def qr(a,overwrite_a=0,lwork=None):
"""QR decomposition of an M x N matrix a.
Description:
Find a unitary matrix, q, and an upper-trapezoidal matrix r
such that q * r = a
Inputs:
a -- the matrix
overwrite_a=0 -- if non-zero then discard the contents of a,
i.e. a is used as a work array if possible.
lwork=None -- >= shape(a)[1]. If None (or -1) compute optimal
work array size.
Outputs:
q, r -- matrices such that q * r = a
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2:
raise ValueError, 'expected matrix'
M,N = a1.shape
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a,'__array__'))
geqrf, = get_lapack_funcs(('geqrf',),(a1,))
if lwork is None or lwork == -1:
# get optimal work array
qr,tau,work,info = geqrf(a1,lwork=-1,overwrite_a=1)
lwork = work[0]
qr,tau,work,info = geqrf(a1,lwork=lwork,overwrite_a=overwrite_a)
if info<0: raise ValueError,\
'illegal value in %-th argument of internal geqrf'%(-info)
gemm, = get_blas_funcs(('gemm',),(qr,))
t = qr.typecode()
R = basic.triu(qr)
Q = scipy_base.identity(M,typecode=t)
ident = scipy_base.identity(M,typecode=t)
zeros = scipy_base.zeros
for i in range(min(M,N)):
v = zeros((M,),t)
v[i] = 1
v[i+1:M] = qr[i+1:M,i]
H = gemm(-tau[i],v,v,1+0j,ident,trans_b=2)
Q = gemm(1,Q,H)
return Q, R
def pinv(a, cond=None):
""" pinv(a, cond=None) -> a_pinv
Compute generalized inverse of A using least-squares solver.
"""
a = asarray_chkfinite(a)
t = a.typecode()
b = scipy_base.identity(a.shape[0],t)
return lstsq(a, b, cond=cond)[0]
