def hessenberg(a,calc_q=0,overwrite_a=0):
""" Compute Hessenberg form of a matrix.
Inputs:
a -- the matrix
calc_q -- if non-zero then calculate unitary similarity
transformation matrix q.
overwrite_a=0 -- if non-zero then discard the contents of a,
i.e. a is used as a work array if possible.
Outputs:
h -- Hessenberg form of a [calc_q=0]
h, q -- matrices such that a = q * h * q^T [calc_q=1]
"""
a1 = asarray(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__'))
gehrd,gebal = get_lapack_funcs(('gehrd','gebal'),(a1,))
ba,lo,hi,pivscale,info = gebal(a,permute=1,overwrite_a = overwrite_a)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal gebal (hessenberg)'%(-info)
n = len(a1)
lwork = calc_lwork.gehrd(gehrd.prefix,n,lo,hi)
hq,tau,info = gehrd(ba,lo=lo,hi=hi,lwork=lwork,overwrite_a=1)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal gehrd (hessenberg)'%(-info)
if not calc_q:
for i in range(lo,hi):
hq[i+2:hi+1,i] = 0.0
return hq
# XXX: Use ORGHR routines to compute q.
ger,gemm = get_blas_funcs(('ger','gemm'),(hq,))
typecode = hq.typecode()
q = None
for i in range(lo,hi):
if tau[i]==0.0:
continue
v = zeros(n,typecode=typecode)
v[i+1] = 1.0
v[i+2:hi+1] = hq[i+2:hi+1,i]
hq[i+2:hi+1,i] = 0.0
h = ger(-tau[i],v,v,a=diag(ones(n,typecode=typecode)),overwrite_a=1)
if q is None:
q = h
else:
q = gemm(1.0,q,h)
if q is None:
q = diag(ones(n,typecode=typecode))
return hq,q
def diagsvd(s,M,N):
"""Return sigma from singular values and original size M,N."""
part = diag(s)
typ = part.typecode()
MorN = len(s)
if MorN == M:
return c_[part,zeros((M,N-M),typ)]
elif MorN == N:
return r_[part,zeros((M-N,N),typ)]
else:
raise ValueError, "Length of s must be M or N."
