magpylib.magnet package
magpylib.magnet package#
The magpylib.magnet subpackage contains all magnet classes.
- class magpylib.magnet.Cuboid(magnetization=None, dimension=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#
Bases:
magpylib._src.obj_classes.class_BaseExcitations.BaseMagnetCuboid magnet with homogeneous magnetization.
Can be used as sources input for magnetic field computation.
When position=(0,0,0) and orientation=None the Cuboid sides are parallel to the global coordinate basis vectors and the geometric center of the Cuboid is located in the origin.
- Parameters
magnetization (array_like, shape (3,), default=`None`) – Magnetization vector (mu0*M, remanence field) in units of [mT] given in the local object coordinates (rotates with object).
dimension (array_like, shape (3,), default=`None`) – Length of the cuboid sides [a,b,c] in units of [mm].
position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
orientation (scipy Rotation object with length 1 or m, default=`None`) – Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
parent (Collection object or None) – The object is a child of it’s parent collection.
style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’.
- Returns
magnet source
- Return type
Cuboid object
Examples
Cuboid magnets are magnetic field sources. Below we compute the H-field [kA/m] of a cubical magnet with magnetization (100,200,300) in units of [mT] and 1 [mm] sides at the observer position (1,1,1) given in units of [mm]:
>>> import magpylib as magpy >>> src = magpy.magnet.Cuboid(magnetization=(100,200,300), dimension=(1,1,1)) >>> H = src.getH((1,1,1)) >>> print(H) [6.21116976 4.9689358 3.72670185]
We rotate the source object, and compute the B-field, this time at a set of observer positions:
>>> src.rotate_from_angax(45, 'x') Cuboid(id=...) >>> B = src.getB([(1,1,1), (2,2,2), (3,3,3)]) >>> print(B) [[4.30496934 6.9363475 0.50728577] [0.54127889 0.86827283 0.05653357] [0.1604214 0.25726266 0.01664045]]
The same result is obtained when the rotated source moves along a path away from an observer at position (1,1,1). Here we use a Sensor object as observer.
>>> sens = magpy.Sensor(position=(1,1,1)) >>> src.move([(-1,-1,-1), (-2,-2,-2)]) Cuboid(id=...) >>> B = src.getB(sens) >>> print(B) [[4.30496934 6.9363475 0.50728577] [0.54127889 0.86827283 0.05653357] [0.1604214 0.25726266 0.01664045]]
- copy(**kwargs)#
Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independant of the original object.
- Parameters
kwargs (dict) – Keyword arguments (for example position=(1,2,3)) are applied to the copy.
Examples
Create a Sensor object and copy to an another position:
>>> import magpylib as magpy >>> sens1 = magpy.Sensor(style_label='sens1') >>> sens2 = sens1.copy(position=(2,6,10), style_label='sens2') >>> print(f"Instance {sens1.style.label} with position {sens1.position}.") Instance sens1 with position [0. 0. 0.]. >>> print(f"Instance {sens2.style.label} with position {sens2.position}.") Instance sens2 with position [ 2. 6. 10.].
- describe(*, exclude=('style', 'field_func'), return_string=False)#
Returns a view of the object properties.
- Parameters
exclude (bool, default=("style",)) – Properties to be excluded in the description view.
return_string (bool, default=`False`) – If False print description with stdout, if True return as string.
- property dimension#
Length of the cuboid sides [a,b,c] in units of [mm].
- property field_func#
The function for B- and H-field computation must have the two positional arguments field and observers. With field=’B’ or field=’H’ the B- or H-field in units of [mT] or [kA/m] must be returned respectively. The observers argument must accept numpy ndarray inputs of shape (n,3), in which case the returned fields must be numpy ndarrays of shape (n,3) themselves.
- getB(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the B-field in units of [mT] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
B-field – B-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [mT]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the B-field of a spherical magnet at three positions:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> B = src.getB(((0,0,0), (1,0,0), (2,0,0))) >>> print(B) [[ 0. 0. 666.66666667] [ 0. 0. -41.66666667] [ 0. 0. -5.20833333]]
Compute the B-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> B = src.getB(sens1, sens2) >>> print(B) [[[ 12.19288783 0. -39.83010025] [-12.19288783 0. -39.83010025]] [[ 0.77638847 0. -5.15004352] [ -0.77638847 0. -5.15004352]]]
- getH(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the H-field in units of [kA/m] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
H-field – H-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [kA/m]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the H-field of a spherical magnet at three positions:
>>> import magpylib as magpy
>>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> H = src.getH(((0,0,0), (1,0,0), (2,0,0))) >>> print(H) [[ 0. 0. -265.25823849] [ 0. 0. -33.15727981] [ 0. 0. -4.14465998]]
Compute the H-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> H = src.getH(sens1, sens2) >>> print(H) [[[ 9.70279185 0. -31.69578669] [ -9.70279185 0. -31.69578669]] [[ 0.61783031 0. -4.09827441] [ -0.61783031 0. -4.09827441]]]
- property magnetization#
Object magnetization attribute getter and setter.
- move(displacement, start='auto')#
Move object by the displacement input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
displacement (array_like, shape (3,) or (n,3)) – Displacement vector in units of [mm].
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Move objects around with scalar input:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,1,1)) >>> print(sens.position) [1. 1. 1.] >>> sens.move((1,1,1)) Sensor(id=...) >>> print(sens.position) [2. 2. 2.]
Create len>1 object paths with vector input:
>>> sens.move([(1,1,1),(2,2,2),(3,3,3)]) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 4.] [5. 5. 5.]]
Apply operations starting with a designated path index:
>>> sens.move((0,0,2), start=2) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 6.] [5. 5. 7.]]
- property orientation#
Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
- property parent#
The object is a child of it’s parent collection.
- property position#
Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
- reset_path()#
Set object position to (0,0,0) and orientation = unit rotation.
- Returns
self
- Return type
magpylib object
Examples
Demonstration of reset_path functionality:
>>> import magpylib as magpy >>> obj = magpy.Sensor(position=(1,2,3)) >>> obj.rotate_from_angax(45, 'z') Sensor... >>> print(obj.position) [1. 2. 3.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
>>> obj.reset_path() Sensor(id=...) >>> print(obj.position) [0. 0. 0.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [0. 0. 0.]
- rotate(rotation: scipy.spatial.transform._rotation.Rotation, anchor=None, start='auto')#
Rotate object about a given anchor.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotation (None or scipy Rotation object) – Rotation to be applied to the object. The scipy Rotation input can be scalar or vector type (see terminology above). None input is interpreted as unit rotation.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> from scipy.spatial.transform import Rotation as R >>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate(R.from_euler('z', 45, degrees=True), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate(R.from_euler('z', 45, degrees=True)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate(R.from_euler('z', (15,30,45), degrees=True), anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_angax(angle, axis, anchor=None, start='auto', degrees=True)#
Rotates object using angle-axis input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
axis (str or array_like, shape (3,)) – The direction of the axis of rotation. Input can be a vector of shape (3,) or a string ‘x’, ‘y’ or ‘z’ to denote respective directions.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_angax(45, axis='z', anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_angax(45, axis=(0,0,1)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_angax((15,30,45), axis='z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_euler(angle, seq, anchor=None, start='auto', degrees=True)#
Rotates object using Euler angle input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
seq (string) – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_euler(45, 'z', anchor=0) Sensor... >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_euler(45, 'z') Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_euler((15,30,45), 'z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_matrix(matrix, anchor=None, start='auto')#
Rotates object using matrix input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
matrix (array_like, shape (n,3,3) or (3,3)) – Rotation input. See scipy.spatial.transform.Rotation for details.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)], anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_mrp(mrp, anchor=None, start='auto')#
Rotates object using Modified Rodrigues Parameters (MRPs) input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
mrp (array_like, shape (n,3) or (3,)) – Rotation input. See scipy Rotation package for details on Modified Rodrigues Parameters (MRPs).
