math module

This module provide basic linear algebra classes.

Classes:

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

class apsg.math.Vector3(*args, **kwargs)

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 geo: Return tuple of plunge direction and signed plunge

is_upper(): Return True if vector points towards negative Z direction

lower(): Change vector direction to point towards positive Z direction

normalized(): Returns normalized (unit length) vector

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)

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

uv(): Returns normalized (unit length) vector

property z: Return z-component of the vector

class apsg.math.Axial3(*args, **kwargs)

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, **kwargs)

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)

property direction: Returns direction of the vector in degrees

normalized(): Returns normalized (unit length) vector

classmethod random(): Random 2D vector

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)

classmethod unit_x(): Create unit length vector in x-direction

classmethod unit_y(): Create unit length vector in y-direction

uv(): Returns normalized (unit length) vector

class apsg.math.Axial2(*args, **kwargs)

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, **kwargs)

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

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

property E1: First eigenvalue

property E2: Second eigenvalue

property E3: Third eigenvalue

property V1: First eigenvector

property V2: Second eigenvector

property V3: Third eigenvector

eigenvectors(): Return tuple of principal eigenvectors as Vector3 objects.

classmethod from_comp(**kwargs)

Return Matrix3 defined by individual components. Default is zero matrix.

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

>>> M = matrix.from_comp(xy=1, zy=-0.5)
>>> M
[[ 0.   1.   0. ]
 [ 0.   0.   0. ]
 [ 0.  -0.5  0. ]]

scaled_eigenvectors(): Return tuple of principal eigenvectors as Vector3 objects with magnitudes of eigenvalues

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

class apsg.math.Matrix2(*args, **kwargs)

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]])

property E1: First eigenvalue

property E2: Second eigenvalue

property V1: First eigenvector

property V2: Second eigenvector

eigenvectors(): Return tuple of principal eigenvectors as Vector3 objects.

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

Return Matrix2 defined by individual components. Default is zero matrix.

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

>>> M = matrix2.from_comp(xy=2)
>>> M
Matrix2
[[0. 2.]
 [0. 0.]]

scaled_eigenvectors(): Return tuple of principal eigenvectors as Vector3 objects with magnitudes of eigenvalues