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85 lines
2.2 KiB
Python
85 lines
2.2 KiB
Python
from . import __nnls
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from numpy import asarray_chkfinite, zeros, double
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__all__ = ['nnls']
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def nnls(A, b, maxiter=None):
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"""
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Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``. This is a wrapper
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for a FORTRAN non-negative least squares solver.
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Parameters
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----------
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A : ndarray
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Matrix ``A`` as shown above.
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b : ndarray
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Right-hand side vector.
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maxiter: int, optional
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Maximum number of iterations, optional.
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Default is ``3 * A.shape[1]``.
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Returns
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-------
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x : ndarray
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Solution vector.
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rnorm : float
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The residual, ``|| Ax-b ||_2``.
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See Also
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--------
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lsq_linear : Linear least squares with bounds on the variables
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Notes
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-----
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The FORTRAN code was published in the book below. The algorithm
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is an active set method. It solves the KKT (Karush-Kuhn-Tucker)
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conditions for the non-negative least squares problem.
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References
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----------
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Lawson C., Hanson R.J., (1987) Solving Least Squares Problems, SIAM
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Examples
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--------
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>>> from scipy.optimize import nnls
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...
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>>> A = np.array([[1, 0], [1, 0], [0, 1]])
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>>> b = np.array([2, 1, 1])
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>>> nnls(A, b)
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(array([1.5, 1. ]), 0.7071067811865475)
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>>> b = np.array([-1, -1, -1])
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>>> nnls(A, b)
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(array([0., 0.]), 1.7320508075688772)
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"""
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A, b = map(asarray_chkfinite, (A, b))
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if len(A.shape) != 2:
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raise ValueError("Expected a two-dimensional array (matrix)" +
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", but the shape of A is %s" % (A.shape, ))
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if len(b.shape) != 1:
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raise ValueError("Expected a one-dimensional array (vector" +
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", but the shape of b is %s" % (b.shape, ))
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m, n = A.shape
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if m != b.shape[0]:
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raise ValueError(
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"Incompatible dimensions. The first dimension of " +
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"A is %s, while the shape of b is %s" % (m, (b.shape[0], )))
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maxiter = -1 if maxiter is None else int(maxiter)
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w = zeros((n,), dtype=double)
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zz = zeros((m,), dtype=double)
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index = zeros((n,), dtype=int)
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x, rnorm, mode = __nnls.nnls(A, m, n, b, w, zz, index, maxiter)
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if mode != 1:
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raise RuntimeError("too many iterations")
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return x, rnorm
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