Use and Examples¶
Importing data from file¶
In some cases the data to process is stored in external files. Due to those cases, this application software is able to import the data from an external tabulate .txt which contains the data of the randomly selected sample. It is done by using the function dataFromFile from the tools.py module.
Some conditions are required in the file format for importing it. It has to be structured as a \((n \times 6)\) array, where math:n is the number of tensors and each row contains a tensor in the vector form with the 6 components sorted like this order \(t_{11}, t_{22}, t_{33}, t_{12}, t_{23}, t_{13}\).
The exampledata.txt file has the following content:
1.02327 1.02946 0.94727 -0.01495 -0.03599 -0.05574
1.02315 1.01803 0.95882 -0.00924 -0.02058 -0.03151
1.02801 1.03572 0.93627 -0.03029 -0.03491 -0.06088
1.02775 1.00633 0.96591 -0.01635 -0.04148 -0.02006
1.02143 1.01775 0.96082 -0.02798 -0.04727 -0.02384
1.01823 1.01203 0.96975 -0.01126 -0.02833 -0.03649
1.01486 1.02067 0.96446 -0.01046 -0.01913 -0.03864
1.04596 1.01133 0.94271 -0.01660 -0.04711 -0.03636
And the minimum script for importing exampledata.txt is the following:
# import the function
from jelinekstat.tools import dataFromFile
sample, numTensors = dataFromFile('exampledata.txt')
Examples¶
Two ways for executing the application software via script are presented below.
Short script¶
The first way is by using the function tensorStat from the jelinekstat.py module in a short script as follow.
# import the functions
from jelinekstat.jelinekstat import tensorStat
# Input data
sample = [[1.02327, 1.02946, 0.94727, -0.01495, -0.03599, -0.05574],
[1.02315, 1.01803, 0.95882, -0.00924, -0.02058, -0.03151],
[1.02801, 1.03572, 0.93627, -0.03029, -0.03491, -0.06088],
[1.02775, 1.00633, 0.96591, -0.01635, -0.04148, -0.02006],
[1.02143, 1.01775, 0.96082, -0.02798, -0.04727, -0.02384],
[1.01823, 1.01203, 0.96975, -0.01126, -0.02833, -0.03649],
[1.01486, 1.02067, 0.96446, -0.01046, -0.01913, -0.03864],
[1.04596, 1.01133, 0.94271, -0.01660, -0.04711, -0.03636]]
confLevel = 0.95
jelinekStatsSummary, stereonetPlot = tensorStat(
sample, confLevel=0.95, want2plot=True, plotName='shortSCRoutcome',
ext='pdf')
stereonetPlot.show()
Long script¶
The second way is by using all the code lines inside the same function used above in a much longer script as follow.
import numpy as np
import matplotlib.pyplot as plt
from jelinekstat.jelinekstat import normalizeTensors, meantensor, \
covMtx2PPlane, eigValsIntervals, localCovMtxs, eigVectsRegions
from jelinekstat.tools import getEigSorted, confRegions2PPlanes, \
eigVects2PlgTrd, proyAllEllipses2LongLat, splitIterables
# Input data.
sample = [[1.02327, 1.02946, 0.94727, -0.01495, -0.03599, -0.05574],
[1.02315, 1.01803, 0.95882, -0.00924, -0.02058, -0.03151],
[1.02801, 1.03572, 0.93627, -0.03029, -0.03491, -0.06088],
[1.02775, 1.00633, 0.96591, -0.01635, -0.04148, -0.02006],
[1.02143, 1.01775, 0.96082, -0.02798, -0.04727, -0.02384],
[1.01823, 1.01203, 0.96975, -0.01126, -0.02833, -0.03649],
[1.01486, 1.02067, 0.96446, -0.01046, -0.01913, -0.03864],
[1.04596, 1.01133, 0.94271, -0.01660, -0.04711, -0.03636]]
confLevel = 0.95
# PERFORMING THE CALCULATION STEP BY STEP.
# Normalization of the imput sample
sample = normalizeTensors(sample)
# Mean tensor from normalized data and sample size (n)
k, K, n = meantensor(sample, True) # k (vector); K (matrix)
# Eigenvalues (kK) and eigenvectors (pK) of the mean tensor
kK, pK = getEigSorted(K)
