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 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 test_aaRot_priv():
A = np.array([22, 133, 244])
AX = np.array([[.1, .2, .3], [3, 4, 5], [-7, -8, -9]])
V = np.array([[1, 2, 3], [2, 3, 4], [4, 5, 6]])
sol = np.array([[
1.,
2.,
3.,
], [2.57438857, 2.86042187, 3.76702936],
[4.77190313, 4.65730779, 5.70424619]])
assert amax(abs(angleAxisRotationV_priv(A, AX, V) -
sol)) < 1e-6, "bad angleAxisRotationV_priv"
def Bfield_CircularCurrentLoopV(I0, D, POS):
R = D / 2 #radius
N = len(D) # vector size
X, Y, Z = POS[:, 0], POS[:, 1], POS[:, 2]
RR, PHI = sqrt(X**2 + Y**2), arctan2(Y, X) # cylindrical coordinates
deltaP = sqrt((RR + R)**2 + Z**2)
deltaM = sqrt((RR - R)**2 + Z**2)
kappa = deltaP**2 / deltaM**2
kappaBar = 1 - kappa
# allocate solution vector
field_R = empty([N])
# avoid discontinuity of Br on z-axis
maskRR0 = RR == np.zeros([N])
field_R[maskRR0] = 0
# R-component computation
notM = np.invert(maskRR0)
field_R[notM] = -2 * 1e-4 * (Z[notM] / RR[notM] / deltaM[notM]) * (
ellipticKV(kappaBar[notM]) - (2 - kappaBar[notM]) /
(2 - 2 * kappaBar[notM]) * ellipticEV(kappaBar[notM]))
# Z-component computation
field_Z = -2 * 1e-4 * (1 / deltaM) * (
-ellipticKV(kappaBar) + (2 - kappaBar - 4 * (R / deltaM)**2) /
(2 - 2 * kappaBar) * ellipticEV(kappaBar))
# transformation to cartesian coordinates
Bcy = np.array([field_R, np.zeros(N), field_Z]).T
AX = np.zeros([N, 3])
AX[:, 2] = 1
Bkart = angleAxisRotationV_priv(PHI / pi * 180, AX, Bcy)
return (Bkart.T * I0).T * 1000 # to mT
def getBv_magnet(type, MAG, DIM, POSm, POSo, ANG=[], AX=[], ANCH=[], Nphi0=50):
"""
Calculate the field of magnets using vectorized performance code.
Parameters
----------
type : string
source type either 'box', 'cylinder', 'sphere'.
MAG : Nx3 numpy array float [mT]
vector of N magnetizations.
DIM : NxY numpy array float [mm]
vector of N dimensions for each evaluation. The form of this vector depends
on the source type. Y=3/2/1 for box/cylinder/sphere
POSo : Nx3 numpy array float [mm]
vector of N positions of the observer.
POSm : Nx3 numpy array float [mm]
vector of N initial source positions. These positions will be adjusted by
the given rotation parameters.
ANG=[] : length M list of size N numpy arrays float [deg]
Angles of M subsequent rotation operations applied to the N-sized POSm and
the implicit source orientation.
AX=[] : length M list of Nx3 numpy arrays float []
Axis vectors of M subsequent rotation operations applied to the N-sized
POSm and the implicit source orientation.
ANCH=[] : length M list of Nx3 numpy arrays float [mm]
Anchor positions of M subsequent rotations applied ot the N-sized POSm and
the implicit source orientation.
Nphi0=50 : integer gives number of iterations used when calculating diametral
magnetized cylindrical magnets.
"""
N = len(POSo)
Q = np.zeros([N, 4])
Q[:, 0] = 1 # init orientation
Pm = POSm #initial position
#apply rotation operations
for ANGLE, AXIS, ANCHOR in zip(ANG, AX, ANCH):
Q = QmultV(getRotQuatV(ANGLE, AXIS), Q)
Pm = angleAxisRotationV_priv(ANGLE, AXIS, Pm - ANCHOR) + ANCHOR
# transform into CS of source
POSrel = POSo - Pm #relative position
Qc = QconjV(Q) #orientierung
POSrot = QrotationV(Qc, POSrel) #rotation der pos in das CS der Quelle
# calculate field
if type == 'box':
Brot = Bfield_BoxV(MAG, POSrot, DIM)
elif type == 'cylinder':
Brot = Bfield_CylinderV(MAG, POSrot, DIM, Nphi0)
elif type == 'sphere':
Brot = Bfield_SphereV(MAG, POSrot, DIM)
else:
print('Bad type or WIP')
return 0
# transform back
B = QrotationV(Q, Brot) #rückrotation des feldes
return B
def getBv_moment(type, MOM, POSm, POSo, ANG=[], AX=[], ANCH=[]):
"""
Calculate the field of magnetic moments using vectorized performance code.
