ee.Array.eigen
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Berechnet die reellen Eigenvektoren und ‑werte eines quadratischen 2D-Arrays mit A Zeilen und A Spalten. Gibt ein Array mit A Zeilen und A+1 Spalten zurück, wobei jede Zeile in der ersten Spalte einen Eigenwert und in den verbleibenden A Spalten den entsprechenden Eigenvektor enthält. Die Zeilen werden in absteigender Reihenfolge nach Eigenwert sortiert.
Bei dieser Implementierung wird DecompositionFactory.eig() aus https://ejml.org verwendet.
| Nutzung | Ausgabe |
|---|
Array.eigen() | Array |
| Argument | Typ | Details |
|---|
So gehts: input | Array | Ein quadratisches 2D-Array, aus dem die Eigenwertzerlegung berechnet werden soll. |
Beispiele
Code-Editor (JavaScript)
print(ee.Array([[0, 0], [0, 0]]).eigen()); // [[0,0,1],[0,1,0]]
print(ee.Array([[1, 0], [0, 0]]).eigen()); // [[1,1,0],[0,0,1]]
print(ee.Array([[0, 1], [0, 0]]).eigen()); // [[0,0,1],[0,1,0]]
print(ee.Array([[0, 0], [1, 0]]).eigen()); // [[0,-1,0],[0,0,-1]]
print(ee.Array([[0, 0], [0, 1]]).eigen()); // [[1,0,1],[0,1,0]]
print(ee.Array([[1, 1], [0, 0]]).eigen()); // [[1,1,0],[0,-1/√2,1/√2]]
print(ee.Array([[0, 0], [1, 1]]).eigen()); // [[1,0,-1],[0,-1/√2,1/√2]]]
print(ee.Array([[1, 0], [1, 0]]).eigen()); // [[1,1/√2,1/√2],[0,0,1]]
print(ee.Array([[1, 0], [0, 1]]).eigen()); // [[1,1,0],[1,0,1]]
print(ee.Array([[0, 1], [1, 0]]).eigen()); // [[1,1/√2,1/√2],[-1,1/√2,-1/√2]]
print(ee.Array([[0, 1], [0, 1]]).eigen()); // [[1,1/√2,1/√2],[0,1,0]]
print(ee.Array([[1, 1], [1, 0]]).eigen()); // [[1.62,0.85,0.53],[-0.62,0.53]]
print(ee.Array([[1, 1], [0, 1]]).eigen()); // [[1,0,1],[1,1,0]]
print(ee.Array([[1, 0], [1, 1]]).eigen()); // [[1,-1,0],[1,0,-1]]
// [[1.62,-0.53,-0.85],[-0.62,-0.85,0.53]]
print(ee.Array([[0, 1], [1, 1]]).eigen());
print(ee.Array([[1, 1], [1, 1]]).eigen()); // [[2,1/√2,1/√2],[0,1/√2,-1/√2]]
var matrix = ee.Array([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]]);
print(matrix.eigen()); // [[1,1,0,0],[1,0,1,0],[1,0,0,1]]
var matrix = ee.Array([
[2, 0, 0],
[0, 3, 0],
[0, 0, 4]]);
print(matrix.eigen()); // [[4,0,0,1],[3,0,1,0],[2,1,0,0]]
matrix = ee.Array([
[1, 0, 0],
[0, 0, 0],
[0, 0, 0]]);
print(matrix.eigen()); // [[1,1,0,0],[0,0,1,0],[0,0,0,1]]
matrix = ee.Array([
[1, 1, 1],
[1, 1, 1],
[1, 1, 1]]);
// [[3,-0.58,-0.58,-0.58],[0,0,-1/√2,1/√2],[0,-0.82,0.41,0.41]]
print(matrix.eigen());
Python einrichten
Informationen zur Python API und zur Verwendung von geemap für die interaktive Entwicklung finden Sie auf der Seite
Python-Umgebung.
