torch.linalg.matrix_exp#

torch.linalg.matrix_exp(A)→Tensor#

Computes the matrix exponential of a square matrix.

Letting$\mathbb{K}$K be$\mathbb{R}$R or$\mathbb{C}$C,this function computes thematrix exponential of$A\in {\mathbb{K}}^{n\times n}$A∈Kn×n, which is defined as

$$\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{x}\mathrm{\_}\mathrm{e}\mathrm{x}\mathrm{p}(A)=\sum _{k=0}^{\mathrm{\infty }}\frac{1}{k!}{A}^k\in {\mathbb{K}}^{n\times n}\mathrm{.}$$matrix_exp(A)=k=0∑∞​k!1​Ak∈Kn×n.

If the matrix$A$A has eigenvalues${\lambda }_i\in \mathbb{C}$λi​∈C,the matrix$\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{x}\mathrm{\_}\mathrm{e}\mathrm{x}\mathrm{p}(A)$matrix_exp(A) has eigenvalues$e^{{\lambda }_i}\in \mathbb{C}$eλi​∈C.

Supports input of bfloat16, float, double, cfloat and cdouble dtypes.Also supports batches of matrices, and ifA is a batch of matrices thenthe output has the same batch dimensions.

Parameters

A (Tensor) – tensor of shape(*, n, n) where* is zero or more batch dimensions.

Example:

>>>A=torch.empty(2,2,2)>>>A[0,:,:]=torch.eye(2,2)>>>A[1,:,:]=2*torch.eye(2,2)>>>Atensor([[[1., 0.],         [0., 1.]],        [[2., 0.],         [0., 2.]]])>>>torch.linalg.matrix_exp(A)tensor([[[2.7183, 0.0000],         [0.0000, 2.7183]],         [[7.3891, 0.0000],          [0.0000, 7.3891]]])>>>importmath>>>A=torch.tensor([[0,math.pi/3],[-math.pi/3,0]])# A is skew-symmetric>>>torch.linalg.matrix_exp(A)# matrix_exp(A) = [[cos(pi/3), sin(pi/3)], [-sin(pi/3), cos(pi/3)]]tensor([[ 0.5000,  0.8660],        [-0.8660,  0.5000]])