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import _nnls
from numpy import asarray_chkfinite, zeros, double
__all__ = ['nnls']
def nnls(A,b):
"""
Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. This is a wrapper
for a FORTAN non-negative least squares solver.
Parameters
----------
A : ndarray
Matrix ``A`` as shown above.
b : ndarray
Right-hand side vector.
Returns
-------
x : ndarray
Solution vector.
rnorm : float
The residual, ``|| Ax-b ||_2``.
Notes
-----
The FORTRAN code was published in the book below. The algorithm
is an active set method. It solves the KKT (Karush-Kuhn-Tucker)
conditions for the non-negative least squares problem.
References
----------
Lawson C., Hanson R.J., (1987) Solving Least Squares Problems, SIAM
"""
A,b = map(asarray_chkfinite, (A,b))
if len(A.shape)!=2:
raise ValueError("expected matrix")
if len(b.shape)!=1:
raise ValueError("expected vector")
m,n = A.shape
if m != b.shape[0]:
raise ValueError("incompatible dimensions")
w = zeros((n,), dtype=double)
zz = zeros((m,), dtype=double)
index=zeros((n,), dtype=int)
x,rnorm,mode = _nnls.nnls(A,m,n,b,w,zz,index)
if mode != 1:
raise RuntimeError("too many iterations")
return x, rnorm
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