/usr/lib/python2.7/dist-packages/dipy/reconst/utils.py is in python-dipy 0.10.1-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | import numpy as np
def dki_design_matrix(gtab):
r""" Constructs B design matrix for DKI
Parameters
---------
gtab : GradientTable
Measurement directions.
Returns
-------
B : array (N, 22)
Design matrix or B matrix for the DKI model
B[j, :] = (Bxx, Bxy, Bzz, Bxz, Byz, Bzz,
Bxxxx, Byyyy, Bzzzz, Bxxxy, Bxxxz,
Bxyyy, Byyyz, Bxzzz, Byzzz, Bxxyy,
Bxxzz, Byyzz, Bxxyz, Bxyyz, Bxyzz,
BlogS0)
"""
b = gtab.bvals
bvec = gtab.bvecs
B = np.zeros((len(b), 22))
B[:, 0] = -b * bvec[:, 0] * bvec[:, 0]
B[:, 1] = -2 * b * bvec[:, 0] * bvec[:, 1]
B[:, 2] = -b * bvec[:, 1] * bvec[:, 1]
B[:, 3] = -2 * b * bvec[:, 0] * bvec[:, 2]
B[:, 4] = -2 * b * bvec[:, 1] * bvec[:, 2]
B[:, 5] = -b * bvec[:, 2] * bvec[:, 2]
B[:, 6] = b * b * bvec[:, 0]**4 / 6
B[:, 7] = b * b * bvec[:, 1]**4 / 6
B[:, 8] = b * b * bvec[:, 2]**4 / 6
B[:, 9] = 4 * b * b * bvec[:, 0]**3 * bvec[:, 1] / 6
B[:, 10] = 4 * b * b * bvec[:, 0]**3 * bvec[:, 2] / 6
B[:, 11] = 4 * b * b * bvec[:, 1]**3 * bvec[:, 0] / 6
B[:, 12] = 4 * b * b * bvec[:, 1]**3 * bvec[:, 2] / 6
B[:, 13] = 4 * b * b * bvec[:, 2]**3 * bvec[:, 0] / 6
B[:, 14] = 4 * b * b * bvec[:, 2]**3 * bvec[:, 1] / 6
B[:, 15] = b * b * bvec[:, 0]**2 * bvec[:, 1]**2
B[:, 16] = b * b * bvec[:, 0]**2 * bvec[:, 2]**2
B[:, 17] = b * b * bvec[:, 1]**2 * bvec[:, 2]**2
B[:, 18] = 2 * b * b * bvec[:, 0]**2 * bvec[:, 1] * bvec[:, 2]
B[:, 19] = 2 * b * b * bvec[:, 1]**2 * bvec[:, 0] * bvec[:, 2]
B[:, 20] = 2 * b * b * bvec[:, 2]**2 * bvec[:, 0] * bvec[:, 1]
B[:, 21] = np.ones(len(b))
return B
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