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_mrp((0,0,1), anchor=0) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. -90.]
- rotate_from_quat(quat, anchor=None, start='auto')#
Rotates object using quaternion input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
quat (array_like, shape (n,4) or (4,)) – Rotation input in quaternion form.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_quat((0,0,1,1), anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_quat((0,0,1,1)) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_rotvec(rotvec, anchor=None, start='auto', degrees=True)#
Rotates object using rotation vector input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotvec (array_like, shape (n,3) or (3,)) – Rotation input. Rotation vector direction is the rotation axis, vector length is the rotation angle in units of [rad].
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_rotvec((0,0,45), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_rotvec((0,0,45)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_rotvec([(0,0,15), (0,0,30), (0,0,45)], anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- show(*, zoom=0, animation=False, markers=None, backend=None, canvas=None, return_fig=False, **kwargs)#
Display objects and paths graphically.
Global graphic styles can be set with kwargs as style dictionary or using style underscore magic.
- Parameters
objects (Magpylib objects (sources, collections, sensors)) – Objects to be displayed.
zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.
animation (bool or float, default=`False`) – If True and at least one object has a path, the paths are rendered. If input is a positive float, the animation time is set to the given value. This feature is only available for the plotly backend.
markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.
backend (string, default=`None`) – Define plotting backend. Must be one of ‘matplotlib’, ‘plotly’. If not set, parameter will default to magpylib.defaults.display.backend which is ‘matplotlib’ by installation default.
canvas (bool, default=False) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes._subplots.AxesSubplot with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. By default a new canvas is created and immediately displayed.
canvas – If True, the function call returns the figure object. - with matplotlib: matplotlib.figure.Figure. - with plotly: plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter.
- Return type
None or figure object
Examples
Display multiple objects, object paths, markers in 3D using Matplotlib or Plotly:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(0,0,1), diameter=1) >>> src.move([(0.1*x,0,0) for x in range(50)]) Sphere... >>> src.rotate_from_angax(angle=[*range(0,400,10)], axis='z', anchor=0, start=11) Sphere... >>> ts = [-.4,0,.4] >>> sens = magpy.Sensor(position=(0,0,2), pixel=[(x,y,0) for x in ts for y in ts]) >>> magpy.show(src, sens) >>> magpy.show(src, sens, backend='plotly') >>> # graphic output
Display output on your own canvas (here a Matplotlib 3d-axes):
>>> import matplotlib.pyplot as plt >>> import magpylib as magpy >>> my_axis = plt.axes(projection='3d') >>> magnet = magpy.magnet.Cuboid(magnetization=(1,1,1), dimension=(1,2,3)) >>> sens = magpy.Sensor(position=(0,0,3)) >>> magpy.show(magnet, sens, canvas=my_axis, zoom=1) >>> plt.show() >>> # graphic output
Use sophisticated figure styling options accessible from defaults, as individual object styles or as global style arguments in display.
>>> import magpylib as magpy >>> src1 = magpy.magnet.Sphere((1,1,1), 1, [(0,0,0), (0,0,3)]) >>> src2 = magpy.magnet.Sphere((1,1,1), 1, [(1,0,0), (1,0,3)], style_path_show=False) >>> magpy.defaults.display.style.magnet.magnetization.size = 2 >>> src1.style.magnetization.size = 1 >>> magpy.show(src1, src2, style_color='r') >>> # graphic output
- property style#
Object style in the form of a BaseStyle object. Input must be in the form of a style dictionary.
- class magpylib.magnet.Cylinder(magnetization=None, dimension=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#
Bases:
magpylib._src.obj_classes.class_BaseExcitations.BaseMagnetCylinder magnet with homogeneous magnetization.
Can be used as sources input for magnetic field computation.
When position=(0,0,0) and orientation=None the geometric center of the cylinder lies in the origin of the global coordinate system and the cylinder axis conincides with the global z-axis.
- Parameters
magnetization (array_like, shape (3,), default=`None`) – Magnetization vector (mu0*M, remanence field) in units of [mT] given in the local object coordinates (rotates with object).
dimension (array_like, shape (2,), default=`None`) – Dimension (d,h) denote diameter and height of the cylinder in units of [mm].
position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
orientation (scipy Rotation object with length 1 or m, default=`None`) – Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
parent (Collection object or None) – The object is a child of it’s parent collection.
style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’.
- Returns
magnet source
- Return type
Cylinder
Examples
Cylinder magnets are magnetic field sources. Below we compute the H-field [kA/m] of a cylinder magnet with magnetization (100,200,300) in units of [mT] and 1 [mm] diameter and height at the observer position (1,1,1) given in units of [mm]:
>>> import magpylib as magpy >>> src = magpy.magnet.Cylinder(magnetization=(100,200,300), dimension=(1,1)) >>> H = src.getH((1,1,1)) >>> print(H) [4.84991343 3.88317816 2.73973202]
We rotate the source object, and compute the B-field, this time at a set of observer positions:
>>> src.rotate_from_angax(45, 'x') Cylinder(id=...) >>> B = src.getB([(1,1,1), (2,2,2), (3,3,3)]) >>> print(B) [[3.31419501 5.26683023 0.37767015] [0.42298405 0.67710536 0.04464932] [0.12571523 0.20144503 0.01312389]]
The same result is obtained when the rotated source moves along a path away from an observer at position (1,1,1). Here we use a Sensor object as observer.
>>> sens = magpy.Sensor(position=(1,1,1)) >>> src.move([(-1,-1,-1), (-2,-2,-2)]) Cylinder(id=...) >>> B = src.getB(sens) >>> print(B) [[3.31419501 5.26683023 0.37767015] [0.42298405 0.67710536 0.04464932] [0.12571523 0.20144503 0.01312389]]
- copy(**kwargs)#
Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independant of the original object.
- Parameters
kwargs (dict) – Keyword arguments (for example position=(1,2,3)) are applied to the copy.
Examples
Create a Sensor object and copy to an another position:
>>> import magpylib as magpy >>> sens1 = magpy.Sensor(style_label='sens1') >>> sens2 = sens1.copy(position=(2,6,10), style_label='sens2') >>> print(f"Instance {sens1.style.label} with position {sens1.position}.") Instance sens1 with position [0. 0. 0.]. >>> print(f"Instance {sens2.style.label} with position {sens2.position}.") Instance sens2 with position [ 2. 6. 10.].
- describe(*, exclude=('style', 'field_func'), return_string=False)#
Returns a view of the object properties.
- Parameters
exclude (bool, default=("style",)) – Properties to be excluded in the description view.
return_string (bool, default=`False`) – If False print description with stdout, if True return as string.
- property dimension#
Dimension (d,h) denote diameter and height of the cylinder in units of [mm].
- property field_func#
The function for B- and H-field computation must have the two positional arguments field and observers. With field=’B’ or field=’H’ the B- or H-field in units of [mT] or [kA/m] must be returned respectively. The observers argument must accept numpy ndarray inputs of shape (n,3), in which case the returned fields must be numpy ndarrays of shape (n,3) themselves.
- getB(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the B-field in units of [mT] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
B-field – B-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [mT]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the B-field of a spherical magnet at three positions:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> B = src.getB(((0,0,0), (1,0,0), (2,0,0))) >>> print(B) [[ 0. 0. 666.66666667] [ 0. 0. -41.66666667] [ 0. 0. -5.20833333]]
Compute the B-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> B = src.getB(sens1, sens2) >>> print(B) [[[ 12.19288783 0. -39.83010025] [-12.19288783 0. -39.83010025]] [[ 0.77638847 0. -5.15004352] [ -0.77638847 0. -5.15004352]]]
- getH(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the H-field in units of [kA/m] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
H-field – H-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [kA/m]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the H-field of a spherical magnet at three positions:
>>> import magpylib as magpy
>>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> H = src.getH(((0,0,0), (1,0,0), (2,0,0))) >>> print(H) [[ 0. 0. -265.25823849] [ 0. 0. -33.15727981] [ 0. 0. -4.14465998]]
Compute the H-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> H = src.getH(sens1, sens2) >>> print(H) [[[ 9.70279185 0. -31.69578669] [ -9.70279185 0. -31.69578669]] [[ 0.61783031 0. -4.09827441] [ -0.61783031 0. -4.09827441]]]
- property magnetization#
Object magnetization attribute getter and setter.
