从下三角矩阵给出一个元素(Giving an element from lower/upper triangular matrix)

从下三角矩阵给出一个元素(Giving an element from lower/upper triangular matrix)

我有一个矩阵的上三角部分，主对角线存储为线性阵列，矩阵元素的（i，j）指数如何从阵列的线性索引中提取？

例如，对于矩阵存储线性阵列： [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10]

a0 a1 a2 a3 0 a4 a5 a6 0 0 a7 a8 0 0 0 a10

我找到了这个问题的解决方案，但没有主对角线，它是：

index = (n*(n-1)/2) - (n-i)*((n-i)-1)/2 + j - i - 1

并解决相同的问题，但对于具有对角线的下三角矩阵：

index = ((i + 1) * i / 2 + i).

问候，

I have the upper triangular portion of a matrix, with the main diagonal stored as a linear array, how can the (i,j) indices of a matrix element be extracted from the linear index of the array?

For example the linear array :[a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10]is storage for the matrix

a0 a1 a2 a3 0 a4 a5 a6 0 0 a7 a8 0 0 0 a10

I've found solutions for this problem but without the main diagonal which is:

index = (n*(n-1)/2) - (n-i)*((n-i)-1)/2 + j - i - 1

And solution for the same problem but for a lower triangular matrix with the diagonal:

index = ((i + 1) * i / 2 + i).

Regards,