Parameters
----------
type : string
source type: 'dipole'
MOM : Nx3 numpy array float [mT]
vector of N dipole moments.
POSo : Nx3 numpy array float [mm]
vector of N positions of the observer.
POSm : Nx3 numpy array float [mm]
vector of N initial source positions. These positions will be adjusted by
the given rotation parameters.
ANG=[] : length M list of size N numpy arrays float [deg]
Angles of M subsequent rotation operations applied to the N-sized POSm and
the implicit source orientation.
AX=[] : length M list of Nx3 numpy arrays float []
Axis vectors of M subsequent rotation operations applied to the N-sized
POSm and the implicit source orientation.
ANCH=[] : length M list of Nx3 numpy arrays float [mm]
Anchor positions of M subsequent rotations applied ot the N-sized POSm and
the implicit source orientation.
"""
N = len(POSo)
Q = np.zeros([N, 4])
Q[:, 0] = 1 # init orientation
Pm = POSm #initial position
#apply rotation operations
for ANGLE, AXIS, ANCHOR in zip(ANG, AX, ANCH):
Q = QmultV(getRotQuatV(ANGLE, AXIS), Q)
Pm = angleAxisRotationV_priv(ANGLE, AXIS, Pm - ANCHOR) + ANCHOR
# transform into CS of source
POSrel = POSo - Pm #relative position
Qc = QconjV(Q) #orientierung
POSrot = QrotationV(Qc, POSrel) #rotation der pos in das CS der Quelle
# calculate field
if type == 'dipole':
Brot = Bfield_DipoleV(MOM, POSrot)
else:
print('Bad type')
return 0
# transform back
B = QrotationV(Q, Brot) #rückrotation des feldes
return B
def getBv_current(type, CURR, DIM, POSm, POSo, ANG=[], AX=[], ANCH=[]):
"""
Calculate the field of currents using vectorized performance code.
Parameters
----------
type : string
source type either 'circular' or 'line'
MAG : Nx3 numpy array float [mT]
vector of N magnetizations.
DIM : NxY numpy array float [mm]
vector of N dimensions for each evaluation. The form of this vector depends
on the source type. Y=1/3x3 for circular/line.
POSo : Nx3 numpy array float [mm]
vector of N positions of the observer.
POSm : Nx3 numpy array float [mm]
vector of N initial source positions. These positions will be adjusted by
the given rotation parameters.
ANG=[] : length M list of size N numpy arrays float [deg]
Angles of M subsequent rotation operations applied to the N-sized POSm and
the implicit source orientation.
AX=[] : length M list of Nx3 numpy arrays float []
Axis vectors of M subsequent rotation operations applied to the N-sized
POSm and the implicit source orientation.
ANCH=[] : length M list of Nx3 numpy arrays float [mm]
Anchor positions of M subsequent rotations applied ot the N-sized POSm and
the implicit source orientation.
"""
N = len(POSo)
Q = np.zeros([N, 4])
Q[:, 0] = 1 # init orientation
Pm = POSm #initial position
#apply rotation operations
for ANGLE, AXIS, ANCHOR in zip(ANG, AX, ANCH):
Q = QmultV(getRotQuatV(ANGLE, AXIS), Q)
Pm = angleAxisRotationV_priv(ANGLE, AXIS, Pm - ANCHOR) + ANCHOR
# transform into CS of source
POSrel = POSo - Pm #relative position
Qc = QconjV(Q) #orientierung
POSrot = QrotationV(Qc, POSrel) #rotation der pos in das CS der Quelle
# calculate field
if type == 'circular':
Brot = Bfield_CircularCurrentLoopV(CURR, DIM, POSrot)
elif type == 'line':
Brot = Bfield_LineSegmentV(POSrot, DIM[:, 0], DIM[:, 1], CURR)
else:
print('Bad type')
return 0
# transform back
B = QrotationV(Q, Brot) #rückrotation des feldes
return B