Beispiel #1
0
def show_x_error_chart(count):
    """ displays x=123 with covariances showing error"""

    plt.cla()
    plt.gca().autoscale(tight=True)

    cov = np.array([[0.03, 0], [0, 8]])
    e = stats.covariance_ellipse(cov)

    cov2 = np.array([[0.03, 0], [0, 4]])
    e2 = stats.covariance_ellipse(cov2)

    cov3 = np.array([[12, 11.95], [11.95, 12]])
    e3 = stats.covariance_ellipse(cov3)

    sigma = [1, 4, 9]

    if count >= 1:
        stats.plot_covariance_ellipse((0, 0), ellipse=e, variance=sigma)

    if count == 2 or count == 3:

        stats.plot_covariance_ellipse((5, 5), ellipse=e, variance=sigma)

    if count == 3:

        stats.plot_covariance_ellipse((5, 5),
                                      ellipse=e3,
                                      variance=sigma,
                                      edgecolor='r')

    if count == 4:
        M1 = np.array([[5, 5]]).T
        m4, cov4 = stats.multivariate_multiply(M1, cov2, M1, cov3)
        e4 = stats.covariance_ellipse(cov4)

        stats.plot_covariance_ellipse((5, 5),
                                      ellipse=e,
                                      variance=sigma,
                                      alpha=0.25)

        stats.plot_covariance_ellipse((5, 5),
                                      ellipse=e3,
                                      variance=sigma,
                                      edgecolor='r',
                                      alpha=0.25)
        stats.plot_covariance_ellipse(m4[:, 0], ellipse=e4, variance=sigma)

    #plt.ylim([0,11])
    #plt.xticks(np.arange(1,4,1))

    plt.xlabel("Position")
    plt.ylabel("Velocity")

    plt.show()
def show_x_error_chart(count):
    """ displays x=123 with covariances showing error"""

    plt.cla()
    plt.gca().autoscale(tight=True)

    cov = np.array([[0.03,0], [0,8]])
    e = stats.covariance_ellipse (cov)

    cov2 = np.array([[0.03,0], [0,4]])
    e2 = stats.covariance_ellipse (cov2)

    cov3 = np.array([[12,11.95], [11.95,12]])
    e3 = stats.covariance_ellipse (cov3)


    sigma=[1, 4, 9]

    if count >= 1:
        stats.plot_covariance_ellipse ((0,0), ellipse=e, variance=sigma)

    if count == 2 or count == 3:

        stats.plot_covariance_ellipse ((5,5), ellipse=e, variance=sigma)

    if count == 3:

        stats.plot_covariance_ellipse ((5,5), ellipse=e3, variance=sigma,
                                       edgecolor='r')

    if count == 4:
        M1 = np.array([[5, 5]]).T
        m4, cov4 = stats.multivariate_multiply(M1, cov2, M1, cov3)
        e4 = stats.covariance_ellipse (cov4)

        stats.plot_covariance_ellipse ((5,5), ellipse=e, variance=sigma,
                                       alpha=0.25)

        stats.plot_covariance_ellipse ((5,5), ellipse=e3, variance=sigma,
                                       edgecolor='r', alpha=0.25)
        stats.plot_covariance_ellipse (m4[:,0], ellipse=e4, variance=sigma)

    #plt.ylim([0,11])
    #plt.xticks(np.arange(1,4,1))

    plt.xlabel("Position")
    plt.ylabel("Velocity")

    plt.show()
def show_x_with_unobserved():
    """ shows x=1,2,3 with velocity superimposed on top """

    # plot velocity
    sigma=[0.5,1.,1.5,2]
    cov = np.array([[1,1],[1,1.1]])
    stats.plot_covariance_ellipse ((2,2), cov=cov, variance=sigma, axis_equal=False)

    # plot positions
    cov = np.array([[0.003,0], [0,12]])
    sigma=[0.5,1.,1.5,2]
    e = stats.covariance_ellipse (cov)

    stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
    stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
    stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)

    # plot intersection cirle
    isct = Ellipse(xy=(2,2), width=.2, height=1.2, edgecolor='r', fc='None', lw=4)
    plt.gca().add_artist(isct)

    plt.ylim([0,11])
    plt.xlim([0,4])
    plt.xticks(np.arange(1,4,1))

    plt.xlabel("Position")
    plt.ylabel("Time")

    plt.show()
def show_x_error_chart():
    """ displays x=123 with covariances showing error"""

    cov = np.array([[0.003, 0], [0, 12]])
    sigma = [0.5, 1., 1.5, 2]
    e = stats.covariance_ellipse(cov)

    stats.plot_covariance_ellipse((1, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)
    stats.plot_covariance_ellipse((2, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)
    stats.plot_covariance_ellipse((3, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)

    plt.ylim([0, 11])
    plt.xticks(np.arange(1, 4, 1))

    plt.xlabel("Position")
    plt.ylabel("Time")

    plt.show()
def plot_3d_sampled_covariance(mean, cov):
    """ plots a 2x2 covariance matrix positioned at mean. mean will be plotted
    in x and y, and the probability in the z axis.

