Transform Tensor

Transformation of a 3D-tensor of any order to another coordinate system.

FUNCTION
otr = transform(itr,tmx)

PARAMETERS
otr = output tensor, after transformation; has the same dimensions as the input tensor
itr = input tensor, before transformation; should be a 3-element vector, a 3x3 matrix, or a 3x3x3x... multidimensional array, each dimension containing 3 elements
tmx = transformation matrix, 3x3 matrix that contains the direction cosines between the old and the new coordinate system

DESCRIPTION
Tensors play an important role in several areas of physics and engineering. Perhaps the most important examples are the stress and strain tensor, which are both 2nd rank tensors. Both tensors are related by a 4th rank elasticity (compliance or stiffness) tensor, which is a material property. Calculation of stress or strain along a certain direction of a crystalline material, consisting of one or more differently oriented crystallites, often requires several coordinate transformations, for which this function might be useful.
It transforms a 3D-tensor (Euclidean or Cartesion tensor) of any order between two coordinate systems. An m-file, a c-file and a PC mex-file have been included. The m-file works for numeric as well as symbolic data, the mex-file only for numeric data. The mex-file is, of course, considerable faster than the m-file. However, if speed of calculation is really an issue a dedicated function for a tensor of a specific order would perform better.