reordering an array changes results by 1021173647741.1094 It's obvious if I calculate 1 / floating_point_noise and floating_point_noise depends on mathematically irrelevant details. But it took me a while to remember that noise doesn't follow the simple math. inv with nonsingular matrix - great
xm = np.corrcoef(x[:,::-2], rowvar=0) np.linalg.inv(xm)[:, -3:] array([[ 0.38794217, 0.40358464, 0.12232308], [ 1.21001936, 0.39702137, -0.10164338], [ 0.39702137, 1.20088551, 0.03021732], [-0.10164338, 0.03021732, 1.03114181]])
np.linalg.inv(xm[::-1,::-1])[::-1,::-1][:, -3:] array([[ 0.38794217, 0.40358464, 0.12232308], [ 1.21001936, 0.39702137, -0.10164338], [ 0.39702137, 1.20088551, 0.03021732], [-0.10164338, 0.03021732, 1.03114181]])
np.max(np.abs(np.linalg.inv(xm[::-1,::-1])[::-1,::-1] - np.linalg.inv(xm))) 1.1102230246251565e-16
inv with singular matrix - blowing up path dependent numerical noise
xm = np.corrcoef(x, rowvar=0) np.linalg.inv(xm)[:, -3:] array([[ 4.68288729e-02, -1.86395743e-01, 1.47198710e-02], [ -1.35971574e-01, 2.90029902e-01, 3.41148182e-01], [ 9.77422379e-03, -1.17494713e-01, -2.43669915e-01], [ -1.00183312e+14, -1.00183312e+14, -1.00183312e+14], [ -1.00183312e+14, -1.00183312e+14, -1.00183312e+14], [ -1.00183312e+14, -1.00183312e+14, -1.00183312e+14], [ -1.00183312e+14, -1.00183312e+14, -1.00183312e+14], [ -1.00183312e+14, -1.00183312e+14, -1.00183312e+14]])
np.linalg.inv(xm[::-1,::-1])[::-1,::-1][:, -3:] array([[ 5.01007835e-02, -1.84819296e-01, 1.57372647e-02], [ -1.46454280e-01, 2.88649950e-01, 3.38451911e-01], [ 1.13948216e-02, -1.18632618e-01, -2.43817631e-01], [ -1.01204486e+14, -1.01204486e+14, -1.01204486e+14], [ -1.01204486e+14, -1.01204486e+14, -1.01204486e+14], [ -1.01204486e+14, -1.01204486e+14, -1.01204486e+14], [ -1.01204486e+14, -1.01204486e+14, -1.01204486e+14], [ -1.01204486e+14, -1.01204486e+14, -1.01204486e+14]])
np.max(np.abs(np.linalg.inv(xm[::-1,::-1])[::-1,::-1] - np.linalg.inv(xm))) 1021173647741.1094
Josef