将 rbf 与 scipy 一起使用时出现内存错误

Question

我想像这里一样用 rbf 函数绘制一些点以获得点的密度分布：

如果我运行下面的代码，它工作正常：

from scipy.interpolate.rbf import Rbf  # radial basis functions
import cv2
import matplotlib.pyplot as plt
import numpy as np

# import data
x = [1, 1, 2 ,3, 2, 7, 8, 6, 6, 7, 6.5, 7.5, 9, 8, 9, 8.5]
y = [0, 2, 5, 6, 1, 2, 9, 2, 3, 3, 2.5, 2, 8, 8, 9, 8.5]
d = np.ones(len(x))
print(d)

ti = np.linspace(-1,10)

xx, yy = np.meshgrid(ti, ti)

rbf = Rbf(x, y, d, function='gaussian')
jet = cm = plt.get_cmap('jet')
zz = rbf(xx, yy)
plt.pcolor(xx, yy, zz, cmap=jet)
plt.colorbar()

# Plotting the original points.
plot3 = plt.plot(x, y, 'ko', markersize=5)  # the original points.

plt.show()

现在我想更改我的输入数据：

# import data
input = "testProbe.jpg"
image = cv2.imread(input)   # load the image
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)  # convert it to grayscale
# threshold the image to reveal light regions in the gray image
thresh = cv2.threshold(gray, 145, 200, cv2.THRESH_BINARY)[1]

x, y = np.where(thresh > 0)
d = np.ones(len(x))

我收到以下错误消息：

Traceback (most recent call last):
  File "C:/Users/.../Python/pythonprojects/03a_test_rbfWithScipy.py", line 32, in <module>
    rbf = Rbf(x, y, z, function='gaussian')
  File "C:\Users\...\Python\Anaconda2\lib\site-packages\scipy\interpolate\rbf.py", line 220, in __init__
    self.nodes = linalg.solve(self.A, self.di)
  File "C:\Users\...\Python\Anaconda2\lib\site-packages\scipy\interpolate\rbf.py", line 226, in A
    r = self._call_norm(self.xi, self.xi)
  File "C:\Users\...\Python\Anaconda2\lib\site-packages\scipy\interpolate\rbf.py", line 236, in _call_norm
    return self.norm(x1, x2)
  File "C:\Users\...\Python\Anaconda2\lib\site-packages\scipy\interpolate\rbf.py", line 118, in _euclidean_norm
    return np.sqrt(((x1 - x2)**2).sum(axis=0))
MemoryError

错误消息出现得非常快，当我查看任务管理器时，PC 并未运行满负荷运行。他立即发出这条消息。那总有些事情是不对的，不是吗？

我尝试使用其他阈值 thresh = cv2.threshold(gray, 250, 255, cv2.THRESH_BINARY)[1] 来获得更少的值并且它有效，但我收到以下错误消息：

C:\Users\...\Python\Anaconda2\lib\site-packages\scipy\interpolate\rbf.py:220: LinAlgWarning: 
scipy.linalg.solve Ill-conditioned matrix detected. Result is not guaranteed to be accurate. 
Reciprocal condition number2.246772e-22 self.nodes = linalg.solve(self.A, self.di)

有什么想法吗？

如果我只剪掉一小部分图片，也可以。也许它对内存进行了一些初步计算并给我内存错误

Answer 1

在我看来 Rbf 插值计算量很大，会导致 O(N^2) 操作（如果我错了请纠正我）。因此，为了避免内存错误，您可以执行以下操作之一，而不是

zz = rbf(xx, yy)

1.用 nditer

迭代

慢，但适用于小型阵列：

for iz, ix, iy in np.nditer(
    [zz, xx, yy],
    flags=['external_loop', 'buffered'], 
    op_flags=['readwrite']
):
    iz[...] = rbf(ix, iy)

2。使用 dask.array

更快的选项并使用线程

import dask.array as da

n1 = xx.shape[1]
ix = da.from_array(xx, chunks=(1, n1))
iy = da.from_array(yy, chunks=(1, n1))
iz = da.map_blocks(rbf, ix, iy)
zz = iz.compute()

希望这对你有用。

P.S：如 another question and scipy docs on Rbf, Rbf also allows you to replace the norm calculation function with a callable (see LowLevelCallable and the Pythran blog 中所建议）。它有点复杂，但它也可能会解决您的问题，同时也会提高性能。

P.P.S：我通过这个修改设法加速了 50 倍：

import numpy as np

def euclidean_norm_numpy(x1, x2):
    return np.linalg.norm(x1 - x2, axis=0)

rbf = Rbf(x, y, d, function='gaussian', norm=euclidean_norm_numpy)

将 rbf 与 scipy 一起使用时出现内存错误

memory error by using rbf with scipy

python

python-3.x

out-of-memory

probability

probability-density