import ee
import geemap.core as geemap
Colab (Python)
display(ee.Array([[0, 0], [0, 0]]).eigen()) # [[0, 0, 1], [0, 1, 0]]
display(ee.Array([[1, 0], [0, 0]]).eigen()) # [[1, 1, 0], [0,0,1]]
display(ee.Array([[0, 1], [0, 0]]).eigen()) # [[0, 0, 1], [0, 1, 0]]
display(ee.Array([[0, 0], [1, 0]]).eigen()) # [[0, -1, 0], [0, 0, -1]]
display(ee.Array([[0, 0], [0, 1]]).eigen()) # [[1, 0, 1], [0, 1, 0]]
# [[1, 1, 0], [0, -1/√2, 1/√2]]
display(ee.Array([[1, 1], [0, 0]]).eigen())
# [[1, 0, -1], [0, -1/√2, 1/√2]]]
display(ee.Array([[0, 0], [1, 1]]).eigen())
# [[1, 1/√2, 1/√2], [0, 0, 1]]
display(ee.Array([[1, 0], [1, 0]]).eigen())
display(ee.Array([[1, 0], [0, 1]]).eigen()) # [[1, 1, 0], [1, 0, 1]]
# [[1, 1/√2, 1/√2], [-1, 1/√2, -1/√2]]
display(ee.Array([[0, 1], [1, 0]]).eigen())
# [[1, 1/√2, 1/√2], [0, 1, 0]]
display(ee.Array([[0, 1], [0, 1]]).eigen())
# [[1.62, 0.85, 0.53], [-0.62, 0.53]]
display(ee.Array([[1, 1], [1, 0]]).eigen())
display(ee.Array([[1, 1], [0, 1]]).eigen()) # [[1, 0, 1], [1, 1, 0]]
display(ee.Array([[1, 0], [1, 1]]).eigen()) # [[1, -1, 0], [1, 0, -1]]
# [[1.62, -0.53, -0.85], [-0.62, -0.85, 0.53]]
display(ee.Array([[0, 1], [1, 1]]).eigen())
# [[2, 1/√2, 1/√2], [0, 1/√2, -1/√2]]
display(ee.Array([[1, 1], [1, 1]]).eigen())
matrix = ee.Array([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
display(matrix.eigen()) # [[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]
matrix = ee.Array([
[2, 0, 0],
[0, 3, 0],
[0, 0, 4]])
display(matrix.eigen()) # [[4, 0, 0, 1], [3, 0, 1, 0], [2, 1, 0, 0]]
matrix = ee.Array([
[1, 0, 0],
[0, 0, 0],
[0, 0, 0]])
display(matrix.eigen()) # [[1, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
matrix = ee.Array([
[1, 1, 1],
[1, 1, 1],
[1, 1, 1]])
# [[3, -0.58, -0.58, -0.58], [0, 0, -1/√2, 1/√2], [0, -0.82, 0.41, 0.41]]
display(matrix.eigen())
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Zuletzt aktualisiert: 2025-07-26 (UTC).
[null,null,["Zuletzt aktualisiert: 2025-07-26 (UTC)."],[[["\u003cp\u003eComputes the real eigenvectors and eigenvalues of a 2D square array.\u003c/p\u003e\n"],["\u003cp\u003eReturns an array where each row represents an eigenvalue and its corresponding eigenvector.\u003c/p\u003e\n"],["\u003cp\u003eEigenvalues are sorted in descending order within the output array.\u003c/p\u003e\n"],["\u003cp\u003eUtilizes the \u003ccode\u003eDecompositionFactory.eig()\u003c/code\u003e method from the EJML library for computation.\u003c/p\u003e\n"],["\u003cp\u003eAccepts a single argument: the input 2D square array.\u003c/p\u003e\n"]]],["The `eigen()` function computes the eigenvalues and eigenvectors of a square 2D array. It takes a square 2D array as input and returns a new array where each row represents an eigenvalue and its corresponding eigenvector. The first column of each row contains the eigenvalue, and the remaining columns contain the eigenvector components. The rows are sorted in descending order by eigenvalue. It uses `DecompositionFactory.eig()` for its core calculations.\n"],null,["# ee.Array.eigen\n\nComputes the real eigenvectors and eigenvalues of a square 2D array of A rows and A columns. Returns an array with A rows and A+1 columns, where each row contains an eigenvalue in the first column, and the corresponding eigenvector in the remaining A columns. The rows are sorted by eigenvalue, in descending order.\n\n\u003cbr /\u003e\n\nThis implementation uses DecompositionFactory.eig() from https://ejml.org.