Welcome to APSG’s documentation!

APSG defines several new python classes to easily manage, analyze and visualize orientational structural geology data. It is under active developement, so until documenation will be finished, you can go trough tutorial to see what APSG can do for you.

Usage

To use APSG in a project:

import apsg

To use APSG interactively it is easier to import into current namespace:

from apsg import *

Changes in classnames and API

Note

APSG has been significantly refactored from version 1.0 and several changes are breaking backward compatibility. The main APSG namespace provides often-used classes in lowercase names as aliases to PascalCase convention used in modules to provide a simplified interface for users. The PascalCase names of classes use longer and plain English names instead acronyms for better readability.

If you already used older versions of APSG, check following table for new names and aliases of most commonly used classes.

alias	class name	Description
vec2	Vector2	A class to represent a 2D vector
vec	Vector3	A class to represent a 3D vector
lin	Lineation	A class to represent non-oriented (axial) linear feature
fol	Foliation	A class to represent non-oriented planar feature
pair	Pair	The class to store pair of planar and linear features
fault	Fault	The class to store pair of planar and linear features together with sense of movement
cone	Cone	The class to store cone with given axis, secant line and revolution angle in degrees
vec2set	Vector2Set	Class to store set of Vector2 features
vecset	Vector3Set	Class to store set of Vector3 features
linset	LineationSet	Class to store set of Lineation features
folset	FoliationSet	Class to store set of Foliation features
pairset	PairSet	Class to store set of Pair features
faultset	FaultSet	Class to store set of Fault features
coneset	ConeSet	Class to store set of Cone features
defgrad2	DeformationGradient2	The class to represent 2D deformation gradient tensor
defgrad	DeformationGradient3	The class to represent 3D deformation gradient tensor
velgrad2	VelocityGradient2	The class to represent 2D velocity gradient tensor
velgrad	VelocityGradient3	The class to represent 3D velocity gradient tensor
stress2	Stress2	The class to represent 2D stress tensor
stress	Stress3	The class to represent 3D stress tensor
ellipse	Ellipse	The class to represent 2D ellipse
ellipsoid	Ellipsoid	The class to represent 3D ellipsoid
ortensor2	OrientationTensor2	Represents an 2D orientation tensor
ortensor	OrientationTensor3	Represents an 3D orientation tensor
ellipseset	EllipseSet	Class to store set of Ellipse features
ortensor2set	OrientationTensor2Set	Class to store set of OrientationTensor2 features
ellipsoidset	EllipsoidSet	Class to store set of Ellipsoid features
ortensorset	OrientationTensor3Set	Class to store set of OrientationTensor3 features

Check tutorials and module API for more details.

Contents

Installation

Using pip

To install APSG from PyPI, just execute:

pip install apsg

To upgrade an existing version of APSG from PyPI, execute

pip install apsg –upgrade –no-deps

Please note that the dependencies (Matplotlib, NumPy and SciPy) will also be upgraded if you omit the --no-deps flag; use the --no-deps (“no dependencies”) flag if you don’t want this.

Master version

The APSG version on PyPI may always one step behind; you can install the latest development version from the GitHub repository by executing:

pip install git+https://github.com/ondrolexa/apsg.git

Using Conda

The APSG package is also available through conda-forge. To install APSG using conda, use the following command:

conda install apsg --channel conda-forge

or simply

conda install apsg

if you added conda-forge to your channels (conda config --add channels conda-forge).

Tutorials

APSG tutorial - Part 1

APSG defines several new python classes to easily manage, analyze and visualize orientation structural geology data. There are several classes to work with orientation data, namely Vector3 for vectorial data and Lineation, Foliation for axial data

Basic usage

APSG module could be imported either into own name space or into active one for easier interactive work.

from apsg import *

Basic operations with vectors in 2D and 3D

Instance of vector object Vector3 could be created by passing 3 arguments correspondig to 3 components to function vec:

u = vec(1, -2, 3)
v = vec(-2, 1, 1)

Alternative ways to create vector is to pass single iterable object as list, tuple or array, or to provide geological orientation according to APSG notation (default is direction of dip and dip angle for planar and trend and plunge for linear features)

coords = (-2, 2, 3)
a = vec(coords)
b = vec(120, 60)
print(a, b)

Vector3(-2, 2, 3) Vector3(-0.25, 0.433, 0.866)

The instance of 2D vector Vector2 could be created passing 2 arguments correspondig to 2 components or single iterable with components to function vec2:

k = vec2(1, 1)
coords = (-1, 2)
l = vec2(coords)
print(k, l)

Vector2(1, 1) Vector2(-1, 2)

Alternatively, single argument is interpreted as direction in degrees (0-top, 90-right, 180-down, 270-left)

m = 5 * vec2(120)
m

Vector2(-2.5, 4.33)

For common vector operation we can use standard mathematical operators or special methods using dot notation

u + v

Vector3(-1, -1, 4)

u - v

Vector3(3, -3, 2)

3*u - 2*v

Vector3(7, -8, 7)

Its magnitude or length is most commonly defined as its Euclidean norm and could be calculated using abs

abs(v)

2.449489742783178

abs(u + v)

4.242640687119285

For dot product we can use dot method or operator @

u.dot(v)

-1

u @ v

-1.0

For cross product we can method cross

u.cross(v)

Vector3(-5, -7, -3)

To project vector u onto vector v we can use method proj

u.proj(v)

Vector3(0.333, -0.167, -0.167)

To find angle (in degrees) between to vectors we use method angle

u.angle(v)

96.26395271992722

Method rotate provide possibility to rotate vector around another vector. For example, to rotate vector u around vector v for 45°

u.rotate(v, 45)

Vector3(2.248, 0.558, 2.939)

Classes Lineation and Foliation

To work with orientation data in structural geology, APSG provide two classes, Foliation class to represent planar features and Lineation class to represent linear features. Both classes support all Vector3 methods and operators, but it should be noted, that dot and angle respect their axial nature, i.e. angle between two lineations cant’t be bigger than 90 degrees.

To create instance of Lineation or Foliation, we can use functions lin and fol. Arguments have similar syntax to vec3.

lin(120, 60), fol(216, 62)

(L:120/60, S:216/62)

We can also cast Vector3 instance to Foliation or Lineation

lin(u), fol(u)

(L:297/53, S:117/37)

Vector methods for Lineation and Foliation

To find angle between two linear or planar features we can use method angle

l1 = lin(110, 40)
l2 = lin(160, 30)
l1.angle(l2)

41.59741268003547

p1 = fol(330, 50)
p2 = fol(250, 40)
p1.angle(p2)

54.69639932197533

We can use cross product to construct planar feature defined by two linear features

l1.cross(l2)

S:113/40

or to construct linear feature defined by intersection of two planar features

p1.cross(p2)

L:278/36

Cross product of planar and linear features could be used to construct plane defined by linear feature and normal of planar feature

l2.cross(p2)

S:96/53

or to find perpendicular linear feature on given plane

p2.cross(l2)

L:276/37

To rotate structural features we can use method rotate

p2.rotate(l2, 45)

S:269/78

Classes Pair and Fault

To work with paired orientation data like foliations and lineations or fault data in structural geology, APSG provide two base Pair class and derived Fault class. Both classes are instantiated providing dip direction and dip of planar and linear measurements, which are automatically orthogonalized. If misfit is too high, warning is raised. The Fault class expects one more argument providing sense of movement information, either 1 or -1 for normal/reverse movement.

To create instance of Pair, we have to pass two arguments for planar and two argumets for linear features following geological notation to function pair:

p = pair(120, 40, 162, 28)
p

P:118/39-163/30

p.misfit

3.5623168411508175

Planar and linear features are accessible using fol and lin properties

p.fol, p.lin

(S:118/39, L:163/30)

To rotate Pair instance we can use rotate method

p.rotate(lin(45, 10), 60)

P:314/83-237/61

Instantiation of Fault class is similar, we just have to provide argument to define sense of movement

f = fault(120, 60, 110, 58, 1)  # 1 for normal fault
f

F:120/59-110/59 +

Note the change in sense of movement after Fault rotation

f.rotate(lin(45, 10), 60)

F:312/62-340/59 -

For simple fault analyses Fault class also provide p, t, m and d properties to get PT-axes, kinematic plane and dihedra separation plane

f.p, f.t, f.m, f.d

(L:315/75, L:116/14, S:27/85, S:290/31)

Class Cone

General feature type to store small or great circles as cone. It could be defined by axis, secant and revolving angle or by axis and apical angle The revolving angle is by default 360° defining full cone. For segments of small circles, the revolving angle could be different.

c = cone(lin(140, 50), lin(140, 75))
c

C:140/50 [25]

To create small circle segment, you can provide revolving angle

c = cone(lin(90, 70), lin(45,30), 115)

The tips of small circle segments could be obtained from cone property secant and rotated_secant

lin(c.secant), lin(c.rotated_secant)

(L:45/30, L:137/30)

To define cone using apical angle, use axis amd number arguments. Note, that revolving angle is 360 by default

c = cone(lin(140, 50), 25)
c

C:140/50 [25]

c.revangle

360.0

Feature sets

APSG provide several classes to process, analyze and visualize the sets of data. There are e.g. vecset, linset and folset classes to store group of vec, lin and fol objects. All these feature sets are created from homogeneous list of data with optional name atribute.

v = vecset([vec(120,60), vec(116,50), vec(132,45), vec(90,60), vec(84,52)], name='Vectors')
v

V3(5) Vectors

l = linset([lin(120,60), lin(116,50), lin(132,45), lin(90,60), lin(84,52)], name='Lineations')
l

L(5) Lineations

f = folset([fol(120,60), fol(116,50), fol(132,45), fol(90,60), fol(84,52)], name='Foliations')
f

S(5) Foliations

To simplify interactive group creation, you can use function G

g = G([lin(120,60), lin(116,50), lin(132,45), lin(90,60), lin(84,52)], name='L1')
g

L(5) L1

Method len returns number of features in group

len(v)

5

Most of the vec, lin and fol methods could be used for feature sets as well. For example, to measure angles between all features in group and another feature, we can use method angle:

l.angle(lin(110,50))

array([11.49989817,  3.85569115, 15.61367789, 15.11039885, 16.3947936 ])

To rotate all features in group around another feature, we can use method rotate

lr = l.rotate(lin(150, 30), 45)

To show data in list you can use data property

l.data

(L:120/60, L:116/50, L:132/45, L:90/60, L:84/52)

lr.data

(L:107/35, L:113/26, L:126/30, L:93/26, L:94/18)

Function R returns resultant of all features in set. Note that Lineation and Foliation are axial in nature, so resultant vector is not reliable. Check the orientation tensor anlysis below.

v.R()

Vector3(-0.941, 2.649, 3.993)

lin(v.R())

L:110/55

There is several methods to infer spherical statistics as spherical variance, Fisher’s statistics, confidence cones on data etc.

l.var()

0.02337168447438498

v.fisher_statistics()

{'k': 34.22945405911087, 'a95': 13.26402990511733, 'csd': 13.844747281750971}

v.fisher_cone_a95()

C:110/55 [13.264]

v.fisher_cone_csd()

C:110/55 [13.8447]

v.delta()

12.411724720740516

v.rdegree()

95.32566310512297

To calculate orientation tensor of all features in group, we can use ortensor method.

v.ortensor()

OrientationTensor3
[[ 0.074 -0.096 -0.143]
 [-0.096  0.284  0.421]
 [-0.143  0.421  0.642]]
(S1:0.977, S2:0.201, S3:0.0758)

APSG tutorial - Part 2

from apsg import *

Matrix like classes and tensors

APSG provides matrix-like classes to work with tensor quantities used commonly in structural geology analysis. It includes DefGrad3 and VelGrad3 for deformation and velocity gradient, Stress3 for stress tensor, Ellipsoid for quadratic forms and Ortensor3 for orientation tensor. All these classes support common matrix mathematical operations and provide basic methods and properties.

All matrix-like objects could be created either by passing nested list or tuple or providing individual components to class method from_comp

F = defgrad([[2, 0, 1], [0, 1, 0], [0, 0, 0.5]])
F

DeformationGradient3
[[2.  0.  1. ]
 [0.  1.  0. ]
 [0.  0.  0.5]]

F = defgrad.from_comp(xx=2, zz=0.5, xz=1)
F

DeformationGradient3
[[2.  0.  1. ]
 [0.  1.  0. ]
 [0.  0.  0.5]]

For multiplifications of matrix or vectors we have to use matmul @ operator

v = vec('z') # unit-length vector in direction af axis z
u = F @ v
u

Vector3(1, 0, 0.5)

I property returns inverse matrix

F.I @ u

Vector3(0, 0, 1)

To transpose matrix, we can use T property and for multiplification we have to use @ operator

F.T @ F

DeformationGradient3
[[4.   0.   2.  ]
 [0.   1.   0.  ]
 [2.   0.   1.25]]

v @ F.T @ F @ v

1.25

Eigenvalues and eigenvectors could be obtained by methods eigenvalues and eigenvectors. Individual eigenvalues and eigen vectors could be accessed by properties E1, E2, E3 and V1, V2, V3

Deformation gradient and rotations

Deformation gradient DeformationGradient3 could describe distorsion, dilation and rigid-body rotation. All APSG features provides transform method which transform then using provided deformation gradient.

The rigid-body rotation could be either extracted from deformation gradient using R method:

R = F.R
R

DeformationGradient3
[[ 0.928  0.     0.371]
 [ 0.     1.     0.   ]
 [-0.371  0.     0.928]]

or could be created of one of the class methods like from_axisangle, defining axis of rotation and angle

R = defgrad.from_axisangle(lin(120, 50), 60)
R

DeformationGradient3
[[ 0.552 -0.753  0.359]
 [ 0.574  0.655  0.492]
 [-0.605 -0.065  0.793]]

from_two_vectors, where axis of rotation is perpendicular to both vectors and angle is angle of vectors

R = defgrad.from_two_vectors(lin(120, 50), lin(270, 80))
R

DeformationGradient3
[[ 0.938  0.074  0.339]
 [ 0.186  0.718 -0.671]
 [-0.294  0.692  0.66 ]]

lin(120, 50).transform(R)

L:270/80

or by from_vectors_axis, where axis do not need to by perpendicular to vectors. Note that rotation axis needs to be adjusted to provide correct rotation of vector.

R = defgrad.from_vectors_axis(lin(45,30), lin(135, 30), lin(90, 70))
R

DeformationGradient3
[[-0.393 -0.864  0.315]
 [ 0.864 -0.23   0.448]
 [-0.315  0.448  0.837]]

lin(45,30).transform(R)

L:135/30

a, ang = R.axisangle()
print(lin(a), ang)

L:90/70 113.1157146919613

from_two_pairs method, to describe rotation between two coordinate systems. Note that pair define X axis as lineation vector and Z axis as foliation vector.

p1 = pair(150, 60, 90, 40)
p2 = pair(45, 30, 10, 25)
R = defgrad.from_two_pairs(p1, p2)
R

DeformationGradient3
[[-0.071  0.97   0.234]
 [-0.874 -0.174  0.453]
 [ 0.48  -0.173  0.86 ]]

p1.transform(R)

P:45/30-10/25

Ellipsoid

In deformation analysis, the quadratic forms are represented by Ellipsoid class. It could be used to represents either ellipsoid objects or finite strain ellipsoid.

