"""

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.])

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.])

f2.close()

#take the antipode for the directions in file 2

D2_flip=[]

for rec in D2:

d,i=(rec[0]-180.)%360.,-rec[1]

D2_flip.append([d,i,1.])

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(.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: ")