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import numpy as np
def matrix_invert(mat):
"""
Pointwise matrix inversion.
Given an array that stores many square matrices (e.g. the values of the
metric tensor at spacetime points), compute the array of corresponding
inverses.
:param array_like mat: N-D array with N>2 and each mat[i0, ..., :, :] a
square matrix to be inverted.
:return: Array (same shape as mat) of inverses.
"""
oldshape = mat.shape
newshape = oldshape[:2] + (np.product(mat.shape[2:]),)
mat = mat.reshape(newshape).transpose((2, 0, 1))
inv = np.linalg.inv(mat)
return inv.transpose((1, 2, 0)).reshape(oldshape)
def matrix_det(mat):
"""
Pointwise matrix determinant.
Given an array that stores many square matrices (e.g. the values of the
metric tensor at spacetime points), compute the array of corresponding
determinants.
:param array_like mat: N-D array with N>2 and each mat[i0, ..., :, :] a
square matrix.
:return: Array of determinants.
"""
oldshape = mat.shape
newshape = oldshape[:2] + (np.product(mat.shape[2:]),)
mat = mat.reshape(newshape).transpose((2, 0, 1))
return np.linalg.det(mat).reshape(oldshape[2:])
def array_reflect(data, parity = 1.0, axis = -1):
"""
Reflect an N-D array with respect to the specified axis. E.g. input
[0, 1, 2, 3] becomes [3, 2, 1, 0, 1, 2, 3] with parity=1.0 and
[-3, -2, -1, 0, 1, 2, 3] with parity=-1.0.
:param array_like data: The array to reflect.
:param float parity: The reflected portion is multiplied by this factor,
typically 1.0 or -1.0.
:param int axis: Index of the axis to reflect along.
:return: Reflected array.
"""
slices0 = [slice(None) for _ in data.shape]
slices1 = [slice(None) for _ in data.shape]
slices0[axis] = slice(None, None, -1)
slices1[axis] = slice(1, None)
return np.concatenate((parity * data[tuple(slices0)], data[tuple(slices1)]), axis)
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