# magpylib.current package#

The magpylib.current subpackage contains all electric current classes.

class magpylib.current.Circle(position=(0, 0, 0), orientation=None, diameter=None, current=None, *, style=None, **kwargs)#

Bases: `BaseCurrent`

Circular current loop.

Can be used as sources input for magnetic field computation.

When position=(0,0,0) and orientation=None the current loop lies in the x-y plane of the global coordinate system, with its center in the origin.

SI units are used for all inputs and outputs.

Parameters:
• position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of m. 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.

• diameter (float, default=`None`) – Diameter of the loop in units of m.

• current (float, default=`None`) – Electrical current in units of A.

• 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:

current source

Return type:

Circle object

Examples

Circle objects are magnetic field sources. In this example we compute the H-field in A/m of such a current loop with 100 A current and a diameter of 2 meters at the observer position (0.01,0.01,0.01) given in units of m:

```>>> import magpylib as magpy
>>> src = magpy.current.Circle(current=100, diameter=2)
>>> H = src.getH((.01,.01,.01))
>>> print(H)
[7.50093701e-03 7.50093701e-03 4.99999967e+01]
```

We rotate the source object, and compute the B-field, this time at a set of observer positions:

```>>> src.rotate_from_angax(90, 'x')
Circle(id=...)
>>> B = src.getB([(.01,.01,.01), (.02,.02,.02), (.03,.03,.03)])
>>> print(B)
[[-9.42595544e-09 -6.28318490e-05 -9.42595544e-09]
[-3.77179218e-08 -6.28317871e-05 -3.77179218e-08]
[-8.49179752e-08 -6.28315185e-05 -8.49179752e-08]]
```
copy(**kwargs)#

Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independent 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.].
```
property current#

Object current attribute getter and setter.

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 loop in units of m.

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 T or A/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', in_out='auto')#

Compute the B-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

B-field – B-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> B = src.getB(((0,0,0), (1,0,0), (2,0,0)))
>>> print(B)
[[ 0.          0.          0.66666667]
[ 0.          0.         -0.04166667]
[ 0.          0.         -0.00520833]]
```

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)
[[[ 0.01219289  0.         -0.0398301 ]
[-0.01219289  0.         -0.0398301 ]]

[[ 0.00077639  0.         -0.00515004]
[-0.00077639  0.         -0.00515004]]]
```
getH(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the H-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

H-field – H-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> H = src.getH(((0,0,0), (1,0,0), (2,0,0)))
>>> print(H)
[[      0.               0.         -265258.23834209]
[      0.               0.          -33157.27979276]
[      0.               0.           -4144.6599741 ]]
```

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)
[[[  9702.79184001      0.         -31695.78667738]
[ -9702.79184001      0.         -31695.78667738]]

[[   617.83031344      0.          -4098.27441249]
[  -617.83031344      0.          -4098.27441249]]]
```
getJ(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the J-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

J-field – J-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

getM(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the M-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

M-field – M-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

get_trace(base=72, **kwargs) Dict[str, Any] | List[Dict[str, Any]]#

Creates the plotly scatter3d parameters for a Circle current in a dictionary based on the provided arguments.

move(displacement, start='auto')#

Move object by the displacement input. SI units are used for all inputs and outputs.

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 m.

• 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 m. 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: 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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(*, backend=<default>, canvas=<default>, animation=<default>, zoom=<default>, markers=<default>, return_fig=<default>, row=<default>, col=<default>, output=<default>, sumup=<default>, pixel_agg=<default>, style=<default>, **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.

• backend (string, default=`None`) – Define plotting backend. Must be one of [‘auto’, ‘matplotlib’, ‘plotly’, ‘pyvista’]. If not set, parameter will default to magpylib.defaults.display.backend which is ‘auto’ by installation default. With ‘auto’, the backend defaults to ‘plotly’ if plotly is installed and the function is called in an IPython environment, otherwise defaults to ‘matplotlib’ which comes installed with magpylib. If the canvas is set, the backend defaults to the one corresponding to the canvas object (see canvas parameter).

• canvas (matplotlib.pyplot AxesSubplot or plotly Figure object, default=`None`) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes.Axes with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter. By default a new canvas is created and immediately displayed.

• 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.

• zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.

• markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.

• return_fig (bool, default=False) –

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.

• row (int or None,) – If provided specifies the row in which the objects will be displayed.

• col (int or None,) – If provided specifies the column in which the objects will be displayed.

• output (tuple or string, default="model3d") – Can be a string or a tuple of strings specifying the plot output type. By default output=’model3d’ displays the 3D representations of the objects. If output is a tuple of strings it must be a combination of ‘B’, ‘H’, ‘M’ or ‘J’ and ‘x’, ‘y’ and/or ‘z’. When having multiple coordinates, the field value is the combined vector length (e.g. (‘Bx’, ‘Hxy’, ‘Byz’)) ‘Bxy’ is equivalent to sqrt(|Bx|^2 + |By|^2). A 2D line plot is then represented accordingly if the objects contain at least one source and one sensor.

• sumup (bool, default=True) – If True, sums the field values of the sources. Applies only if output is not ‘model3d’.

• pixel_agg (bool, default="mean") – 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. Applies only if output is not ‘model3d’.

• style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’. Applies to all objects matching the given style properties.

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(polarization=(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(polarization=(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(position=[(0,0,0), (0,0,3)], diameter=1, polarization=(1,1,1))
>>> src2 = magpy.magnet.Sphere(
...     position=[(1,0,0), (1,0,3)],
...     diameter=1,
...     polarization=(1,1,1),
...     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
```

