?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ssyev/cheev中为单精度浮点型数组。在dsyev/zheev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（复数类型特有）	在ssyev/cheev中为单精度浮点型数组。在dsyev/zheev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：第-info个参数值不合法。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

父主题： 特征值问题函数