]))
pars_p1=pmag.fisher_mean(Dirp)
# get a set of N2 fisher distributed vectors with k2,
# calculate fisher stats
Dirp=[]
for i in range(int(dir2["n"])):
Dirp.append(pmag.fshdev(dir2["k"]))
pars_p2=pmag.fisher_mean(Dirp)
# get the V for these
Vk=pmag.vfunc(pars_p1,pars_p2)
Vp.append(Vk)
# sort the Vs, get Vcrit (95th percentile one)
Vp.sort()
k=int(.95*NumSims)
Vcrit=Vp[k]
# equation 18 of McFadden and McElhinny, 1990 calculates the critical
# value of R (Rwc)
Rwc=Sr-(Vcrit/2)
# following equation 19 of McFadden and McElhinny (1990) the critical
# angle is calculated. If the observed angle (also calculated below)
# between the data set means exceeds the critical angle the hypothesis
# of a common mean direction may be rejected at the 95% confidence
# level. The critical angle is simply a different way to present
# Watson's V parameter so it makes sense to use the Watson V parameter
# in comparison with the critical value of V for considering the test
# results. What calculating the critical angle allows for is the
# classification of McFadden and McElhinny (1990) to be made
# for data sets that are consistent with sharing a common mean.
k1=dir1['k']
k2=dir2['k']
R1=dir1['r']
R2=dir2['r']
critical_angle=np.degrees(np.arccos(((Rwc**2)-((k1*R1)**2)
-((k2*R2)**2))/
(2*k1*R1*k2*R2)))
D1=(dir1['dec'],dir1['inc'])
D2=(dir2['dec'],dir2['inc'])
angle=pmag.angle(D1,D2)
if V<Vcrit:
outcome='Pass'
if critical_angle<5: MM90class='A'
elif critical_angle<10: MM90class='B'
elif critical_angle<20: MM90class='C'
else: MM90class='INDETERMINATE'
else:
outcome='Fail'
MM90class='FAIL'
result=pd.Series([outcome,V,Vcrit,angle[0],critical_angle,MM90class], index=['Outcome','VWatson','Vcrit','angle','critangle','MM90class'])
if plot=='yes':
CDF={'cdf':1}
#pmagplotlib.plot_init(CDF['cdf'],5,5)
p1 = pmagplotlib.plotCDF(CDF['cdf'],Vp,"Watson's V",'r',"")
p2 = pmagplotlib.plotVs(CDF['cdf'],[V],'g','-')
p3 = pmagplotlib.plotVs(CDF['cdf'],[Vp[k]],'b','--')
pmagplotlib.drawFIGS(CDF)
return result
