.. _docs-meteoinfolab-numeric-linalg-lstsq: *********************** Least-squares *********************** .. currentmodule:: numeric.linalg .. function:: lstsq(a, b) Compute least-squares solution to equation Ax = b. Compute a vector x such that the 2-norm |b - A x| is minimized. ``Parameters`` a : (M, N) array Left hand side matrix (2-D array). b : (M,) array Right hand side vector. ``Returns`` x : (N,) array Least-squares solution. Return shape matches shape of b. residues : (0,) or () or (K,) ndarray Sums of residues, squared 2-norm for each column in b - a x. Examples:: x = array([1, 2.5, 3.5, 4, 5, 7, 8.5]) y = array([0.3, 1.1, 1.5, 2.0, 3.2, 6.6, 8.6]) M = ones((len(x),2)) M[:,1] = x**2 p, res = linalg.lstsq(M, y) print p #Plot plot(x, y, 'bo', label='data') xx = linspace(0, 9, 101) yy = p[0] + p[1]*xx**2 plot(xx, yy, label='least squares fit, \$y = a + bx^2\$') xlabel('x') ylabel('y') legend(loc='upper left') grid(alpha=0.25) Result:: >>> run script... array([3.0, 2.23606797749979, 2.0, 0.0]) .. image:: ../../../../_static/lstsq.png