symmetric-tensor-index

symmetric-tensor-index

Index operations for symmetric tensors (aka multinomials). In a r-th order symmetric tensor over a d-dimensional vector spaces, we can think of the indices in 3 different ways:

• As a tensor index (ie an array of length r with values of length d)
• As a polynomial degree (ie an array of length d with values up to r)
• Or a flattened array index (a scalar number between 0 and (d + r - 1) choose r )

The code in this library can be used to convert between these indices. For more details see:

• http://0fps.wordpress.com/2011/08/30/multidimensional-taylor-series-and-symmetric-tensors/

Install

npm install symmetric-tensor-index

API

var sym = require("symmetric-tensor-index")

sym.nextTensor(dimension, rank, seq[, index])

Finds the index of the next entry in the tensor.

• dimension is the dimension of the tensor
• rank is the rank of the tensor
• seq is the tensor index
• index is the array index (optional)

Returns The next array index. seq is updated in place.

sym.tensorToDegree(dimension, rank, seq[, result])

Converts a tensor index to a degree index

• dimension dimension of vector space
• rank rank of the tensor
• seq is the tensor index
• result (optional) gets the resulting computation

Returns result

sym.tensorToArray(dimension, rank, seq)

Converts a tensor index to an array index

• dimension dimension of vector space
• rank rank of the tensor
• seq is the tensor index

Returns The array index of the tensor entry

sym.degreeToTensor(dimension, rank, degrees[, result])

Converts a degree index to a tensor index

• dimension dimension of vector space
• rank rank of the tensor
• degrees is the degree index
• result is the result (optional)

Returns result

sym.degreeToArray(dimension, rank, degrees)

Converts a degree index to an array index

• dimension dimension of vector space
• rank rank of the tensor
• degrees is the degree index

Returns The array index of the degree sequence

Credits

(c) 2013 Mikola Lysenko. MIT License