It provides additional methods and properties including lambda1, lambda2 and lambda3 for square-root of eigenvalues, Woodcock’s shape and strength, k, K, d and D for Flinn’s and Ramsay symmetries and intensities, lode for Lode’s parameter etc. For more check documentation. Eigenvectors could be also represented by linear or planar features using properties eigenlins and eigenfols.

We can create Ellipsoid object similarly to Matrix3 (note that only components of upper triangular part are available in from_comp method due to matrix symmetry), or you can use aditional class methods from_defgrad and from_stretch.

B = ellipsoid.from_defgrad(F)  # Finger deformation tensor
B

Ellipsoid
[[5.   0.   0.5 ]
 [0.   1.   0.  ]
 [0.5  0.   0.25]]
(S1:2.25, S2:1, S3:0.445)

In above example, the Finger deformation tensor B represents finite strain ellipsoid reulting from deformation described by deformation gradient F. We can explore several parameters:

print(f'Principal stretches: Sx={B.S1}, Sy={B.S2}, Sz={B.S3}')
print(f'Principal strain ratios: Rxy={B.Rxy}, Ryz={B.Ryz}')
print(f"Flinn's finite strain parameters: d={B.d}, k={B.k}")
print(f"Ramsay's finite strain parameters: d={B.D}, k={B.K}")
print(f"Woodcock's parameters: strength={B.strength}, shape={B.shape}")
print(f"Watterson's strain intesity: s{B.r}")
print(f"Nadai's natural octahedral unit shear: {B.goct}")
print(f"Nadai's natural octahedral unit strain: {B.eoct}")
print(f"Lode's parameter: {B.lode}")

Principal stretches: Sx=2.2476790206496235, Sy=1.0, Sz=0.44490338291762865
Principal strain ratios: Rxy=2.2476790206496235, Ryz=2.2476790206496235
Flinn's finite strain parameters: d=1.7644845924910786, k=1.0
Ramsay's finite strain parameters: d=1.3118699860194973, k=1.0
Woodcock's parameters: strength=1.6197962748565002, shape=1.0
Watterson's strain intesity: s3.495358041299247
Nadai's natural octahedral unit shear: 1.3225581202197996
Nadai's natural octahedral unit strain: 1.14536893009174
Lode's parameter: 0.0

C = ellipsoid.from_defgrad(F, 'right')  # Green's deformation tensor
C

Ellipsoid
[[4.   0.   2.  ]
 [0.   1.   0.  ]
 [2.   0.   1.25]]
(S1:2.25, S2:1, S3:0.445)

v @ C @ v

1.25

Orientation tensor

OrientationTensor3 class represents orientation tensor of set of vectors, linear or planar features. In adition to Ellipsoid methods and properties, it provides properties to describe orientation distribution, e.g. Vollmer’s P, G, R and B indexes, Intensity for Lisle intensity index and MAD for approximate angular deviation.

l = linset.random_fisher(position=lin(120,40))
ot = l.ortensor()
# or
ot = ortensor.from_features(l)
ot

OrientationTensor3
[[ 0.169 -0.226 -0.218]
 [-0.226  0.423  0.37 ]
 [-0.218  0.37   0.407]]
(S1:0.958, S2:0.214, S3:0.193)

ot.eigenvalues()

array([0.91691349, 0.04592418, 0.03716233])

ot.eigenvectors()

(Vector3(-0.387, 0.66, 0.644),
 Vector3(0.194, -0.625, 0.756),
 Vector3(0.901, 0.418, 0.114))

ot.kind

'L'

The instances of Stress3, Ellipsoid and OrientationTensor3 also provides eigenlins and eigenfols properties to represent principal axes and planes

ot.eigenlins

(L:120/40, L:287/49, L:25/7)

ot.eigenfols

(S:300/50, S:107/41, S:205/83)

ot.strength, ot.shape

(1.6028587004277868, 14.14302389342446)

ot.k, ot.d

(31.063343962312064, 3.4701087058410436)

ot.K, ot.D

(14.14302389342446, 2.252244853321263)

ot.P, ot.G, ot.R

(0.8709893116100177, 0.017523685957085658, 0.11148700243289719)

ot.MAD

16.75305404050666

APSG tutorial - Part 3

from apsg import *

StereoNet class

StereoNet allows to visualize fetaures on stereographic projection. Both equal-area Schmidt (default) and equal-angle Wulff projections are supported.

s = StereoNet()
s.great_circle(fol(150, 40))
s.pole(fol(150, 40))
s.line(lin(112, 30))
s.show()

A small circles (or cones) could be plotted as well

s = StereoNet()
l = linset.random_fisher(position=lin(40, 15), kappa=15)
s.line(l, color='k')
s.cone(l.fisher_cone_a95(), color='r')  # confidence cone on resultant
s.cone(l.fisher_cone_csd(), color='g')  # confidence cone on 63% of data
s.show()

For density contouring a contour method is available

s = StereoNet()
s.contour(l, levels=8, colorbar=True)
s.line(l, color='g', marker='.')
s.show()

APSG also provides pairset and faultset classes to store pair or fault datasets. It can be inicialized by passing list of pair or fault objects as argument or use class methods from_array or from_csv

p = pairset([pair(120, 30, 165, 20),
             pair(215, 60, 280,35),
             pair(324, 70, 35, 40)])
p.misfit

array([0.00000000e+00, 1.42108547e-14, 0.00000000e+00])

StereoNet has two special methods to visualize fault data. Method fault produce classical Angelier plot

f = faultset([fault(170, 60, 182, 59, -1),
              fault(210, 55, 195, 53, -1),
              fault(10, 60, 15, 59, -1),
              fault(355, 48, 22, 45, -1)])
s = StereoNet()
s.fault(f)
s.line(f.p, label='P-axes')
s.line(f.t, label='T-axes')
s.great_circle(f.m, label='M-planes')
s.show()

hoeppner method produce Hoeppner diagram and must be invoked from StereoNet instance

s = StereoNet()
s.hoeppner(f, label=repr(f))
s.show()

StereoGrid class

StereoGrid class allows to visualize any scalar field on StereoNet. It is used for plotting contour diagrams, but it exposes apply_func method to calculate scalar field by any user-defined function. Function must accept three element numpy.array as first argument passed from grid points of StereoGrid.

Following example defines function to calculate resolved shear stress on plane from given stress tensor. StereoGrid accesses via .grid property is used to calculate this value over all directions and finally values are plotted by StereoNet

S = stress([[-10, 2, -3],[2, -5, 1], [-3, 1, 2]])
s = StereoNet()
s.grid.apply_func(S.shear_stress)
s.contour(levels=10)
s.show()

The StereoGrid provide also amgmech (Angelier dihedra) method for paleostress analysis. Results are stored in StereoGrid. Default behavior is to calculate counts (positive in extension, negative in compression)

f = faultset.from_csv('mele.csv')
s = StereoNet()
s.grid.angmech(f)
s.contour()
s.show()

Setting method to probability, maximum likelihood estimate is calculated.

f = faultset.from_csv('mele.csv')
s = StereoNet()
s.grid.angmech(f, method='probability')
s.contour()
s.show()

s.grid

StereoGrid EqualAreaProj 3000 points.
Maximum: 48.3587 at L:250/11
Minimum: -36.1316 at L:158/14

Multiple stereonets in figure

import matplotlib.pyplot as plt

fig = plt.figure(constrained_layout=True, figsize=(10, 4))
subfigs = fig.subfigures(1, 3)

f = folset.random_fisher(position=fol(130, 60))
l = linset.random_fisher(position=fol(230, 30))
# panel 1
s1 = StereoNet()
s1.great_circle(f)
# panel 2
s2 = StereoNet()
s2.contour(l)
s2.line(l, ms=4, color='green')
# panel 3
s3 = StereoNet()
s3.pole(f, color='orange')
# render2fig
s1.render2fig(subfigs[0])
s2.render2fig(subfigs[1])
s3.render2fig(subfigs[2])
plt.show()

APSG tutorial - Part 4

from apsg import *

Fabric plots

Tensor-type objects (ortensor, ellipsoid) could be visualized in several specialized plots. FlinnPlot class provide classical Flinn’s deformation diagram, RamsayPlot class provide Ramsay modification of Flinn’s deformation diagram, VollmerPlot class provide triangular fabric plot (Vollmer, 1989) and HsuPlot class provide Hsu fabric diagram using natural strains.

F = defgrad.from_comp(xx=1/1.1, zz=1.1)
g1 = linset.uniform_sfs(name='Uniform').transform(F)
Fp = defgrad.from_comp(xx=0.5, yy=0.5, zz=4)
g2 = linset.uniform_sfs(name='Cluster').transform(Fp @ F)
Fo = defgrad.from_comp(xx=2, yy=0.25, zz=2)
g3 = linset.uniform_sfs(name='Girdle').transform(Fo @ F)

s = StereoNet()
s.line(g1, label=True)
s.line(g2, label=True)
s.line(g3, label=True)
s.show()

s = FlinnPlot()
s.point(g1.ortensor(), label=g1.name)
s.point(g2.ortensor(), label=g2.name)
s.point(g3.ortensor(), label=g3.name)
s.show()

s = RamsayPlot()
s.point(g1.ortensor(), label=g1.name)
s.point(g2.ortensor(), label=g2.name)
s.point(g3.ortensor(), label=g3.name)
s.show()

s = VollmerPlot()
s.point(g1.ortensor(), label=g1.name)
s.point(g2.ortensor(), label=g2.name)
s.point(g3.ortensor(), label=g3.name)
s.show()

s = HsuPlot()
s.point(g1.ortensor(), label=g1.name)
s.point(g2.ortensor(), label=g2.name)
s.point(g3.ortensor(), label=g3.name)
s.show()

All fabric plots has path method which accepts ellipsoidset or ortensorset objects plotted as line.

F = defgrad.from_comp(xx=2, xy=2, yz=2, zz=0.5)
E = ellipsoid.from_defgrad(F)
L = velgrad.from_comp(xx=-2, zz=2)
Eevol = ellipsoidset([E.transform(L.defgrad(t/50)) for t in range(50)])

r = FlinnPlot()
r.path(Eevol, marker='.')
r.point(E, color='r', marker='o')
r.show()

r = RamsayPlot()
r.path(Eevol, marker='.')
r.point(E, color='r', marker='o')
r.show()

ot = g1.ortensor()
otevol = ortensorset([g1.transform(L.defgrad(t/50)).ortensor() for t in range(50)])
f = VollmerPlot()
f.path(otevol, marker='.')
f.point(ot, color='r', marker='o')
f.show()

r = HsuPlot()
r.path(Eevol, marker='.')
r.point(E, color='r', marker='o')
r.show()

APSG tutorial - Part 5

from apsg import *

Pandas interface

To activate APSG interface for pandas you need to import it.

import pandas as pd
from apsg.pandas import *

We can use pandas to read and manage data. See pandas documentation for more information.

df = pd.read_csv('structures.csv')
df.head()

	site	structure	azi	inc
0	PB3	L3	113	47
1	PB3	L3	118	42
2	PB3	S1	42	79
3	PB3	S1	42	73
4	PB4	S0	195	10

We can split out dataset by type of the structure…

g = df.groupby('structure')

and select only one type…

l = g.get_group('L3')
l.head()

	site	structure	azi	inc
0	PB3	L3	113	47
1	PB3	L3	118	42
5	PB8	L3	167	17
6	PB9	L3	137	9
7	PB9	L3	147	14

Before we can use APSG interface, we need to create column with APSG features. For that we can use apsg accessor and it’s methods create_vecs, create_fols, create_lins or create_faults. Each of this method accepts keyword argument name to provide name of the new column.

l = l.apsg.create_lins(name='L3')
l.head()

	site	structure	azi	inc	L3
0	PB3	L3	113	47	L:113/47
1	PB3	L3	118	42	L:118/42
5	PB8	L3	167	17	L:167/17
6	PB9	L3	137	9	L:137/9
7	PB9	L3	147	14	L:147/14

Once we create column with APSG features, we can use accessors vec, fol, lin or fault providing methods for individual feature types, e.g. to calculate resultant vector

l.lin.R()

L:122/8

or to calculate orientation tensor…

l.lin.ortensor()

OrientationTensor3
[[ 0.29  -0.344 -0.067]
 [-0.344  0.644  0.088]
 [-0.067  0.088  0.065]]
(S1:0.932, S2:0.29, S3:0.216)

or to plot data on stereonet…

l.lin.plot(label=True)

You can also extract APSG column as featureset using accessor property getset

l.lin.getset

L(97) L3

To construct stereonets with more data, you can pass stereonet object using keyword argument snet

s = StereoNet()
l.lin.contour(snet=s)
l.lin.plot(snet=s, label=True)
pp = l.lin.ortensor().eigenfols
s.great_circle(*pp, label='principal\nplanes')
s.show()

f = g.get_group('S2').apsg.create_fols(name='S2')
f.fol.plot()

The fault features could be created from columns containing orientation of fault plane, fault striation and sense of shear (+/-1)

df = pd.read_csv('mele.csv')
df.head()

	fazi	finc	lazi	linc	sense
0	94.997	79.966	119.073	79.032	-1
1	65.923	84.972	154.087	20.008	-1
2	42.354	46.152	109.786	21.778	-1
3	14.093	61.963	295.917	21.045	1
4	126.138	77.947	40.848	21.033	-1

t = df.apsg.create_faults()
t.head()

	fazi	finc	lazi	linc	sense	faults
0	94.997	79.966	119.073	79.032	-1	F:95/80-119/79 -
1	65.923	84.972	154.087	20.008	-1	F:66/85-154/20 -
2	42.354	46.152	109.786	21.778	-1	F:42/46-110/22 -
3	14.093	61.963	295.917	21.045	1	F:14/62-296/21 +
4	126.138	77.947	40.848	21.033	-1	F:126/78-41/21 -

t[:5].fault.plot()

APSG tutorial - Part 6

Various tricks

The apsg_conf dictionary allows to modify APSG settings.

import numpy as np
from apsg import *
apsg_conf['figsize'] = (9, 7)

Some fun with cones…

l1 = lin(110, 40)
l2 = lin(250, 40)
m = l1.slerp(l2, 0.5)
p = lin(l1.cross(l2))

s = StereoNet()

for t in np.linspace(0, 1, 8):
    D = defgrad.from_vectors_axis(l1, l2, m.slerp(p, t))
    a, ang = D.axisangle()
    s.cone(cone(a, l1, ang))

for a in np.linspace(10,25,4):
    s.cone(cone(lin(315, 30), a), cone(lin(45, 30), a))

s.show()

Some tricks

Double cross products are allowed but not easy to understand.

