Python interpolate.griddata函数代码示例

    def undistort_image(self, img, Kundistortion=None):
        """
        Transform grayscale image such that radial distortion is removed.

        :param img: input image
        :type img: np.ndarray, shape=(n, m) or (n, m, 3)
        :param Kundistortion: camera matrix for undistorted view, None for self.K
        :type Kundistortion: array-like, shape=(3, 3)
        :return: transformed image
        :rtype: np.ndarray, shape=(n, m) or (n, m, 3)
        """
        if Kundistortion is None:
            Kundistortion = self.K
        if self.calibration_type == 'opencv':
            return cv2.undistort(img, self.K, self.opencv_dist_coeff, newCameraMatrix=Kundistortion)
        elif self.calibration_type == 'opencv_fisheye':
                return cv2.fisheye.undistortImage(img, self.K, self.opencv_dist_coeff, Knew=Kundistortion)
        else:
            xx, yy = np.meshgrid(np.arange(img.shape[1]), np.arange(img.shape[0]))
            img_coords = np.array([xx.ravel(), yy.ravel()])
            y_l = self.undistort(img_coords, Kundistortion)
            if img.ndim == 2:
                return griddata(y_l.T, img.ravel(), (xx, yy), fill_value=0, method='linear')
            else:
                channels = [griddata(y_l.T, img[:, :, i].ravel(), (xx, yy), fill_value=0, method='linear')
                            for i in xrange(img.shape[2])]
                return np.dstack(channels)

def rasterize(geometry, points):
    """ Create array. """
    envelope = geometry.GetEnvelope()
    # px, py, pz = points.transpose()
    x1 = 4 * math.floor(envelope[0] / 4)
    y1 = 4 * math.floor(envelope[2] / 4)
    x2 = 4 * math.ceil(envelope[1] / 4)
    y2 = 4 * math.ceil(envelope[3] / 4)

    geo_transform = x1, A, 0, y2, 0, D
    array = np.full((4 * (y2 - y1), 4 * (x2 - x1)), NO_DATA_VALUE, 'f4')
    grid = tuple(np.mgrid[y2 + D / 2:y1 + D / 2:D,
                          x1 + A / 2:x2 + A / 2:A][::-1])

    # interpolate
    args = points[:, :2], points[:, 2], grid
    linear = interpolate.griddata(*args, method='linear')
    nearest = interpolate.griddata(*args, method='nearest')
    array = np.where(np.isnan(linear), nearest, linear).astype('f4')

    # clip and return
    kwargs = {
        'array': array[np.newaxis],
        'projection': PROJECTION,
        'no_data_value': NO_DATA_VALUE,
        'geo_transform': geo_transform,
    }
    clip(kwargs=kwargs, geometry=geometry)
    return kwargs

def get_GridFSim(x1, y1, x2, y2, img1):
    ''' Calculate estimated ice drift on first image based on feature tracking vectors'''
    
    # # initial drift inter-/extrapolation
    # linear triangulation
    x1Grid, y1Grid = np.meshgrid(range(img1.shape[1]), range(img1.shape[0]))
    x2GridFSim = griddata(np.array([y1, x1]).T, x2, np.array([y1Grid, x1Grid]).T, method='linear').T
    y2GridFSim = griddata(np.array([y1, x1]).T, y2, np.array([y1Grid, x1Grid]).T, method='linear').T
    # linear fit for entire grid
    A = np.vstack([np.ones(len(x1)), x1, y1 ]).T
    # find B in x2 = B * [x1, y1]
    Bx = np.linalg.lstsq(A, x2)[0]
    By = np.linalg.lstsq(A, y2)[0]
    # calculate simulated x2sim = B * [x1, y1]
    x1GridF = x1Grid.flatten()
    y1GridF = y1Grid.flatten()
    A = np.vstack([np.ones(len(x1GridF)), x1GridF, y1GridF]).T
    x2GridFSim_lf = np.dot(A, Bx).reshape(img1.shape)
    y2GridFSim_lf = np.dot(A, By).reshape(img1.shape)
    # fill NaN with lf
    gpi = np.isnan(x2GridFSim)
    x2GridFSim[gpi] = x2GridFSim_lf[gpi]
    y2GridFSim[gpi] = y2GridFSim_lf[gpi]

    return x2GridFSim, y2GridFSim

def bin_confint_lookup(pc, nsamp, ci = .05):
  """Return the confidence interval from the lookup table.
  Inputs:
    pc - array (get back several cis) or single value (get back one ci) of percent corrects
    nsamp - number of trials used to obtain each pc
    ci - confidence level (e.g. 0.01, 0.05)
    bootstraps - number of bootstraps to use
    use_table - if true then use a precomputed table instead of doing the bootstraps

