SciPy和Numpy之间的伪逆的区别 [英] The difference of pseudo-inverse between SciPy and Numpy

问题描述

我发现有pinv()函数的两个版本，可以计算Scipy和numpy中矩阵的伪逆，可以在以下位置查看文档:

I found that there're two versions of pinv() function, which calculates the pseudo-inverse of a matrix in Scipy and numpy, the documents can be viewed at:

http://docs.scipy.org/doc/numpy/reference /generation/numpy.linalg.pinv.html

http://docs.scipy.org/doc/scipy/reference /generation/scipy.linalg.pinv.html

问题是我有一个50000 * 5000的矩阵，使用scipy.linalg.pinv时，它花费了我超过20GB的内存.但是当我使用numpy.linalg.pinv时，仅使用了不到1GB的内存.

The problem is that I have a 50000*5000 matrix, when using scipy.linalg.pinv, it costs me more than 20GB of memory. But when I use numpy.linalg.pinv, only less than 1GB of memory is used..

我想知道为什么numpy和scipy都在不同的实现下都具有pinv.以及为什么他们的表现如此不同.

I was wondering why numpy and scipy both have a pinv under different implemention. And why their performances are so different.

推荐答案

我不能说为什么scipy和numpy都有实现，但是我可以解释为什么行为不同.

I can't speak as to why there are implementations in both scipy and numpy, but I can explain why the behaviour is different.

numpy.linalg.pinv使用SVD逼近Moore-Penrose伪逆(精确地说是lapack方法dgesdd)，而scipy.linalg.pinv在最小二乘意义上求解模型线性系统以近似伪逆(使用dgelss).这就是为什么它们的性能不同的原因.我希望得到的伪逆估计的总体准确性也会有所不同.

numpy.linalg.pinv approximates the Moore-Penrose psuedo inverse using an SVD (the lapack method dgesdd to be precise), whereas scipy.linalg.pinv solves a model linear system in the least squares sense to approximate the pseudo inverse (using dgelss). This is why their performance is different. I would expect the overall accuracy of the resulting pseudo inverse estimates to be somewhat different as well.

您可能会发现scipy.linalg.pinv2的性能与numpy.linalg.pinv更加相似，因为它也使用SVD方法，而不是最小二乘方近似.

You might find that scipy.linalg.pinv2 performs more similarly to numpy.linalg.pinv, as it too uses an SVD method, rather than a least sqaures approximation.

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