For example p**l**p is interpreted as p**(l**p): a) l**p is plane defined by l and p normal b) intersection of this plane and p is calculated

p = fol(250,40)
l = lin(160,25)
s = StereoNet()
s.great_circle(p, label='p')
s.pole(p, label='p')
s.line(l, label='l')
s.great_circle(l**p, label='l**p')
s.line(p**l, label='p**l')
s.great_circle(l**p**l, label='l**p**l')
s.line(p**l**p, label='p**l**p')
s.show()

Pair class could be used to correct measurements of planar linear features which should spatialy overlap

pl = pair(250, 40, 160, 25)
pl.misfit

18.889520432245405

s = StereoNet()
s.great_circle(fol(250, 40), color='b', label='Original')
s.line(lin(160, 25), color='b', label='Original')
s.great_circle(pl.fol, color='g', label='Corrected')
s.line(pl.lin, color='g', label='Corrected')
s.show()

StereoNet has method arrow to draw arrow. Here is example of Hoeppner plot for variable fault orientation within given stress field

R = defgrad.from_pair(pair(180, 45, 240, 27))
S = stress([[-8, 0, 0],[0, -5, 0],[0, 0, -1]]).transform(R)
d = vecset.uniform_gss(n=600)
d = d[~d.is_upper()]
s = StereoNet()
s.great_circle(*S.eigenfols, lw=2)
s.line(S.sigma1dir, ms=10, color='red', label='Sig1')
s.line(S.sigma2dir, ms=10, color='k', label='Sig2')
s.line(S.sigma3dir, ms=10, color='green', label='Sig3')
for n in d:
    f = S.fault(n)
    if f.sense == 1:
        s.arrow(f.fvec, f.lvec, sense=f.sense, color='coral')
    else:
        s.arrow(f.fvec, f.lvec, sense=f.sense, color='skyblue')
s.show()

ClusterSet class

ClusterSet class provide access to scipy hierarchical clustering. Distance matrix is calculated as mutual angles of features within FeatureSet keeping axial and/or vectorial nature in mind. ClusterSet.elbow() method allows to explore explained variance versus number of clusters relation. Actual cluster is done by ClusterSet.cluster() method, using distance or maxclust criterion. Using of ClusterSet is explained in following example. We generate some data and plot dendrogram:

g1 = linset.random_fisher(position=lin(45,30))
g2 = linset.random_fisher(position=lin(320,56))
g3 = linset.random_fisher(position=lin(150,40))
g = g1 + g2 + g3
cl = cluster(g)
cl.dendrogram(no_labels=True)

Now we can explore evolution of within-groups variance versus number of clusters on Elbow plot (Note change in slope for three clusters)

cl.elbow()

Finally we can do clustering with chosen number of clusters and plot them

cl.cluster(maxclust=3)
cl.R.data  # Restored centres of clusters

(L:151/38, L:324/60, L:48/31)

s = StereoNet()
for gid, color in zip(range(3), ['orange', 'red', 'green']):
    s.line(cl.groups[gid], color=color, alpha=0.4, mec='none')
    s.line(cl.R[gid], ms=16, color=color, marker='*', label=True)
s.show()

Package modules

APSG provides following modules:

feature module

This module provide basic classes to store and analyze various type of structural data.

Classes:

Lineation(*args)	A class to represent axial (non-oriented) linear feature (lineation).
Foliation(*args)	A class to represent non-oriented planar feature (foliation).
Pair(*args)	The class to store pair of planar and linear feature.
Fault(*args)	The class to store Pair with associated sense of movement.
Cone(*args)	The class to store cone with given axis, secant line and revolution angle in degrees.
DeformationGradient3(*args)	The class to represent 3D deformation gradient tensor.
VelocityGradient3(*args)	The class to represent 3D velocity gradient tensor.
Stress3(*args)	The class to represent 3D stress tensor.
Ellipsoid(*args)	The class to represent 3D ellipsoid.
OrientationTensor3(*args)	Represents an 3D orientation tensor, which characterize data distribution using eigenvalue method.
DeformationGradient2(*args)	The class to represent 2D deformation gradient tensor.
VelocityGradient2(*args)	The class to represent 2D velocity gradient tensor.
Stress2(*args)	The class to represent 2D stress tensor.
Ellipse(*args)	The class to represent 2D ellipse
OrientationTensor2(*args)	Represents an 2D orientation tensor, which characterize data distribution using eigenvalue method.
Vector2Set(data[, name])	Class to store set of Vector2 features
FeatureSet(data[, name])	Base class for containers
Vector3Set(data[, name])	Class to store set of Vector3 features
LineationSet(data[, name])	Class to store set of Lineation features
FoliationSet(data[, name])	Class to store set of Foliation features
PairSet(data[, name])	Class to store set of Pair features
FaultSet(data[, name])	Class to store set of Fault features
ConeSet(data[, name])	Class to store set of Cone features
EllipseSet(data[, name])	Class to store set of Ellipse features
EllipsoidSet(data[, name])	Class to store set of Ellipsoid features
OrientationTensor2Set(data[, name])	Class to store set of OrientationTensor2 features
OrientationTensor3Set(data[, name])	Class to store set of OrientationTensor3 features
ClusterSet(d, **kwargs)	Provides a hierarchical clustering using scipy.cluster routines.
Core(**kwargs)	Core class to store palemomagnetic analysis data

Functions:

G(lst[, name])

Function to create appropriate container (FeatueSet) from list of features.

class apsg.feature.Lineation(*args)

Bases: Axial3

A class to represent axial (non-oriented) linear feature (lineation).

There are different way to create Lineation object:

• without arguments create default Lineation L:0/0

• with single argument l, where:

  • l could be Vector3-like object

  • l could be string ‘x’, ‘y’ or ‘z’ - principal axes of coordinate system

  • l could be tuple of (x, y, z) - vector components

• with 2 arguments plunge direction and plunge

• with 3 numerical arguments defining vector components

Parameters

• azi (float) – plunge direction of linear feature in degrees

• inc (float) – plunge of linear feature in degrees

Example

>>> lin()
>>> lin('y')
>>> lin(1,2,-1)
>>> l = lin(110, 26)

cross(other)

Return Foliation defined by two linear features

property geo

Return tuple of plunge direction and plunge

to_json()

Return as JSON dict

class apsg.feature.Foliation(*args)

Bases: Axial3

A class to represent non-oriented planar feature (foliation).

There are different way to create Foliation object:

• without arguments create default Foliation S:180/0

• with single argument f, where:

  • f could be Vector3-like object

  • f could be string ‘x’, ‘y’ or ‘z’ - principal planes of coordinate system

  • f could be tuple of (x, y, z) - vector components

• with 2 arguments follows active notation. See apsg_conf[“notation”]

• with 3 numerical arguments defining vector components of plane normal

Parameters

• azi (float) – dip direction (or strike) of planar feature in degrees.

• inc (float) – dip of planar feature in degrees

Example

>>> fol()
>>> fol('y')
>>> fol(1,2,-1)
>>> f = fol(250, 30)

cross(other)

Return Lineation defined by intersection of planar features

property geo

Return tuple of dip direction and dip

to_json()

Return as JSON dict

dipvec()

Return dip vector

pole()

Return plane normal as vector

rake(rake)

Return rake vector

transform(F, **kwargs)

Return affine transformation by matrix F.

Parameters

F – transformation matrix

Keyword Arguments

norm – normalize transformed Foliation. [True or False] Default False

Returns

vector representation of affine transformation (dot product) of self by F

Example

>>> # Reflexion of `y` axis.
>>> F = [[1, 0, 0], [0, -1, 0], [0, 0, 1]]
>>> f = fol(45, 20)
>>> f.transform(F)
S:315/20

class apsg.feature.Pair(*args)

Bases: object

The class to store pair of planar and linear feature.

When Pair object is created, both planar and linear feature are adjusted, so linear feature perfectly fit onto planar one. Warning is issued, when misfit angle is bigger than 20 degrees.

There are different way to create Pair object:

• without arguments create default Pair with fol(0,0) and lin(0,0)

• with single argument p, where:

  • p could be Pair

  • p could be tuple of (fazi, finc, lazi, linc)

  • p could be tuple of (fx, fy ,fz, lx, ly, lz)

• with 2 arguments f and l could be Vector3 like objects, e.g. Foliation and Lineation

• with four numerical arguments defining fol(fazi, finc) and lin(lazi, linc)

Parameters

• fazi (float) – dip azimuth of planar feature in degrees

• finc (float) – dip of planar feature in degrees

• lazi (float) – plunge direction of linear feature in degrees

• linc (float) – plunge of linear feature in degrees

fvec

corrected vector normal to plane

Type

Vector3

lvec

corrected vector of linear feature

Type

Vector3

Example

>>> pair()
>>> pair(p)
>>> pair(f, l)
>>> pair(fazi, finc, lazi, linc)
>>> p = pair(140, 30, 110, 26)

label()

Return label

to_json()

Return as JSON dict

classmethod random()

Random Pair

property fol

Return a planar feature of Pair as Foliation.

property lin

Return a linear feature of Pair as Lineation.

transform(F, **kwargs)

Return an affine transformation of Pair by matrix F.

Parameters

F – transformation matrix

Keyword Arguments

norm – normalize transformed vectors. True or False. Default False

Returns

representation of affine transformation (dot product) of self by F

Example

>>> F = defgrad.from_axisangle(lin(0,0), 60)
>>> p = pair(90, 90, 0, 50)
>>> p.transform(F)
P:270/30-314/23

class apsg.feature.Fault(*args)

Bases: Pair

The class to store Pair with associated sense of movement.

When Fault object is created, both planar and linear feature are adjusted, so linear feature perfectly fit onto planar one. Warning is issued, when misfit angle is bigger than 20 degrees.

There are different way to create Fault object:

• without arguments create default Fault with fol(0,0) and lin(0,0)

• with single argument p:

  • p could be Fault

  • p could be tuple of (fazi, finc, lazi, linc, sense)

  • p could be tuple of (fx, fy ,fz, lx, ly, lz)

• with 2 arguments f and l could be Vector3 like objects, e.g. Foliation and Lineation

• with 5 numerical arguments defining fol(fazi, finc), lin(lazi, linc) and sense

Parameters

• fazi (float) – dip azimuth of planar feature in degrees

• finc (float) – dip of planar feature in degrees

• lazi (float) – plunge direction of linear feature in degrees

• linc (float) – plunge of linear feature in degrees

• sense (float) – sense of movement -/+1 hanging-wall up/down reverse/normal

fvec

corrected vector normal to plane

Type

Vector3

lvec

corrected vector of linear feature

Type

Vector3

sense

sense of movement (+/-1)

Type

int

Example

>>> fault()
>>> fault(p)
>>> fault(f, l)
>>> fault(fazi, finc, lazi, linc, sense)
>>> f = fault(140, 30, 110, 26, -1)

to_json()

Return as JSON dict

classmethod random()

Random Fault

p_vector(ptangle=90)

Return P axis as Vector3

t_vector(ptangle=90)

Return T-axis as Vector3.

property p

Return P-axis as Lineation

property t

Return T-axis as Lineation

property m

Return kinematic M-plane as Foliation

property d

Return dihedra plane as Fol

class apsg.feature.Cone(*args)

Bases: object

The class to store cone with given axis, secant line and revolution angle in degrees.

There are different way to create Cone object according to number of arguments:

• without args, you can create default``Cone`` with axis lin(0, 90), secant lin(0, 0) angle 360°

• with single argument c, where c could be Cone, 5-tuple of (aazi, ainc, sazi, sinc, revangle) or 7-tuple of (ax, ay ,az, sx, sy, sz, revangle)

• with 3 arguments, where axis and secant line could be Vector3 like objects, e.g. Lineation and third argument is revolution angle

• with 5 arguments defining axis lin(aazi, ainc), secant line lin(sazi, sinc) and angle of revolution

axis

axis of the cone

Type

Vector3

secant

secant line

Type

Vector3

revangle

revolution angle

Type

float

Example

>>> cone()
>>> cone(c)
>>> cone(a, s, revangle)
>>> cone(aazi, ainc, sazi, sinc, revangle)
>>> c = cone(140, 30, 110, 26, 360)

label()

Return label

to_json()

Return as JSON dict

classmethod random()

Random Cone

apical_angle()

Return apical angle

property rotated_secant

Return revangle rotated secant vector

class apsg.feature.DeformationGradient3(*args)

Bases: Matrix3

The class to represent 3D deformation gradient tensor.

Parameters

a (3x3 array_like) – Input data, that can be converted to 3x3 2D array. This includes lists, tuples and ndarrays.

Returns

DeformationGradient3 object

Example

>>> F = defgrad(np.diag([2, 1, 0.5]))

classmethod from_ratios(Rxy=1, Ryz=1)

Return isochoric DeformationGradient3 tensor with axial stretches defined by strain ratios. Default is identity tensor.

Keyword Arguments

• Rxy (float) – XY strain ratio

• Ryz (float) – YZ strain ratio

Example

>>> F = defgrad.from_ratios(Rxy=2, Ryz=3)
>>> F
DeformationGradient3
[[2.289 0.    0.   ]
 [0.    1.145 0.   ]
 [0.    0.    0.382]]

classmethod from_two_pairs(p1, p2, symmetry=False)

Return DeformationGradient3 representing rotation of coordinates from system defined by Pair p1 to system defined by Pair p2.

Lineation in pair define x axis and normal to foliation in pair define z axis

Parameters

• p1 (Pair) – from

• p2 (Pair) – to

Keyword Arguments

symmetry (bool) – If True, returns minimum angle rotation of axial pairs

Returns

Defgrad3 rotational matrix

Example

>>> p1 = pair(58, 36, 81, 34)
>>> p2 = pair(217,42, 162, 27)
>>> R = defgrad.from_two_pairs(p1, p2)
>>> p1.transform(R) == p2
True

property R

Return rotation part of DeformationGradient3 from polar decomposition.

property U

Return stretching part of DeformationGradient3 from right polar decomposition.

property V

Return stretching part of DeformationGradient3 from left polar decomposition.

axisangle()

Return rotation part of DeformationGradient3 as axis, angle tuple.

velgrad(time=1)

Return VelocityGradient3 calculated as matrix logarithm divided by given time.

Keyword Arguments

time (float) – total time. Default 1

Example

>>> F = defgrad.from_comp(xx=2, xy=1, zz=0.5)
>>> L = F.velgrad(time=10)
>>> L
VelocityGradient3
[[ 0.069  0.069  0.   ]
 [ 0.     0.     0.   ]
 [ 0.     0.    -0.069]]
>>> L.defgrad(time=10)
DeformationGradient3
[[2.  1.  0. ]
 [0.  1.  0. ]
 [0.  0.  0.5]]

class apsg.feature.VelocityGradient3(*args)

Bases: Matrix3

The class to represent 3D velocity gradient tensor.

Parameters

a (3x3 array_like) – Input data, that can be converted to 3x3 2D array. This includes lists, tuples and ndarrays.

Returns

VelocityGradient3 matrix

Example

>>> L = velgrad(np.diag([0.1, 0, -0.1]))

defgrad(time=1, steps=1)

Return DeformationGradient3 tensor accumulated after given time.

Keyword Arguments

• time (float) – time of deformation. Default 1

• steps (int) – when bigger than 1, will return a list of DeformationGradient3 tensors for each timestep.

rate()

Return rate of deformation tensor

spin()

Return spin tensor

class apsg.feature.Stress3(*args)

Bases: Tensor3

The class to represent 3D stress tensor.

The real eigenvalues of the stress tensor are what we call the principal stresses. There are 3 of these in 3D, available as properties E1, E2, and E3 in descending order of magnitude (max, intermediate, and minimum principal stresses) with orientations available as properties V1, V2 and V3. The minimum principal stress is simply the eigenvalue that has the lowest magnitude. Therefore, the maximum principal stress is the most tensile (least compressive) and the minimum principal stress is the least tensile (most compressive). Tensile normal stresses have positive values, and compressive normal stresses have negative values. If the maximum principal stress is <=0 and the minimum principal stress is negative then the stresses are completely compressive.