    Parameters
    ----------
    mean :  2x1 tuple-like object
        mean for x and y coordinates. For example (2.3, 7.5)

    cov : 2x2 nd.array
       the covariance matrix

    """

    # compute width and height of covariance ellipse so we can choose
    # appropriate ranges for x and y
    o,w,h = stats.covariance_ellipse(cov,3)
    # rotate width and height to x,y axis
    wx = abs(w*np.cos(o) + h*np.sin(o))*1.2
    wy = abs(h*np.cos(o) - w*np.sin(o))*1.2


    # ensure axis are of the same size so everything is plotted with the same
    # scale
    if wx > wy:
        w = wx
    else:
        w = wy

    minx = mean[0] - w
    maxx = mean[0] + w
    miny = mean[1] - w
    maxy = mean[1] + w

    count = 1000
    x,y = multivariate_normal(mean=mean, cov=cov, size=count).T

    xs = np.arange(minx, maxx, (maxx-minx)/40.)
    ys = np.arange(miny, maxy, (maxy-miny)/40.)
    xv, yv = np.meshgrid (xs, ys)

    zs = np.array([100.* stats.multivariate_gaussian(np.array([xx,yy]),mean,cov) \
                   for xx,yy in zip(np.ravel(xv), np.ravel(yv))])
    zv = zs.reshape(xv.shape)

    ax = plt.figure().add_subplot(111, projection='3d')
    ax.scatter(x,y, [0]*count, marker='.')

    ax.set_xlabel('X')
    ax.set_ylabel('Y')

    ax.contour(xv, yv, zv, zdir='x', offset=minx-1, cmap=cm.autumn)
    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)
Beispiel #6
0
def plot_3d_sampled_covariance(mean, cov):
    """ plots a 2x2 covariance matrix positioned at mean. mean will be plotted
    in x and y, and the probability in the z axis.

    Parameters
    ----------
    mean :  2x1 tuple-like object
        mean for x and y coordinates. For example (2.3, 7.5)

    cov : 2x2 nd.array
       the covariance matrix

    """

    # compute width and height of covariance ellipse so we can choose
    # appropriate ranges for x and y
    o, w, h = stats.covariance_ellipse(cov, 3)
    # rotate width and height to x,y axis
    wx = abs(w * np.cos(o) + h * np.sin(o)) * 1.2
    wy = abs(h * np.cos(o) - w * np.sin(o)) * 1.2

    # ensure axis are of the same size so everything is plotted with the same
    # scale
    if wx > wy:
        w = wx
    else:
        w = wy

    minx = mean[0] - w
    maxx = mean[0] + w
    miny = mean[1] - w
    maxy = mean[1] + w

    count = 1000
    x, y = multivariate_normal(mean=mean, cov=cov, size=count).T

    xs = np.arange(minx, maxx, (maxx - minx) / 40.)
    ys = np.arange(miny, maxy, (maxy - miny) / 40.)
    xv, yv = np.meshgrid(xs, ys)

    zs = np.array([100.* stats.multivariate_gaussian(np.array([xx,yy]),mean,cov) \
                   for xx,yy in zip(np.ravel(xv), np.ravel(yv))])
    zv = zs.reshape(xv.shape)

    ax = plt.figure().add_subplot(111, projection='3d')
    ax.scatter(x, y, [0] * count, marker='.')

    ax.set_xlabel('X')
    ax.set_ylabel('Y')

    ax.contour(xv, yv, zv, zdir='x', offset=minx - 1, cmap=cm.autumn)
    ax.contour(xv, yv, zv, zdir='y', offset=maxy, cmap=cm.BuGn)
def show_x_with_unobserved():
    """ shows x=1,2,3 with velocity superimposed on top """

    # plot velocity
    sigma = [0.5, 1., 1.5, 2]
    cov = np.array([[1, 1], [1, 1.1]])
    stats.plot_covariance_ellipse((2, 2),
                                  cov=cov,
                                  variance=sigma,
                                  axis_equal=False)

    # plot positions
    cov = np.array([[0.003, 0], [0, 12]])
    sigma = [0.5, 1., 1.5, 2]
    e = stats.covariance_ellipse(cov)

    stats.plot_covariance_ellipse((1, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)
    stats.plot_covariance_ellipse((2, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)
    stats.plot_covariance_ellipse((3, 1),
                                  ellipse=e,
                                  variance=sigma,
                                  axis_equal=False)

    # plot intersection cirle
    isct = Ellipse(xy=(2, 2),
                   width=.2,
                   height=1.2,
                   edgecolor='r',
                   fc='None',
                   lw=4)
    plt.gca().add_artist(isct)

    plt.ylim([0, 11])
    plt.xlim([0, 4])
    plt.xticks(np.arange(1, 4, 1))

    plt.xlabel("Position")
    plt.ylabel("Time")

    plt.show()
def show_x_error_chart():
    """ displays x=123 with covariances showing error"""

    cov = np.array([[0.003,0], [0,12]])
    sigma=[0.5,1.,1.5,2]
    e = stats.covariance_ellipse (cov)

    stats.plot_covariance_ellipse ((1,1), ellipse=e, variance=sigma, axis_equal=False)
    stats.plot_covariance_ellipse ((2,1), ellipse=e, variance=sigma, axis_equal=False)
    stats.plot_covariance_ellipse ((3,1), ellipse=e, variance=sigma, axis_equal=False)


    plt.ylim([0,11])
    plt.xticks(np.arange(1,4,1))

    plt.xlabel("Position")
    plt.ylabel("Time")

    plt.show()