{ "__type": "IngestedDoc", "__tag": 4010, "_content": { "Notes": { "__type": "Section", "__tag": 4015, "children": [ { "__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": "from_davenport", "reference": { "__type": "LocalRef", "__tag": 4022, "kind": "module", "path": "scipy.spatial.transform._rotation:Rotation.from_davenport" }, "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": "rotation", "annotation": "`Rotation` instance", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Object containing the rotation represented by the sequence of rotations around given axes with given angles." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Initialize from Davenport angles." } ] } ], "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": [ { "__type": "Parameters", "__tag": 4026, "children": [ { "__type": "DocParam", "__tag": 4016, "name": "axes", "annotation": "array_like, shape (3,) or (..., [1 or 2 or 3], 3)", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Axis of rotation, if one dimensional. If two or more dimensional, describes the sequence of axes for rotations, where each axes[..., i, :] is the ith axis. If more than one axis is given, then the second axis must be orthogonal to both the first and third axes." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "order", "annotation": "string", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If it is equal to 'e' or 'extrinsic', the sequence will be extrinsic. If it is equal to 'i' or 'intrinsic', sequence will be treated as intrinsic." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "angles", "annotation": "float or array_like, shape (..., [1 or 2 or 3])", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Angles specified in radians (" }, { "__type": "ParamRef", "__tag": 4071, "name": "degrees" }, { "__type": "Text", "__tag": 4046, "value": " is False) or degrees (" }, { "__type": "ParamRef", "__tag": 4071, "name": "degrees" }, { "__type": "Text", "__tag": 4046, "value": " is True). Each angle i in the last dimension of " }, { "__type": "ParamRef", "__tag": 4071, "name": "angles" }, { "__type": "Text", "__tag": 4046, "value": " turns around the corresponding axis axis[..., i, :]. The resulting rotation has the shape np.broadcast_shapes(np.atleast_2d(axes).shape[:-2], np.atleast_1d(angles).shape[:-1]) Dimensionless angles are thus only valid for a single axis." } ] } ] }, { "__type": "DocParam", "__tag": 4016, "name": "degrees", "annotation": "bool, optional", "desc": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "If True, then the given angles are assumed to be in degrees. Default is False." } ] } ] } ] } ], "title": [], "level": 0, "target": null }, "Extended Summary": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "Rotations in 3-D can be represented by a sequence of 3 rotations around a sequence of axes." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "The three rotations can either be in a global frame of reference (extrinsic) or in a body centred frame of reference (intrinsic), which is attached to, and moves with, the object under rotation " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "1" }, { "__type": "Text", "__tag": 4046, "value": "." } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For both Euler angles and Davenport angles, consecutive axes must be are orthogonal (" }, { "__type": "InlineCode", "__tag": 4051, "value": "axis2" }, { "__type": "Text", "__tag": 4046, "value": " is orthogonal to both " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis3" }, { "__type": "Text", "__tag": 4046, "value": "). For Euler angles, there is an additional relationship between " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis1" }, { "__type": "Text", "__tag": 4046, "value": " or " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis3" }, { "__type": "Text", "__tag": 4046, "value": ", with two possibilities:" } ] }, { "__type": "Blockquote", "__tag": 4059, "children": [ { "__type": "BulletList", "__tag": 4053, "ordered": false, "start": 1, "children": [ { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "axis1" }, { "__type": "Text", "__tag": 4046, "value": " and " }, { "__type": "InlineCode", "__tag": 4051, "value": "axis3" }, { "__type": "Text", "__tag": 4046, "value": " are also orthogonal (asymmetric sequence)" } ] } ] }, { "__type": "ListItem", "__tag": 4054, "children": [ { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "InlineCode", "__tag": 4051, "value": "axis1 == axis3" }, { "__type": "Text", "__tag": 4046, "value": " (symmetric sequence)" } ] } ] } ] } ] }, { "__type": "Paragraph", "__tag": 4045, "children": [ { "__type": "Text", "__tag": 4046, "value": "For Davenport angles, this last relationship is relaxed " }, { "__type": "FootnoteReference", "__tag": 4066, "label": "2" }, { "__type": "Text", "__tag": 4046, "value": ", and only the consecutive orthogonal axes requirement is maintained." } ] } ], "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": 768, "item_type": "staticmethod", "aliases": [ "scipy.spatial.transform.Rotation.from_davenport" ], "example_section_data": { "__type": "Section", "__tag": 4015, "children": [ { "__type": "Code", "__tag": 4050, "value": "from scipy.spatial.transform import Rotation as R\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nDavenport angles are a generalization of Euler angles, when we use the\ncanonical basis axes:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "ex = [1, 0, 0]\ney = [0, 1, 0]\nez = [0, 0, 1]\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nInitialize a single rotation with a given axis sequence:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "axes = [ez, ey, ex]\nr = R.from_davenport(axes, 'extrinsic', [90, 0, 0], degrees=True)\nr.as_quat().shape\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nIt is equivalent to Euler angles in this case:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r.as_euler('zyx', degrees=True)\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nInitialize multiple rotations in one object:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r = R.from_davenport(axes, 'extrinsic', [[90, 45, 30], [35, 45, 90]], degrees=True)\nr.as_quat().shape\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nUsing only one or two axes is also possible:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "r = R.from_davenport([ez, ex], 'extrinsic', [[90, 45], [35, 45]], degrees=True)\nr.as_quat().shape\n", "execution_status": "success" }, { "__type": "Text", "__tag": 4046, "value": "\nNon-canonical axes are possible, and they do not need to be normalized,\nas long as consecutive axes are orthogonal:\n\n" }, { "__type": "Code", "__tag": 4050, "value": "e1 = [2, 0, 0]\ne2 = [0, 1, 0]\ne3 = [1, 0, 1]\naxes = [e1, e2, e3]\nr = R.from_davenport(axes, 'extrinsic', [90, 45, 30], degrees=True)\n", "execution_status": "success" }, { "__type": "Code", "__tag": 4050, "value": "r.as_quat()\n", "execution_status": "failure" } ], "title": [], "level": 0, "target": null }, "see_also": [], "signature": { "__type": "SignatureNode", "__tag": 4029, "kind": "function", "parameters": [ { "__type": "SigParam", "__tag": 4030, "name": "axes", "annotation": "ArrayLike", "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "order", "annotation": "str", "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "angles", "annotation": "ArrayLike | float", "kind": "POSITIONAL_OR_KEYWORD", "default": { "__type": "Empty", "__tag": 4031 } }, { "__type": "SigParam", "__tag": 4030, "name": "degrees", "annotation": "bool", "kind": "POSITIONAL_OR_KEYWORD", "default": "False" } ], "return_annotation": "Rotation", "target_name": "from_davenport" }, "references": [ ".. [1] https://en.wikipedia.org/wiki/Euler_angles#Definition_by_intrinsic_rotations", ".. [2] Shuster, Malcolm & Markley, Landis. (2003). Generalization of", " the Euler Angles. Journal of the Astronautical Sciences. 51. 123-132.", " 10.1007/BF03546304." ], "qa": "scipy.spatial.transform._rotation:Rotation.from_davenport", "arbitrary": [], "local_refs": [ "angles", "axes", "degrees", "order", "rotation" ] }