Note: Stress tensor has a special properties sigma1, sigma2 and sigma3 to follow common geological terminology. sigma1 is most compressive (least tensile) while sigma3 is most tensile (least compressive). Their orientation could be accessed with properties sigma1dir, sigma2dir and sigma3dir.

Parameters

a (3x3 array_like) – Input data, that can be converted to 3x3 2D array. This includes lists, tuples and ndarrays.

Returns

Stress3 object

Example

>>> S = stress([[-8, 0, 0],[0, -5, 0],[0, 0, -1]])

classmethod from_comp(xx=0, xy=0, xz=0, yy=0, yz=0, zz=0)

Return Stress tensor. Default is zero tensor.

Note that stress tensor must be symmetrical.

Keyword Arguments

zz (xx, xy, xz, yy, yz,) – tensor components

Example

>>> S = stress.from_comp(xx=-5, yy=-2, zz=10, xy=1)
>>> S
Stress3
[[-5.  1.  0.]
 [ 1. -2.  0.]
 [ 0.  0. 10.]]

property mean_stress

Mean stress

property hydrostatic

Mean hydrostatic stress tensor component

property deviatoric

A stress deviator tensor component

effective(fp)

A effective stress tensor reduced by fluid pressure

Parameters

fp (flot) – fluid pressure

property sigma1

A maximum principal stress (max compressive)

property sigma2

A intermediate principal stress

property sigma3

A minimum principal stress (max tensile)

property sigma1dir

Return unit length vector in direction of maximum principal stress (max compressive)

property sigma2dir

Return unit length vector in direction of intermediate principal stress

property sigma3dir

Return unit length vector in direction of minimum principal stress (max tensile)

property sigma1vec

Return maximum principal stress vector (max compressive)

property sigma2vec

Return intermediate principal stress vector

property sigma3vec

Return minimum principal stress vector (max tensile)

property I1

First invariant

property I2

Second invariant

property I3

Third invariant

property diagonalized

Returns diagonalized Stress tensor and orthogonal matrix R, which transforms actual coordinate system to the principal one.

cauchy(n)

Return stress vector associated with plane given by normal vector.

Parameters

n – normal given as Vector3 or Foliation object

Example

>>> S = stress.from_comp(xx=-5, yy=-2, zz=10, xy=1)
>>> S.cauchy(fol(160, 30))
Vector3(-2.52, 0.812, 8.66)

fault(n)

Return Fault object derived from given by normal vector.

Parameters

n – normal given as Vector3 or Foliation object

Example

>>> S = stress.from_comp(xx=-5, yy=-2, zz=10, xy=8)
>>> S.fault(fol(160, 30))
F:160/30-141/29 +

stress_comp(n)

Return normal and shear stress Vector3 components on plane given by normal vector.

normal_stress(n)

Return normal stress magnitude on plane given by normal vector.

shear_stress(n)

Return shear stress magnitude on plane given by normal vector.

slip_tendency(n, fp=0, log=False)

Return slip tendency calculated as the ratio of shear stress to normal stress acting on the plane.

Note: Providing fluid pressure effective normal stress is calculated

Keyword Arguments

• fp (float) – fluid pressure. Default 0

• log (bool) – when True, returns logarithm of slip tendency

dilation_tendency(n, fp=0)

Return dilation tendency of the plane.

Note: Providing fluid pressure effective stress is used

Keyword Arguments

fp (float) – fluid pressure. Default 0

property shape_ratio

Return shape ratio R (Gephart & Forsyth 1984)

class apsg.feature.Ellipsoid(*args)

Bases: Tensor3

The class to represent 3D ellipsoid.

See following methods and properties for additional operations.

Parameters

matrix (3x3 array_like) – Input data, that can be converted to 3x3 2D matrix. This includes lists, tuples and ndarrays.

Returns

Ellipsoid object

Example

>>> E = ellipsoid([[8, 0, 0], [0, 2, 0], [0, 0, 1]])
>>> E
Ellipsoid
[[8 0 0]
 [0 2 0]
 [0 0 1]]
(S1:2.83, S2:1.41, S3:1)

classmethod from_defgrad(F, form='left', **kwargs) → Ellipsoid

Return deformation tensor from Defgrad3.

Kwargs:

form: ‘left’ or ‘B’ for left Cauchy–Green deformation tensor or

Finger deformation tensor ‘right’ or ‘C’ for right Cauchy–Green deformation tensor or Green’s deformation tensor. Default is ‘left’.

classmethod from_stretch(x=1, y=1, z=1, **kwargs) → Ellipsoid

Return diagonal tensor defined by magnitudes of principal stretches.

property kind: str

Return descriptive type of ellipsoid

property strength: float

Return the Woodcock strength.

property shape: float

return the Woodcock shape.

property S1: float

Return the maximum principal stretch.

property S2: float

Return the middle principal stretch.

property S3: float

Return the minimum principal stretch.

property e1: float

Return the maximum natural principal strain.

property e2: float

Return the middle natural principal strain.

property e3: float

Return the minimum natural principal strain.

property Rxy: float

Return the Rxy ratio.

property Ryz: float

Return the Ryz ratio.

property e12: float

Return the e1 - e2.

property e13: float

Return the e1 - e3.

property e23: float

Return the e2 - e3.

property k: float

Return the strain symmetry.

property d: float

Return the strain intensity.

property K: float

Return the strain symmetry (Ramsay, 1983).

property D: float

Return the strain intensity.

property r: float

Return the strain intensity (Watterson, 1968).

property goct: float

Return the natural octahedral unit shear (Nadai, 1963).

property eoct: float

Return the natural octahedral unit strain (Nadai, 1963).

property lode: float

Return Lode parameter (Lode, 1926).

property P: float

Point index (Vollmer, 1990).

property G: float

Girdle index (Vollmer, 1990).

property R: float

Random index (Vollmer, 1990).

property B: float

Cylindricity index (Vollmer, 1990).

property Intensity: float

Intensity index (Lisle, 1985).

property aMAD_l: float

Return approximate angular deviation from the major axis along E1.

property aMAD_p: float

Return approximate deviation from the plane normal to E3.

property aMAD: float

Return approximate deviation according to shape

property MAD_l: float

Return maximum angular deviation (MAD) of linearly distributed vectors.

Kirschvink 1980

property MAD_p: float

Return maximum angular deviation (MAD) of planarly distributed vectors.

Kirschvink 1980

property MAD: float

Return maximum angular deviation (MAD)

class apsg.feature.OrientationTensor3(*args)

Bases: Ellipsoid

Represents an 3D orientation tensor, which characterize data distribution using eigenvalue method. See (Watson 1966, Scheidegger 1965).

See following methods and properties for additional operations.

Parameters

matrix (3x3 array_like) – Input data, that can be converted to 3x3 2D matrix. This includes lists, tuples and ndarrays. Array could be also Group (for backward compatibility)

Returns

OrientationTensor3 object

Example

>>> ot = ortensor([[8, 0, 0], [0, 2, 0], [0, 0, 1]])
>>> ot
OrientationTensor3
[[8 0 0]
 [0 2 0]
 [0 0 1]]
(S1:2.83, S2:1.41, S3:1)

classmethod from_features(g) → OrientationTensor3

Return Ortensor of data in Vector3Set of features

Parameters

g (Vector3Set) – Set of features

Example

>>> g = linset.random_fisher(position=lin(120,50))
>>> ot = ortensor.from_features(g)
>>> ot
OrientationTensor3
[[ 0.126 -0.149 -0.202]
 [-0.149  0.308  0.373]
 [-0.202  0.373  0.566]]
(S1:0.955, S2:0.219, S3:0.2)
>>> ot.eigenlins
(L:119/51, L:341/31, L:237/21)

classmethod from_pairs(p, shift=True) → OrientationTensor3

Return Lisle (1989) Ortensor of orthogonal data in PairSet

Lisle, R. (1989). The Statistical Analysis of Orthogonal Orientation Data.

The Journal of Geology, 97(3), 360-364.

Note: Tensor is by default shifted towards positive eigenvalues, so it

could be used as Scheidegger orientation tensor for plotting. When original Lisle tensor is needed, set shift to False.

Parameters

p – PairSet

Keyword Arguments

shift (bool) – When True the tensor is shifted. Default True

Example

>>> p = pairset([pair(109, 82, 21, 10),
                 pair(118, 76, 30, 11),
                 pair(97, 86, 7, 3),
                 pair(109, 75, 23, 14)])
>>> ot = ortensor.from_pairs(p)
>>> ot
OrientationTensor3
[[0.577 0.192 0.029]
 [0.192 0.092 0.075]
 [0.029 0.075 0.332]]
(S1:0.807, S2:0.579, S3:0.114)

class apsg.feature.DeformationGradient2(*args)

Bases: Matrix2

The class to represent 2D deformation gradient tensor.

Parameters

a (2x2 array_like) – Input data, that can be converted to 2x2 2D array. This includes lists, tuples and ndarrays.

Returns

DeformationGradient2 object

Example

>>> F = defgrad2(np.diag([2, 0.5]))

classmethod from_ratio(R=1)

Return isochoric DeformationGradient2 tensor with axial stretches defined by strain ratio. Default is identity tensor.

Keyword Arguments

R (float) – strain ratio

Example

>>> F = defgrad2.from_ratio(R=4)
>> F
DeformationGradient2
[[2.  0. ]
 [0.  0.5]]

classmethod from_angle(theta)

Return DeformationGradient2 representing rotation by angle theta.

Parameters

theta – Angle of rotation in degrees

Example

>>> F = defgrad2.from_angle(45)
>>> F
DeformationGradient2
[[ 0.707 -0.707]
 [ 0.707  0.707]]

property R

Return rotation part of DeformationGradient2 from polar decomposition.

property U

Return stretching part of DeformationGradient2 from right polar decomposition.

property V

Return stretching part of DeformationGradient2 from left polar decomposition.

angle()

Return rotation part of DeformationGradient2 as angle.

velgrad(time=1)

Return VelocityGradient2 for given time

class apsg.feature.VelocityGradient2(*args)

Bases: Matrix2

The class to represent 2D velocity gradient tensor.

Parameters

a (2x2 array_like) – Input data, that can be converted to 2x2 2D array. This includes lists, tuples and ndarrays.

Returns

VelocityGradient2 object

Example

>>> L = velgrad2(np.diag([0.1, -0.1]))

defgrad(time=1, steps=1)

Return DeformationGradient2 tensor accumulated after given time.

Keyword Arguments

• time (float) – time of deformation. Default 1

• steps (int) – when bigger than 1, will return a list of DeformationGradient2 tensors for each timestep.

rate()

Return rate of deformation tensor

spin()

Return spin tensor

class apsg.feature.Stress2(*args)

Bases: Tensor2

The class to represent 2D stress tensor.

Parameters

a (2x2 array_like) – Input data, that can be converted to 2x2 2D array. This includes lists, tuples and ndarrays.

Returns

Stress2 object

Example

>>> S = Stress2([[-8, 0, 0],[0, -5, 0],[0, 0, -1]])

classmethod from_comp(xx=0, xy=0, yy=0)

Return Stress2 tensor. Default is zero tensor.

Note that stress tensor must be symmetrical.

Keyword Arguments

yy (xx, xy,) – tensor components

Example

>>> S = stress2.from_comp(xx=-5, yy=-2, xy=1)
>>> S
Stress2
[[-5.  1.]
 [ 1. -2.]]

property mean_stress

Mean stress

property hydrostatic

Mean hydrostatic stress tensor component

property deviatoric

A stress deviator tensor component

property sigma1

A maximum principal stress (max compressive)

property sigma2

A minimum principal stress

property sigma1dir

Return unit length vector in direction of maximum principal stress (max compressive)

property sigma2dir

Return unit length vector in direction of minimum principal stress

property sigma1vec

Return maximum principal stress vector (max compressive)

property sigma2vec

Return minimum principal stress vector

property I1

First invariant

property I2

Second invariant

property I3

Third invariant

property diagonalized

Returns diagonalized Stress tensor and orthogonal matrix R, which transforms actual coordinate system to the principal one.

cauchy(n)

Return stress vector associated with plane given by normal vector.

Parameters

n – normal given as Vector2 object

Example

>>> S = Stress.from_comp(xx=-5, yy=-2, xy=1)
>>> S.cauchy(vec2(1,1))
V(-2.520, 0.812, 8.660)

stress_comp(n)

Return normal and shear stress Vector2 components on plane given by normal vector.

normal_stress(n)

Return normal stress magnitude on plane given by normal vector.

shear_stress(n)

Return shear stress magnitude on plane given by normal vector.

signed_shear_stress(n)

Return signed shear stress magnitude on plane given by normal vector.

class apsg.feature.Ellipse(*args)

Bases: Tensor2

The class to represent 2D ellipse

See following methods and properties for additional operations.

Parameters

matrix (2x2 array_like) – Input data, that can be converted to 2x2 2D matrix. This includes lists, tuples and ndarrays.

Returns

Ellipse object

Example

>>> E = ellipse([[8, 0], [0, 2]])
>>> E
Ellipse
[[8. 0.]
 [0. 2.]]
(ar:2, ori:0)

classmethod from_defgrad(F, form='left', **kwargs) → Ellipse

Return deformation tensor from Defgrad2.

Kwargs:

form: ‘left’ or ‘B’ for left Cauchy–Green deformation tensor or

Finger deformation tensor ‘right’ or ‘C’ for right Cauchy–Green deformation tensor or Green’s deformation tensor. Default is ‘left’.

classmethod from_stretch(x=1, y=1, **kwargs) → Ellipse

Return diagonal tensor defined by magnitudes of principal stretches.

property S1: float

Return the maximum principal stretch.

property S2: float

Return the minimum principal stretch.

property e1: float

Return the maximum natural principal strain.

property e2: float

Return the minimum natural principal strain.

property ar: float

Return the ellipse axial ratio.

property orientation

Return the orientation of the maximum eigenvector.

property e12: float

Return the difference between natural principal strains.

class apsg.feature.OrientationTensor2(*args)

Bases: Ellipse

Represents an 2D orientation tensor, which characterize data distribution using eigenvalue method. See (Watson 1966, Scheidegger 1965).

See following methods and properties for additional operations.

Parameters

matrix (2x2 array_like) – Input data, that can be converted to 2x2 2D matrix. This includes lists, tuples and ndarrays. Array could be also Group (for backward compatibility)

Returns

OrientationTensor2 object

Example

>>> v = vec2set.random(n=1000)
>>> ot = v.ortensor()
>>> ot
OrientationTensor2
[[ 0.502 -0.011]
 [-0.011  0.498]]
(ar:1.02, ori:140)

classmethod from_features(g) → OrientationTensor2

Return Ortensor of data in Vector2Set features

Parameters

g (Vector2Set) – Set of features

Example

>>> v = vec2set.random_vonmises(position=120)
>>> ot = v.ortensor()
>>> ot
OrientationTensor2
[[ 0.377 -0.282]
 [-0.282  0.623]]
(ar:2.05, ori:123)

class apsg.feature.Vector2Set(data, name='Default')

Bases: FeatureSet

Class to store set of Vector2 features

property x

Return numpy array of x-components

property y

Return numpy array of y-components

property direction

Return array of direction angles

proj(vec)

Return projections of all features in Vector2Set onto vector.

dot(vec)

Return array of dot products of all features in Vector2Set with vector.

cross(other=None)

Return cross products of all features in Vector2Set

Without arguments it returns cross product of all pairs in dataset. If argument is Vector2Set of same length or single data object element-wise cross-products are calculated.

angle(other=None)

Return angles of all data in Vector2Set object

Without arguments it returns angles of all pairs in dataset. If argument is Vector2Set of same length or single data object element-wise angles are calculated.

normalized()

Return Vector2Set object with normalized (unit length) elements.

uv()

Return Vector2Set object with normalized (unit length) elements.

transform(F, **kwargs)

Return affine transformation of all features Vector2Set by matrix ‘F’.