- move(displacement, start='auto')#
Move object by the displacement input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
displacement (array_like, shape (3,) or (n,3)) – Displacement vector in units of [mm].
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Move objects around with scalar input:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,1,1)) >>> print(sens.position) [1. 1. 1.] >>> sens.move((1,1,1)) Sensor(id=...) >>> print(sens.position) [2. 2. 2.]
Create len>1 object paths with vector input:
>>> sens.move([(1,1,1),(2,2,2),(3,3,3)]) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 4.] [5. 5. 5.]]
Apply operations starting with a designated path index:
>>> sens.move((0,0,2), start=2) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 6.] [5. 5. 7.]]
- property orientation#
Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
- property parent#
The object is a child of it’s parent collection.
- property position#
Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
- reset_path()#
Set object position to (0,0,0) and orientation = unit rotation.
- Returns
self
- Return type
magpylib object
Examples
Demonstration of reset_path functionality:
>>> import magpylib as magpy >>> obj = magpy.Sensor(position=(1,2,3)) >>> obj.rotate_from_angax(45, 'z') Sensor... >>> print(obj.position) [1. 2. 3.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
>>> obj.reset_path() Sensor(id=...) >>> print(obj.position) [0. 0. 0.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [0. 0. 0.]
- rotate(rotation: scipy.spatial.transform._rotation.Rotation, anchor=None, start='auto')#
Rotate object about a given anchor.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotation (None or scipy Rotation object) – Rotation to be applied to the object. The scipy Rotation input can be scalar or vector type (see terminology above). None input is interpreted as unit rotation.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> from scipy.spatial.transform import Rotation as R >>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate(R.from_euler('z', 45, degrees=True), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate(R.from_euler('z', 45, degrees=True)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate(R.from_euler('z', (15,30,45), degrees=True), anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_angax(angle, axis, anchor=None, start='auto', degrees=True)#
Rotates object using angle-axis input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
axis (str or array_like, shape (3,)) – The direction of the axis of rotation. Input can be a vector of shape (3,) or a string ‘x’, ‘y’ or ‘z’ to denote respective directions.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_angax(45, axis='z', anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_angax(45, axis=(0,0,1)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_angax((15,30,45), axis='z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_euler(angle, seq, anchor=None, start='auto', degrees=True)#
Rotates object using Euler angle input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
seq (string) – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_euler(45, 'z', anchor=0) Sensor... >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_euler(45, 'z') Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_euler((15,30,45), 'z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_matrix(matrix, anchor=None, start='auto')#
Rotates object using matrix input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
matrix (array_like, shape (n,3,3) or (3,3)) – Rotation input. See scipy.spatial.transform.Rotation for details.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)], anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_mrp(mrp, anchor=None, start='auto')#
Rotates object using Modified Rodrigues Parameters (MRPs) input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
mrp (array_like, shape (n,3) or (3,)) – Rotation input. See scipy Rotation package for details on Modified Rodrigues Parameters (MRPs).
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_mrp((0,0,1), anchor=0) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. -90.]
- rotate_from_quat(quat, anchor=None, start='auto')#
Rotates object using quaternion input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
quat (array_like, shape (n,4) or (4,)) – Rotation input in quaternion form.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_quat((0,0,1,1), anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_quat((0,0,1,1)) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_rotvec(rotvec, anchor=None, start='auto', degrees=True)#
Rotates object using rotation vector input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotvec (array_like, shape (n,3) or (3,)) – Rotation input. Rotation vector direction is the rotation axis, vector length is the rotation angle in units of [rad].
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_rotvec((0,0,45), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_rotvec((0,0,45)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_rotvec([(0,0,15), (0,0,30), (0,0,45)], anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- show(*, zoom=0, animation=False, markers=None, backend=None, canvas=None, return_fig=False, **kwargs)#
Display objects and paths graphically.
Global graphic styles can be set with kwargs as style dictionary or using style underscore magic.
- Parameters
objects (Magpylib objects (sources, collections, sensors)) – Objects to be displayed.
zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.
animation (bool or float, default=`False`) – If True and at least one object has a path, the paths are rendered. If input is a positive float, the animation time is set to the given value. This feature is only available for the plotly backend.
markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.
backend (string, default=`None`) – Define plotting backend. Must be one of ‘matplotlib’, ‘plotly’. If not set, parameter will default to magpylib.defaults.display.backend which is ‘matplotlib’ by installation default.
canvas (bool, default=False) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes._subplots.AxesSubplot with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. By default a new canvas is created and immediately displayed.
canvas – If True, the function call returns the figure object. - with matplotlib: matplotlib.figure.Figure. - with plotly: plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter.
- Return type
None or figure object
Examples
Display multiple objects, object paths, markers in 3D using Matplotlib or Plotly:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(0,0,1), diameter=1) >>> src.move([(0.1*x,0,0) for x in range(50)]) Sphere... >>> src.rotate_from_angax(angle=[*range(0,400,10)], axis='z', anchor=0, start=11) Sphere... >>> ts = [-.4,0,.4] >>> sens = magpy.Sensor(position=(0,0,2), pixel=[(x,y,0) for x in ts for y in ts]) >>> magpy.show(src, sens) >>> magpy.show(src, sens, backend='plotly') >>> # graphic output
Display output on your own canvas (here a Matplotlib 3d-axes):
>>> import matplotlib.pyplot as plt >>> import magpylib as magpy >>> my_axis = plt.axes(projection='3d') >>> magnet = magpy.magnet.Cuboid(magnetization=(1,1,1), dimension=(1,2,3)) >>> sens = magpy.Sensor(position=(0,0,3)) >>> magpy.show(magnet, sens, canvas=my_axis, zoom=1) >>> plt.show() >>> # graphic output
Use sophisticated figure styling options accessible from defaults, as individual object styles or as global style arguments in display.
>>> import magpylib as magpy >>> src1 = magpy.magnet.Sphere((1,1,1), 1, [(0,0,0), (0,0,3)]) >>> src2 = magpy.magnet.Sphere((1,1,1), 1, [(1,0,0), (1,0,3)], style_path_show=False) >>> magpy.defaults.display.style.magnet.magnetization.size = 2 >>> src1.style.magnetization.size = 1 >>> magpy.show(src1, src2, style_color='r') >>> # graphic output
- property style#
Object style in the form of a BaseStyle object. Input must be in the form of a style dictionary.
- class magpylib.magnet.CylinderSegment(magnetization=None, dimension=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#
Bases:
magpylib._src.obj_classes.class_BaseExcitations.BaseMagnetCylinder segment (ring-section) magnet with homogeneous magnetization.
Can be used as sources input for magnetic field computation.
When position=(0,0,0) and orientation=None the geometric center of the cylinder lies in the origin of the global coordinate system and the cylinder axis conincides with the global z-axis. Section angle 0 corresponds to an x-z plane section of the cylinder.
