Python: module mat3

mat3

3x3 matrix class In addition to the classes and functions described here, there is the function rotVector(vec, angle) - return matrix corresponding to rotation about 3-vector vec by angle (in radians)

Classes

cdsMatrix.CDSMatrix_double(builtins.object)

Mat3

cdsMatrix.SymMatrix_double(builtins.object)

SymMat3

class Mat3(cdsMatrix.CDSMatrix_double)

Mat3(m11=0, m12=0, m13=0, m21=0, m22=0, m23=0, m31=0, m32=0, m33=0, colVecs=None, rowVecs=None)

Method resolution order:: Mat3; cdsMatrix.CDSMatrix_double; builtins.object

Methods defined here:

__init__(s, m11=0, m12=0, m13=0, m21=0, m22=0, m23=0, m31=0, m32=0, m33=0, colVecs=None, rowVecs=None): Mat3 has a specialized constructor which allows all matrix elements
to be enumerated as arguments. example:
m=Mat3(1,2,3,
4,5,6,
7,8,9)

Matrix elements can alternatively be specified by passng 3 3-vecs,
specified as column- or row- vectors.

__mul__(s, x)

Methods inherited from cdsMatrix.CDSMatrix_double:

__add__(self, *args, **kwargs) -> 'CDSMatrix< double >'

__getitem__(self, *args, **kwargs) -> 'double'

__iadd__(self, *args, **kwargs) -> 'CDSMatrix< double >'

__neg__(self, *args, **kwargs) -> 'CDSMatrix< double >'

__repr__(self, *args, **kwargs) -> 'String': Return repr(self).

__rmul__(self, *args, **kwargs) -> 'CDSMatrix< double >'

__setitem__(self, *args, **kwargs) -> 'void'

__str__(self, *args, **kwargs) -> 'String': Return str(self).

__sub__(self, *args, **kwargs) -> 'CDSMatrix< double >'

add(self, *args, **kwargs) -> 'void'

cols(self, *args, **kwargs) -> 'int'

fromList(s, l)

get(self, *args, **kwargs) -> 'double'

rawData(self, *args, **kwargs) -> 'CDSVector< double >'

resize(self, *args, **kwargs) -> 'void'

rows(self, *args, **kwargs) -> 'int'

scale(self, *args, **kwargs) -> 'void'

set(self, *args) -> 'void'

setDiag(self, *args) -> 'void'

Static methods inherited from cdsMatrix.CDSMatrix_double:

__swig_destroy__ = delete_CDSMatrix_double(...)

Data descriptors inherited from cdsMatrix.CDSMatrix_double:

__dict__: dictionary for instance variables (if defined)

__weakref__: list of weak references to the object (if defined)

thisown: The membership flag

class SymMat3(cdsMatrix.SymMatrix_double)

SymMat3(a=0, b=0, c=0, d=0, e=0, f=0)

Method resolution order:: SymMat3; cdsMatrix.SymMatrix_double; builtins.object

Methods defined here:

__init__(s, a=0, b=0, c=0, d=0, e=0, f=0): SymMat3 has a specialized constructor which allows lower triangular
elements to be enumerated as arguments. example:
m=SymMat3(m11,
m12,m22,
m13,m23,m33)

Methods inherited from cdsMatrix.SymMatrix_double:

__add__(self, *args, **kwargs) -> 'SymMatrix< double >'

__getitem__(self, *args, **kwargs) -> 'double'

__iadd__(self, *args, **kwargs) -> 'SymMatrix< double >'

__mul__(self, *args) -> 'CDSVector< double >'

__repr__(self, *args, **kwargs) -> 'String': Return repr(self).

__rmul__(self, *args, **kwargs) -> 'SymMatrix< double >'

__setitem__(self, *args, **kwargs) -> 'void'

__str__(self, *args, **kwargs) -> 'String': Return str(self).

__sub__(self, *args, **kwargs) -> 'SymMatrix< double >'

cols(self, *args, **kwargs) -> 'int'

rows(self, *args, **kwargs) -> 'int'

scale(self, *args, **kwargs) -> 'void'

set(self, *args) -> 'void'

setDiag(self, *args, **kwargs) -> 'void'

Static methods inherited from cdsMatrix.SymMatrix_double:

__swig_destroy__ = delete_SymMatrix_double(...)

Data descriptors inherited from cdsMatrix.SymMatrix_double:

__dict__: dictionary for instance variables (if defined)

__weakref__: list of weak references to the object (if defined)

thisown: The membership flag

Functions

outerProd(v1, v2)

randOrient(): Return a random orientation :math:`u`, which is
performed in
spherical polar coordinates- with the these variables sampled
uniformly: azimuthal angle :math:`  heta` in the range :math:`-\pi..\pi`,
and the
cosine of the polar angle :math:`\phi` in the range -1..1.

A vec3.Vec3 is returned: :math:`(\cos(  heta)\sin(\phi),
                              \sin( heta)\sin(\phi),
                              \cos(\phi))`

randRot(deltaAngle=3.141592653589793): Return a random rotation by an amount up to deltaAngle.
This is accomplished by first choosing an random direction using
randOrient(), and the choosing a random rotation amount 0..deltaAngle,
with the distribution

   P(alpha) = 2/deltaAngle sin^2(alpha / 2)

such that the distributions of rotations are biased away from zero
rotation.

Reference: Rotation, Reflection, and Frame Changes
    Orthogonal tensors in computational engineering mechanics
                    R M Brannon
IOP Publishing (2018)

DOI: 10.1088/978-0-7503-1454-1

rotVector(uvec, angle): uvec, angle) - return matrix corresponding to rotation about
3-vector uvec by angle (in radians).

R = c * I + (1-c) * uvec * uvec^T + s * crossMat(uvec)

where c = cos(angle), s = sin(angle), and crossMat(v) is the matrix
associated with vector v s.t. crossMat(v) u = u X v.

rotationAmount(R): given rotation matrix R, determine and return the magnitude of the
associated rotation, in radians.

Data
		pi = 3.141592653589793