{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Admonition",
          "__tag": 4056,
          "kind": "versionadded",
          "base_type": "neutral",
          "children": [
            {
              "__type": "AdmonitionTitle",
              "__tag": 4055,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "versionadded 1.6.0"
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Strong",
              "__tag": 4048,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "Array API Standard Support"
                }
              ]
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "CrossRef",
              "__tag": 4002,
              "value": "as_mrp",
              "reference": {
                "__type": "LocalRef",
                "__tag": 4022,
                "kind": "module",
                "path": "scipy.spatial.transform._rotation:Rotation.as_mrp"
              },
              "kind": "module"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "SCIPY_ARRAY_API=1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported."
            }
          ]
        },
        {
          "__type": "Code",
          "__tag": 4050,
          "value": "====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 ✅                     n/a                 \nCuPy                  n/a                   ✅                   \nPyTorch               ✅                     ✅                   \nJAX                   ✅                     ✅                   \nDask                  ⛔                     n/a                 \n====================  ====================  ====================",
          "execution_status": null
        },
        {
          "__type": "Blockquote",
          "__tag": 4059,
          "children": [
            {
              "__type": "Paragraph",
              "__tag": 4045,
              "children": [
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": "See "
                },
                {
                  "__type": "InlineRole",
                  "__tag": 4003,
                  "value": "dev-arrayapi",
                  "domain": null,
                  "role": "ref",
                  "inventory": null
                },
                {
                  "__type": "Text",
                  "__tag": 4046,
                  "value": " for more information."
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "mrps",
              "annotation": "ndarray, shape (..., 3)",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Shape depends on shape of inputs used for initialization."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Represent as Modified Rodrigues Parameters (MRPs)."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "MRPs are a 3 dimensional vector co-directional to the axis of rotation and whose magnitude is equal to "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "tan(theta / 4)"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ", where "
            },
            {
              "__type": "InlineCode",
              "__tag": 4051,
              "value": "theta"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " is the angle of rotation (in radians) "
            },
            {
              "__type": "FootnoteReference",
              "__tag": 4066,
              "label": "1"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "."
            }
          ]
        },
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "MRPs have a singularity at 360 degrees which can be avoided by ensuring the angle of rotation does not exceed 180 degrees, i.e. switching the direction of the rotation when it is past 180 degrees. This function will always return MRPs corresponding to a rotation of less than or equal to 180 degrees."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/scipy/spatial/transform/_rotation.py",
  "item_line": 1424,
  "item_type": "function",
  "aliases": [
    "scipy.spatial.transform.Rotation.as_mrp"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "from scipy.spatial.transform import Rotation as R\nimport numpy as np\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nRepresent a single rotation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r = R.from_rotvec([0, 0, np.pi])\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp()\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp().shape\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nRepresent a stack with a single rotation:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r = R.from_euler('xyz', [[180, 0, 0]], degrees=True)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp()\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp().shape\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nRepresent multiple rotations:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r = R.from_rotvec([[np.pi/2, 0, 0], [0, 0, np.pi/2]])\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp()\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "r.as_mrp().shape\n",
        "execution_status": "success"
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [],
  "signature": {
    "__type": "SignatureNode",
    "__tag": 4029,
    "kind": "function",
    "parameters": [
      {
        "__type": "SigParam",
        "__tag": 4030,
        "name": "self",
        "annotation": {
          "__type": "Empty",
          "__tag": 4031
        },
        "kind": "POSITIONAL_OR_KEYWORD",
        "default": {
          "__type": "Empty",
          "__tag": 4031
        }
      }
    ],
    "return_annotation": "Array",
    "target_name": "as_mrp"
  },
  "references": [
    ".. [1] Shuster, M. D. \"A Survey of Attitude Representations\",",
    "       The Journal of Astronautical Sciences, Vol. 41, No.4, 1993,",
    "       pp. 475-476"
  ],
  "qa": "scipy.spatial.transform._rotation:Rotation.as_mrp",
  "arbitrary": [],
  "local_refs": [
    "mrps"
  ]
}