Function eigs #
Compute eigenvalues and eigenvectors of a matrix. The eigenvalues are sorted by their absolute value, ascending.
An eigenvalue with multiplicity k will be listed k times. The eigenvectors are returned as columns of a matrix –
the eigenvector that belongs to the j-th eigenvalue in the list (eg. values[j]) is the j-th column (eg. column(vectors, j)).
If the algorithm fails to converge, it will throw an error – in that case, however, you may still find useful information
in err.values and err.vectors.
Syntax #
math.eigs(x, [prec])
Parameters #
| Parameter | Type | Description |
|---|---|---|
x |
Array | Matrix | Matrix to be diagonalized |
prec |
number | BigNumber | Precision, default value: 1e-15 |
Returns #
| Type | Description |
|---|---|
| {values: Array | Matrix, vectors: Array | Matrix} | Object containing an array of eigenvalues and a matrix with eigenvectors as columns. |
Throws #
Type | Description —- | ———–
Examples #
const { eigs, multiply, column, transpose } = math
const H = [[5, 2.3], [2.3, 1]]
const ans = eigs(H) // returns {values: [E1,E2...sorted], vectors: [v1,v2.... corresponding vectors as columns]}
const E = ans.values
const U = ans.vectors
multiply(H, column(U, 0)) // returns multiply(E[0], column(U, 0))
const UTxHxU = multiply(transpose(U), H, U) // diagonalizes H
E[0] == UTxHxU[0][0] // returns true
