我一直在尝试使用scipy.interpolate.bisplrep()和scipy.interpolate.interp2d()来查找我(218x135)2D球面极坐标网格上数据的插值。对于这些,我传递了我的网格节点的笛卡尔位置的2D数组X和Y.我不断收到如下错误(对于interp2d的线性插入):
“警告:不能添加结,因为额外的结会重合 与旧的。可能原因:重量太小或太大 到一个不准确的数据点。 (FP> S) kx,ky = 1,1 nx,ny = 4,5 m = 29430 fp = 1390609718.902140 s = 0.000000“
我得到了二变量样条的类似结果和平滑参数s的默认值等。我的数据是平滑的。我已经在下面附上了我的代码,以防我做错了。
有什么想法吗? 谢谢! 凯尔
class Field(object):
Nr = 0
Ntheta = 0
grid = np.array([])
def __init__(self, Nr, Ntheta, f):
self.Nr = Nr
self.Ntheta = Ntheta
self.grid = np.empty([Nr, Ntheta])
for i in range(Nr):
for j in range(Ntheta):
self.grid[i,j] = f[i*Ntheta + j]
def calculate_lines(filename):
ri,ti,r,t,Br,Bt,Bphi,Bmag = np.loadtxt(filename, skiprows=3,\
usecols=(1,2,3,4,5,6,7,9), unpack=True)
Nr = int(max(ri)) + 1
Ntheta = int(max(ti)) + 1
### Initialise coordinate grids ###
X = np.empty([Nr, Ntheta])
Y = np.empty([Nr, Ntheta])
for i in range(Nr):
for j in range(Ntheta):
indx = i*Ntheta + j
X[i,j] = r[indx]*sin(t[indx])
Y[i,j] = r[indx]*cos(t[indx])
### Initialise field objects ###
Bradial = Field(Nr=Nr, Ntheta=Ntheta, f=Br)
### Interpolate the fields ###
intp_Br = interpolate.interp2d(X, Y, Bradial.grid, kind='linear')
#rbf_0 = interpolate.Rbf(X,Y, Bradial.grid, epsilon=2)
return
答案 0 :(得分:15)
已添加27Aug:凯尔接着这样做了 scipy-user thread
30Aug:@Kyle,看起来Cartesion X,Y和极地Xnew,Ynew之间有混淆。 请参阅下面的长篇笔记中的“极性”。
# griddata vs SmoothBivariateSpline
# http://stackoverflow.com/questions/3526514/
# problem-with-2d-interpolation-in-scipy-non-rectangular-grid
# http://www.scipy.org/Cookbook/Matplotlib/Gridding_irregularly_spaced_data
# http://en.wikipedia.org/wiki/Natural_neighbor
# http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html
from __future__ import division
import sys
import numpy as np
from scipy.interpolate import SmoothBivariateSpline # $scipy/interpolate/fitpack2.py
from matplotlib.mlab import griddata
__date__ = "2010-10-08 Oct" # plot diffs, ypow
# "2010-09-13 Sep" # smooth relative
def avminmax( X ):
absx = np.abs( X[ - np.isnan(X) ])
av = np.mean(absx)
m, M = np.nanmin(X), np.nanmax(X)
histo = np.histogram( X, bins=5, range=(m,M) ) [0]
return "av %.2g min %.2g max %.2g histo %s" % (av, m, M, histo)
def cosr( x, y ):
return 10 * np.cos( np.hypot(x,y) / np.sqrt(2) * 2*np.pi * cycle )
def cosx( x, y ):
return 10 * np.cos( x * 2*np.pi * cycle )
def dipole( x, y ):
r = .1 + np.hypot( x, y )
t = np.arctan2( y, x )
return np.cos(t) / r**3
#...............................................................................
testfunc = cosx
Nx = Ny = 20 # interpolate random Nx x Ny points -> Newx x Newy grid
Newx = Newy = 100
cycle = 3
noise = 0
ypow = 2 # denser => smaller error
imclip = (-5., 5.) # plot trierr, splineerr to same scale
kx = ky = 3
smooth = .01 # Spline s = smooth * z2sum, see note
# s is a target for sum (Z() - spline())**2 ~ Ndata and Z**2;
# smooth is relative, s absolute
# s too small => interpolate/fitpack2.py:580: UserWarning: ier=988, junk out
# grr error message once only per ipython session
seed = 1
plot = 0
exec "\n".join( sys.argv[1:] ) # run this.py N= ...
np.random.seed(seed)
np.set_printoptions( 1, threshold=100, suppress=True ) # .1f
print 80 * "-"
print "%s Nx %d Ny %d -> Newx %d Newy %d cycle %.2g noise %.2g kx %d ky %d smooth %s" % (
testfunc.__name__, Nx, Ny, Newx, Newy, cycle, noise, kx, ky, smooth)
#...............................................................................