Parameters

F – Transformation matrix. Array-like value e.g. DeformationGradient3

Keyword Arguments

norm – normalize transformed features. True or False. Default False

R(mean=False)

Return resultant of data in Vector2Set object.

Resultant is of same type as features in Vector2Set. Note that Axial2 is axial in nature so resultant can give other result than expected. Anyway for axial data orientation tensor analysis will give you right answer.

Parameters

mean – if True returns mean resultant. Default False

fisher_statistics()

Fisher’s statistics

fisher_statistics returns dictionary with keys:

k estimated precision parameter, csd estimated angular standard deviation a95 confidence limit

var()

Spherical variance based on resultant length (Mardia 1972).

var = 1 - abs(R) / n

delta()

Cone angle containing ~63% of the data in degrees.

For enough large sample it approach angular standard deviation (csd) of Fisher statistics

rdegree()

Degree of preffered orientation of vectors in Vector2Set.

D = 100 * (2 * abs(R) - n) / n

ortensor()

Return orientation tensor Ortensor of Group.

halfspace()

Change orientation of vectors in Vector2Set, so all have angle<=90 with resultant.

classmethod from_direction(angles, name='Default')

Create Vector2Set object from arrays of direction angles

Parameters

angles – list or angles

Keyword Arguments

name – name of Vector2Set object. Default is ‘Default’

Example

>>> f = vec2set.from_angles([120,130,140,125, 132. 131])

classmethod from_xy(x, y, name='Default')

Create Vector2Set object from arrays of x and y components

Parameters

• x – list or array of x components

• y – list or array of y components

Keyword Arguments

name – name of Vector2Set object. Default is ‘Default’

Example

>>> v = vec2set.from_xy([-0.4330127, -0.4330127, -0.66793414],
                        [0.75, 0.25, 0.60141061])

classmethod random(n=100, name='Default')

Method to create Vector2Set of features with uniformly distributed random orientation.

Keyword Arguments

• n – number of objects to be generated

• name – name of dataset. Default is ‘Default’

Example

>>> np.random.seed(58463123)
>>> l = vec2set.random(100)

classmethod random_vonmises(n=100, position=0, kappa=5, name='Default')

Return Vector2Set of random vectors sampled from von Mises distribution around center position with concentration kappa.

Parameters

• n – number of objects to be generated

• position – mean orientation given as angle. Default 0

• kappa – precision parameter of the distribution. Default 20

• name – name of dataset. Default is ‘Default’

Example

>>> l = linset.random_fisher(position=lin(120,50))

class apsg.feature.FeatureSet(data, name='Default')

Bases: object

Base class for containers

to_json()

Return as JSON dict

label()

Return label

rotate(axis, phi)

Rotate FeatureSet object phi degress about axis.

bootstrap(n=100, size=None)

Return generator of bootstraped samples from FeatureSet.

Parameters

• n – number of samples to be generated. Default 100.

• size – number of data in sample. Default is same as FeatureSet.

Example

>>> np.random.seed(6034782)
>>> l = Vector3Set.random_fisher(n=100, position=lin(120,40))
>>> sm = [lb.R() for lb in l.bootstrap()]
>>> l.fisher_statistics()
{'k': 19.91236110604979, 'a95': 3.249027370399397, 'csd': 18.15196473425630}
>>> Vector3Set(sm).fisher_statistics()
{'k': 1735.360206701859, 'a95': 0.3393224356447341, 'csd': 1.944420546779801}

class apsg.feature.Vector3Set(data, name='Default')

Bases: FeatureSet

Class to store set of Vector3 features

property x

Return numpy array of x-components

property y

Return numpy array of y-components

property z

Return numpy array of z-components

property geo

Return arrays of azi and inc according to apsg_conf[‘notation’]

to_lin()

Return LineationSet object with all data converted to Lineation.

to_fol()

Return FoliationSet object with all data converted to Foliation.

to_vec()

Return Vector3Set object with all data converted to Vector3.

project(vec)

Return projections of all features in FeatureSet onto vector.

proj(vec)

Return projections of all features in FeatureSet onto vector.

reject(vec)

Return rejections of all features in FeatureSet onto vector.

dot(vec)

Return array of dot products of all features in FeatureSet with vector.

cross(other=None)

Return cross products of all features in FeatureSet

Without arguments it returns cross product of all pairs in dataset. If argument is FeatureSet of same length or single data object element-wise cross-products are calculated.

angle(other=None)

Return angles of all data in FeatureSet object

Without arguments it returns angles of all pairs in dataset. If argument is FeatureSet of same length or single data object element-wise angles are calculated.

normalized()

Return FeatureSet object with normalized (unit length) elements.

uv()

Return FeatureSet object with normalized (unit length) elements.

transform(F, **kwargs)

Return affine transformation of all features FeatureSet by matrix ‘F’.

Parameters

F – Transformation matrix. Array-like value e.g. DeformationGradient3

Keyword Arguments

norm – normalize transformed features. True or False. Default False

is_upper()

Return boolean array of z-coordinate negative test

R(mean=False)

Return resultant of data in FeatureSet object.

Resultant is of same type as features in FeatureSet. Note that Foliation and Lineation are axial in nature so resultant can give other result than expected. Anyway for axial data orientation tensor analysis will give you right answer.

Parameters

mean – if True returns mean resultant. Default False

fisher_statistics()

Fisher’s statistics

fisher_statistics returns dictionary with keys:

k estimated precision parameter, csd estimated angular standard deviation a95 confidence limit

fisher_cone_a95()

Confidence limit cone based on Fisher’s statistics

Cone axis is resultant and apical angle is a95 confidence limit

fisher_cone_csd()

Angular standard deviation cone based on Fisher’s statistics

Cone axis is resultant and apical angle is angular standard deviation

var()

Spherical variance based on resultant length (Mardia 1972).

var = 1 - abs(R) / n

delta()

Cone angle containing ~63% of the data in degrees.

For enough large sample it approach angular standard deviation (csd) of Fisher statistics

rdegree()

Degree of preffered orientation of vectors in FeatureSet.

D = 100 * (2 * abs(R) - n) / n

ortensor()

Return orientation tensor Ortensor of Group.

centered(max_vertical=False)

Rotate FeatureSet object to position that eigenvectors are parallel to axes of coordinate system: E1||X (north-south), E2||X(east-west), E3||X(vertical)

Parameters

max_vertical – If True E1 is rotated to vertical. Default False

halfspace()

Change orientation of vectors in FeatureSet, so all have angle<=90 with resultant.

classmethod from_csv(filename, acol=0, icol=1)

Create FeatureSet object from csv file of azimuths and inclinations

Parameters

filename (str) – name of CSV file to load

Keyword Arguments

• acol (int or str) – azimuth column (starts from 0). Default 0

• icol (int or str) – inclination column (starts from 0). Default 1 When acol and icol are strings they are used as column headers.

Example

>>> gf = folset.from_csv('file1.csv')                 
>>> gl = linset.from_csv('file2.csv', acol=1, icol=2) 

to_csv(filename, delimiter=',')

Save FeatureSet object to csv file of azimuths and inclinations

Parameters

filename (str) – name of CSV file to save.

Keyword Arguments

delimiter (str) – values delimiter. Default ‘,’

Note: Written values are rounded according to ndigits settings in apsg_conf

classmethod from_array(azis, incs, name='Default')

Create FeatureSet object from arrays of azimuths and inclinations

Parameters

• azis – list or array of azimuths

• incs – list or array of inclinations

Keyword Arguments

name – name of FeatureSet object. Default is ‘Default’

Example

>>> f = folset.from_array([120,130,140], [10,20,30])
>>> l = linset.from_array([120,130,140], [10,20,30])

classmethod from_xyz(x, y, z, name='Default')

Create FeatureSet object from arrays of x, y and z components

Parameters

• x – list or array of x components

• y – list or array of y components

• z – list or array of z components

Keyword Arguments

name – name of FeatureSet object. Default is ‘Default’

Example

>>> v = vecset.from_xyz([-0.4330127, -0.4330127, -0.66793414],
                        [0.75, 0.25, 0.60141061],
                        [0.5, 0.8660254, 0.43837115])

classmethod random_normal(n=100, position=Vector3(0, 0, 1), sigma=20, name='Default')

Method to create FeatureSet of normaly distributed features.

Keyword Arguments

• n – number of objects to be generated

• position – mean orientation given as Vector3. Default Vector3(0, 0, 1)

• sigma – sigma of normal distribution. Default 20

• name – name of dataset. Default is ‘Default’

Example

>>> np.random.seed(58463123)
>>> l = linset.random_normal(100, lin(120, 40))
>>> l.R
L:120/39

classmethod random_fisher(n=100, position=Vector3(0, 0, 1), kappa=20, name='Default')

Return FeatureSet of random vectors sampled from von Mises Fisher distribution around center position with concentration kappa.

Parameters

• n – number of objects to be generated

• position – mean orientation given as Vector3. Default Vector3(0, 0, 1)

• kappa – precision parameter of the distribution. Default 20

• name – name of dataset. Default is ‘Default’

Example

>>> l = linset.random_fisher(position=lin(120,50))

classmethod random_fisher2(n=100, position=Vector3(0, 0, 1), kappa=20, name='Default')

Method to create FeatureSet of vectors distributed according to Fisher distribution.

Note: For proper von Mises Fisher distrinbution implementation use random.fisher method.

Parameters

• n – number of objects to be generated

• position – mean orientation given as Vector3. Default Vector3(0, 0, 1)

• kappa – precision parameter of the distribution. Default 20

• name – name of dataset. Default is ‘Default’

Example

>>> l = linset.random_fisher2(position=lin(120,50))

classmethod random_kent(p, n=100, kappa=20, beta=None, name='Default')

Return FeatureSet of random vectors sampled from Kent distribution (Kent, 1982) - The 5-parameter Fisher–Bingham distribution.

Parameters

• p – Pair object defining orientation of data

• N – number of objects to be generated

• kappa – concentration parameter. Default 20

• beta – ellipticity 0 <= beta < kappa

• name – name of dataset. Default is ‘Default’

Example

>>> p = pair(150, 40, 150, 40)
>>> l = linset.random_kent(p, n=300, kappa=30)

classmethod uniform_sfs(n=100, name='Default')

Method to create FeatureSet of uniformly distributed vectors. Spherical Fibonacci Spiral points on a sphere algorithm adopted from John Burkardt.

http://people.sc.fsu.edu/~jburkardt/

Keyword Arguments

• n – number of objects to be generated. Default 1000

• name – name of dataset. Default is ‘Default’

Example

>>> v = vecset.uniform_sfs(300)
>>> v.ortensor().eigenvalues()
(0.3334645347163635, 0.33333474915201167, 0.33320071613162483)

classmethod uniform_gss(n=100, name='Default')

Method to create FeatureSet of uniformly distributed vectors. Golden Section Spiral points on a sphere algorithm.

http://www.softimageblog.com/archives/115

Parameters

• n – number of objects to be generated. Default 1000

• name – name of dataset. Default is ‘Default’

Example

>>> v = vecset.uniform_gss(300)
>>> v.ortensor().eigenvalues()
(0.33335688569571587, 0.33332315115436933, 0.33331996314991513)

class apsg.feature.LineationSet(data, name='Default')

Bases: Vector3Set

Class to store set of Lineation features

class apsg.feature.FoliationSet(data, name='Default')

Bases: Vector3Set

Class to store set of Foliation features

dipvec()

Return FeatureSet object with plane dip vector.

class apsg.feature.PairSet(data, name='Default')

Bases: FeatureSet

Class to store set of Pair features

property fol

Return Foliations of pairs as FoliationSet

property fvec

Return planar normal vectors of pairs as Vector3Set

property lin

Return Lineation of pairs as LineationSet

property lvec

Return lineation vectors of pairs as Vector3Set

property misfit

Return array of misfits

property rax

Return vectors perpendicular to both planar and linear parts of pairs as Vector3Set

property ortensor

Return Lisle (1989) orientation tensor OrientationTensor3 of orientations defined by pairs

label()

Return label

classmethod random(n=25)

Create PairSet of random pairs

classmethod from_csv(filename, delimiter=',', facol=0, ficol=1, lacol=2, licol=3)

Read PairSet from csv file

to_csv(filename, delimiter=',')

Save PairSet object to csv file

Parameters

filename (str) – name of CSV file to save.

Keyword Arguments

delimiter (str) – values delimiter. Default ‘,’

Note: Written values are rounded according to ndigits settings in apsg_conf

classmethod from_array(fazis, fincs, lazis, lincs, name='Default')

Create PairSet from arrays of azimuths and inclinations

Parameters

• azis – list or array of azimuths

• incs – list or array of inclinations

Keyword Arguments

name – name of PairSet object. Default is ‘Default’

class apsg.feature.FaultSet(data, name='Default')

Bases: PairSet

Class to store set of Fault features

property sense

Return array of sense values

property p_vector

Return p-axes of FaultSet as Vector3Set

property t_vector

Return t-axes of FaultSet as Vector3Set

property p

Return p-axes of FaultSet as LineationSet

property t

Return t-axes of FaultSet as LineationSet

property m

Return m-planes of FaultSet as FoliationSet

property d

Return dihedra planes of FaultSet as FoliationSet

classmethod random(n=25)

Create PairSet of random pairs

classmethod from_csv(filename, delimiter=',', facol=0, ficol=1, lacol=2, licol=3, scol=4)

Read FaultSet from csv file

to_csv(filename, delimiter=',')

Save FaultSet object to csv file

Parameters

filename (str) – name of CSV file to save.

