---
title: ?sy(he)ev
description: "计算对称（Hermite）矩阵的所有特征值与特征向量。"
url: https://www.hikunpeng.com/document/detail/zh/kunpengboostkithistory/2200/accel/kunpengaccel_kml_16_0329.html
sourcePath: /source/zh/kunpengboostkithistory/2200/accel/kunpengaccel_kml_16_0329.html
indexId: a524ec526dc30b01f9e100d4e860b1d42c25ce5933db7b1cc44fbef9deb7692074
---
# ?sy(he)ev

计算对称（Hermite）矩阵的所有特征值与特征向量。

#### 接口定义

C Interface：

ssyev_(const char *jobz, const char *uplo, const int *n, float *A, const int *lda, float *w, float *work, const int *lwork, int * info);

dsyev_(const char *jobz, const char *uplo, const int *n, double *A, const int *lda, double *w, double *work, const int *lwork, int * info);

cheev_(const char *jobz, const char *uplo, const int *n, float _Complex *A, const int *lda, float *w, float _Complex *work, const int *lwork, float* rwork, int * info);

zheev_(const char *jobz, const char *uplo, const int *n, double _Complex *A, const int *lda, double *w, double _Complex *work, const int *lwork, double* rwork, int * info);

Fortran Interface：

SSYEV(jobz, uplo, n, a, lda, w, work, lwork, info);

DSYEV(jobz, uplo, n, a, lda, w, work, lwork, info);

CHEEV(jobz, uplo, n, a, lda, w, work, lwork, rwork, info);

ZHEEV(jobz, uplo, n, a, lda, w, work, lwork, rwork, info);


#### 参数

| 参数 | 类型 | 说明 | 输入/输出 |
| --- | --- | --- | --- |
| jobz | 字符型 | ‘N’：只计算特征值。 ‘V’：计算特征值及特征向量。 | 输入 |
| uplo | 字符型 | ‘U’：存储A的上三角部分。 ‘L’：存储A的下三角部分。 | 输入 |
| n | 整数型 | 矩阵A的维度，大于或等于0。 | 输入 |
| a | 在ssyev中为单精度浮点型数组。 在dsyev中为双精度浮点型数组。 在cheev中为单精度复数型数组。 在zheev中为双精度复数型数组。 | 调用前保存待分解的对称矩阵。 调用后保存特征向量。 | 输入，输出 |
| lda | 整数型 | 矩阵A的主维，大于或等于max(1,N)。 | 输入 |
| w | 在ssyevd/cheevd中为单精度浮点型数组。 在dsyevd/zheevd中为双精度浮点型数组。 | Info=0时，以升序存储特征值，长度为N。 | 输出 |
| work | 在ssyev中为单精度浮点型数组。 在dsyev中为双精度浮点型数组。 在cheev中为单精度复数型数组。 在zheev中为双精度复数型数组。 | Info=0时，work(0)返回最优lwork大小。 | 输出 |
| lwork | 整数型 | Work数组的长度。 lwork=\-1时查询最优work大小，结果保存在work[0]中。且lwork ≥ max(1, 2\*n\-1)。 | 输入 |
| rwork（复数特有） | 在ssyevd/cheevd中为单精度浮点型数组。 在dsyevd/zheevd中为双精度浮点型数组。 | 工作数组，取值max(1,3\*n\-1)。 | 输出 |
| info | 整数型 | 状态值： 等于0：表示成功。 小于0：info=\-i，表示第i个参数非法。 大于0：算法出错。 | 输出 |


#### 依赖

#include "klapack.h"


#### 示例

C Interface：

```
char jobz = 'V';
char uplo = 'L';
int n = 5;
int lda = 5;
int info = 0;
double w[5];
double *work = NULL;
double qwork;
int lwork = -1;
/*
* Symmetric A (stored in column-major):
*   7.027  8.710  1.015  6.929  7.584
*   8.710  0.839  2.469  3.850  0.559
*   1.015  2.469  1.930  6.761  7.207
*   6.929  3.850  6.761  4.344  4.804
*   7.584  0.559  7.207  4.804  6.177
*/
double a[] = {7.027, 8.710, 1.015, 6.929, 7.584,
8.710, 0.839, 2.469, 3.850, 0.559,
1.015, 2.469, 1.930, 6.761, 7.207,
6.929, 3.850, 6.761, 4.344, 4.804,
7.584, 0.559, 7.207, 4.804, 6.177};
/* Query optimal work size */
dsyev_(&jobz, &uplo, &n, a, &lda, w, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate eigenvalues and eigenvectors */
dsyev_(&jobz, &uplo, &n, a, &lda, w, work, &lwork, &info);
free(work);
/*
* Output:
* Eigenvalues (in w)
*  -1.770722   -0.845606   -0.203058   -5.712058   3.044889
* Eigenvectors (in a, stored in column-major)
*  0.547211        -0.528441       0.339953        -0.172302       -0.531245
*  0.050685        -16.554919      -5.702155       2.261598        15.521155
*  -0.456110       0.988485        0.587808        -3.161022       -1.099502
* -0.443428       -1.398420       0.424293        0.800628        0.016423
* -0.541596       -1.770722       -0.845606       -0.203058       -5.712058
*/
```

Fortran Interface：

```
CHARACTER :: jobz = "V"
CHARACTER :: uplo = "L"
PARAMETER (n = 5)
PARAMETER (lda = 5)
INTEGER :: info = 0
REAL(8) :: w(5);
REAL(8) :: qwork(1)
REAL(8), ALLOCATABLE :: work(:)
INTEGER :: lwork = -1
*       Symmetric A (stored in column-major):
*         7.027  8.710  1.015  6.929  7.584
*         8.710  0.839  2.469  3.850  0.559
*         1.015  2.469  1.930  6.761  7.207
*         6.929  3.850  6.761  4.344  4.804
*         7.584  0.559  7.207  4.804  6.177
REAL(8) :: a(n, n)
DATA a / 7.027, 8.710, 1.015, 6.929, 7.584,
$           8.710, 0.839, 2.469, 3.850, 0.559,
$           1.015, 2.469, 1.930, 6.761, 7.207,
$           6.929, 3.850, 6.761, 4.344, 4.804,
$           7.584, 0.559, 7.207, 4.804, 6.177 /
*       Query optimal work size
EXTERNAL DSYEVD
CALL DSYEV(jobz, uplo, n, a, lda, w, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
*       Calculate eigenvalues and eigenvectors
CALL DSYEV(jobz, uplo, n, a, lda, w, work, lwork, info)
DEALLOCATE(work);
*       Output:
*       Eigenvalues (in w)
*        -1.770722   -0.845606   -0.203058   -5.712058   3.044889
*       Eigenvectors (in a, stored in column-major)
*         0.547211        -0.528441       0.339953        -0.172302       -0.531245
*         0.050685        -16.554919      -5.702155       2.261598        15.521155
*         -0.456110       0.988485        0.587808        -3.161022       -1.099502
*         -0.443428       -1.398420       0.424293        0.800628        0.016423
*         -0.541596       -1.770722       -0.845606       -0.203058       -5.71205
```