- Parameters
magnetization (array_like, shape (3,), default=`None`) – Magnetization vector (mu0*M, remanence field) in units of [mT] given in the local object coordinates (rotates with object).
dimension (array_like, shape (5,), default=`None`) – Dimension/Size of the cylinder segment of the form (r1, r2, h, phi1, phi2) where r1<r2 denote inner and outer radii in units of [mm], phi1<phi2 denote the cylinder section angles in units of [deg] and h is the cylinder height in units of [mm].
position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
barycenter (array_like, shape (3,)) – Read only property that returns the geometric barycenter (=center of mass) of the object.
orientation (scipy Rotation object with length 1 or m, default=`None`) – Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
parent (Collection object or None) – The object is a child of it’s parent collection.
style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’.
- Returns
magnet source
- Return type
CylinderSegment object
Examples
CylinderSegment magnets are magnetic field sources. In this example we compute the H-field [kA/m] of such a cylinder segment magnet with magnetization (100,200,300) in units of [mT], inner radius 1 [mm], outer radius 2 [mm], height 1 [mm], and section angles 0 and 45 [deg] at the observer position (2,2,2) in units of [mm]:
>>> import magpylib as magpy >>> src = magpy.magnet.CylinderSegment(magnetization=(100,200,300), dimension=(1,2,1,0,45)) >>> H = src.getH((2,2,2)) >>> print(H) [0.80784692 1.93422813 2.74116805]
We rotate the source object, and compute the B-field, this time at a set of observer positions:
>>> src.rotate_from_angax(45, 'x') CylinderSegment(id=...) >>> B = src.getB([(1,1,1), (2,2,2), (3,3,3)]) >>> print(B) [[-32.82849635 30.15882073 -16.32885658] [ 0.62876075 3.97579164 0.73297829] [ 0.25439493 0.74331628 0.11682542]]
The same result is obtained when the rotated source moves along a path away from an observer at position (1,1,1). Here we use a Sensor object as observer.
>>> sens = magpy.Sensor(position=(1,1,1)) >>> src.move([(-1,-1,-1), (-2,-2,-2)]) CylinderSegment(id=...) >>> B = src.getB(sens) >>> print(B) [[-32.82849635 30.15882073 -16.32885658] [ 0.62876075 3.97579164 0.73297829] [ 0.25439493 0.74331628 0.11682542]]
- property barycenter#
Object barycenter.
- copy(**kwargs)#
Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independant of the original object.
- Parameters
kwargs (dict) – Keyword arguments (for example position=(1,2,3)) are applied to the copy.
Examples
Create a Sensor object and copy to an another position:
>>> import magpylib as magpy >>> sens1 = magpy.Sensor(style_label='sens1') >>> sens2 = sens1.copy(position=(2,6,10), style_label='sens2') >>> print(f"Instance {sens1.style.label} with position {sens1.position}.") Instance sens1 with position [0. 0. 0.]. >>> print(f"Instance {sens2.style.label} with position {sens2.position}.") Instance sens2 with position [ 2. 6. 10.].
- describe(*, exclude=('style', 'field_func'), return_string=False)#
Returns a view of the object properties.
- Parameters
exclude (bool, default=("style",)) – Properties to be excluded in the description view.
return_string (bool, default=`False`) – If False print description with stdout, if True return as string.
- property dimension#
Dimension/Size of the cylinder segment of the form (r1, r2, h, phi1, phi2) where r1<r2 denote inner and outer radii in units of [mm], phi1<phi2 denote the cylinder section angles in units of [deg] and h is the cylinder height in units of [mm].
- property field_func#
The function for B- and H-field computation must have the two positional arguments field and observers. With field=’B’ or field=’H’ the B- or H-field in units of [mT] or [kA/m] must be returned respectively. The observers argument must accept numpy ndarray inputs of shape (n,3), in which case the returned fields must be numpy ndarrays of shape (n,3) themselves.
- getB(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the B-field in units of [mT] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
B-field – B-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [mT]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the B-field of a spherical magnet at three positions:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> B = src.getB(((0,0,0), (1,0,0), (2,0,0))) >>> print(B) [[ 0. 0. 666.66666667] [ 0. 0. -41.66666667] [ 0. 0. -5.20833333]]
Compute the B-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> B = src.getB(sens1, sens2) >>> print(B) [[[ 12.19288783 0. -39.83010025] [-12.19288783 0. -39.83010025]] [[ 0.77638847 0. -5.15004352] [ -0.77638847 0. -5.15004352]]]
- getH(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the H-field in units of [kA/m] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
H-field – H-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [kA/m]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the H-field of a spherical magnet at three positions:
>>> import magpylib as magpy
>>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> H = src.getH(((0,0,0), (1,0,0), (2,0,0))) >>> print(H) [[ 0. 0. -265.25823849] [ 0. 0. -33.15727981] [ 0. 0. -4.14465998]]
Compute the H-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> H = src.getH(sens1, sens2) >>> print(H) [[[ 9.70279185 0. -31.69578669] [ -9.70279185 0. -31.69578669]] [[ 0.61783031 0. -4.09827441] [ -0.61783031 0. -4.09827441]]]
- property magnetization#
Object magnetization attribute getter and setter.
- move(displacement, start='auto')#
Move object by the displacement input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
displacement (array_like, shape (3,) or (n,3)) – Displacement vector in units of [mm].
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Move objects around with scalar input:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,1,1)) >>> print(sens.position) [1. 1. 1.] >>> sens.move((1,1,1)) Sensor(id=...) >>> print(sens.position) [2. 2. 2.]
Create len>1 object paths with vector input:
>>> sens.move([(1,1,1),(2,2,2),(3,3,3)]) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 4.] [5. 5. 5.]]
Apply operations starting with a designated path index:
>>> sens.move((0,0,2), start=2) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 6.] [5. 5. 7.]]
- property orientation#
Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
- property parent#
The object is a child of it’s parent collection.
- property position#
Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
- reset_path()#
Set object position to (0,0,0) and orientation = unit rotation.
- Returns
self
- Return type
magpylib object
Examples
Demonstration of reset_path functionality:
>>> import magpylib as magpy >>> obj = magpy.Sensor(position=(1,2,3)) >>> obj.rotate_from_angax(45, 'z') Sensor... >>> print(obj.position) [1. 2. 3.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
>>> obj.reset_path() Sensor(id=...) >>> print(obj.position) [0. 0. 0.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [0. 0. 0.]
- rotate(rotation: scipy.spatial.transform._rotation.Rotation, anchor=None, start='auto')#
Rotate object about a given anchor.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotation (None or scipy Rotation object) – Rotation to be applied to the object. The scipy Rotation input can be scalar or vector type (see terminology above). None input is interpreted as unit rotation.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> from scipy.spatial.transform import Rotation as R >>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate(R.from_euler('z', 45, degrees=True), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate(R.from_euler('z', 45, degrees=True)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate(R.from_euler('z', (15,30,45), degrees=True), anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_angax(angle, axis, anchor=None, start='auto', degrees=True)#
Rotates object using angle-axis input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
axis (str or array_like, shape (3,)) – The direction of the axis of rotation. Input can be a vector of shape (3,) or a string ‘x’, ‘y’ or ‘z’ to denote respective directions.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_angax(45, axis='z', anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_angax(45, axis=(0,0,1)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_angax((15,30,45), axis='z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_euler(angle, seq, anchor=None, start='auto', degrees=True)#
Rotates object using Euler angle input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
seq (string) – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_euler(45, 'z', anchor=0) Sensor... >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_euler(45, 'z') Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_euler((15,30,45), 'z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_matrix(matrix, anchor=None, start='auto')#
Rotates object using matrix input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
matrix (array_like, shape (n,3,3) or (3,3)) – Rotation input. See scipy.spatial.transform.Rotation for details.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)], anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_mrp(mrp, anchor=None, start='auto')#
Rotates object using Modified Rodrigues Parameters (MRPs) input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
mrp (array_like, shape (n,3) or (3,)) – Rotation input. See scipy Rotation package for details on Modified Rodrigues Parameters (MRPs).
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_mrp((0,0,1), anchor=0) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. -90.]