# Unbiased covariance matrix (V).
V = np.cov(sample.T, bias=False)
# Covariance matrix (V) in the system of the k's principal vectors (pV).
pV = covMtx2PPlane(V, k, n)
# Confidence intervals of eigenvalues of mean tensor (kIntervals).
kIntervals = eigValsIntervals(pV, n, confLevel)
# Local covariance matrices (W) in each P-plane of each confidence region.
W, eigValW, eigVectW = localCovMtxs(k, pV)
# Length and orientation of ellipses semi-axis.
majorAxis, minorAxis, theta = eigVectsRegions(
W, eigValW, eigVectW, n, confLevel)
# Coordiantes of the three ellipses in each P-plane.
x, y, PPlanePlots = confRegions2PPlanes(
majorAxis, minorAxis, theta, True, confLevel)
# Stereographic notation to plot the mean tensor's principal vectors (pK).
pKPlg, pKTrd = eigVects2PlgTrd(k) # Plg (plunge); Trd (trend)
# (plunge,trend) notation to plot principal axis of all tensors.
samplePlgTrd = list(map(eigVects2PlgTrd, sample))
# (lon, lat) notation of each confidence region.
kRegionsLong, kRegionsLat = proyAllEllipses2LongLat(x, y, k)
# Summary of the Jelinek (1978) statistic proposal for 2nd-order tensors.
jelinekStatSummary = {
'k': k,
'n': n,
'k1': {'mean': kK[0], 'variability': kIntervals[0]},
'k2': {'mean': kK[1], 'variability': kIntervals[1]},
'k3': {'mean': kK[2], 'variability': kIntervals[2]},
'p1': {'coords': pK[:, 0], 'plg': pKPlg[0], 'trd': pKTrd[0],
'majAx': majorAxis[0], 'minAx': minorAxis[0],
'incl': np.degrees(theta[0])},
'p2': {'coords': pK[:, 1], 'plg': pKPlg[1], 'trd': pKTrd[1],
'majAx': majorAxis[1], 'minAx': minorAxis[1],
'incl': np.degrees(theta[1])},
'p3': {'coords': pK[:, 2], 'plg': pKPlg[2], 'trd': pKTrd[2],
'majAx': majorAxis[2], 'minAx': minorAxis[2],
'incl': np.degrees(theta[2])}
}
# Plotting.
fig = plt.figure(num='Jelinek plot summary')
plt.ioff()
markers = ['s', '^', 'o']
labels = ['$k_1 = ' + str(round(kK[0], 3)) + '\pm' +
str(round(kIntervals[0], 3)) + '$',
'$k_2 = ' + str(round(kK[1], 3)) + '\pm' +
str(round(kIntervals[1], 3)) + '$',
'$k_3 = ' + str(round(kK[2], 3)) + '\\pm' +
str(round(kIntervals[2], 3)) + '$']
ax = fig.add_subplot(111, projection='stereonet')
# Eigenvectors of all tensors
for tensor in samplePlgTrd:
for i in range(3):
ax.line(tensor[0][i], tensor[1][i], markers[i], color='0.3',
ms=5, fillstyle='none')
# Eigenvectors of mean tensor
for i in range(3):
ax.line(pKPlg[i], pKTrd[i], markers[i], color='k', ms=7,
label=labels[i])
# Confidence regions
for i in range(3):
kRegionsLongSplitted, kRegionsLatSplitted = splitIterables(
kRegionsLong[i], kRegionsLat[i])
for i in range(len(kRegionsLongSplitted)):
ax.plot(kRegionsLongSplitted[i], kRegionsLatSplitted[i], ':k',
lw=1)
# Empty plot to add the confidence region legends.
confLvl = str(round(confLevel * 100, 1))
ax.line(0, 0, ':k', lw=1, label='$'+confLvl + '\%$ conf. regions')
ax.legend(loc=tuple(np.radians([45, -7])), fontsize='x-small')
ax.grid(True, ls='--', lw=0.5)
fig.savefig('longSCRoutcome.pdf', bbox_inches='tight')
fig.show()
Since it is the same picture than the obtained with the short script, it is not displayed again.