def getB(self, pos): # Particular Line current B field calculation. Check RCS for getB() interface
# vectorized code if input is an Nx3 array
if type(pos) == ndarray:
if len(shape(pos))==2: # list of positions - use vectorized code
# vector size
NN = shape(pos)[0]
# prepare vector inputs
POSREL = pos - self.position
ANG = ones(NN)*self.angle
AX = tile(self.axis,(NN,1))
# compute rotations and field
ROTATEDPOS = angleAxisRotationV_priv(ANG, -AX, POSREL)
BB = Bfield_CurrentLineVV(self.vertices,self.current,ROTATEDPOS)
BCM = angleAxisRotationV_priv(ANG, AX, BB)
return BCM
# secure input type and check input format
p1 = array(pos, dtype=float64, copy=False)
# relative position between mag and obs
posRel = p1 - self.position
# rotate this vector into the CS of the magnet (inverse rotation)
rotatedPos = angleAxisRotation_priv(self.angle, -self.axis, posRel) # pylint: disable=invalid-unary-operand-type
# rotate field vector back
BCm = angleAxisRotation_priv(self.angle, self.axis, Bfield_CurrentLineV(self.vertices, self.current,rotatedPos))
# BCm is the obtained magnetic field in Cm
# the field is well known in the magnet coordinates.
return BCm
def getB(self, pos):
# vectorized code if input is an Nx3 array
if type(pos) == ndarray:
if len(np.shape(
pos)) == 2: # list of positions - use vectorized code
# vector size
NN = np.shape(pos)[0]
# prepare vector inputs
POSREL = pos - self.position
ANG = np.ones(NN) * self.angle
AX = np.tile(self.axis, (NN, 1))
MAG = np.tile(self.magnetization, (NN, 1))
DIM = np.ones(NN) * self.dimension
# compute rotations and field
ROTATEDPOS = angleAxisRotationV_priv(ANG, -AX, POSREL)
BB = Bfield_SphereV(MAG, ROTATEDPOS, DIM)
BCM = angleAxisRotationV_priv(ANG, AX, BB)
return BCM
# secure input type and check input format
p1 = array(pos, dtype=float64, copy=False)
# relative position between mag and obs
posRel = p1 - self.position
# rotate this vector into the CS of the magnet (inverse rotation)
rotatedPos = angleAxisRotation_priv(self.angle, -self.axis, posRel) # pylint: disable=invalid-unary-operand-type
# rotate field vector back
BCm = angleAxisRotation_priv(
self.angle, self.axis,
Bfield_Sphere(self.magnetization, rotatedPos, self.dimension))
# BCm is the obtained magnetic field in Cm
# the field is well known in the magnet coordinates.
return BCm
def test_Quaternion():
Qmult([1, 2, 3, 4], [4, 3, 2, 1]) == [-12, 6, 24, 12]
Qconj([1, 2, 3, 4]) == [1, -2, -3, -4]
Qnorm2([1, 2, 3, 4]) == 30
Q = Qunit([1, 2, 3, 4])
sol = [0.1826, 0.3651, 0.5477, 0.7303]
for q, s in zip(Q, sol):
assert round(q, 4) == s, "bad Qunit"
Q = getRotQuat(33, [1, 2, 3])
sol = [0.9588, 0.0759, 0.1518, 0.2277]
for q, s in zip(Q, sol):
assert round(q, 4) == s, "bad getRotQuat"
V = angleAxisRotation_priv(33, [1, 2, 3], [4, 5, 6])
sol = [3.2868, 5.8042, 5.7016]
for v, s in zip(V, sol):
assert round(v, 4) == s, "bad getRotQuat"
def displaySystem(sources,
markers=listOfPos,
subplotAx=None,
sensors=listOfSensors,
suppress=False,
direc=False,
figsize=(8, 8)):
"""
Shows the collection system in an interactive pyplot and returns a matplotlib figure identifier.
WARNING
-------
As a result of an inherent problem in matplotlib the
Poly3DCollections z-ordering fails when bounding boxes intersect.
Parameters
----------
markers : list[scalar,scalar,scalar,[label]]
List of position vectors to add visual markers to the display, optional label.
Default: [[0,0,0]]
Example
-------
>>> from magpylib import Collection, source
>>> c=source.current.Circular(3,7)
>>> x = Collection(c)
>>> marker0 = [0,0,0,"Neutral Position"]
>>> marker1 = [10,10,10]
>>> x.displaySystem(markers=[ marker0,
... marker1])
Parameters
----------
sensors : list[sensor]
List of :class:`~magpylib.Sensor` objects to add the display.
Default: None
Example
-------
>>> from magpylib import Collection, source
>>> c=source.current.Circular(3,7)
>>> x = Collection(c)
>>> sensor0 = Sensor()
>>> sensor1 = Sensor(pos=[1,2,3], angle=180)
>>> x.displaySystem(sensors=[ sensor0,
... sensor1])
Parameters
----------
suppress : bool
If True, only return Figure information, do not show. Interactive mode must be off.