Use a context manager to jointly animate 3d and 2d subplots

```>>> import magpylib as magpy
>>> import numpy as np
>>> import plotly.graph_objects as go
>>> path_len = 40
>>> sensor = magpy.Sensor()
>>> cyl1 = magpy.magnet.Cylinder(
...    polarization=(.1, 0, 0),
...    dimension=(1, 2),
...    position=(4, 0, 0),
...    style_label="Cylinder1",
... )
>>> sensor.move(np.linspace((0, 0, -3), (0, 0, 3), path_len), start=0)
Sensor(id=...)
>>> cyl1.rotate_from_angax(angle=np.linspace(0, 300, path_len), start=0, axis="z", anchor=0)
Cylinder(id=...)
>>> cyl2 = cyl1.copy().move((0, 0, 5))
>>> fig = go.Figure()
>>> with magpy.show_context(cyl1, cyl2, sensor, canvas=fig, backend="plotly", animation=True):
...    magpy.show(col=1, output="model3d")
...    magpy.show(col=2, output="Bxy", sumup=True)
...    magpy.show(col=3, output="Bz", sumup=False)
>>> fig.show()
>>> # 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.current.Line(*args, **kwargs)#

Bases: `Polyline`

Line is deprecated, see Polyline

copy(**kwargs)#

Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independent 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.].
```
property current#

Object current attribute getter and setter.

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 T or A/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', in_out='auto')#

Compute the B-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

B-field – B-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> B = src.getB(((0,0,0), (1,0,0), (2,0,0)))
>>> print(B)
[[ 0.          0.          0.66666667]
[ 0.          0.         -0.04166667]
[ 0.          0.         -0.00520833]]
```

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)
[[[ 0.01219289  0.         -0.0398301 ]
[-0.01219289  0.         -0.0398301 ]]

[[ 0.00077639  0.         -0.00515004]
[-0.00077639  0.         -0.00515004]]]
```
getH(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the H-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

H-field – H-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> H = src.getH(((0,0,0), (1,0,0), (2,0,0)))
>>> print(H)
[[      0.               0.         -265258.23834209]
[      0.               0.          -33157.27979276]
[      0.               0.           -4144.6599741 ]]
```

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)
[[[  9702.79184001      0.         -31695.78667738]
[ -9702.79184001      0.         -31695.78667738]]

[[   617.83031344      0.          -4098.27441249]
[  -617.83031344      0.          -4098.27441249]]]
```
getJ(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the J-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

J-field – J-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

getM(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the M-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

M-field – M-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

get_trace(**kwargs) Dict[str, Any] | List[Dict[str, Any]]#

Creates the plotly scatter3d parameters for a Polyline current in a dictionary based on the provided arguments.

move(displacement, start='auto')#

Move object by the displacement input. SI units are used for all inputs and outputs.

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 m.

• 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 m. 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: 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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(*, backend=<default>, canvas=<default>, animation=<default>, zoom=<default>, markers=<default>, return_fig=<default>, row=<default>, col=<default>, output=<default>, sumup=<default>, pixel_agg=<default>, style=<default>, **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.

