# expm

## 语法

``Y = expm(X)``

## 说明

``Y = expm(X)` 计算 `X` 的矩阵指数。虽然不按此种方式计算，但是如果 `X` 包含一组完整的特征向量 `V` 和对应特征值 `D`，则 `[V,D] = eig(X)` 且expm(X) = V*diag(exp(diag(D)))/V对于逐个元素的指数运算，请使用 `exp`。`

## 示例

```A = [1 1 0; 0 0 2; 0 0 -1]; exp(A)```
```ans = 3×3 2.7183 2.7183 1.0000 1.0000 1.0000 7.3891 1.0000 1.0000 0.3679 ```
`expm(A)`
```ans = 3×3 2.7183 1.7183 1.0862 0 1.0000 1.2642 0 0 0.3679 ```

## 算法

`expm` 使用的算法如 [1][2] 中所述。

## 参考

[1] Higham, N. J., “The Scaling and Squaring Method for the Matrix Exponential Revisited,” SIAM J. Matrix Anal. Appl., 26(4) (2005), pp. 1179–1193.

[2] Al-Mohy, A. H. and N. J. Higham, “A new scaling and squaring algorithm for the matrix exponential,” SIAM J. Matrix Anal. Appl., 31(3) (2009), pp. 970–989.

[3] Golub, G. H. and C. F. Van Loan, Matrix Computation, p. 384, Johns Hopkins University Press, 1983.

[4] Moler, C. B. and C. F. Van Loan, “Nineteen Dubious Ways to Compute the Exponential of a Matrix,” SIAM Review 20, 1978, pp. 801–836. Reprinted and updated as “Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,” SIAM Review 45, 2003, pp. 3–49.