- rotate_from_quat(quat, anchor=None, start='auto')#
Rotates object using quaternion input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
quat (array_like, shape (n,4) or (4,)) – Rotation input in quaternion form.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_quat((0,0,1,1), anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_quat((0,0,1,1)) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_rotvec(rotvec, anchor=None, start='auto', degrees=True)#
Rotates object using rotation vector input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotvec (array_like, shape (n,3) or (3,)) – Rotation input. Rotation vector direction is the rotation axis, vector length is the rotation angle in units of [rad].
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_rotvec((0,0,45), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_rotvec((0,0,45)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_rotvec([(0,0,15), (0,0,30), (0,0,45)], anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- show(*, zoom=0, animation=False, markers=None, backend=None, canvas=None, return_fig=False, **kwargs)#
Display objects and paths graphically.
Global graphic styles can be set with kwargs as style dictionary or using style underscore magic.
- Parameters
objects (Magpylib objects (sources, collections, sensors)) – Objects to be displayed.
zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.
animation (bool or float, default=`False`) – If True and at least one object has a path, the paths are rendered. If input is a positive float, the animation time is set to the given value. This feature is only available for the plotly backend.
markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.
backend (string, default=`None`) – Define plotting backend. Must be one of ‘matplotlib’, ‘plotly’. If not set, parameter will default to magpylib.defaults.display.backend which is ‘matplotlib’ by installation default.
canvas (bool, default=False) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes._subplots.AxesSubplot with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. By default a new canvas is created and immediately displayed.
canvas – If True, the function call returns the figure object. - with matplotlib: matplotlib.figure.Figure. - with plotly: plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter.
- Return type
None or figure object
Examples
Display multiple objects, object paths, markers in 3D using Matplotlib or Plotly:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(0,0,1), diameter=1) >>> src.move([(0.1*x,0,0) for x in range(50)]) Sphere... >>> src.rotate_from_angax(angle=[*range(0,400,10)], axis='z', anchor=0, start=11) Sphere... >>> ts = [-.4,0,.4] >>> sens = magpy.Sensor(position=(0,0,2), pixel=[(x,y,0) for x in ts for y in ts]) >>> magpy.show(src, sens) >>> magpy.show(src, sens, backend='plotly') >>> # graphic output
Display output on your own canvas (here a Matplotlib 3d-axes):
>>> import matplotlib.pyplot as plt >>> import magpylib as magpy >>> my_axis = plt.axes(projection='3d') >>> magnet = magpy.magnet.Cuboid(magnetization=(1,1,1), dimension=(1,2,3)) >>> sens = magpy.Sensor(position=(0,0,3)) >>> magpy.show(magnet, sens, canvas=my_axis, zoom=1) >>> plt.show() >>> # graphic output
Use sophisticated figure styling options accessible from defaults, as individual object styles or as global style arguments in display.
>>> import magpylib as magpy >>> src1 = magpy.magnet.Sphere((1,1,1), 1, [(0,0,0), (0,0,3)]) >>> src2 = magpy.magnet.Sphere((1,1,1), 1, [(1,0,0), (1,0,3)], style_path_show=False) >>> magpy.defaults.display.style.magnet.magnetization.size = 2 >>> src1.style.magnetization.size = 1 >>> magpy.show(src1, src2, style_color='r') >>> # graphic output
- property style#
Object style in the form of a BaseStyle object. Input must be in the form of a style dictionary.
- class magpylib.magnet.Sphere(magnetization=None, diameter=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#
Bases:
magpylib._src.obj_classes.class_BaseExcitations.BaseMagnetSpherical magnet with homogeneous magnetization.
Can be used as sources input for magnetic field computation.
When position=(0,0,0) and orientation=None the sphere center is located in the origin of the global coordinate system.
- Parameters
magnetization (array_like, shape (3,), default=`None`) – Magnetization vector (mu0*M, remanence field) in units of [mT] given in the local object coordinates (rotates with object).
diameter (float, default=`None`) – Diameter of the sphere in units of [mm].
position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
orientation (scipy Rotation object with length 1 or m, default=`None`) – Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
parent (Collection object or None) – The object is a child of it’s parent collection.
style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’.
- Returns
magnet source
- Return type
Sphere object
Examples
Sphere objects are magnetic field sources. In this example we compute the H-field [kA/m] of a spherical magnet with magnetization (100,200,300) in units of [mT] and diameter of 1 [mm] at the observer position (1,1,1) given in units of [mm]:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(100,200,300), diameter=1) >>> H = src.getH((1,1,1)) >>> print(H) [3.19056074 2.55244859 1.91433644]
We rotate the source object, and compute the B-field, this time at a set of observer positions:
>>> src.rotate_from_angax(45, 'x') Sphere(id=...) >>> B = src.getB([(1,1,1), (2,2,2), (3,3,3)]) >>> print(B) [[2.26804606 3.63693295 0.23486386] [0.28350576 0.45461662 0.02935798] [0.08400171 0.13470122 0.00869866]]
The same result is obtained when the rotated source moves along a path away from an observer at position (1,1,1). This time we use a Sensor object as observer.
>>> src.move([(-1,-1,-1), (-2,-2,-2)]) Sphere(id=...) >>> sens = magpy.Sensor(position=(1,1,1)) >>> B = src.getB(sens) >>> print(B) [[2.26804606 3.63693295 0.23486386] [0.28350576 0.45461662 0.02935798] [0.08400171 0.13470122 0.00869866]]
- copy(**kwargs)#
Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independant of the original object.
- Parameters
kwargs (dict) – Keyword arguments (for example position=(1,2,3)) are applied to the copy.
Examples
Create a Sensor object and copy to an another position:
>>> import magpylib as magpy >>> sens1 = magpy.Sensor(style_label='sens1') >>> sens2 = sens1.copy(position=(2,6,10), style_label='sens2') >>> print(f"Instance {sens1.style.label} with position {sens1.position}.") Instance sens1 with position [0. 0. 0.]. >>> print(f"Instance {sens2.style.label} with position {sens2.position}.") Instance sens2 with position [ 2. 6. 10.].
- describe(*, exclude=('style', 'field_func'), return_string=False)#
Returns a view of the object properties.
- Parameters
exclude (bool, default=("style",)) – Properties to be excluded in the description view.
return_string (bool, default=`False`) – If False print description with stdout, if True return as string.
- property diameter#
Diameter of the sphere in units of [mm].
- property field_func#
The function for B- and H-field computation must have the two positional arguments field and observers. With field=’B’ or field=’H’ the B- or H-field in units of [mT] or [kA/m] must be returned respectively. The observers argument must accept numpy ndarray inputs of shape (n,3), in which case the returned fields must be numpy ndarrays of shape (n,3) themselves.
- getB(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the B-field in units of [mT] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
B-field – B-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [mT]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the B-field of a spherical magnet at three positions:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> B = src.getB(((0,0,0), (1,0,0), (2,0,0))) >>> print(B) [[ 0. 0. 666.66666667] [ 0. 0. -41.66666667] [ 0. 0. -5.20833333]]
Compute the B-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> B = src.getB(sens1, sens2) >>> print(B) [[[ 12.19288783 0. -39.83010025] [-12.19288783 0. -39.83010025]] [[ 0.77638847 0. -5.15004352] [ -0.77638847 0. -5.15004352]]]
- getH(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the H-field in units of [kA/m] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
H-field – H-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [kA/m]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the H-field of a spherical magnet at three positions:
>>> import magpylib as magpy
>>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> H = src.getH(((0,0,0), (1,0,0), (2,0,0))) >>> print(H) [[ 0. 0. -265.25823849] [ 0. 0. -33.15727981] [ 0. 0. -4.14465998]]
Compute the H-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> H = src.getH(sens1, sens2) >>> print(H) [[[ 9.70279185 0. -31.69578669] [ -9.70279185 0. -31.69578669]] [[ 0.61783031 0. -4.09827441] [ -0.61783031 0. -4.09827441]]]
- property magnetization#
Object magnetization attribute getter and setter.
