def eigenvectors(a):
"""eigenvectors(a) returns u,v where u is the eigenvalues and
v is a matrix of eigenvectors with vector v[i] corresponds to
eigenvalue u[i]. Satisfies the equation dot(a, v[i]) = u[i]*v[i]
"""
_assertRank2(a)
_assertSquareness(a)
t =_commonType(a)
real_t = _array_type[0][_array_precision[t]]
a = _fastCopyAndTranspose(t, a)
n = a.getshape()[0]
dummy = num.zeros((1,), t)
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite2.zgeev
w = num.zeros((n,), t)
v = num.zeros((n,n), t)
lwork = 1
work = num.zeros((lwork,),t)
rwork = num.zeros((2*n,),real_t)
results = lapack_routine('N', 'V', n, a, n, w,
dummy, 1, v, n, work, -1, rwork, 0)
lwork = int(abs(work[0]))
work = num.zeros((lwork,),t)
results = lapack_routine('N', 'V', n, a, n, w,
dummy, 1, v, n, work, lwork, rwork, 0)
else:
lapack_routine = lapack_lite2.dgeev
wr = num.zeros((n,), t)
wi = num.zeros((n,), t)
vr = num.zeros((n,n), t)
lwork = 1
work = num.zeros((lwork,),t)
results = lapack_routine('N', 'V', n, a, n, wr, wi,
dummy, 1, vr, n, work, -1, 0)
lwork = int(work[0])
work = num.zeros((lwork,),t)
results = lapack_routine('N', 'V', n, a, n, wr, wi,
dummy, 1, vr, n, work, lwork, 0)
if num.logical_and.reduce(num.equal(wi, 0.)):
w = wr
v = vr
else:
w = wr+1j*wi
v = num.array(vr,type=num.Complex)
ind = num.nonzero(
num.equal(
num.equal(wi,0.0) # true for real e-vals
,0) # true for complex e-vals
) # indices of complex e-vals
for i in range(len(ind)/2):
v[ind[2*i]] = vr[ind[2*i]] + 1j*vr[ind[2*i+1]]
v[ind[2*i+1]] = vr[ind[2*i]] - 1j*vr[ind[2*i+1]]
if results['info'] > 0:
raise LinAlgError, 'Eigenvalues did not converge'
return w,v
def eigenvalues(a):
_assertRank2(a)
_assertSquareness(a)
t =_commonType(a)
real_t = _array_type[0][_array_precision[t]]
a = _fastCopyAndTranspose(t, a)
n = a.getshape()[0]
dummy = num.zeros((1,), t)
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite2.zgeev
w = num.zeros((n,), t)
rwork = num.zeros((n,),real_t)
lwork = 1
work = num.zeros((lwork,), t)
results = lapack_routine('N', 'N', n, a, n, w,
dummy, 1, dummy, 1, work, -1, rwork, 0)
lwork = int(abs(work[0]))
work = num.zeros((lwork,), t)
results = lapack_routine('N', 'N', n, a, n, w,
dummy, 1, dummy, 1, work, lwork, rwork, 0)
else:
lapack_routine = lapack_lite2.dgeev
wr = num.zeros((n,), t)
wi = num.zeros((n,), t)
lwork = 1
work = num.zeros((lwork,), t)
results = lapack_routine('N', 'N', n, a, n, wr, wi,
dummy, 1, dummy, 1, work, -1, 0)
lwork = int(work[0])
work = num.zeros((lwork,), t)
results = lapack_routine('N', 'N', n, a, n, wr, wi,
dummy, 1, dummy, 1, work, lwork, 0)
if num.logical_and.reduce(num.equal(wi, 0.)):
w = wr
else:
w = wr+1j*wi
if results['info'] > 0:
raise LinAlgError, 'Eigenvalues did not converge'
return w