  Output:
    3xN array - first row is pc
                last two rows are lower and upper ci as expected by pylab.errorbar
  """
  points = ci_table['points']
  values_lo = ci_table['values_lo']
  values_high = ci_table['values_high']

  from scipy.interpolate import griddata
  if pylab.isscalar(pc):
    pc = pylab.array([pc])
    nsamp = pylab.array([nsamp])
  ci_a = pylab.ones(pc.size)*ci
  xi = pylab.array((pc,nsamp,ci_a)).T

  low_ci = griddata(points, values_lo, xi, method='linear')
  high_ci = griddata(points, values_high, xi, method='linear')

  return pylab.array((pc,low_ci,high_ci))

def make_grid(points, values, grid, method=None):
    """Abstraction of two different versions of griddata

    points: Nx2 array of points where data is known
    values: corresponding values
    grid: Tuple of X, Y - Regular grid (e.g. obtained from meshgrid)
    """


    if griddata_version == 'scipy':
        if method is None:
            m = 'cubic'
        else:
            m = method

        return griddata(points, values, grid, method=m)
    elif griddata_version == 'pylab':
        if method is None:
            m = 'nn'
        else:
            m = method

        x = points[:,0]
        y = points[:,0]
        z = values
        X, Y = grid
        return griddata(x, y, z, X, Y, interp=m)

def plot_QU_gd(x, y, Q, U, irad, Req):
    """ using griddata 
    """
    fig = _plt.figure()
    lins, cols = (1, 2)
    gs = _gridspec.GridSpec(lins, cols)

    axq = _plt.subplot(gs[0, 0])  
    axu = _plt.subplot(gs[0, 1])  

    xmin = _np.min(x)/Req
    xmax = _np.max(x)/Req
    ymin = _np.min(y)/Req
    ymax = _np.max(y)/Req
    xx, yy = _np.meshgrid(_np.linspace(xmin, xmax, 32), 
        _np.linspace(ymin, ymax, 32)[::-1])
    yo = y*_np.cos(irad)
    q = _interpolate.griddata( _np.array([x, yo]).T/Req, Q, 
        _np.array([xx.flatten(), yy.flatten()]).T )
    u = _interpolate.griddata( _np.array([x, yo]).T/Req, U, 
        _np.array([xx.flatten(), yy.flatten()]).T )

    axq.imshow(q.reshape(32, 32), origin='lower', extent=[xmin, xmax, 
        ymin, ymax])
    axu.imshow(u.reshape(32, 32), origin='lower', extent=[xmin, xmax, 
        ymin, ymax])
    return fig, [axq, axu]

def mesh2grid(v, mesh):
    """ Interpolates from an unstructured coordinates (mesh) to a structured 
        coordinates (grid)
    """
    x = mesh[:,0]
    z = mesh[:,1]
    lx = x.max() - x.min()
    lz = z.max() - z.min()
    nn = v.size

    nx = np.around(np.sqrt(nn*lx/lz))
    nz = np.around(np.sqrt(nn*lz/lx))
    dx = lx/nx
    dz = lz/nz

    # construct structured grid
    x = np.linspace(x.min(), x.max(), nx)
    z = np.linspace(z.min(), z.max(), nz)
    X, Z = np.meshgrid(x, z)
    grid = stack(X.flatten(), Z.flatten())

    # interpolate to structured grid
    V = _interp.griddata(mesh, v, grid, 'linear')

    # workaround edge issues
    if np.any(np.isnan(V)):
        W = _interp.griddata(mesh, v, grid, 'nearest')
        for i in np.where(np.isnan(V)):
            V[i] = W[i]

