def determinant(a):
"""determinant(a) -> ||a||
*a* may be either rank-2 or rank-3. If it is rank-2, it must square.
>>> A = [[1,2,3], [3,4,5], [5,6,7]]
>>> _isClose(determinant(A), 0)
1
If *a* is rank-3, it is treated as an array of rank-2 matrices and
must be square along the last 2 axes.
>>> A = [[[1, 3], [2j, 3j]], [[2, 4], [4j, 4j]], [[3, 5], [6j, 5j]]]
>>> _isClose(determinant(A), [-3j, -8j, -15j])
1
If *a* is not square along its last two axes, a LinAlgError is raised.
>>> determinant(na.asarray(A)[...,:1])
Traceback (most recent call last):
...
LinearAlgebraError: Array (or it submatrices) must be square
"""
a = na.asarray(a)
_assertRank((2,3), a)
_assertSubmatrixSquareness(a)
stretched = (len(a.shape) == 2)
if stretched:
a = a[na.NewAxis,]
t = _commonType(a)
a = _castCopyAndTranspose(t, a, indices=(0,2,1))
n_cases, n = a.shape[:2]
if _array_kind[t] == 1:
lapack_routine = lapack_lite2.zgetrf
else:
lapack_routine = lapack_lite2.dgetrf
no_pivoting = na.arrayrange(1, n+1)
pivots = na.zeros((n,), 'l')
all_pivots = na.zeros((n_cases, n,), 'l')
sum , not_equal = na.sum, na.not_equal
stride = n * n * a.itemsize()
pivots_stride = n * pivots.itemsize()
view = a[0].view()
view_pivots = all_pivots[0]
a_i = view.copy()
for i in range(n_cases):
if i:
a_i._copyFrom(view)
outcome = lapack_routine(n, n, a_i, n, pivots, 0)
view_pivots._copyFrom(pivots)
view._copyFrom(a_i)
view._byteoffset += stride
view_pivots._byteoffset += pivots_stride
signs = na.where(sum(not_equal(all_pivots, no_pivoting), 1) % 2, -1, 1).astype(t)
for i in range(n):
signs *= a[:,i,i]
if stretched:
signs = signs[0]
return signs