加权最小二乘矩阵维数

Question

我想执行以下加权最小二乘运算：

L = ((x^t * W * x)^-1)(X^t *W*y)
Where x is(240, 60) matrix
y is (240, 1) matrix
W is diagonal matrix of shape (60, 60)

我试图在计算倒数x^t*W*x之前实现第一部分，如下所示：

np.dot(x.transpose(),W,x) 

我得到错误：

shapes (60,240) and (60,240) not aligned: 240 (dim 1) != 60 (dim 0)

同时实施

numpy.transpose(x)*W*y

给出错误

operands could not be broadcast together with shapes (60,240) (240,1)

完成乘法运算的最佳方法是什么？然后我想实现SVD方法来获得项(x^t*W*x(的逆

Answer 1

import numpy as numpy
x = numpy.random.random((240, 60))
y = numpy.random.random((240, 1))
W = numpy.random.random((60, 60))
second_part = numpy.dot(numpy.transpose(numpy.dot(x,W)),y)