    V = np.reshape(V, (nz, nx))
    return V, grid

def test_imshow_heatmap():
    from scipy.interpolate import griddata
    from matplotlib import pyplot as plt

    mesh3D = mesh(200)
    mesh2D = proj_to_2D(mesh3D)

    data = np.zeros((3,3))
    data[0,1] += 2

    vals = np.exp(log_dirichlet_density(mesh3D,2.,data=data.sum(0)))
    temp = log_censored_dirichlet_density(mesh3D,2.,data=data)
    censored_vals = np.exp(temp - temp.max())

    xi = np.linspace(-1,1,1000)
    yi = np.linspace(-0.5,1,1000)

    plt.figure()
    plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),vals,(xi[None,:],yi[:,None]),method='cubic'))
    plt.axis('off')
    plt.title('uncensored likelihood')

    plt.figure()
    plt.imshow(griddata((mesh2D[:,0],mesh2D[:,1]),censored_vals,(xi[None,:],yi[:,None]),method='cubic'))
    plt.axis('off')
    plt.title('censored likelihood')

 def plot(x,y,field,filename,c=200):
     plt.figure()
     # define grid.
     xi = np.linspace(min(x),max(x),100)
     yi = np.linspace(min(y),max(y),100)
     # grid the data.
     si_lin = griddata((x, y), field, (xi[None,:], yi[:,None]), method='linear')
     si_cub = griddata((x, y), field, (xi[None,:], yi[:,None]), method='linear')
     print np.min(field)
     print np.max(field)
     plt.subplot(211)
     # contour the gridded data, plotting dots at the randomly spaced data points.
     CS = plt.contour(xi,yi,si_lin,c,linewidths=0.5,colors='k')
     CS = plt.contourf(xi,yi,si_lin,c,cmap=plt.cm.jet)
     plt.colorbar() # draw colorbar
     # plot data points.
     #    plt.scatter(x,y,marker='o',c='b',s=5)
     plt.xlim(min(x),max(x))
     plt.ylim(min(y),max(y))
     plt.title('Lineaarinen interpolointi')
     #plt.tight_layout()
     plt.subplot(212)
     # contour the gridded data, plotting dots at the randomly spaced data points.
     CS = plt.contour(xi,yi,si_cub,c,linewidths=0.5,colors='k')
     CS = plt.contourf(xi,yi,si_cub,c,cmap=plt.cm.jet)
     plt.colorbar() # draw colorbar
     # plot data points.
     #    plt.scatter(x,y,marker='o',c='b',s=5)
     plt.xlim(min(x),max(x))
     plt.ylim(min(y),max(y))
     plt.title('Kuubinen interpolointi')
     plt.savefig(filename)

def interpolateData(binaryDataFile):
    file = open(binaryDataFile, 'rb')
    if os.name == 'nt':
        rawTimeHistory = numpy.array(pickle.load(file, encoding='latin1')).transpose()
        rawStressHistory = numpy.array(pickle.load(file, encoding='latin1')).transpose()
        rawStrainHistory = numpy.array(pickle.load(file, encoding='latin1')).transpose()
    elif os.name == 'posix':
        rawTimeHistory = numpy.array(pickle.load(file)).transpose()
        rawStressHistory = numpy.array(pickle.load(file)).transpose()
        rawStrainHistory = numpy.array(pickle.load(file)).transpose()
    
    timeHistory = numpy.linspace(0, simulationTime, numberOfSteps+1)
    stressHistory = numpy.empty([3, numberOfSteps+1]);
    strainHistory = numpy.empty([3, numberOfSteps+1]);
    for i in range(3):
        stressHistory[i, :] = griddata(rawTimeHistory, rawStressHistory[i], timeHistory)
        strainHistory[i, :] = griddata(rawTimeHistory, rawStrainHistory[i], timeHistory)
    stressHistory = stressHistory.transpose()
    strainHistory = strainHistory.transpose()
    
    with open('output.dat', 'w') as f:
        f.write('time S11 S22 S12 LE11 LE22 LE12\n')
        for i in range(len(timeHistory)):
            f.write(str(timeHistory[i])+' ')
            for j in range(len(stressHistory[i])):
                f.write(str(stressHistory[i][j])+' ')
            for j in range(len(strainHistory[i])):
                f.write(str(strainHistory[i][j])+' ')
            f.write('\n')

