def _geneig(a1,b,left,right,overwrite_a,overwrite_b):
b1 = asarray(b)
overwrite_b = overwrite_b or (b1 is not b and not hasattry(b,'__array__'))
if len(b1.shape) != 2 or b1.shape[0] != b1.shape[1]:
raise ValueError, 'expected square matrix'
ggev, = get_lapack_funcs(('ggev',),(a1,b1))
cvl,cvr = left,right
if ggev.module_name[:7] == 'clapack':
raise NotImplementedError,'calling ggev from %s' % (ggev.module_name)
res = ggev(a1,b1,lwork=-1)
lwork = res[-2][0]
if ggev.prefix in 'cz':
alpha,beta,vl,vr,work,info = ggev(a1,b1,cvl,cvr,lwork,
overwrite_a,overwrite_b)
w = alpha / beta
else:
alphar,alphai,beta,vl,vr,work,info = ggev(a1,b1,cvl,cvr,lwork,
overwrite_a,overwrite_b)
w = (alphar+_I*alphai)/beta
if info<0: raise ValueError,\
'illegal value in %-th argument of internal ggev'%(-info)
if info>0: raise LinAlgError,"generalized eig algorithm did not converge"
only_real = scipy_base.logical_and.reduce(scipy_base.equal(w.imag,0.0))
if not (ggev.prefix in 'cz' or only_real):
t = w.typecode()
if left:
vl = _make_complex_eigvecs(w, vl, t)
if right:
vr = _make_complex_eigvecs(w, vr, t)
if not (left or right):
return w
if left:
if right:
return w, vl, vr
return w, vl
return w, vr
def eig(a,b=None,left=0,right=1,overwrite_a=0,overwrite_b=0):
""" Solve ordinary and generalized eigenvalue problem
of a square matrix.
Inputs:
a -- An N x N matrix.
b -- An N x N matrix [default is identity(N)].
left -- Return left eigenvectors [disabled].
right -- Return right eigenvectors [enabled].
Outputs:
w -- eigenvalues [left==right==0].
w,vr -- w and right eigenvectors [left==0,right=1].
w,vl -- w and left eigenvectors [left==1,right==0].
w,vl,vr -- [left==right==1].
Definitions:
a * vr[:,i] = w[i] * b * vr[:,i]
a^H * vl[:,i] = conjugate(w[i]) * b^H * vl[:,i]
where a^H denotes transpose(conjugate(a)).
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError, 'expected square matrix'
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a,'__array__'))
if b is not None:
b = asarray_chkfinite(b)
return _geneig(a1,b,left,right,overwrite_a,overwrite_b)
geev, = get_lapack_funcs(('geev',),(a1,))
compute_vl,compute_vr=left,right
if geev.module_name[:7] == 'flapack':
lwork = calc_lwork.geev(geev.prefix,a1.shape[0],
compute_vl,compute_vr)[1]
if geev.prefix in 'cz':
w,vl,vr,info = geev(a1,lwork = lwork,
compute_vl=compute_vl,
compute_vr=compute_vr,
overwrite_a=overwrite_a)
else:
wr,wi,vl,vr,info = geev(a1,lwork = lwork,
compute_vl=compute_vl,
compute_vr=compute_vr,
overwrite_a=overwrite_a)
t = {'f':'F','d':'D'}[wr.typecode()]
w = wr+_I*wi
else: # 'clapack'
if geev.prefix in 'cz':
w,vl,vr,info = geev(a1,
compute_vl=compute_vl,
compute_vr=compute_vr,
overwrite_a=overwrite_a)
else:
wr,wi,vl,vr,info = geev(a1,
compute_vl=compute_vl,
compute_vr=compute_vr,
overwrite_a=overwrite_a)
t = {'f':'F','d':'D'}[wr.typecode()]
w = wr+_I*wi
if info<0: raise ValueError,\
'illegal value in %-th argument of internal geev'%(-info)
if info>0: raise LinAlgError,"eig algorithm did not converge"
only_real = scipy_base.logical_and.reduce(scipy_base.equal(w.imag,0.0))
if not (geev.prefix in 'cz' or only_real):
t = w.typecode()
if left:
vl = _make_complex_eigvecs(w, vl, t)
if right:
vr = _make_complex_eigvecs(w, vr, t)
if not (left or right):
return w
if left:
if right:
return w, vl, vr
return w, vl
return w, vr