Keyword Arguments

delimiter (str) – values delimiter. Default ‘,’

Note: Written values are rounded according to ndigits settings in apsg_conf

classmethod from_array(fazis, fincs, lazis, lincs, senses, name='Default')

Create PairSet from arrays of azimuths and inclinations

Parameters

• azis – list or array of azimuths

• incs – list or array of inclinations

Keyword Arguments

name – name of PairSet object. Default is ‘Default’

class apsg.feature.ConeSet(data, name='Default')

Bases: FeatureSet

Class to store set of Cone features

class apsg.feature.EllipseSet(data, name='Default')

Bases: FeatureSet

Class to store set of Ellipse features

property S1: ndarray

Return the array of maximum principal stretches.

property S2: ndarray

Return the array of minimum principal stretches.

property e1: ndarray

Return the maximum natural principal strains.

property e2: ndarray

Return the array of minimum natural principal strains.

property ar: ndarray

Return the array of axial ratios.

property orientation: ndarray

Return the array of orientations of the maximum eigenvector.

property e12: ndarray

Return the array of differences between natural principal strains.

class apsg.feature.EllipsoidSet(data, name='Default')

Bases: FeatureSet

Class to store set of Ellipsoid features

property strength: ndarray

Return the array of the Woodcock strength.

property shape: ndarray

Return the array of the Woodcock shape.

property S1: ndarray

Return the array of maximum principal stretches.

property S2: ndarray

Return the array of middle principal stretches.

property S3: ndarray

Return the array of minimum principal stretches.

property e1: ndarray

Return the array of the maximum natural principal strain.

property e2: ndarray

Return the array of the middle natural principal strain.

property e3: ndarray

Return the array of the minimum natural principal strain.

property Rxy: ndarray

Return the array of the Rxy ratios.

property Ryz: ndarray

Return the array of the Ryz ratios.

property e12: ndarray

Return the array of the e1 - e2 values.

property e13: ndarray

Return the array of the e1 - e3 values.

property e23: ndarray

Return the array of the e2 - e3 values.

property k: ndarray

Return the array of the strain symmetries.

property d: ndarray

Return the array of the strain intensities.

property K: ndarray

Return the array of the strain symmetries K (Ramsay, 1983).

property D: ndarray

Return the array of the strain intensities D (Ramsay, 1983)..

property r: ndarray

Return the array of the strain intensities (Watterson, 1968).

property goct: ndarray

Return the array of the natural octahedral unit shears (Nadai, 1963).

property eoct: ndarray

Return the array of the natural octahedral unit strains (Nadai, 1963).

property lode: ndarray

Return the array of Lode parameters (Lode, 1926).

property P: ndarray

Return the array of Point indexes (Vollmer, 1990).

property G: ndarray

Return the array of Girdle indexes (Vollmer, 1990).

property R: ndarray

Return the array of Random indexes (Vollmer, 1990).

property B: ndarray

Return the array of Cylindricity indexes (Vollmer, 1990).

property Intensity: ndarray

Return the array of Intensity indexes (Lisle, 1985).

property aMAD_l: ndarray

Return approximate angular deviation from the major axis along E1.

property aMAD_p: ndarray

Return approximate deviation from the plane normal to E3.

property aMAD: ndarray

Return approximate deviation according to the shape

property MAD_l: ndarray

Return maximum angular deviation (MAD) of linearly distributed vectors. Kirschvink 1980

property MAD_p: ndarray

Return maximum angular deviation (MAD) of planarly distributed vectors. Kirschvink 1980

property MAD: ndarray

Return approximate deviation according to shape

class apsg.feature.OrientationTensor2Set(data, name='Default')

Bases: EllipseSet

Class to store set of OrientationTensor2 features

class apsg.feature.OrientationTensor3Set(data, name='Default')

Bases: EllipsoidSet

Class to store set of OrientationTensor3 features

apsg.feature.G(lst, name='Default')

Function to create appropriate container (FeatueSet) from list of features.

Parameters

lst (list) – Homogeneous list of objects of Vector2, Vector3, Lineation, Foliation, Pair, Cone, Ellipse or OrientationTensor3.

Keyword Arguments

name (str) – name of feature set. Default Default

Example

>>> fols = [fol(120,30), fol(130, 40), fol(126, 37)]
>>> f = G(fols)

class apsg.feature.ClusterSet(d, **kwargs)

Bases: object

Provides a hierarchical clustering using scipy.cluster routines. The distance matrix is calculated as an angle between features, where Foliation and Lineation use axial angles while Vector3 uses direction angles.

cluster(**kwargs)

Do clustering on data

Result is stored as tuple of Groups in groups property.

Keyword Arguments

• maxclust – number of clusters

• distance – maximum cophenetic distance in clusters

linkage(**kwargs)

Do linkage of distance matrix

Keyword Arguments

method – The linkage algorithm to use

dendrogram(**kwargs)

Show dendrogram

See scipy.cluster.hierarchy.dendrogram for possible kwargs.

elbow(no_plot=False, n=None)

Plot within groups variance vs. number of clusters. Elbow criterion could be used to determine number of clusters.

property R

Return group of clusters resultants.

class apsg.feature.Core(**kwargs)

Bases: object

Core class to store palemomagnetic analysis data

Keyword Arguments

• info –

• specimen –

• filename –

• alpha –

• beta –

• strike –

• dip –

• volume –

• date –

• steps –

• a95 –

• comments –

• vectors –

Returns

Core object instance

classmethod from_pmd(filename)

Return Core instance generated from PMD file.

Parameters

filename – PMD file

write_pmd(filename=None)

Save Core instance to PMD file.

Parameters

filename – PMD file

classmethod from_rs3(filename, exclude=['C', 'G'])

Return Core instance generated from PMD file.

Parameters

filename – Remasoft rs3 file

Kwargs:

exclude: Labels to be excluded. Default [‘C’, ‘G’]

write_rs3(filename=None)

Save Core instance to RS3 file.

Parameters

filename – RS3 file

property datatable

Return data list of strings

show()

Show data

property MAG

Returns numpy array of MAG values

property nsteps

Returns steps as numpy array of numbers

property V

Returns Vector3Set of vectors in sample (or core) coordinates system

property geo

Returns Vector3Set of vectors in in-situ coordinates system

property tilt

Returns Vector3Set of vectors in tilt‐corrected coordinates system

pca(kind='geo', origin=False)

PCA analysis to calculate principal component and MAD

Keyword Arguments

• kind (str) – “V”, “geo” or “tilt”. Default “geo”

• origin (bool) – Whether to include origin. Default False

plotting module

Classes:

StereoNet(**kwargs)	Plot features on stereographic projection
StereoGrid(**kwargs)	The class to store values with associated uniformly positions.
RosePlot(**kwargs)	RosePlot class for rose histogram plotting.
VollmerPlot(*args, **kwargs)	Represents the triangular fabric plot (Vollmer, 1989).
RamsayPlot(*args, **kwargs)	Represents the Ramsay deformation plot.
FlinnPlot(*args, **kwargs)	Represents the Ramsay deformation plot.
HsuPlot(*args, **kwargs)	Represents the Hsu fabric plot.

Functions:

quicknet(*args, **kwargs)

Function to quickly show or save StereoNet from args

class apsg.plotting.StereoNet(**kwargs)

Bases: object

Plot features on stereographic projection

Keyword Arguments

• title (str) – figure title. Default None.

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• tight_layout (bool) – Matplotlib figure tight_layout. Default False

• kind (str) – Equal area (“equal-area”, “schmidt” or “earea”) or equal angle (“equal-angle”, “wulff” or “eangle”) projection. Default is “equal-area”

• hemisphere (str) – “lower” or “upper”. Default is “lower”

• overlay_position (tuple or Pair) – Position of overlay X, Y, Z given by Pair. X is direction of linear element, Z is normal to planar. Default is (0, 0, 0, 0)

• rotate_data (bool) – Whether data should be rotated together with overlay. Default False

• minor_ticks (None or float) – Default None

• major_ticks (None or float) – Default None

• overlay (bool) – Whether to show overlay. Default is True

• overlay_step (float) – Grid step of overlay. Default 15

• overlay_resolution (float) – Resolution of overlay. Default 181

• clip_pole (float) – Clipped cone around poles. Default 15

• grid_type (str) – Type of contouring grid “gss” or “sfs”. Default “gss”

• grid_n (int) – Number of counting points in grid. Default 3000

Examples

>>> l = linset.random_fisher(position=lin(120, 40))
>>> s = StereoNet(title="Random linear features")
>>> s.contour(l)
>>> s.line(l)
>>> s.show()

clear()

Clear plot

to_json()

Return stereonet as JSON dict

classmethod from_json(json_dict)

Create stereonet from JSON dict

save(filename)

Save stereonet to pickle file

Parameters

filename (str) – name of picke file

classmethod load(filename)

Load stereonet from pickle file

Parameters

filename (str) – name of picke file

render2fig(fig)

Plot stereonet to already existing figure or subfigure

Parameters

fig (Figure) – A mtplotlib Figure artist

format_coord(x, y)

Format stereonet coordinates

show()

Show stereonet

savefig(filename='stereonet.png', **kwargs)

Save stereonet figure to graphics file

Keyword Arguments

filename (str) – filename

All others kwargs are passed to matplotlib Figure.savefig

line(*args, **kwargs)

Plot linear feature(s) as point(s)

Parameters

feature (Vector3 or Vector3Set like) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• mec (color) – Set the edge color. Default None

• mfc (color) – Set the face color. Default None

• mew (float) – Set the marker edge width. Default 1

• ms (float) – Set the marker size. Default 6

• marker (str) – Marker style string. Default “o”

• ls (str) – Line style string (only for multiple features). Default None

pole(*args, **kwargs)

Plot pole of planar feature(s) as point(s)

Parameters

feature (Foliation or FoliationSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• mec (color) – Set the edge color. Default None

• mfc (color) – Set the face color. Default None

• mew (float) – Set the marker edge width. Default 1

• ms (float) – Set the marker size. Default 6

• marker (str) – Marker style string. Default “o”

• ls (str) – Line style string (only for multiple features). Default None

vector(*args, **kwargs)

Plot vector feature(s) as point(s)

Note: Markers are filled on lower and open on upper hemisphere.

Parameters

feature (Vector3 or Vector3Set like) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• mec (color) – Set the edge color. Default None

• mfc (color) – Set the face color. Default None

• mew (float) – Set the marker edge width. Default 1

• ms (float) – Set the marker size. Default 6

• marker (str) – Marker style string. Default “o”

• ls (str) – Line style string (only for multiple features). Default None

scatter(*args, **kwargs)

Plot vector-like feature(s) as point(s)

Note: This method is using scatter plot to allow variable colors

or sizes of points

Parameters

feature (Vector3 or Vector3Set like) –

Keyword Arguments

• s (list or array) –

• c (list or array) –

• alpha (scalar) – Set the alpha value. Default None

• linewidths (float) – The linewidth of the marker edges. Default 1.5

• marker (str) – Marker style string. Default “o”

• cmap (str) – Mtplotlib colormap. Default None

• legend (bool) – Whether to show legend. Default False

• num (int) – NUmber of legend items. Default “auto”

great_circle(*args, **kwargs)

Plot planar feature(s) as great circle(s)

Note: great_circle has also alias gc

Parameters

feature (Foliation or FoliationSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

gc(*args, **kwargs)

Plot planar feature(s) as great circle(s)

Note: great_circle has also alias gc

Parameters

feature (Foliation or FoliationSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

arc(*args, **kwargs)

Plot arc bewtween vectors along great circle(s)

Note: You should pass several features in connection order

Parameters

feature (Vector3 or Vector3Set like) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

pair(*args, **kwargs)

Plot pair feature(s) as great circle and point

Parameters

feature (Pair or PairSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

• line_marker (str) – Marker style string for point. Default “o”

fault(*args, **kwargs)

Plot fault feature(s) as great circle and arrow

Note: Arrow is styled according to default arrow config

Parameters

feature (Fault or FaultSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

hoeppner(*args, **kwargs)

Plot fault feature(s) on Hoeppner (tangent lineation) plot

Note: Arrow is styled according to default arrow config

Parameters

feature (Fault or FaultSet) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

arrow(*args, **kwargs)

Plot arrow at position of first argument and oriented in direction of second

Note: You should pass two features

Parameters

feature (Vector3 or Vector3Set like) –

Keyword Arguments

• color (color) – Set the color of the arrow. Default None

• width (int) – Width of arrow. Default 2

• headwidth (int) – Width of arrow head. Default 5

• pivot (str) – Arrow pivot. Default “mid”

• units (str) – Arrow size units. Default “dots”

tensor(*args, **kwargs)

Plot principal planes or principal directions of tensor

Parameters

feature (OrientationTensor3 like) –

Keyword Arguments

• planes (bool) – When True, plot principal planes, otherwise principal directions. Default True

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color. Default is red, green, blue for s1, s2, s3

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

• mew (float) – Set the marker edge width. Default 1

• ms (float) – Set the marker size. Default 9

• marker (str) – Marker style string. Default “o”

contour(*args, **kwargs)

Plot filled contours using modified Kamb contouring technique with exponential smoothing.

Parameters

feature (Vector3Set like) –

Keyword Arguments

• levels (int or list) – number or values of contours. Default 6

• cmap – matplotlib colormap used for filled contours. Default “Greys”

• colorbar (bool) – Show colorbar. Default False

• alpha (float) – transparency. Default None

• antialiased (bool) – Default True

• sigma (float) – If None it is automatically calculated

• sigmanorm (bool) – If True scaled counts are normalized by sigma. Default True

• trimzero (bool) – Remove values equal to 0. Default True

• clines (bool) – Show contour lines instead filled contours. Default False

• linewidths (float) – contour lines width

• linestyles (str) – contour lines style

• show_data (bool) – Show data as points. Default False

• data_kws (dict) – arguments passed to point factory when show_data True

class apsg.plotting.StereoGrid(**kwargs)

Bases: object

The class to store values with associated uniformly positions.

StereoGrid is used to calculate continous functions on sphere e.g. density distribution.

Keyword Arguments

• kind (str) – Equal area (“equal-area”, “schmidt” or “earea”) or equal angle (“equal-angle”, “wulff” or “eangle”) projection. Default is “equal-area”

• hemisphere (str) – “lower” or “upper”. Default is “lower”

• overlay_position (tuple or Pair) – Position of overlay X, Y, Z given by Pair. X is direction of linear element, Z is normal to planar. Default is (0, 0, 0, 0)

• rotate_data (bool) – Whether data should be rotated together with overlay. Default False

• minor_ticks (None or float) – Default None

• major_ticks (None or float) – Default None

• overlay (bool) – Whether to show overlay. Default is True

• overlay_step (float) – Grid step of overlay. Default 15

• overlay_resolution (float) – Resolution of overlay. Default 181

• clip_pole (float) – Clipped cone around poles. Default 15

• grid_type (str) – Type of contouring grid “gss” or “sfs”. Default “gss”

• grid_n (int) – Number of counting points in grid. Default 3000

Note: Euclidean norms are used as weights. Normalize data if you dont want to use weigths.

min()

Returns minimum value of the grid

max()

Returns maximum value of the grid

min_at()

Returns position of minimum value of the grid as Lineation

max_at()

Returns position of maximum value of the grid as Lineation

calculate_density(features, **kwargs)

Calculate density distribution of vectors from FeatureSet object.

The modified Kamb contouring technique with exponential smoothing is used.

Parameters

• sigma (float) – if none sigma is calculated automatically. Default None

• sigmanorm (bool) – If True counting is normalized to sigma multiples. Default True

• trimzero – if True, zero contour is not drawn. Default True

density_lookup(v)

Calculate density distribution value at position given by vector

Note: you need to calculate density before using this method

Parameters

v – Vector3 like object

Keyword Arguments

p (int) – power. Default 2

apply_func(func, *args, **kwargs)

Calculate values of user-defined function on sphere.

Function must accept Vector3 like (or 3 elements array) as first argument and return scalar value.

Parameters

• func (function) – function used to calculate values

• *args – passed to function func as args

• **kwargs – passed to function func as kwargs

contourf(*args, **kwargs)

Draw filled contours of values using tricontourf.

Keyword Arguments

• levels (int or list) – number or values of contours. Default 6

• cmap – matplotlib colormap used for filled contours. Default “Greys”

• colorbar (bool) – Show colorbar. Default False

• alpha (float) – transparency. Default None

• antialiased (bool) – Default True

contour(*args, **kwargs)

Draw contour lines of values using tricontour.

