nnls#
- scipy.optimize.nnls(A, b, *, maxiter=None, atol=<object object>)[source]#
- Solve - argmin_x || Ax - b ||_2for- x>=0.- This problem, often called as NonNegative Least Squares, is a convex optimization problem with convex constraints. It typically arises when the - xmodels quantities for which only nonnegative values are attainable; weight of ingredients, component costs and so on.- Deprecated since version 1.18.0: Use of argument(s) - {'maxiter'}by position is deprecated; beginning in SciPy 1.18.0, these will be keyword-only. Argument(s)- {'atol'}are deprecated, whether passed by position or keyword; they will be removed in SciPy 1.18.0.- Parameters:
- A(m, n) ndarray
- Coefficient array 
- b(m,) ndarray, float
- Right-hand side vector. 
- maxiter: int, optional
- Maximum number of iterations, optional. Default value is - 3 * n.
- atolfloat, optional
- Deprecated since version 1.18.0: This parameter is deprecated and will be removed in SciPy 1.18.0. It is not used in the implementation. 
 
- Returns:
- xndarray
- Solution vector. 
- rnormfloat
- The 2-norm of the residual, - || Ax-b ||_2.
 
 - See also - lsq_linear
- Linear least squares with bounds on the variables 
 - Notes - The code is based on the classical algorithm of [1]. It utilizes an active set method and solves the KKK (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem. - References [1]- : Lawson C., Hanson R.J., “Solving Least Squares Problems”, SIAM, 1995, DOI:10.1137/1.9781611971217 - 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)