• backend (string, default=`None`) – Define plotting backend. Must be one of [‘auto’, ‘matplotlib’, ‘plotly’, ‘pyvista’]. If not set, parameter will default to magpylib.defaults.display.backend which is ‘auto’ by installation default. With ‘auto’, the backend defaults to ‘plotly’ if plotly is installed and the function is called in an IPython environment, otherwise defaults to ‘matplotlib’ which comes installed with magpylib. If the canvas is set, the backend defaults to the one corresponding to the canvas object (see canvas parameter).

• canvas (matplotlib.pyplot AxesSubplot or plotly Figure object, default=`None`) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes.Axes with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter. By default a new canvas is created and immediately displayed.

• 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.

• zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.

• markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.

• return_fig (bool, default=False) –

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.

• row (int or None,) – If provided specifies the row in which the objects will be displayed.

• col (int or None,) – If provided specifies the column in which the objects will be displayed.

• output (tuple or string, default="model3d") – Can be a string or a tuple of strings specifying the plot output type. By default output=’model3d’ displays the 3D representations of the objects. If output is a tuple of strings it must be a combination of ‘B’, ‘H’, ‘M’ or ‘J’ and ‘x’, ‘y’ and/or ‘z’. When having multiple coordinates, the field value is the combined vector length (e.g. (‘Bx’, ‘Hxy’, ‘Byz’)) ‘Bxy’ is equivalent to sqrt(|Bx|^2 + |By|^2). A 2D line plot is then represented accordingly if the objects contain at least one source and one sensor.

• sumup (bool, default=True) – If True, sums the field values of the sources. Applies only if output is not ‘model3d’.

• pixel_agg (bool, default="mean") – 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. Applies only if output is not ‘model3d’.

• style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’. Applies to all objects matching the given style properties.

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(polarization=(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(polarization=(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(position=[(0,0,0), (0,0,3)], diameter=1, polarization=(1,1,1))
>>> src2 = magpy.magnet.Sphere(
...     position=[(1,0,0), (1,0,3)],
...     diameter=1,
...     polarization=(1,1,1),
...     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
```

Use a context manager to jointly animate 3d and 2d subplots

```>>> import magpylib as magpy
>>> import numpy as np
>>> import plotly.graph_objects as go
>>> path_len = 40
>>> sensor = magpy.Sensor()
>>> cyl1 = magpy.magnet.Cylinder(
...    polarization=(.1, 0, 0),
...    dimension=(1, 2),
...    position=(4, 0, 0),
...    style_label="Cylinder1",
... )
>>> sensor.move(np.linspace((0, 0, -3), (0, 0, 3), path_len), start=0)
Sensor(id=...)
>>> cyl1.rotate_from_angax(angle=np.linspace(0, 300, path_len), start=0, axis="z", anchor=0)
Cylinder(id=...)
>>> cyl2 = cyl1.copy().move((0, 0, 5))
>>> fig = go.Figure()
>>> with magpy.show_context(cyl1, cyl2, sensor, canvas=fig, backend="plotly", animation=True):
...    magpy.show(col=1, output="model3d")
...    magpy.show(col=2, output="Bxy", sumup=True)
...    magpy.show(col=3, output="Bz", sumup=False)
>>> fig.show()
>>> # 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#

The current flows along the vertices which are given in units of m in the local object coordinates (move/rotate with object). At least two vertices must be given.

class magpylib.current.Loop(*args, **kwargs)#

Bases: `Circle`

Loop is deprecated, see Circle

copy(**kwargs)#

Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independent 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.].
```
property current#

Object current attribute getter and setter.

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 loop in units of m.

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 T or A/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', in_out='auto')#

Compute the B-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

B-field – B-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> B = src.getB(((0,0,0), (1,0,0), (2,0,0)))
>>> print(B)
[[ 0.          0.          0.66666667]
[ 0.          0.         -0.04166667]
[ 0.          0.         -0.00520833]]
```

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)
[[[ 0.01219289  0.         -0.0398301 ]
[-0.01219289  0.         -0.0398301 ]]

[[ 0.00077639  0.         -0.00515004]
[-0.00077639  0.         -0.00515004]]]
```
getH(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the H-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

H-field – H-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> H = src.getH(((0,0,0), (1,0,0), (2,0,0)))
>>> print(H)
[[      0.               0.         -265258.23834209]
[      0.               0.          -33157.27979276]
[      0.               0.           -4144.6599741 ]]
```

