def test_QV():
x = array([[1, 2, 3, 4], [2, 3, 4, 5]])
y = array([[4, 3, 2, 1], [5, 4, 3, 2]])
v = array([[1, 2, 3], [2, 3, 4]])
assert (QmultV(x, y) == array([[-12, 6, 24, 12],
[-24, 16, 40, 22]])).all(), "bad QmultV"
assert (QconjV(x) == array([[1, -2, -3, -4], [2, -3, -4,
-5]])).all(), "bad Qconj"
assert (QrotationV(x, v) == array([[54, 60, 78],
[140, 158,
200]])).all(), "bad Qrotation"
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_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_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