Default: False.
Example
-------
>>> ## Suppress matplotlib.pyplot.show()
>>> ## and returning figure from showing up
>>> from matplotlib import pyplot
>>> pyplot.ioff()
>>> figureData = Collection.displayFigure(suppress=True)
Parameters
----------
direc : bool
Set to True to show current directions and magnetization vectors.
Default: False
Return
------
matplotlib Figure object
graphics object is displayed through plt.show()
Example
-------
>>> from magpylib import source, Collection
>>> pm1 = source.magnet.Box(mag=[0,0,1000],dim=[1,1,1],pos=[-1,-1,-1],angle=45,axis=[0,0,1])
>>> pm2 = source.magnet.Cylinder(mag=[0,0,1000],dim=[2,2],pos=[0,-1,1],angle=45,axis=[1,0,0])
>>> pm3 = source.magnet.Sphere(mag=[0,0,1000],dim=3,pos=[-2,1,2],angle=45,axis=[1,0,0])
>>> C1 = source.current.Circular(curr=100,dim=6)
>>> col = Collection(pm1,pm2,pm3,C1)
>>> col.displaySystem()
Parameters
----------
subplotAx : matplotlib subplot axe instance
Use an existing matplotlib subplot instance to draw the 3D system plot into.
Default: None
Example
-------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from magpylib.source.magnet import Box
>>> from magpylib import Collection
>>> #create collection of one magnet
>>> s1 = Box(mag=[ 500,0, 500], dim=[3,3,3], pos=[ 0,0, 3], angle=45, axis=[0,1,0])
>>> c = Collection(s1)
>>> #create positions
>>> xs = np.linspace(-8,8,100)
>>> zs = np.linspace(-6,6,100)
>>> posis = [[x,0,z] for z in zs for x in xs]
>>> #calculate fields
>>> Bs = c.getBsweep(posis)
>>> #reshape array and calculate amplitude
>>> Bs = np.array(Bs).reshape([100,100,3])
>>> Bamp = np.linalg.norm(Bs,axis=2)
>>> X,Z = np.meshgrid(xs,zs)
>>> # Define figure
>>> fig = plt.figure()
>>> ## Define ax for 2D
>>> ax1 = fig.add_subplot(1, 2, 1, axisbelow=True)
>>> ## Define ax for 3D displaySystem
>>> ax2 = fig.add_subplot(1, 2, 2, axisbelow=True,projection='3d')
>>> ## field plot 2D
>>> ax1.contourf(X,Z,Bamp,100,cmap='rainbow')
>>> U,V = Bs[:,:,0], Bs[:,:,2]
>>> ax1.streamplot(X, Z, U, V, color='k', density=2)
>>> ## plot Collection system in 3D ax subplot
>>> c.displaySystem(subplotAx=ax2)
Raises
------
AssertionError
If Marker position list is poorly defined. i.e. listOfPos=(x,y,z) instead of lisOfPos=[(x,y,z)]
"""
collection = Collection(sources)
if subplotAx is None:
fig = plt.figure(dpi=80, figsize=figsize)
ax = fig.gca(projection='3d')
else:
ax = subplotAx
# count magnets
Nm = 0
for s in collection.sources:
if type(s) is Box or type(s) is Cylinder or type(s) is Sphere:
Nm += 1
cm = plt.cm.hsv # Linter complains about this but it is working pylint: disable=no-member
# select colors
colors = [cm(x) for x in linspace(0, 1, Nm + 1)]
ii = -1
SYSSIZE = finfo(float).eps # Machine Epsilon for moment
dipolesList = []
magnetsList = []
sensorsList = []
currentsList = []
markersList = []
# Check input and Add markers to the Markers list before plotting
for m in markers:
assert isDisplayMarker(
m), "Invalid marker definition in displaySystem:" + str(
m) + ". Needs to be [vec3] or [vec3,string]"
markersList += [m]
for s in sensors:
if s == sensor1:
continue
else:
assert isSensor(
s), "Invalid sensor definition in displaySystem:" + str(s)
sensorsList.append(s)
for s in collection.sources:
if type(s) is Box:
ii += 1 # increase color counter
P = s.position
D = s.dimension / 2
# create vertices in canonical basis
v0 = array([
D, D * array([1, 1, -1]), D * array([1, -1, -1]),
D * array([1, -1, 1]), D * array([-1, 1, 1]),
D * array([-1, 1, -1]), -D, D * array([-1, -1, 1])
])
# rotate vertices + displace
v = array(
[angleAxisRotation_priv(s.angle, s.axis, d) + P for d in v0])
# create faces
faces = [[v[0], v[1], v[2], v[3]], [v[0], v[1], v[5], v[4]],
[v[4], v[5], v[6], v[7]], [v[2], v[3], v[7], v[6]],
[v[0], v[3], v[7], v[4]], [v[1], v[2], v[6], v[5]]]
# plot
boxf = Poly3DCollection(faces,
facecolors=colors[ii],
linewidths=0.5,
edgecolors='k',
alpha=1)
ax.add_collection3d(boxf)