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)
[[[  9702.79184001      0.         -31695.78667738]
[ -9702.79184001      0.         -31695.78667738]]

[[   617.83031344      0.          -4098.27441249]
[  -617.83031344      0.          -4098.27441249]]]
```
getJ(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the J-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

J-field – J-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

getM(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the M-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

M-field – M-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

get_trace(base=72, **kwargs) Dict[str, Any] | List[Dict[str, Any]]#

Creates the plotly scatter3d parameters for a Circle current in a dictionary based on the provided arguments.

move(displacement, start='auto')#

Move object by the displacement input. SI units are used for all inputs and outputs.

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 m.

• 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 m. 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: 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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(*, backend=<default>, canvas=<default>, animation=<default>, zoom=<default>, markers=<default>, return_fig=<default>, row=<default>, col=<default>, output=<default>, sumup=<default>, pixel_agg=<default>, style=<default>, **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.

• backend (string, default=`None`) – Define plotting backend. Must be one of [‘auto’, ‘matplotlib’, ‘plotly’, ‘pyvista’]. If not set, parameter will default to magpylib.defaults.display.backend which is ‘auto’ by installation default. With ‘auto’, the backend defaults to ‘plotly’ if plotly is installed and the function is called in an IPython environment, otherwise defaults to ‘matplotlib’ which comes installed with magpylib. If the canvas is set, the backend defaults to the one corresponding to the canvas object (see canvas parameter).

• canvas (matplotlib.pyplot AxesSubplot or plotly Figure object, default=`None`) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes.Axes with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter. By default a new canvas is created and immediately displayed.

• 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.

• zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.

• markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.

• return_fig (bool, default=False) –

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.

• row (int or None,) – If provided specifies the row in which the objects will be displayed.

• col (int or None,) – If provided specifies the column in which the objects will be displayed.

• output (tuple or string, default="model3d") – Can be a string or a tuple of strings specifying the plot output type. By default output=’model3d’ displays the 3D representations of the objects. If output is a tuple of strings it must be a combination of ‘B’, ‘H’, ‘M’ or ‘J’ and ‘x’, ‘y’ and/or ‘z’. When having multiple coordinates, the field value is the combined vector length (e.g. (‘Bx’, ‘Hxy’, ‘Byz’)) ‘Bxy’ is equivalent to sqrt(|Bx|^2 + |By|^2). A 2D line plot is then represented accordingly if the objects contain at least one source and one sensor.

• sumup (bool, default=True) – If True, sums the field values of the sources. Applies only if output is not ‘model3d’.

• pixel_agg (bool, default="mean") – 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. Applies only if output is not ‘model3d’.

• style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’. Applies to all objects matching the given style properties.

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(polarization=(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(polarization=(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(position=[(0,0,0), (0,0,3)], diameter=1, polarization=(1,1,1))
>>> src2 = magpy.magnet.Sphere(
...     position=[(1,0,0), (1,0,3)],
...     diameter=1,
...     polarization=(1,1,1),
...     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
```

Use a context manager to jointly animate 3d and 2d subplots

```>>> import magpylib as magpy
>>> import numpy as np
>>> import plotly.graph_objects as go
>>> path_len = 40
>>> sensor = magpy.Sensor()
>>> cyl1 = magpy.magnet.Cylinder(
...    polarization=(.1, 0, 0),
...    dimension=(1, 2),
...    position=(4, 0, 0),
...    style_label="Cylinder1",
... )
>>> sensor.move(np.linspace((0, 0, -3), (0, 0, 3), path_len), start=0)
Sensor(id=...)
>>> cyl1.rotate_from_angax(angle=np.linspace(0, 300, path_len), start=0, axis="z", anchor=0)
Cylinder(id=...)
>>> cyl2 = cyl1.copy().move((0, 0, 5))
>>> fig = go.Figure()
>>> with magpy.show_context(cyl1, cyl2, sensor, canvas=fig, backend="plotly", animation=True):
...    magpy.show(col=1, output="model3d")
...    magpy.show(col=2, output="Bxy", sumup=True)
...    magpy.show(col=3, output="Bz", sumup=False)
>>> fig.show()
>>> # 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.current.Polyline(current=None, vertices=None, position=(0, 0, 0), orientation=None, style=None, **kwargs)#

Bases: `BaseCurrent`

Line current flowing in straight paths from vertex to vertex.

Can be used as sources input for magnetic field computation.

The vertex positions are defined in the local object coordinates (rotate with object). When position=(0,0,0) and orientation=None global and local coordinates coincide.

SI units are used for all inputs and outputs.

Parameters:
• position (array_like, shape (3,) or (m,3), default=`(0,0,0)`) – Object position(s) in the global coordinates in units of m. 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.

• vertices (array_like, shape (n,3), default=`None`) – The current flows along the vertices which are given in units of m in the local object coordinates (move/rotate with object). At least two vertices must be given.

• current (float, default=`None`) – Electrical current in units of A.

• 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:

current source

Return type:

Polyline object

Examples

Polyline objects are magnetic field sources. In this example we compute the H-field in A/m of a square-shaped line-current with 1 A current at the observer position (1,1,1) given in units of m:

```>>> import magpylib as magpy
>>> src = magpy.current.Polyline(
...     current=1,
...     vertices=((.01,0,0), (0,.01,0), (-.01,0,0), (0,-.01,0), (.01,0,0)),
... )
>>> H = src.getH((.01,.01,.01))
>>> print(H)
[3.16063859 3.16063859 0.76687556]
```

We rotate the source object, and compute the B-field, this time at a set of observer positions:

```>>> src.rotate_from_angax(90, 'x')
Polyline(id=...)
>>> B = src.getB([(.01,.01,.01), (.02,.02,.02), (.03,.03,.03)])
>>> print(B)
[[-3.97177559e-06 -9.63684251e-07 -3.97177559e-06]
[-4.90331150e-07 -3.11039072e-08 -4.90331150e-07]
[-1.43908549e-07 -4.10438492e-09 -1.43908549e-07]]
```
copy(**kwargs)#

Returns a copy of the current object instance. The copy method returns a deep copy of the object, that is independent 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.].
```
property current#

Object current attribute getter and setter.

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 T or A/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', in_out='auto')#

Compute the B-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

B-field – B-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> B = src.getB(((0,0,0), (1,0,0), (2,0,0)))
>>> print(B)
[[ 0.          0.          0.66666667]
[ 0.          0.         -0.04166667]
[ 0.          0.         -0.00520833]]
```

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)
[[[ 0.01219289  0.         -0.0398301 ]
[-0.01219289  0.         -0.0398301 ]]

[[ 0.00077639  0.         -0.00515004]
[-0.00077639  0.         -0.00515004]]]
```
getH(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the H-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

H-field – H-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index 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(polarization=(0,0,1.), diameter=1)
>>> H = src.getH(((0,0,0), (1,0,0), (2,0,0)))
>>> print(H)
[[      0.               0.         -265258.23834209]
[      0.               0.          -33157.27979276]
[      0.               0.           -4144.6599741 ]]
```

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)
[[[  9702.79184001      0.         -31695.78667738]
[ -9702.79184001      0.         -31695.78667738]]

[[   617.83031344      0.          -4098.27441249]
[  -617.83031344      0.          -4098.27441249]]]
```
getJ(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the J-field at observers in units of T generated by the source.

SI units are used for all inputs and outputs.

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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

J-field – J-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of T. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

getM(*observers, squeeze=True, pixel_agg=None, output='ndarray', in_out='auto')#

Compute the M-field in units of A/m at observers 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 m.

• 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).

• in_out ({'auto', 'inside', 'outside'}) –

This parameter only applies for magnet bodies. It specifies the location of the observers relative to the magnet body, affecting the calculation of the magnetic field. The options are: - ‘auto’: The location (inside or outside the cuboid) is determined automatically for each observer. - ‘inside’: All observers are considered to be inside the cuboid; use this for

performance optimization if applicable.

• ’outside’: All observers are considered to be outside the cuboid; use this for performance optimization if applicable.

Choosing ‘auto’ is fail-safe but may be computationally intensive if the mix of observer locations is unknown.

Returns:

M-field – M-field at each path position (index m) for each sensor (index k) and each sensor pixel position (indices n1,n2,…) in units of A/m. Sensor pixel positions are equivalent to simple observer positions. Paths of objects that are shorter than index m will be considered as static beyond their end.

Return type:

ndarray, shape squeeze(m, k, n1, n2, …, 3) or DataFrame

get_trace(**kwargs) Dict[str, Any] | List[Dict[str, Any]]#

Creates the plotly scatter3d parameters for a Polyline current in a dictionary based on the provided arguments.

move(displacement, start='auto')#

Move object by the displacement input. SI units are used for all inputs and outputs.

