如何仅在八度中计算矩阵乘积的对角线? [英] How to compute only the diagonal of a matrix product in Octave?

问题描述

八度中是否有一种方法可以仅计算和存储矩阵乘积的对角线?

Is there a way in Octave to compute and store only the diagonal of a matrix product?

基本上喜欢这样做:vector = diag(A*B);

除了对角线上的那些值，我不在乎A*B的任何值.矩阵大小在80k x 12和12 x 80k左右，所以即使我不在乎速度/额外的内存，它也根本无法放入RAM.

I don't care about any of the values of A*B except those on the diagonal. The matrix sizes are around 80k x 12 and 12 x 80k, so even if I didn't care about the speed/extra memory it simply wont fit in RAM.

奇怪，因为Octave是用于存储大量数据集的程序包，对角线非常重要，所以应该有可能.

Strange, since Octave is a package for huge data sets and diagonals are very important, so it should be possible.

推荐答案

对角线上的第一个元素是A的第一行与B的第一列的标量积.对角线上的第二个元素是标量积A的第二行和B的第二列.

The first element in the diagonal is the scalar product of the first row of A with the first column of B. The second element in the diagonal is the scalar product of the second row of A with the second column of B.

换句话说:

vector = sum(A.*B',2);

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