- move(displacement, start='auto')#
Move object by the displacement input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
displacement (array_like, shape (3,) or (n,3)) – Displacement vector in units of [mm].
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Move objects around with scalar input:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,1,1)) >>> print(sens.position) [1. 1. 1.] >>> sens.move((1,1,1)) Sensor(id=...) >>> print(sens.position) [2. 2. 2.]
Create len>1 object paths with vector input:
>>> sens.move([(1,1,1),(2,2,2),(3,3,3)]) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 4.] [5. 5. 5.]]
Apply operations starting with a designated path index:
>>> sens.move((0,0,2), start=2) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 6.] [5. 5. 7.]]
- property orientation#
Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
- property parent#
The object is a child of it’s parent collection.
- property position#
Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
- reset_path()#
Set object position to (0,0,0) and orientation = unit rotation.
- Returns
self
- Return type
magpylib object
Examples
Demonstration of reset_path functionality:
>>> import magpylib as magpy >>> obj = magpy.Sensor(position=(1,2,3)) >>> obj.rotate_from_angax(45, 'z') Sensor... >>> print(obj.position) [1. 2. 3.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
>>> obj.reset_path() Sensor(id=...) >>> print(obj.position) [0. 0. 0.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [0. 0. 0.]
- rotate(rotation: scipy.spatial.transform._rotation.Rotation, anchor=None, start='auto')#
Rotate object about a given anchor.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotation (None or scipy Rotation object) – Rotation to be applied to the object. The scipy Rotation input can be scalar or vector type (see terminology above). None input is interpreted as unit rotation.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> from scipy.spatial.transform import Rotation as R >>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate(R.from_euler('z', 45, degrees=True), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate(R.from_euler('z', 45, degrees=True)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate(R.from_euler('z', (15,30,45), degrees=True), anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_angax(angle, axis, anchor=None, start='auto', degrees=True)#
Rotates object using angle-axis input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
axis (str or array_like, shape (3,)) – The direction of the axis of rotation. Input can be a vector of shape (3,) or a string ‘x’, ‘y’ or ‘z’ to denote respective directions.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_angax(45, axis='z', anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_angax(45, axis=(0,0,1)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_angax((15,30,45), axis='z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_euler(angle, seq, anchor=None, start='auto', degrees=True)#
Rotates object using Euler angle input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
seq (string) – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_euler(45, 'z', anchor=0) Sensor... >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_euler(45, 'z') Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_euler((15,30,45), 'z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_matrix(matrix, anchor=None, start='auto')#
Rotates object using matrix input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
matrix (array_like, shape (n,3,3) or (3,3)) – Rotation input. See scipy.spatial.transform.Rotation for details.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)], anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_mrp(mrp, anchor=None, start='auto')#
Rotates object using Modified Rodrigues Parameters (MRPs) input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
mrp (array_like, shape (n,3) or (3,)) – Rotation input. See scipy Rotation package for details on Modified Rodrigues Parameters (MRPs).
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_mrp((0,0,1), anchor=0) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. -90.]
- rotate_from_quat(quat, anchor=None, start='auto')#
Rotates object using quaternion input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
quat (array_like, shape (n,4) or (4,)) – Rotation input in quaternion form.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_quat((0,0,1,1), anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_quat((0,0,1,1)) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_rotvec(rotvec, anchor=None, start='auto', degrees=True)#
Rotates object using rotation vector input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotvec (array_like, shape (n,3) or (3,)) – Rotation input. Rotation vector direction is the rotation axis, vector length is the rotation angle in units of [rad].
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_rotvec((0,0,45), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_rotvec((0,0,45)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_rotvec([(0,0,15), (0,0,30), (0,0,45)], anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- show(*, zoom=0, animation=False, markers=None, backend=None, canvas=None, return_fig=False, **kwargs)#
Display objects and paths graphically.
Global graphic styles can be set with kwargs as style dictionary or using style underscore magic.
- Parameters
objects (Magpylib objects (sources, collections, sensors)) – Objects to be displayed.
zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.
animation (bool or float, default=`False`) – If True and at least one object has a path, the paths are rendered. If input is a positive float, the animation time is set to the given value. This feature is only available for the plotly backend.
markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.
backend (string, default=`None`) – Define plotting backend. Must be one of ‘matplotlib’, ‘plotly’. If not set, parameter will default to magpylib.defaults.display.backend which is ‘matplotlib’ by installation default.
canvas (bool, default=False) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes._subplots.AxesSubplot with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. By default a new canvas is created and immediately displayed.
canvas – If True, the function call returns the figure object. - with matplotlib: matplotlib.figure.Figure. - with plotly: plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter.
- Return type
None or figure object
Examples
Display multiple objects, object paths, markers in 3D using Matplotlib or Plotly:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(0,0,1), diameter=1) >>> src.move([(0.1*x,0,0) for x in range(50)]) Sphere... >>> src.rotate_from_angax(angle=[*range(0,400,10)], axis='z', anchor=0, start=11) Sphere... >>> ts = [-.4,0,.4] >>> sens = magpy.Sensor(position=(0,0,2), pixel=[(x,y,0) for x in ts for y in ts]) >>> magpy.show(src, sens) >>> magpy.show(src, sens, backend='plotly') >>> # graphic output
Display output on your own canvas (here a Matplotlib 3d-axes):
>>> import matplotlib.pyplot as plt >>> import magpylib as magpy >>> my_axis = plt.axes(projection='3d') >>> magnet = magpy.magnet.Cuboid(magnetization=(1,1,1), dimension=(1,2,3)) >>> sens = magpy.Sensor(position=(0,0,3)) >>> magpy.show(magnet, sens, canvas=my_axis, zoom=1) >>> plt.show() >>> # graphic output
Use sophisticated figure styling options accessible from defaults, as individual object styles or as global style arguments in display.
>>> import magpylib as magpy >>> src1 = magpy.magnet.Sphere((1,1,1), 1, [(0,0,0), (0,0,3)]) >>> src2 = magpy.magnet.Sphere((1,1,1), 1, [(1,0,0), (1,0,3)], style_path_show=False) >>> magpy.defaults.display.style.magnet.magnetization.size = 2 >>> src1.style.magnetization.size = 1 >>> magpy.show(src1, src2, style_color='r') >>> # graphic output
- property style#
Object style in the form of a BaseStyle object. Input must be in the form of a style dictionary.
- class magpylib.magnet.Tetrahedron(magnetization=None, vertices=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#
Bases:
magpylib._src.obj_classes.class_BaseExcitations.BaseMagnetTetrahedron magnet with homogeneous magnetization.
Can be used as sources input for magnetic field computation.
When position=(0,0,0) and orientation=None the Tetrahedron vertices coordinates are the same as in the global coordinate system. The geometric center of the Tetrahedron is determined by its vertices and. It is not necessarily located in the origin an can be computed with the barycenter property.
- Parameters
magnetization (array_like, shape (3,), default=`None`) – Magnetization vector (mu0*M, remanence field) in units of [mT] given in the local object coordinates (rotates with object).
vertices (ndarray, shape (4,3)) – Vertices [(x1,y1,z1), (x2,y2,z2), (x3,y3,z3), (x4,y4,z4)], in the relative coordinate system of the tetrahedron.
position (array_like, shape (3,) or (m,3)) – Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path. When setting vertices, the initial position is set to the barycenter.
barycenter (array_like, shape (3,)) – Read only property that returns the geometric barycenter (=center of mass) of the object.
orientation (scipy Rotation object with length 1 or m, default=`None`) – Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
parent (Collection object or None) – The object is a child of it’s parent collection.
style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’.
