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Merge pull request #25 from nicolasaunai/mva
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add minimum variance analysis
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nicolasaunai authored Apr 3, 2024
2 parents c814b8c + f70e62b commit a1693d9
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100 changes: 100 additions & 0 deletions space/analysis/mva.py
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import numpy as np

# L,M,N constants
L = 2
M = 1
N = 0


class MVA(object):
"""
Minimum Variance Analysis
"""

def __init__(self, B):
"""
@param B : magnetic field
"""

self._B = B.copy() # magnetic field

# not normalizing anymore...
# B2 = B[:,0]**2 + B[:,1]**2 + B[:,2]**2
# self._B[:,0]/=np.sqrt(B2)
# self._B[:,1]/=np.sqrt(B2)
# self._B[:,2]/=np.sqrt(B2)

self._LMN = np.ndarray(shape=(3, 3)) # LMN matrix
self._eigen = None

varM = np.ndarray(shape=(3, 3))

# build the variance matrix <BiBj> - <Bi><Bj>
for i in np.arange(3):
for j in np.arange(3):
varM[i, j] = np.mean(self._B[:, i] * self._B[:, j]) - np.mean(
self._B[:, i]
) * np.mean(self._B[:, j])

# find the eigenvalues of varM and the associated eigenvectors
w, v = np.linalg.eigh(varM)

# now we want to sort the eigenvalues
ind = np.argsort(w) # return the indices that would sort 'w'
self._eigen = w[ind]

vt = v.transpose() # eigh returns v[:,i] associated with w[i]
# and we want the line v[i,:] with w[i]
# so that vB is Blmn

# then put the vectors in the same order as the eigenvalues
for h in np.arange(3):
self._LMN[h, :] = vt[ind[h], :]

# legacy magnetopause : reverse N if pointing inside the magnetosphere
# can be convention that Nx >0
if self._LMN[N, 0] < 0:
self._LMN[N, :] *= -1

# same kind of convention we want Lz >0
if self._LMN[L, 2] < 0:
self._LMN[L, :] *= -1

# M defined as cross product LxN
self._LMN[1, 0] = (
self._LMN[0, 1] * self._LMN[2, 2] - self._LMN[0, 2] * self._LMN[2, 1]
)
self._LMN[1, 1] = (
self._LMN[2, 0] * self._LMN[0, 2] - self._LMN[2, 2] * self._LMN[0, 0]
)
self._LMN[1, 2] = (
self._LMN[0, 0] * self._LMN[2, 1] - self._LMN[0, 1] * self._LMN[2, 0]
)

# ==========================================================
# ==========================================================
def to_LMN(self, vector):
"""
transforms vector[:,3] into the LMN coord. syst.
"""
vlmn = np.ndarray(vector.shape)
for i in np.arange(3):
vlmn[:, i] = (
self._LMN[i, 0] * vector[:, 0]
+ self._LMN[i, 1] * vector[:, 1]
+ self._LMN[i, 2] * vector[:, 2]
)

return vlmn

# ==========================================================

# ==========================================================
# ==========================================================
def quality(self):
"""
returns the quality of MVA as the ratio intermediate/min eigenvalues
"""
return self._eigen[1] / self._eigen[0]

# ==========================================================

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