# check system size
maxSize = amax(abs(v))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Cylinder:
ii += 1 # increase color counter
P = s.position
R, H = s.dimension / 2
resolution = 20
# vertices
phis = linspace(0, 2 * pi, resolution)
vertB0 = array([[R * cos(p), R * sin(p), -H] for p in phis])
vertT0 = array([[R * cos(p), R * sin(p), H] for p in phis])
# rotate vertices+displacement
vB = array([
angleAxisRotation_priv(s.angle, s.axis, d) + P for d in vertB0
])
vT = array([
angleAxisRotation_priv(s.angle, s.axis, d) + P for d in vertT0
])
# faces
faces = [[vT[i], vB[i], vB[i + 1], vT[i + 1]]
for i in range(resolution - 1)]
faces += [vT, vB]
# plot
coll = Poly3DCollection(faces,
facecolors=colors[ii],
linewidths=0.5,
edgecolors='k',
alpha=1)
ax.add_collection3d(coll)
# check system size
maxSize = max([amax(abs(vB)), amax(abs(vT))])
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Sphere:
ii += 1 # increase color counter
P = s.position
R = s.dimension / 2
resolution = 12
# vertices
phis = linspace(0, 2 * pi, resolution)
thetas = linspace(0, pi, resolution)
vs0 = [[[
R * cos(phi) * sin(th), R * sin(phi) * sin(th), R * cos(th)
] for phi in phis] for th in thetas]
# rotate vertices + displacement
vs = array(
[[angleAxisRotation_priv(s.angle, s.axis, v) + P for v in vss]
for vss in vs0])
# faces
faces = []
for j in range(resolution - 1):
faces += [[
vs[i, j], vs[i + 1, j], vs[i + 1, j + 1], vs[i, j + 1]
] for i in range(resolution - 1)]
# plot
boxf = Poly3DCollection(faces,
facecolors=colors[ii],
linewidths=0.5,
edgecolors='k',
alpha=1)
ax.add_collection3d(boxf)
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Line:
P = s.position
vs0 = s.vertices
# rotate vertices + displacement
vs = array(
[angleAxisRotation_priv(s.angle, s.axis, v) + P for v in vs0])
# plot
ax.plot(vs[:, 0], vs[:, 1], vs[:, 2], lw=1, color='k')
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
# These don't move in the original object,
sCopyWithVertices = deepcopy(s)
sCopyWithVertices.vertices = vs # We just draw the frame rotation, discard changes
currentsList.append(sCopyWithVertices)
elif type(s) is Circular:
P = s.position
R = s.dimension / 2
resolution = 20
# vertices
phis = linspace(0, 2 * pi, resolution)
vs0 = array([[R * cos(p), R * sin(p), 0] for p in phis])
# rotate vertices + displacement
vs = array(
[angleAxisRotation_priv(s.angle, s.axis, v) + P for v in vs0])
# plot
ax.plot(vs[:, 0], vs[:, 1], vs[:, 2], lw=1, color='k')
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
# Send the Circular vertice information
sCopyWithVertices = deepcopy(s)
sCopyWithVertices.vertices = vs # to the object drawing list
currentsList.append(sCopyWithVertices)
elif type(s) is Dipole:
P = angleAxisRotation(s.position, s.angle, s.axis)
maxSize = amax(abs(P))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
dipolesList.append(s)
for m in markersList: # Draw Markers
ax.scatter(m[0], m[1], m[2], s=20, marker='x')
if (len(m) > 3):
zdir = None
ax.text(m[0], m[1], m[2], m[3], zdir)
# Goes up to 3rd Position
maxSize = max([abs(pos) for pos in m[:3]])
if maxSize > SYSSIZE:
SYSSIZE = maxSize
for s in sensorsList: # Draw Sensors
maxSize = max([abs(pos) for pos in s.position])
if maxSize > SYSSIZE:
SYSSIZE = maxSize
drawSensor(s, SYSSIZE, ax)
for d in dipolesList:
drawDipole(d.position, d.moment, d.angle, d.axis, SYSSIZE, ax)
if direc is True: # Draw the Magnetization axes and current directions
drawCurrentArrows(currentsList, SYSSIZE, ax)
drawMagAxis(magnetsList, SYSSIZE, ax)
#for tick in ax.xaxis.get_ticklabels()+ax.yaxis.get_ticklabels()+ax.zaxis.get_ticklabels():
# tick.set_fontsize(12)
ax.set_xlabel('x[mm]') #, fontsize=12)
ax.set_ylabel(
'y[mm]') #, fontsize=12) #change font size through rc parameters
ax.set_zlabel('z[mm]') #, fontsize=12)
ax.set(
xlim=(-SYSSIZE, SYSSIZE),
ylim=(-SYSSIZE, SYSSIZE),
zlim=(-SYSSIZE, SYSSIZE),
)
plt.tight_layout()
if suppress == True:
return plt.gcf()
else:
plt.show()