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 m.

• 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 m. 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: 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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 m. 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(*, backend=<default>, canvas=<default>, animation=<default>, zoom=<default>, markers=<default>, return_fig=<default>, row=<default>, col=<default>, output=<default>, sumup=<default>, pixel_agg=<default>, style=<default>, **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.

• backend (string, default=`None`) – Define plotting backend. Must be one of [‘auto’, ‘matplotlib’, ‘plotly’, ‘pyvista’]. If not set, parameter will default to magpylib.defaults.display.backend which is ‘auto’ by installation default. With ‘auto’, the backend defaults to ‘plotly’ if plotly is installed and the function is called in an IPython environment, otherwise defaults to ‘matplotlib’ which comes installed with magpylib. If the canvas is set, the backend defaults to the one corresponding to the canvas object (see canvas parameter).

• canvas (matplotlib.pyplot AxesSubplot or plotly Figure object, default=`None`) – Display graphical output on a given canvas: - with matplotlib: matplotlib.axes.Axes with projection=3d. - with plotly: `plotly.graph_objects.Figure or plotly.graph_objects.FigureWidget. - with pyvista: pyvista.Plotter. By default a new canvas is created and immediately displayed.

• 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.

• zoom (float, default=`0`) – Adjust plot zoom-level. When zoom=0 3D-figure boundaries are tight.

• markers (array_like, shape (n,3), default=`None`) – Display position markers in the global coordinate system.

• return_fig (bool, default=False) –

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.

• row (int or None,) – If provided specifies the row in which the objects will be displayed.

• col (int or None,) – If provided specifies the column in which the objects will be displayed.

• output (tuple or string, default="model3d") – Can be a string or a tuple of strings specifying the plot output type. By default output=’model3d’ displays the 3D representations of the objects. If output is a tuple of strings it must be a combination of ‘B’, ‘H’, ‘M’ or ‘J’ and ‘x’, ‘y’ and/or ‘z’. When having multiple coordinates, the field value is the combined vector length (e.g. (‘Bx’, ‘Hxy’, ‘Byz’)) ‘Bxy’ is equivalent to sqrt(|Bx|^2 + |By|^2). A 2D line plot is then represented accordingly if the objects contain at least one source and one sensor.

• sumup (bool, default=True) – If True, sums the field values of the sources. Applies only if output is not ‘model3d’.

• pixel_agg (bool, default="mean") – 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. Applies only if output is not ‘model3d’.

• style (dict) – Object style inputs must be in dictionary form, e.g. {‘color’:’red’} or using style underscore magic, e.g. style_color=’red’. Applies to all objects matching the given style properties.

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(polarization=(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(polarization=(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(position=[(0,0,0), (0,0,3)], diameter=1, polarization=(1,1,1))
>>> src2 = magpy.magnet.Sphere(
...     position=[(1,0,0), (1,0,3)],
...     diameter=1,
...     polarization=(1,1,1),
...     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
```

Use a context manager to jointly animate 3d and 2d subplots

```>>> import magpylib as magpy
>>> import numpy as np
>>> import plotly.graph_objects as go
>>> path_len = 40
>>> sensor = magpy.Sensor()
>>> cyl1 = magpy.magnet.Cylinder(
...    polarization=(.1, 0, 0),
...    dimension=(1, 2),
...    position=(4, 0, 0),
...    style_label="Cylinder1",
... )
>>> sensor.move(np.linspace((0, 0, -3), (0, 0, 3), path_len), start=0)
Sensor(id=...)
>>> cyl1.rotate_from_angax(angle=np.linspace(0, 300, path_len), start=0, axis="z", anchor=0)
Cylinder(id=...)
>>> cyl2 = cyl1.copy().move((0, 0, 5))
>>> fig = go.Figure()
>>> with magpy.show_context(cyl1, cyl2, sensor, canvas=fig, backend="plotly", animation=True):
...    magpy.show(col=1, output="model3d")
...    magpy.show(col=2, output="Bxy", sumup=True)
...    magpy.show(col=3, output="Bz", sumup=False)
>>> fig.show()
>>> # 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#

The current flows along the vertices which are given in units of m in the local object coordinates (move/rotate with object). At least two vertices must be given.