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, by using the colVecs or rowVecs keyword arguments, respectively:   m=Mat3(colVecs=[v1,v2,v3]) or m=Mat3(rowVecs=[v1,v2,v3]) __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