Keyword Arguments

• levels (int or list) – number or values of contours. Default 6

• cmap – matplotlib colormap used for filled contours. Default “Greys”

• colorbar (bool) – Show colorbar. Default False

• alpha (float) – transparency. Default None

• antialiased (bool) – Default True

• linewidths (float) – contour lines width

• linestyles (str) – contour lines style

plotcountgrid(**kwargs)

Show counting grid.

angmech(faults, **kwargs)

Implementation of Angelier-Mechler dihedra method

Parameters

faults – FaultSet of data

Kwargs:

method: ‘probability’ or ‘classic’. Classic method assigns +/-1 to individual positions, while ‘probability’ returns maximum likelihood estimate. Other kwargs are passed to contourf

class apsg.plotting.RosePlot(**kwargs)

Bases: object

RosePlot class for rose histogram plotting.

Keyword Arguments

• title (str) – figure title. Default None

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• bins (int) – Number of bins. Default 36

• axial (bool) – Directional data are axial. Defaut True

• density (bool) – Use density instead of counts. Default False

• pdf (bool) – Plot Von Mises density function instead histogram. Default False

• pdf_res (int) – Resolution of pdf. Default 901

• kappa (float) – Shape parameter of Von Mises pdf. Default 250

• scaled (bool) – Bins scaled by area instead value. Default False

• ticks (bool) – show ticks. Default True

• grid (bool) – show grid lines. Default False

• grid_kws (dict) – Dict passed to Axes.grid. Default {}

• plot. (Other keyword arguments are passed to matplotlib) –

Examples

>>> v = vec2set.random_vonmises(position=120)
>>> p = RosePlot(grid=False)
>>> p.pdf(v)
>>> p.bar(v, fc='none', ec='k', lw=1)
>>> p.muci(v)
>>> p.show()

clear()

Clear plot

to_json()

Return rose plot as JSON dict

classmethod from_json(json_dict)

Create rose plot from JSON dict

save(filename)

Save stereonet to pickle file

Parameters

filename (str) – name of picke file

classmethod load(filename)

Load stereonet from pickle file

Parameters

filename (str) – name of picke file

render2fig(fig)

Plot stereonet to already existing figure or subfigure

Parameters

fig (Figure) – A mtplotlib Figure artist

show()

Show rose plot

savefig(filename='roseplot.png', **kwargs)

Save rose plot figure to graphics file

Keyword Arguments

filename (str) – filename

All others kwargs are passed to matplotlib Figure.savefig

bar(*args, **kwargs)

Plot rose histogram of angles

Parameters

feature (Vector2Set) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ec (color) – Patch edge color. Default None

• fc (color) – Patch face color. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

• legend (bool) – Whether to show legend. Default False

pdf(*args, **kwargs)

Plot Von Mises probability density function from angles

Parameters

feature (Vector2Set) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ec (color) – Patch edge color. Default None

• fc (color) – Patch face color. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

• legend (bool) – Whether to show legend. Default False

• weight (float) – Factor to scale probability density function Default 1

muci(*args, **kwargs)

Plot circular mean with bootstrapped confidence interval

Parameters

feature (Vector2Set) –

Keyword Arguments

• alpha (scalar) – Set the alpha value. Default None

• color (color) – Set the color of the point. Default None

• ls (str) – Line style string (only for multiple features). Default “-”

• lw (float) – Set line width. Default 1.5

• confidence_level (float) – Confidence interval. Default 95

• n_resamples (int) – Number of bootstrapped samples. Default 9999

class apsg.plotting.VollmerPlot(*args, **kwargs)

Bases: FabricPlot

Represents the triangular fabric plot (Vollmer, 1989).

Keyword Arguments

• title (str) – figure title. Default None.

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• ticks (bool) – Show ticks. Default True

• n_ticks (int) – Number of ticks. Default 10

• tick_size (float) – Size of ticks. Default 0.2

• margin (float) – Size of margin. Default 0.05

• grid (bool) – Show grid. Default is True

• grid_color (str) – Matplotlib color of the grid. Default “k”

• grid_style (str) – Matplotlib style of the grid. Default “:”

Examples

>>> l = linset.random_fisher(position=lin(120, 40))
>>> ot = l.ortensor()
>>> s = VollmerPlot(title="Point distribution")
>>> s.point(ot)
>>> s.show()

point(*args, **kwargs)

Plot ellipsoid as point

path(*args, **kwargs)

Plot EllipsoidSet as path

class apsg.plotting.RamsayPlot(*args, **kwargs)

Bases: FabricPlot

Represents the Ramsay deformation plot.

Keyword Arguments

• title (str) – figure title. Default None.

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• ticks (bool) – Show ticks. Default True

• n_ticks (int) – Number of ticks. Default 10

• tick_size (float) – Size of ticks. Default 0.2

• margin (float) – Size of margin. Default 0.05

• grid (bool) – Show grid. Default is True

• grid_color (str) – Matplotlib color of the grid. Default “k”

• grid_style (str) – Matplotlib style of the grid. Default “:”

Examples

>>> l = linset.random_fisher(position=lin(120, 40))
>>> ot = l.ortensor()
>>> s = RamsayPlot(title="Point distribution")
>>> s.point(ot)
>>> s.show()

point(*args, **kwargs)

Plot ellipsoid as point

path(*args, **kwargs)

Plot EllipsoidSet as path

class apsg.plotting.FlinnPlot(*args, **kwargs)

Bases: FabricPlot

Represents the Ramsay deformation plot.

Keyword Arguments

• title (str) – figure title. Default None.

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• ticks (bool) – Show ticks. Default True

• n_ticks (int) – Number of ticks. Default 10

• tick_size (float) – Size of ticks. Default 0.2

• margin (float) – Size of margin. Default 0.05

• grid (bool) – Show grid. Default is True

• grid_color (str) – Matplotlib color of the grid. Default “k”

• grid_style (str) – Matplotlib style of the grid. Default “:”

Examples

>>> l = linset.random_fisher(position=lin(120, 40))
>>> ot = l.ortensor()
>>> s = FlinnPlot(title="Point distribution")
>>> s.point(ot)
>>> s.show()

point(*args, **kwargs)

Plot Ellipsoid as point

path(*args, **kwargs)

Plot EllipsoidSet as path

class apsg.plotting.HsuPlot(*args, **kwargs)

Bases: FabricPlot

Represents the Hsu fabric plot.

Keyword Arguments

• title (str) – figure title. Default None.

• title_kws (dict) – dictionary of keyword arguments passed to matplotlib suptitle method.

• ticks (bool) – Show ticks. Default True

• n_ticks (int) – Number of ticks. Default 10

• tick_size (float) – Size of ticks. Default 0.2

• margin (float) – Size of margin. Default 0.05

• grid (bool) – Show grid. Default is True

• grid_color (str) – Matplotlib color of the grid. Default “k”

• grid_style (str) – Matplotlib style of the grid. Default “:”

Examples

>>> l = linset.random_fisher(position=lin(120, 40))
>>> ot = l.ortensor()
>>> s = HsuPlot(title="Point distribution")
>>> s.point(ot)
>>> s.show()

point(*args, **kwargs)

Plot Ellipsoid as point

path(*args, **kwargs)

Plot EllipsoidSet as path

apsg.plotting.quicknet(*args, **kwargs)

Function to quickly show or save StereoNet from args

Parameters

args – object(s) to be plotted. Instaces of Vector3, Foliation, Lineation, Pair, Fault, Cone, Vector3Set, FoliationSet, LineationSet, PairSet or FaultSet.

Keyword Arguments

• savefig (bool) – True to save figure. Default False

• filename (str) – filename for figure. Default stereonet.png

• savefig_kwargs (dict) – dict passed to plt.savefig

• fol_as_pole (bool) – True to plot planar features as poles, False for plotting as great circle. Default True

Example

>>> l = linset.random_fisher(position=lin(120, 50))
>>> f = folset.random_fisher(position=lin(300, 40))
>>> quicknet(f, l, fol_as_pole=False)

pandas module

This module provide basic integration with pandas.

Classes:

VectorSetBaseAccessor(pandas_obj)	Base class of DataFrame accessors provides methods for FeatureSet
APSGAccessor(pandas_obj)	apsg DataFrame accessor to create aspg columns from data
Vec3Accessor(pandas_obj)	vec DataFrame accessor provides methods for Vector3Set
FolAccessor(pandas_obj)	fol DataFrame accessor provides methods for FoliationSet
LinAccessor(pandas_obj)	lin DataFrame accessor provides methods for LineationSet
FaultAccessor(pandas_obj)	fault DataFrame accessor provides methods for FaultSet
Vector3Array(vecs)	Custom Extension Array type for an array of Vector3
FolArray(fols)	Custom Extension Array type for an array of fols
LinArray(lins)	Custom Extension Array type for an array of lins
FaultArray(faults)	Custom Extension Array type for an array of faults

class apsg.pandas.VectorSetBaseAccessor(pandas_obj)

Bases: object

Base class of DataFrame accessors provides methods for FeatureSet

property getset

Get FeatureSet

R()

Return resultant of data in FeatureSet.

fisher_k()

Precision parameter based on Fisher’s statistics

fisher_csd()

Angular standard deviation based on Fisher’s statistics

fisher_a95()

95% confidence limit based on Fisher’s statistics

var()

Spherical variance based on resultant length (Mardia 1972).

var = 1 - abs(R) / n

delta()

Cone angle containing ~63% of the data in degrees.

For enough large sample it approach angular standard deviation (csd) of Fisher statistics

rdegree()

Degree of preffered orientation of vectors in FeatureSet.

D = 100 * (2 * abs(R) - n) / n

ortensor()

Return orientation tensor Ortensor of vectors in FeatureSet.

contour(snet=None, **kwargs)

Plot data contours on StereoNet

class apsg.pandas.APSGAccessor(pandas_obj)

Bases: object

apsg DataFrame accessor to create aspg columns from data

create_vecs(columns=['x', 'y', 'z'], name='vecs')

Create column with Vector3 features

Keyword Arguments

• columns (list) – Columns containing either x, y and z components or azi and inc. Default [“x”, “y”, “z”]

• name (str) – Name of created column. Default ‘vecs’

create_fols(columns=['azi', 'inc'], name='fols')

Create column with Foliation features

Keyword Arguments

• columns (list) – Columns containing azi and inc. Default [“azi”, “inc”]

• name (str) – Name of created column. Default ‘fols’

create_lins(columns=['azi', 'inc'], name='lins')

Create column with Lineation features

Keyword Arguments

• columns (list) – Columns containing azi and inc. Default [“azi”, “inc”]

• name (str) – Name of created column. Default ‘lins’

create_faults(columns=['fazi', 'finc', 'lazi', 'linc', 'sense'], name='faults')

Create column with Fault features

Keyword Arguments

• columns (list) – Columns containing azi and inc. Default [‘fazi’, ‘finc’, ‘lazi’, ‘linc’, ‘sense’]

• name (str) – Name of created column. Default ‘lins’

class apsg.pandas.Vec3Accessor(pandas_obj)

Bases: VectorSetBaseAccessor

vec DataFrame accessor provides methods for Vector3Set

plot(snet=None, **kwargs)

Plot vecs as vectors on StereoNet

class apsg.pandas.FolAccessor(pandas_obj)

Bases: VectorSetBaseAccessor

fol DataFrame accessor provides methods for FoliationSet

plot(snet=None, aspole=False, **kwargs)

Plot fols as great circles on StereoNet

class apsg.pandas.LinAccessor(pandas_obj)

Bases: VectorSetBaseAccessor

lin DataFrame accessor provides methods for LineationSet

plot(snet=None, **kwargs)

Plot lins as line on StereoNet

class apsg.pandas.FaultAccessor(pandas_obj)

Bases: object

fault DataFrame accessor provides methods for FaultSet

property getset

Get FeatureSet

plot(snet=None, **kwargs)

Plot vecs as vectors on StereoNet

class apsg.pandas.Vector3Array(vecs)

Bases: ExtensionArray

Custom Extension Array type for an array of Vector3

property dtype

Return Dtype instance (not class) associated with this Array

property nbytes

The number of bytes needed to store this object in memory.

isna()

Returns a 1-D array indicating if each value is missing

take(indices, *, allow_fill=False, fill_value=None)

Take element from array using positional indexing

copy()

Return copy of array

class apsg.pandas.FolArray(fols)

Bases: Vector3Array

Custom Extension Array type for an array of fols

property dtype

Return Dtype instance (not class) associated with this Array

class apsg.pandas.LinArray(lins)

Bases: Vector3Array

Custom Extension Array type for an array of lins

property dtype

Return Dtype instance (not class) associated with this Array

class apsg.pandas.FaultArray(faults)

Bases: Vector3Array

Custom Extension Array type for an array of faults

property dtype

Return Dtype instance (not class) associated with this Array

database module

sqlalchemy interface to PySDB database

PySDB database is a simple sqlite3-based relational database to store structural data from the field. You can use apsg to manipulate the data or you can use the GUI application pysdb. There is also the QGIS plugin readsdb to plot data on a map or use map-based select to plot stereonets.

The following snippet demonstrate how to create database programmatically

>>> # Create database
>>> from apsg.database import SDBSession
>>> db = SDBSession('database.sdb', create=True)
>>> # Create unit
>>> unit = db.unit(name='DMU', description='Deamonic Magmatic Unit')
>>> # Create site
>>> site = db.site(unit=unit, name='LX001', x_coord=25934.36, y_coord=564122.5, description='diorite dyke')
>>> # Create structural types
>>> S2 = db.structype(structure='S2', description='Solid-state foliation', planar=1)
>>> L2 = db.structype(structure='L2', description='Solid-state lineation', planar=0)
>>> # Add measurement
>>> fol = db.add_structdata(site=site, structype=S2, azimuth=150, inclination=36)
>>> # Close database
>>> db.close()

You can tag individual data

>>> db = SDBSession('database.sdb')
>>> site = db.site(name='LX001')
>>> struct = db.structype(structure='S2')
>>> tag_plot = db.tag(name='plot')
>>> tag_ap = db.tag(name='AP')
>>> fol = db.add_structdata(site=site, structype=struct, azimuth=324, inclination=78, tags=[tag_plot, tag_ap])
>>> db.close()

or you can attach linear and planar features (e.g. fault data)

>>> db = SDBSession('database.sdb')
>>> unit = db.unit(name='DMU')
>>> site = db.site(name='LX001')
>>> S = db.structype(structure='S')
>>> L = db.structype(structure='L')
>>> fol = db.add_structdata(site=site, structype=S, azimuth=220, inclination=28)
>>> lin = db.add_structdata(site=site, structype=L, azimuth=212, inclination=26)
>>> pair = db.attach(fol, lin)
>>> db.close()

You can open existing database and select existing site and type of structure

>>> db = SDBSession('database.sdb')
>>> site = db.site(name='LX003')
>>> S2 = db.structype(structure='S2')
>>> L2 = db.structype(structure='L2')

and insert Foliation, Lineation or Pair directly

>>> f = fol(196, 39)
>>> l = lin(210, 37)
>>> db.add_fol(f, site=site, structype=S2)
>>> db.add_lin(l, site=site, structype=L2)
>>> p = Pair(258, 42, 220, 30)
>>> db.add_pair(p, S2, L2, site=site)
>>> db.close()

To retrieve data as FeatureSet you can use getset method:

>>> db = SDBSession('database.sdb')
>>> S2 = db.structype(structure='S2')
>>> g = db.getset(structype=S2)

or directly

>>> g = db.getset('S2')

Classes:

