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