- Returns
magnet source
- Return type
Tetrahedron object
Examples
Tetrahedron magnets are magnetic field sources. Below we compute the H-field [kA/m] of a tetrahedron magnet with magnetization (100,200,300) in units of [mT] dimensions defined through the vertices (0,0,0), (1,0,0), (0,1,0) and (0,0,1) in units of [mm] at the observer position (1,1,1) given in units of [mm]:
>>> import magpylib as magpy >>> verts = [(0,0,0), (1,0,0), (0,1,0), (0,0,1)] >>> src = magpy.magnet.Tetrahedron(magnetization=(100,200,300), vertices=verts) >>> H = src.getH((1,1,1)) >>> print(H) [2.07089783 1.65671826 1.2425387 ]
We rotate the source object, and compute the B-field, this time at a set of observer positions:
src.rotate_from_angax(45, ‘x’) Tetrahedron(id=…) B = src.getB([(1,1,1), (2,2,2), (3,3,3)]) print(B) [[ 8.68006559e-01 2.00895792e+00 -5.03469140e-01] [ 1.01357229e-01 1.93731796e-01 -1.59677364e-02] [ 2.90426931e-02 5.22556994e-02 -1.70596096e-03]]
The same result is obtained when the rotated source moves along a path away from an observer at position (1,1,1). Here we use a Sensor object as observer.
sens = magpy.Sensor(position=(1,1,1)) src.move([(-1,-1,-1), (-2,-2,-2)]) Sensor(id=…) B = src.getB(sens) print(B) [[ 8.68006559e-01 2.00895792e+00 -5.03469140e-01] [ 1.01357229e-01 1.93731796e-01 -1.59677364e-02] [ 2.90426931e-02 5.22556994e-02 -1.70596096e-03]]
- property barycenter#
Object barycenter.
- copy(**kwargs)#
Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independant of the original object.
- Parameters
kwargs (dict) – Keyword arguments (for example position=(1,2,3)) are applied to the copy.
Examples
Create a Sensor object and copy to an another position:
>>> import magpylib as magpy >>> sens1 = magpy.Sensor(style_label='sens1') >>> sens2 = sens1.copy(position=(2,6,10), style_label='sens2') >>> print(f"Instance {sens1.style.label} with position {sens1.position}.") Instance sens1 with position [0. 0. 0.]. >>> print(f"Instance {sens2.style.label} with position {sens2.position}.") Instance sens2 with position [ 2. 6. 10.].
- describe(*, exclude=('style', 'field_func'), return_string=False)#
Returns a view of the object properties.
- Parameters
exclude (bool, default=("style",)) – Properties to be excluded in the description view.
return_string (bool, default=`False`) – If False print description with stdout, if True return as string.
- property field_func#
The function for B- and H-field computation must have the two positional arguments field and observers. With field=’B’ or field=’H’ the B- or H-field in units of [mT] or [kA/m] must be returned respectively. The observers argument must accept numpy ndarray inputs of shape (n,3), in which case the returned fields must be numpy ndarrays of shape (n,3) themselves.
- getB(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the B-field in units of [mT] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
B-field – B-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [mT]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the B-field of a spherical magnet at three positions:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> B = src.getB(((0,0,0), (1,0,0), (2,0,0))) >>> print(B) [[ 0. 0. 666.66666667] [ 0. 0. -41.66666667] [ 0. 0. -5.20833333]]
Compute the B-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> B = src.getB(sens1, sens2) >>> print(B) [[[ 12.19288783 0. -39.83010025] [-12.19288783 0. -39.83010025]] [[ 0.77638847 0. -5.15004352] [ -0.77638847 0. -5.15004352]]]
- getH(*observers, squeeze=True, pixel_agg=None, output='ndarray')#
Compute the H-field in units of [kA/m] generated by the source.
- Parameters
observers (array_like or (list of) Sensor objects) – Can be array_like positions of shape (n1, n2, …, 3) where the field should be evaluated, a Sensor object with pixel shape (n1, n2, …, 3) or a list of such sensor objects (must all have similar pixel shapes). All positions are given in units of [mm].
squeeze (bool, default=`True`) – If True, the output is squeezed, i.e. all axes of length 1 in the output (e.g. only a single source) are eliminated.
pixel_agg (str, default=`None`) – Reference to a compatible numpy aggregator function like ‘min’ or ‘mean’, which is applied to observer output values, e.g. mean of all sensor pixel outputs. With this option, observers input with different (pixel) shapes is allowed.
output (str, default='ndarray') – Output type, which must be one of (‘ndarray’, ‘dataframe’). By default a multi- dimensional array (‘ndarray’) is returned. If ‘dataframe’ is chosen, the function returns a 2D-table as a pandas.DataFrame object (the Pandas library must be installed).
- Returns
H-field – H-field at each path position (m) for each sensor (k) and each sensor pixel position (n1,n2,…) in units of [kA/m]. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than m will be considered as static beyond their end.
- Return type
ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame
Examples
Compute the H-field of a spherical magnet at three positions:
>>> import magpylib as magpy
>>> src = magpy.magnet.Sphere((0,0,1000), 1) >>> H = src.getH(((0,0,0), (1,0,0), (2,0,0))) >>> print(H) [[ 0. 0. -265.25823849] [ 0. 0. -33.15727981] [ 0. 0. -4.14465998]]
Compute the H-field at two sensors, each one with two pixels
>>> sens1 = magpy.Sensor(position=(1,0,0), pixel=((0,0,.1), (0,0,-.1))) >>> sens2 = sens1.copy(position=(2,0,0)) >>> H = src.getH(sens1, sens2) >>> print(H) [[[ 9.70279185 0. -31.69578669] [ -9.70279185 0. -31.69578669]] [[ 0.61783031 0. -4.09827441] [ -0.61783031 0. -4.09827441]]]
- property magnetization#
Object magnetization attribute getter and setter.
- move(displacement, start='auto')#
Move object by the displacement input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
displacement (array_like, shape (3,) or (n,3)) – Displacement vector in units of [mm].
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Move objects around with scalar input:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,1,1)) >>> print(sens.position) [1. 1. 1.] >>> sens.move((1,1,1)) Sensor(id=...) >>> print(sens.position) [2. 2. 2.]
Create len>1 object paths with vector input:
>>> sens.move([(1,1,1),(2,2,2),(3,3,3)]) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 4.] [5. 5. 5.]]
Apply operations starting with a designated path index:
>>> sens.move((0,0,2), start=2) Sensor(id=...) >>> print(sens.position) [[2. 2. 2.] [3. 3. 3.] [4. 4. 6.] [5. 5. 7.]]
- property orientation#
Object orientation(s) in the global coordinates. None corresponds to a unit-rotation. For m>1, the position and orientation attributes together represent an object path.
- property parent#
The object is a child of it’s parent collection.
- property position#
Object position(s) in the global coordinates in units of [mm]. For m>1, the position and orientation attributes together represent an object path.
- reset_path()#
Set object position to (0,0,0) and orientation = unit rotation.
- Returns
self
- Return type
magpylib object
Examples
Demonstration of reset_path functionality:
>>> import magpylib as magpy >>> obj = magpy.Sensor(position=(1,2,3)) >>> obj.rotate_from_angax(45, 'z') Sensor... >>> print(obj.position) [1. 2. 3.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
>>> obj.reset_path() Sensor(id=...) >>> print(obj.position) [0. 0. 0.] >>> print(obj.orientation.as_euler('xyz', degrees=True)) [0. 0. 0.]