\n\n| Usage | Returns |\n|-----------------|---------|\n| Array.eigen`()` | Array |\n\n| Argument | Type | Details |\n|---------------|-------|------------------------------------------------------------------------|\n| this: `input` | Array | A square, 2D array from which to compute the eigenvalue decomposition. |\n\nExamples\n--------\n\n### Code Editor (JavaScript)\n\n```javascript\nprint(ee.Array([[0, 0], [0, 0]]).eigen()); // [[0,0,1],[0,1,0]]\n\nprint(ee.Array([[1, 0], [0, 0]]).eigen()); // [[1,1,0],[0,0,1]]\nprint(ee.Array([[0, 1], [0, 0]]).eigen()); // [[0,0,1],[0,1,0]]\nprint(ee.Array([[0, 0], [1, 0]]).eigen()); // [[0,-1,0],[0,0,-1]]\nprint(ee.Array([[0, 0], [0, 1]]).eigen()); // [[1,0,1],[0,1,0]]\n\nprint(ee.Array([[1, 1], [0, 0]]).eigen()); // [[1,1,0],[0,-1/√2,1/√2]]\nprint(ee.Array([[0, 0], [1, 1]]).eigen()); // [[1,0,-1],[0,-1/√2,1/√2]]]\n\nprint(ee.Array([[1, 0], [1, 0]]).eigen()); // [[1,1/√2,1/√2],[0,0,1]]\nprint(ee.Array([[1, 0], [0, 1]]).eigen()); // [[1,1,0],[1,0,1]]\nprint(ee.Array([[0, 1], [1, 0]]).eigen()); // [[1,1/√2,1/√2],[-1,1/√2,-1/√2]]\nprint(ee.Array([[0, 1], [0, 1]]).eigen()); // [[1,1/√2,1/√2],[0,1,0]]\n\nprint(ee.Array([[1, 1], [1, 0]]).eigen()); // [[1.62,0.85,0.53],[-0.62,0.53]]\nprint(ee.Array([[1, 1], [0, 1]]).eigen()); // [[1,0,1],[1,1,0]]\nprint(ee.Array([[1, 0], [1, 1]]).eigen()); // [[1,-1,0],[1,0,-1]]\n// [[1.62,-0.53,-0.85],[-0.62,-0.85,0.53]]\nprint(ee.Array([[0, 1], [1, 1]]).eigen());\n\nprint(ee.Array([[1, 1], [1, 1]]).eigen()); // [[2,1/√2,1/√2],[0,1/√2,-1/√2]]\n\nvar matrix = ee.Array([\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]]);\nprint(matrix.eigen()); // [[1,1,0,0],[1,0,1,0],[1,0,0,1]]\n\nvar matrix = ee.Array([\n [2, 0, 0],\n [0, 3, 0],\n [0, 0, 4]]);\nprint(matrix.eigen()); // [[4,0,0,1],[3,0,1,0],[2,1,0,0]]\n\nmatrix = ee.Array([\n [1, 0, 0],\n [0, 0, 0],\n [0, 0, 0]]);\nprint(matrix.eigen()); // [[1,1,0,0],[0,0,1,0],[0,0,0,1]]\n\nmatrix = ee.Array([\n [1, 1, 1],\n [1, 1, 1],\n [1, 1, 1]]);\n// [[3,-0.58,-0.58,-0.58],[0,0,-1/√2,1/√2],[0,-0.82,0.41,0.41]]\nprint(matrix.eigen());\n```\nPython setup\n\nSee the [Python Environment](/earth-engine/guides/python_install) page for information on the Python API and using\n`geemap` for interactive development. \n\n```python\nimport ee\nimport geemap.core as geemap\n```\n\n### Colab (Python)\n\n```python\ndisplay(ee.Array([[0, 0], [0, 0]]).eigen()) # [[0, 0, 1], [0, 1, 0]]\n\ndisplay(ee.Array([[1, 0], [0, 0]]).eigen()) # [[1, 1, 0], [0,0,1]]\ndisplay(ee.Array([[0, 1], [0, 0]]).eigen()) # [[0, 0, 1], [0, 1, 0]]\ndisplay(ee.Array([[0, 0], [1, 0]]).eigen()) # [[0, -1, 0], [0, 0, -1]]\ndisplay(ee.Array([[0, 0], [0, 1]]).eigen()) # [[1, 0, 1], [0, 1, 0]]\n\n# [[1, 1, 0], [0, -1/√2, 1/√2]]\ndisplay(ee.Array([[1, 1], [0, 0]]).eigen())\n\n# [[1, 0, -1], [0, -1/√2, 1/√2]]]\ndisplay(ee.Array([[0, 0], [1, 1]]).eigen())\n\n# [[1, 1/√2, 1/√2], [0, 0, 1]]\ndisplay(ee.Array([[1, 0], [1, 0]]).eigen())\ndisplay(ee.Array([[1, 0], [0, 1]]).eigen()) # [[1, 1, 0], [1, 0, 1]]\n\n# [[1, 1/√2, 1/√2], [-1, 1/√2, -1/√2]]\ndisplay(ee.Array([[0, 1], [1, 0]]).eigen())\n\n# [[1, 1/√2, 1/√2], [0, 1, 0]]\ndisplay(ee.Array([[0, 1], [0, 1]]).eigen())\n\n# [[1.62, 0.85, 0.53], [-0.62, 0.53]]\ndisplay(ee.Array([[1, 1], [1, 0]]).eigen())\ndisplay(ee.Array([[1, 1], [0, 1]]).eigen()) # [[1, 0, 1], [1, 1, 0]]\ndisplay(ee.Array([[1, 0], [1, 1]]).eigen()) # [[1, -1, 0], [1, 0, -1]]\n\n# [[1.62, -0.53, -0.85], [-0.62, -0.85, 0.53]]\ndisplay(ee.Array([[0, 1], [1, 1]]).eigen())\n\n# [[2, 1/√2, 1/√2], [0, 1/√2, -1/√2]]\ndisplay(ee.Array([[1, 1], [1, 1]]).eigen())\n\nmatrix = ee.Array([\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1]])\ndisplay(matrix.eigen()) # [[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]\n\nmatrix = ee.Array([\n [2, 0, 0],\n [0, 3, 0],\n [0, 0, 4]])\ndisplay(matrix.eigen()) # [[4, 0, 0, 1], [3, 0, 1, 0], [2, 1, 0, 0]]\n\nmatrix = ee.Array([\n [1, 0, 0],\n [0, 0, 0],\n [0, 0, 0]])\ndisplay(matrix.eigen()) # [[1, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]\n\nmatrix = ee.Array([\n [1, 1, 1],\n [1, 1, 1],\n [1, 1, 1]])\n# [[3, -0.58, -0.58, -0.58], [0, 0, -1/√2, 1/√2], [0, -0.82, 0.41, 0.41]]\ndisplay(matrix.eigen())\n```"]]
