GooseTensor

Python module to perform simple tensor multiplications. This module is extremely compact and simple, as it just provides a front-end for the C++ library <cppmat/tensor.h>.

The module is based on three types of tensors, which are each NumPy arrays (below exemplified using zero-tensors):

The cppmat tensors with a special structure (i.e. cppmat::tensor2s and cppmat::tensor2d) are not available from Python.

The following functions are available, whereby the trailing (two) number(s) of both the functions and the variables are indicative for the rank of the input tensor(s).

• C4 = ddot44 ( A4, B4 )

  Double tensor contraction C_ijmn = A_ijkl B_lkmn

• C2 = ddot42 ( A4 , B2 )

  Double tensor contraction C_ij = A_ijkl B_lk

• C2 = ddot24 ( A2 , B4 )

  Double tensor contraction C_kl = A_ij B_jikl

• C = ddot22 ( A2 , B2 )

  Double tensor contraction C = A_ij B_ji

• C2 = dot22 ( A2 , B2 )

  Tensor contraction C_ik = A_ij B_jk

• C1 = dot21 ( A2 , B1 )

  Tensor contraction C_i = A_ij B_j

• C1 = dot12 ( A1 , B2 )

  Tensor contraction C_j = A_i B_ij

• C = dot11 ( A1 , B1 )

  Tensor contraction C = A_i B_i

• C4 = dyadic22 ( A2 , B2 )

  Dyadic product C_ijkl = A_ij B_kl

• C2 = dyadic11 ( A1 , B1 )

  Dyadic product C_ij = A_i B_j

• C1 = cross ( A1 , B1 )

  Cross product C_i

• C4 = transpose4 ( A4 )

  Transposition C_lkji = A_ijkl

• C4 = transpose4L ( A4 )

  Left-transposition C_jikl = A_ijkl

• C4 = transpose4R ( A4 )

  Right-transposition C_ijlk = A_ijkl

• C2 = transpose2 ( A2 )

  Transposition C_ji = A_ij

• C = trace2 ( A2 )

  The trace of the tensor (i.e. the sum of the diagonal components) C = A_ii

• C = det2 ( A2 )

  The determinant C

• C2 = inv2 ( A2 )

  The inverse C_ij

Installation

Pre-compiled version using PyPi

Use

pip3 install GooseTensor

(replace pip3 with the Python version you'd want to use, e.g. by pip).

Local build

To compile and install this module use

python3 setup.py build
python3 setup.py install

(replace python3 with the executable of the Python version you'd want to use, e.g. by python).

Develop

Create a new release

1. Update the version number by modifying __version__ in setup.py.

2. Upload the changes to GitHub and create a new release there (with the correct version number).

3. Upload the package to PyPi:

   $ python3 setup.py bdist_wheel --universal
   $ twine upload dist/*