tensor
A tensor from its shape and its entries in row-major order (rank up to 4). A matrix or an array is accepted wherever a tensor is.
shape(array) -- e.g. [2, 2]data(array) -- row-major entries
Tensors
zeroTensor
The all-zero tensor of a given shape.
shape(array) --
kroneckerDelta
The identity tensor delta_ij of dimension n.
n(integer) --
leviCivita
The Levi-Civita (permutation) symbol epsilon of dimension n.
n(integer) --
euclideanMetric
The Euclidean metric of dimension n (the identity).
n(integer) --
minkowskiMetric
The Minkowski metric diag(-1, 1, 1, 1).
rank
The number of indices of a tensor.
t(tensor) --
tensorGet
One entry, by a list of indices (from 0).
t(tensor) --index(array) --
outer
The outer (tensor) product a (x) b.
a(tensor) --b(tensor) --
contract
Contracts axis axA of a with axis axB of b (a generalized dot product).
a(tensor) --b(tensor) --axA(integer) --axB(integer) --
contractSelf
Contracts two axes of one tensor.
t(tensor) --ax0(integer) --ax1(integer) --
tensorTrace
The trace over two axes, as a number.
t(tensor) --ax0(integer) --ax1(integer) --
doubleContract
A : B, the sum of a_ij b_ij.
a(tensor) --b(tensor) --
transpose
Reverses the order of all axes (the transpose of a matrix).
t(tensor) --
transposeAxes
Swaps two axes.
t(tensor) --ax0(integer) --ax1(integer) --
symmetrize
The symmetric part (T + T^T)/2 of a rank-2 tensor.
t(tensor) --
antisymmetrize
The antisymmetric part (T - T^T)/2 of a rank-2 tensor.
t(tensor) --
invertMetric
The inverse metric g^ij of a metric g_ij.
g(tensor) --
raiseIndex
Raises the first index of t with the metric g.
t(tensor) --g(tensor) --
lowerIndex
Lowers the first index of t with the metric g.
t(tensor) --g(tensor) --
reshape
The same entries with a new shape (same total size).
t(tensor) --shape(array) --
tensorSlice
The sub-tensor with axis ax fixed at index k.
t(tensor) --ax(integer) --k(integer) --