    def __init__(self, vmec_file, ntheta=None, nzeta=None, nr=32, nz=32):
        # Only needed here
        from scipy.interpolate import griddata, RegularGridInterpolator

        self.read_vmec_file(vmec_file, ntheta, nzeta)

        self.nr = nr
        self.nz = nz

        # Make a new rectangular grid in (R,Z)
        self.r_1D = np.linspace(self.r_stz.min(), self.r_stz.max(), nr)
        self.z_1D = np.linspace(self.z_stz.min(), self.z_stz.max(), nz)
        self.R_2D, self.Z_2D = np.meshgrid(self.r_1D, self.z_1D, indexing='ij')

        # First, interpolate the magnetic field components onto (R,Z)
        self.br_rz = np.zeros( (nr, nz, self.nzeta) )
        self.bz_rz = np.zeros( (nr, nz, self.nzeta) )
        self.bphi_rz = np.zeros( (nr, nz, self.nzeta) )
        # No need to interpolate in zeta, so do this one slice at a time
        for k, (br, bz, bphi, r, z) in enumerate(zip(self.br.T, self.bz.T, self.bphi.T, self.r_stz.T, self.z_stz.T)):
            points = np.column_stack( (r.flatten(), z.flatten()) )
            self.br_rz[...,k] = griddata(points, br.flatten(), (self.R_2D, self.Z_2D),
                                         method='linear', fill_value=0.0)
            self.bz_rz[...,k] = griddata(points, bz.flatten(), (self.R_2D, self.Z_2D),
                                         method='linear', fill_value=0.0)
            self.bphi_rz[...,k] = griddata(points, bphi.flatten(), (self.R_2D, self.Z_2D),
                                           method='linear', fill_value=1.0)

        # Now we have a regular grid in (R,Z,phi) (as zeta==phi), so
        # we can get an interpolation function in 3D
        points = ( self.r_1D, self.z_1D, self.zeta )

        self.br_interp = RegularGridInterpolator(points, self.br_rz, bounds_error=False, fill_value=0.0)
        self.bz_interp = RegularGridInterpolator(points, self.bz_rz, bounds_error=False, fill_value=0.0)
        self.bphi_interp = RegularGridInterpolator(points, self.bphi_rz, bounds_error=False, fill_value=1.0)

    def get_apriori(self, latres=0.25, lonres=0.3125):
        '''
        Read GC HCHO sigma shape factor and regrid to lat/lon res.
        temporal resolution is one month
        inputs:
            latres, lonres for resolution of GC 2x2.5 hcho columns to be regridded onto
        '''
        assert False, "Method is old and wrong currently"
        # new latitude longitude we interpolate to.
        newlats= np.arange(-90,90, latres) + latres/2.0
        newlons= np.arange(-180,180, lonres) + lonres/2.0

        # Mesh[lat,lon]
        mlons,mlats = np.meshgrid(self.lons,self.lats)
        mnewlons,mnewlats = np.meshgrid(newlons,newlats)

        ## Get sigma apriori and regrid it
        #
        newS_s = np.zeros([72,len(newlats),len(newlons)])
        newSigma = np.zeros([72,len(newlats),len(newlons)])

        # interpolate at each pressure level...
        for ii in range(72):
            newS_s[ii,:,:] = griddata( (mlats.ravel(), mlons.ravel()),
                                       self.Shape_s[ii,:,:].ravel(),
                                       (mnewlats, mnewlons),
                                       method='nearest')
            newSigma[ii,:,:]=griddata( (mlats.ravel(), mlons.ravel()),
                                     self.sigmas[ii,:,:].ravel(),
                                     (mnewlats, mnewlons),
                                     method='nearest')

        # return the normalised sigma apriori used to recalculate AMF
        return newS_s, newlats, newlons, newSigma

def autocorr(
    A, B, pointsA, pointsB, nregrid, rrange=[0.0, 1.5e18], phirange=[0.0, 6.283185307179586], zrange=[-1.5e18, 1.5e18]
):
    """Calculates the angular average of <a(t)b(t+s)>"""

    print "=== Obtaining correlation ==="
    # create r_i, phi_j and z_k arrays:
    ri = np.linspace(rrange[0], rrange[1], nregrid[0])
    phij = np.linspace(phirange[0], phirange[1], nregrid[1])
    zk = np.linspace(zrange[0], zrange[1], nregrid[2])

