---
title: ?potri
description: "计算对称正定矩阵的逆。"
url: https://www.hikunpeng.com/document/detail/zh/kunpengboostkithistory/240RC1/accel/kunpengaccel_kml_16_0276.html
sourcePath: /source/zh/kunpengboostkithistory/240RC1/accel/kunpengaccel_kml_16_0276.html
indexId: 9871f2ab39914d5e8b25437d619fc84e30cd7f3ff89eba9d4c4b132a8849bfe976
---
# ?potri

计算对称正定矩阵的逆。

#### 接口定义

C interface：

void spotri_(const char *UPLO, const int *N, const float *A, const int *LDA, int *INFO);

void dpotri_(const char *UPLO, const int *N, const double *A, const int *LDA, int *INFO);

void cpotri_(const char *UPLO, const int *N, const float _Complex *A, const int *LDA, int *INFO);

void zpotri_(const char *UPLO, const int *N, const double _Complex *A, const int *LDA, int *INFO);

Fortran Interface：

SPOTRI(UPLO, N, A, LDA, INFO);

DPOTRI(UPLO, N, A, LDA, INFO);

CPOTRI(UPLO, N, A, LDA, INFO);

ZPOTRI(UPLO, N, A, LDA, INFO);


#### 参数

| 参数名 | 类型 | 描述 | 输入/输出 |
| --- | --- | --- | --- |
| UPLO | 字符型 | 'U'：保存A的上三角矩阵。 'L'：保存A的下三角矩阵。 | 输入 |
| N | 整数型 | 矩阵A的维数，n ≥ 0。 | 输入 |
| A | 在spotri中为单精度浮点型数组。 在dpotri中为双精度浮点型数组。 在cpotri中为单精度复数型数组。 在zpotri中为双精度复数型数组。 | 调用前保存矩阵A的Cholesky分解结果（由?potrf得到）。 调用后保存原矩阵A的逆矩阵。 | 输入、输出 |
| LDA | 整数型 | A的leading dimension大小，lda ≥ max(1,n)。 | 输入 |
| INFO | 整数型 | 执行结果： 等于0：成功。 小于0：第\-info个参数值不合法。 大于0：U的对角线上第info个元素为0，矩阵不可逆。 | 输出 |


#### 依赖

#include "klapack.h"


#### 示例

C Interface：

```
char uplo = 'L'
int n = 4;
int lda = n;
int info = 0;
/*
* A: After Cholesky factorization (via potrf, stored in column-major):
*  231.8009    33.9545    9.4153   11.1156
*   33.9454   162.2902   6.6684   53.2023
*   9.4153   6.6684  100.3220  71.5384
*   11.1156   53.2023    71.5384  123.4425
*/
double a[] = {231.8009,   33.9545,   9.4143,   11.1156,
33.9495,  162.2902,   6.6684,   53.2033,
9.4143,    6.6684,  100.322,   71.5384,
11.1156,   53.2033,  71.5384,  106.5638 };
dpotri_(&uplo, &n, a, &lda, &info);
/*
* Output:
*   0.000020  -0.000006  -0.000005   0.000002
*   33.949500  0.000046   0.000015  -0.000026
*   9.414300   6.668400   0.000144  -0.000063
*   11.115600  53.203300  71.538400  0.000088
*/
```

Fortran Interface：

```
CHARACTER :: uplo = "L"
PARAMETER (n = 4)
PARAMETER (lda = 4)
INTEGER :: info = 0
REAL(8) :: a(n,n)
* A: After Cholesky factorization (via potrf, stored in column-major):
*  231.8009    33.9545    9.4153   11.1156
*   33.9454   162.2902   6.6684   53.2023
*   9.4153   6.6684  100.3220  71.5384
*   11.1156   53.2023    71.5384  123.4425
DATA a / 231.8009,  33.9545,  9.4143, 11.1156,
$           33.9495,  162.2902, 6.6684, 53.2033,
$           9.4143,    6.6684,  100.322, 71.5384,
$           11.1156,   53.2033, 71.5384, 106.5638 /
EXTERNAL DPOTRF
CALL DPOTRI (uplo, n, a, lda, info);
*
* Output:
*   0.000020  -0.000006  -0.000005   0.000002
*   33.949500  0.000046   0.000015  -0.000026
*   9.414300   6.668400   0.000144  -0.000063
*   11.115600  53.203300  71.538400  0.000088
*
```