86 lines
2.2 KiB
Python
86 lines
2.2 KiB
Python
|
from . import __nnls
|
||
|
|
from numpy import asarray_chkfinite, zeros, double
|
||
|
|
|
||
|
|
__all__ = ['nnls']
|
||
|
|
|
||
|
|
|
||
|
|
def nnls(A, b, maxiter=None):
|
||
|
|
"""
|
||
|
|
Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. This is a wrapper
|
||
|
|
for a FORTRAN non-negative least squares solver.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
A : ndarray
|
||
|
|
Matrix ``A`` as shown above.
|
||
|
|
b : ndarray
|
||
|
|
Right-hand side vector.
|
||
|
|
maxiter: int, optional
|
||
|
|
Maximum number of iterations, optional.
|
||
|
|
Default is ``3 * A.shape[1]``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
x : ndarray
|
||
|
|
Solution vector.
|
||
|
|
rnorm : float
|
||
|
|
The residual, ``|| Ax-b ||_2``.
|
||
|
|
|
||
|
|
See Also
|
||
|
|
--------
|
||
|
|
lsq_linear : Linear least squares with bounds on the variables
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from scipy.optimize import nnls
|
||
|
|
...
|
||
|
|
>>> A = np.array([[1, 0], [1, 0], [0, 1]])
|
||
|
|
>>> b = np.array([2, 1, 1])
|
||
|
|
>>> nnls(A, b)
|
||
|
|
(array([1.5, 1. ]), 0.7071067811865475)
|
||
|
|
|
||
|
|
>>> b = np.array([-1, -1, -1])
|
||
|
|
>>> nnls(A, b)
|
||
|
|
(array([0., 0.]), 1.7320508075688772)
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
A, b = map(asarray_chkfinite, (A, b))
|
||
|
|
|
||
|
|
if len(A.shape) != 2:
|
||
|
|
raise ValueError("Expected a two-dimensional array (matrix)" +
|
||
|
|
", but the shape of A is %s" % (A.shape, ))
|
||
|
|
if len(b.shape) != 1:
|
||
|
|
raise ValueError("Expected a one-dimensional array (vector)" +
|
||
|
|
", but the shape of b is %s" % (b.shape, ))
|
||
|
|
|
||
|
|
m, n = A.shape
|
||
|
|
|
||
|
|
if m != b.shape[0]:
|
||
|
|
raise ValueError(
|
||
|
|
"Incompatible dimensions. The first dimension of " +
|
||
|
|
"A is %s, while the shape of b is %s" % (m, (b.shape[0], )))
|
||
|
|
|
||
|
|
maxiter = -1 if maxiter is None else int(maxiter)
|
||
|
|
|
||
|
|
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, maxiter)
|
||
|
|
if mode != 1:
|
||
|
|
raise RuntimeError("too many iterations")
|
||
|
|
|
||
|
|
return x, rnorm
|