    (xijk, yijk, zijk) = cylKernel(ri, phij, zk, np.array(nregrid, dtype=np.int32))
    # griddata to points:
    dataA = griddata(
        (pointsA[:, 0], pointsA[:, 1], pointsA[:, 2]),
        np.array(A, dtype=np.float64),
        (xijk, yijk, zijk),
        method="nearest",
    )
    dataB = griddata(
        (pointsB[:, 0], pointsB[:, 1], pointsB[:, 2]),
        np.array(B, dtype=np.float64),
        (xijk, yijk, zijk),
        method="nearest",
    )

    correlation = autocorrKernel(dataA, dataB, np.array(nregrid, dtype=np.int32))

    print "=== Done with correlation ==="
    return np.ma.masked_array(correlation, np.isnan(correlation))

def velovect(u1,u2,d,minvel=1e-40,nvect=None,scalevar=None,scale=100,color='k',fig=None):
    '''Plots normalized velocity vectors'''


    if fig==None:
        ax=plt.gca()
    else:
        ax=fig.ax

    CC=d.getCenterPoints()
    n=np.sqrt(u1**2+u2**2)
    # remove zero velocity:
    m=n<minvel
    vr=np.ma.filled(np.ma.masked_array(u1/n,m),0.)
    vz=np.ma.filled(np.ma.masked_array(u2/n,m),0.)
    if scalevar != None:
        vr = vr*scalevar
        vz = vz*scalevar
    if nvect==None:
        Q=ax.quiver(CC[:,0],CC[:,1],vr,vz,pivot='middle',width=1e-3,minlength=0.,scale=scale,
                    headwidth=6)
    else:
        # regrid the data:
        tmp0=np.complex(0,nvect[0])
        tmp1=np.complex(0,nvect[1])
        grid_r, grid_z = np.mgrid[ax.get_xlim()[0]:ax.get_xlim()[1]:tmp0, ax.get_ylim()[0]:ax.get_ylim()[1]:tmp1]
        grid_vr = griddata(CC, vr, (grid_r, grid_z), method='nearest')
        grid_vz = griddata(CC, vz, (grid_r, grid_z), method='nearest')
        Q=ax.quiver(grid_r,grid_z,grid_vr,grid_vz,pivot='middle',width=2e-3,minlength=minvel,scale=scale,
                    headwidth=10,headlength=10,color=color,edgecolor=color,rasterized=True)

    plt.draw()
    return Q     

def interpolate_data_2d(all_points, data, param1_space_int=None, param2_space_int=None, interpolation_numpoints=200, interpolation_method='linear', mask_when_nearest=True, show_scatter=True, show_colorbar=True, mask_x_condition=None, mask_y_condition=None):

    # Construct the interpolation
    if param1_space_int is None:
        param1_space_int = np.linspace(all_points[:, 0].min(), all_points[:, 0].max(), interpolation_numpoints)
    if param2_space_int is None:
        param2_space_int = np.linspace(all_points[:, 1].min(), all_points[:, 1].max(), interpolation_numpoints)

    data_interpol = spint.griddata(all_points, data, (param1_space_int[None, :], param2_space_int[:, None]), method=interpolation_method)

    if interpolation_method == 'nearest' and mask_when_nearest:
        # Let's mask the points outside of the convex hull

        # The linear interpolation will have nan's on points outside of the convex hull of the all_points
        data_interpol_lin = spint.griddata(all_points, data, (param1_space_int[None, :], param2_space_int[:, None]), method='linear')

        # Mask
        data_interpol[np.isnan(data_interpol_lin)] = np.nan

    # Mask it based on some conditions
    if mask_x_condition is not None:
        data_interpol[mask_x_condition(param1_space_int), :] = 0.0
    if mask_y_condition is not None:
        data_interpol[:, mask_y_condition(param2_space_int)] = 0.0

    return data_interpol