- rotate(rotation: scipy.spatial.transform._rotation.Rotation, anchor=None, start='auto')#
Rotate object about a given anchor.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotation (None or scipy Rotation object) – Rotation to be applied to the object. The scipy Rotation input can be scalar or vector type (see terminology above). None input is interpreted as unit rotation.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> from scipy.spatial.transform import Rotation as R >>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate(R.from_euler('z', 45, degrees=True), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate(R.from_euler('z', 45, degrees=True)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate(R.from_euler('z', (15,30,45), degrees=True), anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_angax(angle, axis, anchor=None, start='auto', degrees=True)#
Rotates object using angle-axis input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
axis (str or array_like, shape (3,)) – The direction of the axis of rotation. Input can be a vector of shape (3,) or a string ‘x’, ‘y’ or ‘z’ to denote respective directions.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_angax(45, axis='z', anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_angax(45, axis=(0,0,1)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_angax((15,30,45), axis='z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_euler(angle, seq, anchor=None, start='auto', degrees=True)#
Rotates object using Euler angle input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
angle (int, float or array_like with shape (n,)) – Angle(s) of rotation in units of [deg] (by default).
seq (string) – Specifies sequence of axes for rotations. Up to 3 characters belonging to the set {‘X’, ‘Y’, ‘Z’} for intrinsic rotations, or {‘x’, ‘y’, ‘z’} for extrinsic rotations. Extrinsic and intrinsic rotations cannot be mixed in one function call.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_euler(45, 'z', anchor=0) Sensor... >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_euler(45, 'z') Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_euler((15,30,45), 'z', anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- rotate_from_matrix(matrix, anchor=None, start='auto')#
Rotates object using matrix input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
matrix (array_like, shape (n,3,3) or (3,3)) – Rotation input. See scipy.spatial.transform.Rotation for details.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)], anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_mrp(mrp, anchor=None, start='auto')#
Rotates object using Modified Rodrigues Parameters (MRPs) input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
mrp (array_like, shape (n,3) or (3,)) – Rotation input. See scipy Rotation package for details on Modified Rodrigues Parameters (MRPs).
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_mrp((0,0,1), anchor=0) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
Rotate the object about itself:
>>> sens.rotate_from_matrix([(0,-1,0),(1,0,0),(0,0,1)]) Sensor(id=...) >>> print(sens.position) [-1. 0. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. -90.]
- rotate_from_quat(quat, anchor=None, start='auto')#
Rotates object using quaternion input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
quat (array_like, shape (n,4) or (4,)) – Rotation input in quaternion form.
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_quat((0,0,1,1), anchor=0) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Rotate the object about itself:
>>> sens.rotate_from_quat((0,0,1,1)) Sensor(id=...) >>> print(sens.position) [0. 1. 0.] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 180.]
- rotate_from_rotvec(rotvec, anchor=None, start='auto', degrees=True)#
Rotates object using rotation vector input.
Terminology for move/rotate methods: - ‘path’ refers to position and orientation of an object. - When an input is just a single operation (e.g. one displacement vector or one angle) we call it ‘scalar input’. When it is an array_like of multiple scalars, we refer to it as ‘vector input’.
General move/rotate behavior: - Scalar input is applied to the whole object path, starting with path index start. - Vector input of length n applies the individual n operations to n object path entries, starting with path index start. - When an input extends beyond the object path, the object path will be padded by its edge-entries before the operation is applied. - By default (start=’auto’) the index is set to start=0 for scalar input [=move whole object path], and to start=len(object path) for vector input [=append to existing object path].
- Parameters
rotvec (array_like, shape (n,3) or (3,)) – Rotation input. Rotation vector direction is the rotation axis, vector length is the rotation angle in units of [rad].
anchor (None, 0 or array_like with shape (3,) or (n,3), default=`None`) – The axis of rotation passes through the anchor point given in units of [mm]. By default (anchor=None) the object will rotate about its own center. anchor=0 rotates the object about the origin (0,0,0).
start (int or str, default=`'auto'`) – Starting index when applying operations. See ‘General move/rotate behavior’ above for details.
degrees (bool, default=`True`) – Interpret input in units of [deg] or [rad].
- Returns
self
- Return type
Magpylib object
Examples
Rotate an object about the origin:
>>> import magpylib as magpy >>> sens = magpy.Sensor(position=(1,0,0)) >>> sens.rotate_from_rotvec((0,0,45), anchor=0) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 45.]
Rotate the object about itself:
>>> sens.rotate_from_rotvec((0,0,45)) Sensor(id=...) >>> print(sens.position) [0.70710678 0.70710678 0. ] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [ 0. 0. 90.]
Create a rotation path by rotating in several steps about an anchor:
>>> sens.rotate_from_rotvec([(0,0,15), (0,0,30), (0,0,45)], anchor=(0,0,0)) Sensor(id=...) >>> print(sens.position) [[ 7.07106781e-01 7.07106781e-01 0.00000000e+00] [ 5.00000000e-01 8.66025404e-01 0.00000000e+00] [ 2.58819045e-01 9.65925826e-01 0.00000000e+00] [-2.22044605e-16 1.00000000e+00 0.00000000e+00]] >>> print(sens.orientation.as_euler('xyz', degrees=True)) [[ 0. 0. 90.] [ 0. 0. 105.] [ 0. 0. 120.] [ 0. 0. 135.]]
- show(*, zoom=0, animation=False, markers=None, backend=None, canvas=None, return_fig=False, **kwargs)#
Display objects and paths graphically.
Global graphic styles can be set with kwargs as style dictionary or using style underscore magic.
- Parameters
objects (Magpylib objects (sources, collections, sensors)) – Objects to be displayed.
zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.
animation (bool or float, default=`False`) – If True and at least one object has a path, the paths are rendered. If input is a positive float, the animation time is set to the given value. This feature is only available for the plotly backend.
markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.
backend (string, default=`None`) – Define plotting backend. Must be one of ‘matplotlib’, ‘plotly’. If not set, parameter will default to magpylib.defaults.display.backend which is ‘matplotlib’ by installation default.
canvas (bool, default=False) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes._subplots.AxesSubplot with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. By default a new canvas is created and immediately displayed.
canvas – If True, the function call returns the figure object. - with matplotlib: matplotlib.figure.Figure. - with plotly: plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter.
- Return type
None or figure object
Examples
Display multiple objects, object paths, markers in 3D using Matplotlib or Plotly:
>>> import magpylib as magpy >>> src = magpy.magnet.Sphere(magnetization=(0,0,1), diameter=1) >>> src.move([(0.1*x,0,0) for x in range(50)]) Sphere... >>> src.rotate_from_angax(angle=[*range(0,400,10)], axis='z', anchor=0, start=11) Sphere... >>> ts = [-.4,0,.4] >>> sens = magpy.Sensor(position=(0,0,2), pixel=[(x,y,0) for x in ts for y in ts]) >>> magpy.show(src, sens) >>> magpy.show(src, sens, backend='plotly') >>> # graphic output
Display output on your own canvas (here a Matplotlib 3d-axes):
>>> import matplotlib.pyplot as plt >>> import magpylib as magpy >>> my_axis = plt.axes(projection='3d') >>> magnet = magpy.magnet.Cuboid(magnetization=(1,1,1), dimension=(1,2,3)) >>> sens = magpy.Sensor(position=(0,0,3)) >>> magpy.show(magnet, sens, canvas=my_axis, zoom=1) >>> plt.show() >>> # graphic output
Use sophisticated figure styling options accessible from defaults, as individual object styles or as global style arguments in display.
>>> import magpylib as magpy >>> src1 = magpy.magnet.Sphere((1,1,1), 1, [(0,0,0), (0,0,3)]) >>> src2 = magpy.magnet.Sphere((1,1,1), 1, [(1,0,0), (1,0,3)], style_path_show=False) >>> magpy.defaults.display.style.magnet.magnetization.size = 2 >>> src1.style.magnetization.size = 1 >>> magpy.show(src1, src2, style_color='r') >>> # graphic output
- property style#
Object style in the form of a BaseStyle object. Input must be in the form of a style dictionary.
- property vertices#
Length of the Tetrahedron sides [a,b,c] in units of [mm].