问题描述
我有以下向量。
x = np.array([[ 0.87695113],[ 0.3284933 ],[-0.35078323]])
当我调用 numpy 版本的 qr
from numpy.linalg import qr as qr_numpy
qr_numpy(x)
我得到
(array([[-0.87695113],[-0.3284933 ],[ 0.35078323]]),array([[-1.]]))
而当我运行 scipy 版本时,我得到了完全不同的东西。
from scipy.linalg import qr as qr_scipy
qr_scipy(x)
有输出
(array([[-0.87695113,-0.3284933,0.35078323],[-0.3284933,0.94250897,0.06139208],[ 0.35078323,0.06139208,0.93444215]]),array([[-1.],[ 0.],[ 0.]]))
这是怎么回事??
解决方法
numpy.linalg.qr()
的默认 mode
是 'reduced'
,而 scipy.linalg.qr()
的默认 'full'
。
因此,要获得相同的结果,请对 scipy-qr 使用 'economic'
或对 numpy-qr 使用 'complete'
:
from numpy.linalg import qr as qr_numpy
qr_numpy(x)
(array([[-0.87695113],[-0.3284933 ],[ 0.35078323]]),array([[-1.]]))
与 scipy-qr 的输出匹配:
from scipy.linalg import qr as qr_scipy
qr_scipy(x,mode='economic')
(array([[-0.87695113],array([[-1.]]))
并获得两者的“完整”版本:
from numpy.linalg import qr as qr_numpy
qr_numpy(x,mode='complete')
(array([[-0.87695113,-0.3284933,0.35078323],[-0.3284933,0.94250897,0.06139208],[ 0.35078323,0.06139208,0.93444215]]),array([[-1.],[ 0.],[ 0.]]))
from scipy.linalg import qr as qr_scipy
qr_scipy(x)
(array([[-0.87695113,[ 0.]]))