# interpolate X Y Z to xnew x ynew --
X, Y = np.random.uniform( size=(Nx*Ny, 2) ) .T
Y **= ypow
# 1d xlin ylin -> 2d X Y Z, Ny x Nx --
# xlin = np.linspace( 0, 1, Nx )
# ylin = np.linspace( 0, 1, Ny )
# X, Y = np.meshgrid( xlin, ylin )
Z = testfunc( X, Y ) # Ny x Nx
if noise:
Z += np.random.normal( 0, noise, Z.shape )
# print "Z:\n", Z
z2sum = np.sum( Z**2 )
xnew = np.linspace( 0, 1, Newx )
ynew = np.linspace( 0, 1, Newy )
Zexact = testfunc( *np.meshgrid( xnew, ynew ))
if imclip is None:
imclip = np.min(Zexact), np.max(Zexact)
xflat, yflat, zflat = X.flatten(), Y.flatten(), Z.flatten()
#...............................................................................
print "SmoothBivariateSpline:"
fit = SmoothBivariateSpline( xflat, yflat, zflat, kx=kx, ky=ky, s = smooth * z2sum )
Zspline = fit( xnew, ynew ) .T # .T ??
splineerr = Zspline - Zexact
print "Zspline - Z:", avminmax(splineerr)
print "Zspline: ", avminmax(Zspline)
print "Z: ", avminmax(Zexact)
res = fit.get_residual()
print "residual %.0f res/z2sum %.2g" % (res, res / z2sum)
# print "knots:", fit.get_knots()
# print "Zspline:", Zspline.shape, "\n", Zspline
print ""
#...............................................................................
print "griddata:"
Ztri = griddata( xflat, yflat, zflat, xnew, ynew )
# 1d x y z -> 2d Ztri on meshgrid(xnew,ynew)
nmask = np.ma.count_masked(Ztri)
if nmask > 0:
print "info: griddata: %d of %d points are masked, not interpolated" % (
nmask, Ztri.size)
Ztri = Ztri.data # Nans outside convex hull
trierr = Ztri - Zexact
print "Ztri - Z:", avminmax(trierr)
print "Ztri: ", avminmax(Ztri)
print "Z: ", avminmax(Zexact)
print ""
#...............................................................................
if plot:
import pylab as pl
nplot = 2
fig = pl.figure( figsize=(10, 10/nplot + .5) )
pl.suptitle( "Interpolation error: griddata - %s, BivariateSpline - %s" % (
testfunc.__name__, testfunc.__name__ ), fontsize=11 )
def subplot( z, jplot, label ):
ax = pl.subplot( 1, nplot, jplot )
im = pl.imshow(
np.clip( z, *imclip ), # plot to same scale
cmap=pl.cm.RdYlBu,
interpolation="nearest" )
# nearest: squares, else imshow interpolates too
# todo: centre the pixels
ny, nx = z.shape
pl.scatter( X*nx, Y*ny, edgecolor="y", s=1 ) # for random XY
pl.xlabel(label)
return [ax, im]
subplot( trierr, 1,
"griddata, Delaunay triangulation + Natural neighbor: max %.2g" %
np.nanmax(np.abs(trierr)) )
ax, im = subplot( splineerr, 2,
"SmoothBivariateSpline kx %d ky %d smooth %.3g: max %.2g" % (
kx, ky, smooth, np.nanmax(np.abs(splineerr)) ))
pl.subplots_adjust( .02, .01, .92, .98, .05, .05 ) # l b r t
cax = pl.axes([.95, .05, .02, .9]) # l b w h
pl.colorbar( im, cax=cax ) # -1.5 .. 9 ??
if plot >= 2:
pl.savefig( "tmp.png" )
pl.show()
关于2d插值的注释,BivariateSpline与griddata。
scipy.interpolate.*BivariateSpline
和matplotlib.mlab.griddata
都将1d数组作为参数:
Znew = griddata( X,Y,Z, Xnew,Ynew )
# 1d X Y Z Xnew Ynew -> interpolated 2d Znew on meshgrid(Xnew,Ynew)
assert X.ndim == Y.ndim == Z.ndim == 1 and len(X) == len(Y) == len(Z)
输入X,Y,Z
描述3空间中的点或表面云:
飞机上的X,Y
(或纬度,经度或......)点,
和Z
上方的表面或地形。
X,Y
可填充大部分矩形[Xmin .. Xmax] x [Ymin .. Ymax],
或者可能只是里面的一个波浪形的S或Y.
