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 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 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
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 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