SDBSession(sdb_file, **kwargs)	SqlAlchemy interface to PySDB database
Meta(*args, **kwargs)
Site(*args, **kwargs)
Structdata(*args, **kwargs)
Structype(*args, **kwargs)
Tag(*args, **kwargs)
Unit(*args, **kwargs)
SDB(sdb_file)	sqlite3 based read-only interface to PySDB database

class apsg.database.SDBSession(sdb_file, **kwargs)

Bases: object

SqlAlchemy interface to PySDB database

Parameters

sdbfile (str) – filename of PySDB database

Keyword Arguments

• create (bool) – if True existing sdbfile will be deleted and new database will be created

• autocommit (bool) – if True, each operation is autocommitted

Example

>>> db = SDBSession('database.sdb', create=True)

close()

Close session

commit()

commit session

rollback()

rollback session

meta(name, **kwargs)

Insert, update or retrieve (when kwargs empty) Meta

Parameters

name (str) – meta name

Keyword Arguments

value (str) – meta value

Returns

Meta

site(name, **kwargs)

Insert, update or retrieve (when kwargs empty) Site

Parameters

name (str) – site name

Keyword Arguments

• x_coord (float) – x coord or longitude

• y_coord (float) – y coord or latitude

• description (str) – site description

• unit (Unit) – unit instance (mus be provided)

Returns

Site

unit(name, **kwargs)

Insert, update or retrieve (when kwargs empty) Unit

Parameters

name (str) – unit name

Keyword Arguments

description (str) – unit description

Returns

Unit

tag(name, **kwargs)

Insert, update or retrieve (when kwargs empty) Tag

Parameters

name (str) – tag name

Keyword Arguments

description (str) – tag description

Returns

Tag

structype(structure, **kwargs)

Insert, update or retrieve (when kwargs empty) Structype

Parameters

structure (str) – label for structure

Keyword Arguments

• description (str) – structype description

• planar (int) – 1 for planar 0 for linear

• structcode (int) – structcode (optional)

• groupcode (int) – groupcode (optional)

Returns

Structype

add_structdata(site, structype, azimuth, inclination, **kwargs)

Add structdata to site

Parameters

• site (Site) – site instance

• structype (Structype) – structype instance

• azimuth (float) – dip direction or plunge direction

• inclination (float) – dip or plunge

Keyword Arguments

description (str) – structdata description

Returns

Structdata

add_fol(site, structype, fol, **kwargs)

Add Foliation to site

Parameters

• site (Site) – site instance

• structype (Structype) – structype instance

• fol (Foliation) – foliation instance

Keyword Arguments

description (str) – structdata description

Returns

Structdata

add_lin(site, structype, lin, **kwargs)

Add Lineation to site

Parameters

• site (Site) – site instance

• structype (Structype) – structype instance

• lin (Lineation) – lineation instance

Keyword Arguments

description (str) – structdata description

Returns

Structdata

attach(fol, lin)

Add Lineation to site

Parameters

• fol (Foliation) – foliation instance

• lin (Lineation) – lineation instance

Returns

Attached

add_pair(pair, foltype, lintype, **kwargs)

Add attached foliation and lineation to database

Parameters

• pair (Pair) – pair instance

• foltype (Structype) – structype instance

• lintype (Structype) – structype instance

Returns

Attached

sites(**kwargs)

Retrieve Site or list of Sites based on criteria in kwargs

Keyword arguments are passed to sqlalchemy filter_by method

units(**kwargs)

Retrieve Unit or list of Units based on criteria in kwargs

Keyword arguments are passed to sqlalchemy filter_by method

structypes(**kwargs)

Retrieve Structype or list of Structypes based on criteria in kwargs

Keyword arguments are passed to sqlalchemy filter_by method

tags(**kwargs)

Retrieve Tag or list of Tags based on criteria in kwargs

Keyword arguments are passed to sqlalchemy filter_by method

getset(structype, **kwargs)

Method to retrieve data from SDB database to FeatureSet.

Parameters

structype (str, Structype) – structure or list of structures to retrieve

Keyword arguments are passed to sqlalchemy filter_by method

class apsg.database.Meta(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.Site(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.Structdata(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.Structype(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.Tag(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.Unit(*args: Any, **kwargs: Any)

Bases: declarative_base

class apsg.database.SDB(sdb_file)

Bases: object

sqlite3 based read-only interface to PySDB database

Parameters

sdbfile (str) – filename of PySDB database

Example

>>> db = SDB('database.sdb')

structures(**kwargs)

Return list of structures in database.

For kwargs see getset method

sites(**kwargs)

Return list of sites in database.

For kwargs see getset method.

units(**kwargs)

Return list of units in database.

For kwargs see getset method.

tags(**kwargs)

Return list of tags in database.

For kwargs see getset method.

getset(structs, **kwargs)

Method to retrieve data from SDB database to FeatureSet.

Parameters

structs (str) – structure or list of structures to retrieve

Keyword Arguments

• sites (str) – name or list of names of sites to retrieve from

• units (str) – name or list of names of units to retrieve from

• tags (str) – tag or list of tags to retrieve

• labels (bool) – if True return also list of sites. Default False

math module

This module provide basic linear algebra classes.

Classes:

Vector3(*args)	A class to represent a 3D vector.
Axial3(*args)	A class to represent a 3D axial vector.
Vector2(*args)	A class to represent a 2D vector.
Axial2(*args)	A class to represent a 2D axial vector.
Matrix3(*args)	A class to represent a 3x3 matrix.
Matrix2(*args)	A class to represent a 2x2 matrix.

class apsg.math.Vector3(*args)

Bases: Vector

A class to represent a 3D vector.

There are different way to create Vector3 object:

• without arguments create default Vector3 (1, 0, 0)

• with single argument v, where

  • v could be Vector3-like object

  • v could be string ‘x’, ‘y’ or ‘z’ - principal axes of coordinate system

  • v could be tuple of (x, y, z) - vector components

• with 2 arguments plunge direction and plunge

• with 3 numerical arguments defining vector components

Parameters

• azi (float) – plunge direction of linear feature in degrees

• inc (float) – plunge of linear feature in degrees

Example

>>> vec()
>>> vec(1,2,-1)
>>> vec('y')
>>> vec(120, 30)
>>> v = vec(1, -2, 1)

property z

Return z-component of the vector

normalized()

Returns normalized (unit length) vector

uv()

Returns normalized (unit length) vector

lower()

Change vector direction to point towards positive Z direction

is_upper()

Return True if vector points towards negative Z direction

property geo

Return tuple of plunge direction and signed plunge

classmethod unit_x()

Create unit length vector in x-direction

classmethod unit_y()

Create unit length vector in y-direction

classmethod unit_z()

Create unit length vector in z-direction

classmethod random()

Create random 3D vector

transform(F, **kwargs)

Return affine transformation of vector u by matrix F.

Parameters

F – transformation matrix

Keyword Arguments

norm – normalize transformed vectors. [True or False] Default False

Returns

vector representation of affine transformation (dot product) of self by F

Example

# Reflexion of y axis. >>> F = [[1, 0, 0], [0, -1, 0], [0, 0, 1]] >>> u = Vector3([1, 1, 1]) >>> u.transform(F) Vector3(1, -1, 1)

class apsg.math.Axial3(*args)

Bases: Vector3

A class to represent a 3D axial vector.

Note: the angle between axial data cannot be more than 90°

class apsg.math.Vector2(*args)

Bases: Vector

A class to represent a 2D vector.

There are different way to create Vector2 object:

• without arguments create default Vector2 (0, 0, 1)

• with single argument v, where

  • v could be Vector2-like object

  • v could be string ‘x’ or ‘y’ - principal axes of coordinate system

  • v could be tuple of (x, y) - vector components

  • v could be float - unit vector with given angle to ‘x’ axis

• with 2 numerical arguments defining vector components

Parameters

ang (float) – angle between ‘x’ axis and vector in degrees

Example

>>> vec2()
>>> vec2(1, -1)
>>> vec2('y')
>>> vec2(50)
>>> v = vec2(1, -2)

normalized()

Returns normalized (unit length) vector

uv()

Returns normalized (unit length) vector

property direction

Returns direction of the vector in degrees

classmethod random()

Random 2D vector

classmethod unit_x()

Create unit length vector in x-direction

classmethod unit_y()

Create unit length vector in y-direction

transform(*args, **kwargs)

Return affine transformation of vector u by matrix F.

Parameters

F – transformation matrix

Keyword Arguments

norm – normalize transformed vectors. [True or False] Default False

Returns

vector representation of affine transformation (dot product) of self by F

Example

# Reflexion of y axis. >>> F = [[1, 0], [0, -1]] >>> u = vec2([1, 1]) >>> u.transform(F) Vector2(1, -1)

class apsg.math.Axial2(*args)

Bases: Vector2

A class to represent a 2D axial vector.

Note: the angle between axial data cannot be more than 90°

class apsg.math.Matrix3(*args)

Bases: Matrix

A class to represent a 3x3 matrix.

There are different way to create Matrix3 object:

• without arguments create default identity Matrix3

• with single argument of Matrix3-like object

Parameters

v – 2-dimensional array-like object

Example

>>> Matrix3()
Matrix3
[[1 0 0]
 [0 1 0]
 [0 0 1]]
>>> A = Matrix3([[2, 1, 0], [0, 0.5, 0], [0, -0.5, 1]])

classmethod from_comp(xx=1, xy=0, xz=0, yx=0, yy=1, yz=0, zx=0, zy=0, zz=1)

Return Matrix3 defined by individual components. Default is identity tensor.

Keyword Arguments

• xx (float) – tensor component M_xx

• xy (float) – tensor component M_xy

• xz (float) – tensor component M_xz

• yx (float) – tensor component M_yx

• yy (float) – tensor component M_yy

• yz (float) – tensor component M_yz

• zx (float) – tensor component M_zx

• zy (float) – tensor component M_zy

• zz (float) – tensor component M_zz

Example

>>> F = Matrix3.from_comp(xy=1, zy=-0.5)
>>> F
[[ 1.   1.   0. ]
 [ 0.   1.   0. ]
 [ 0.  -0.5  1. ]]

property xz

Return xz-element of the matrix

property yz

Return yz-element of the matrix

property zx

Return zx-element of the matrix

property zy

Return zy-element of the matrix

property zz

Return zz-element of the matrix

property E3

Third eigenvalue

property V3

Third eigenvector

eigenvectors()

Return tuple of principal eigenvectors as Vector3 objects.

scaled_eigenvectors()

Return tuple of principal eigenvectors as Vector3 objects with magnitudes of eigenvalues

class apsg.math.Matrix2(*args)

Bases: Matrix

A class to represent a 2x2 matrix.

There are different way to create Matrix2 object:

• without arguments create default identity Matrix2

• with single argument of Matrix2-like object

Parameters

v – 2-dimensional array-like object

Example

>>> Matrix2()
Matrix2
[[1 0]
 [0 1]]
>>> A = Matrix2([[2, 1],[0, 0.5]])

classmethod from_comp(xx=1, xy=0, yx=0, yy=1)

Return Matrix2 defined by individual components. Default is identity tensor.

Keyword Arguments

• xx (float) – tensor component M_xx

• xy (float) – tensor component M_xy

• yx (float) – tensor component M_yx

• yy (float) – tensor component M_yy

Example

>>> F = Matrix2.from_comp(xy=2)
>>> F
[[1. 2.]
 [0. 1.]]

eigenvectors()

Return tuple of principal eigenvectors as Vector3 objects.

scaled_eigenvectors()

Return tuple of principal eigenvectors as Vector3 objects with magnitudes of eigenvalues

helpers module

apsg.helpers.sind(x)

Calculate sine of angle in degrees

apsg.helpers.cosd(x)

Calculate cosine of angle in degrees

apsg.helpers.tand(x)

Calculate tangent of angle in degrees

apsg.helpers.acosd(x)

Calculate arc cosine in degrees

apsg.helpers.asind(x)

Calculate arc sine in degrees

apsg.helpers.atand(x)

Calculate arc tangent in degrees

apsg.helpers.atan2d(y, x)

Calculate arc tangent in degrees in the range from pi to -pi.

Parameters

• y (float) – y coordinate

• x (float) – x coordinate

apsg.helpers.geo2vec_planar(*args)

Function to transform geological measurement of plane to normal vector

Conversion is done according to notation configuration

Parameters

• azi (float) – dip direction or strike

• inc (float) – dip

apsg.helpers.geo2vec_linear(*args)

Function to transform geological measurement of line to vector

Parameters

• azi (float) – plunge direction

• inc (float) – plunge

apsg.helpers.vec2geo_planar(arg)

Function to transform normal vector to geological measurement of plane

Conversion is done according to notation configuration

Parameters

v (Vector3) – Vector3 like object

apsg.helpers.vec2geo_linear(arg)

Function to transform vector to geological measurement of line

Parameters

v (Vector3) – Vector3 like object

Contributing

Contributions are welcome, and they are greatly appreciated! Every little bit helps, and credit will always be given.

You can contribute in many ways:

Types of Contributions

Report Bugs

Report bugs at https://github.com/ondrolexa/apsg/issues.

If you are reporting a bug, please include:

• Your operating system name and version.

• Any details about your local setup that might be helpful in troubleshooting.

• Detailed steps to reproduce the bug.

Fix Bugs

Look through the GitHub issues for bugs. Anything tagged with “bug” is open to whoever wants to implement it.

Implement Features

Look through the GitHub issues for features. Anything tagged with “feature” is open to whoever wants to implement it.

Write Documentation

APSG could always use more documentation, whether as part of the official APSG docs, in docstrings, or even on the web in blog posts, articles, and such.

Submit Feedback

The best way to send feedback is to file an issue at https://github.com/ondrolexa/apsg/issues.

If you are proposing a feature:

• Explain in detail how it would work.

• Keep the scope as narrow as possible, to make it easier to implement.

• Remember that this is a volunteer-driven project, and that contributions are welcome :)

Get Started!

Ready to contribute? Here’s how to set up apsg for local development.

1. Fork the apsg repo on GitHub.

2. Clone your fork locally with SSH or HTTPS:

   $ git clone git@github.com:ondrolexa/apsg.git
   
   $ git clone https://github.com/ondrolexa/apsg.git
   

3. Install your local copy and activate the virtual environment via pipenv.

   $ cd apsg/ $ pipenv shell $ pipenv install –dev

4. Create a branch for local development:

   $ git checkout -b name-of-your-bugfix-or-feature
   

6. Now you can make your changes locally.

7. When you’re done making changes, check that your changes pass flake8 and the tests, including testing other Python versions with tox:

   $ flake8 apsg tests
   $ python setup.py test
   $ tox
   

8. Commit your changes and push your branch to GitHub:

   $ git add .
   $ git commit -m "Your detailed description of your changes."
   $ git push origin name-of-your-bugfix-or-feature
   

9. Submit a pull request through the GitHub website.

Pull Request Guidelines

Before you submit a pull request, check that it meets these guidelines:

1. The pull request should include tests.

2. If the pull request adds functionality, the docs should be updated. Put your new functionality into a function with a docstring, and add the feature to the list in README.rst.

3. The pull request should work for Python 2.7, 3.5, and 3.6, and for PyPy. Check https://travis-ci.org/ondrolexa/apsg/pull_requests and make sure that the tests pass for all supported Python versions.

Credits

Development Lead

• Ondrej Lexa <lexa.ondrej@gmail.com>

Contributors

• David Landa <david.landa@natur.cuni.cz>