Z
表面可能是平滑的,也可能是平滑的+有点噪音,
或者根本不光滑,粗糙的火山山脉。
Xnew和Ynew通常也是1d,描述了一个矩形网格
of | Xnew | x | Ynew |想要插值或估计Z的点。
Znew = griddata(...)在这个网格上返回一个2d数组,np.meshgrid(Xnew,Ynew):
Znew[Xnew0,Ynew0], Znew[Xnew1,Ynew0], Znew[Xnew2,Ynew0] ...
Znew[Xnew0,Ynew1] ...
Znew[Xnew0,Ynew2] ...
...
Xnew,Ynew远远没有任何输入X,Y的拼写麻烦。
griddata
检查一下:
如果任何网格点在凸面之外,则返回蒙版数组 由输入数据定义的船体(未进行外推)。
(“凸壳”是想象中的区域 所有X,Y点周围都有橡皮筋。)
griddata
首先构建Delaunay三角剖分
输入X,Y,然后做
Natural neighbor
插值。这很强大而且非常快。
BivariateSpline可以推断,
在没有警告的情况下生成狂野的摇摆 。
此外,Fitpack中的所有* Spline例程
对平滑参数S非常敏感。
Dierckx的书(books.google isbn 019853440X p.89)说:
如果S太小,则样条逼近过于晃动
并且拾起太多噪音(过度装配);
如果S太大,样条曲线将太平滑
并且信号将丢失(低调)。
分散数据的插值很难,平滑不容易,两者都很难。 内插器应该用XY中的大孔或者非常嘈杂的Z来做什么? (“如果你想出售它,你将不得不描述它。”)
更多的笔记,精美的印刷品:
1d vs 2d:一些内插器将X,Y,Z取为1d或2d。 其他人仅采用1d,因此在插值前展平:
Xmesh, Ymesh = np.meshgrid( np.linspace(0,1,Nx), np.linspace(0,1,Ny) )
Z = f( Xmesh, Ymesh ) # Nx x Ny
Znew = griddata( Xmesh.flatten(), Ymesh.flatten(), Z.flatten(), Xnew, Ynew )
在蒙面数组上:matplotlib处理它们很好, 仅绘制未掩盖/非NaN点。 但我不敢打赌,一个bozo numpy / scipy函数会起作用。 检查X,Y凸包外的插值,如下所示:
Znew = griddata(...)
nmask = np.ma.count_masked(Znew)
if nmask > 0:
print "info: griddata: %d of %d points are masked, not interpolated" % (
nmask, Znew.size)
# Znew = Znew.data # array with NaNs
在极坐标上: X,Y和Xnew,Ynew应该在同一个空间, Cartesion或两者都是[rmin .. rmax] x [tmin ... tmax] 在3d中绘制(r,theta,z)点:
from mpl_toolkits.mplot3d import Axes3D
Znew = griddata( R,T,Z, Rnew,Tnew )
ax = Axes3D(fig)
ax.plot_surface( Rnew * np.cos(Tnew), Rnew * np.sin(Tnew), Znew )
另见(尚未尝试过):
ax = subplot(1,1,1, projection="polar", aspect=1.)
ax.pcolormesh(theta, r, Z)
<小时/> 谨慎的程序员的两个提示:
检查异常值或有趣的缩放:
def minavmax( X ):
m = np.nanmin(X)
M = np.nanmax(X)
av = np.mean( X[ - np.isnan(X) ]) # masked ?
histo = np.histogram( X, bins=5, range=(m,M) ) [0]
return "min %.2g av %.2g max %.2g histo %s" % (m, av, M, histo)
for nm, x in zip( "X Y Z Xnew Ynew Znew".split(),
(X,Y,Z, Xnew,Ynew,Znew) ):
print nm, minavmax(x)
用简单数据检查插值:
interpolate( X,Y,Z, X,Y ) -- interpolate at the same points
interpolate( X,Y, np.ones(len(X)), Xnew,Ynew ) -- constant 1 ?