?sy(he)trd_2stage
将对称矩阵或Hermite矩阵A转为对称或Hermite三对角矩阵T，即A**H*A*Q=T，其中Q为正交矩阵。
接口定义
C Interface：
void ssytrd_2stage(const char *VECT, const char *UPLO, const int *N, float *A, const int *LDA, float *D, float *E, float *TAU, float *HOUS2, int *LHOUS2, float *WORK, const int *LWORK, int *INFO);
void dsytrd_2stage(const char *VECT, const char *UPLO, const int *N, double *A, const int *LDA, double *D, double *E, double *TAU, double *HOUS2, int *LHOUS2, double *WORK, const int *LWORK, int *INFO);
void chetrd_2stage(const char *VECT, const char *UPLO, const int *N, float _Complex *A, const int *LDA, float *D, float *E, float _Complex *TAU, float _Complex *HOUS2, int *LHOUS2, float _Complex *WORK, const int *LWORK, int *INFO);
void zhetrd_2stage(const char *VECT, const char *UPLO, const int *N, double _Complex *A, const int *LDA, double *D, double *E, double _Complex *TAU, double _Complex *HOUS2, int *LHOUS2, double _Complex *WORK, const int *LWORK, int *INFO);
Fortran Interface：
SSYTRD_2STAGE(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO);
DSYTRD_2STAGE(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO);
CHETRD_2STAGE(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO);
ZHETRD_2STAGE(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO);
参数
参数名 |
类型 |
描述 |
输入/输出 |
|---|---|---|---|
VECT |
字符型 |
|
输入 |
UPLO |
字符型 |
|
输入 |
N |
|
矩阵A的列数，N ≥ 0。 |
输入 |
A |
|
矩阵A，维度为（LDA, N）。 |
输入、输出 |
LDA |
整数型 |
矩阵A的主维， LDA ≥ max(1, N)。 |
输入 |
D |
|
对称三对角矩阵T的对角元素，大小为N。 |
输出 |
E |
|
对称三对角矩阵T的非对角元素，大小为N-1。 |
输出 |
TAU |
|
基本反射器的标量因子。 |
输出 |
HOUS2 |
|
存放第二阶段中Householder表达形式。 |
输出 |
LHOUS2 |
整数型 |
HOUS2的长度。
|
输入 |
WORK |
|
工作数组，大小为LWORK。 |
输出 |
LWORK |
整数型 |
工作数组的长度，LWORK ≥ max(1, dimension)。其中，dimension= max(stage1,stage2) + (KD+1)*N = N*KD + N*max(KD+1,FACTOPTNB) + max(2*KD*KD, KD*NTHREADS) + (KD+1)*N，当LWORK=-1时，返回最优LWORK值。 |
输入 |
INFO |
整数型 |
|
输出 |
依赖
include "klapack.h"
示例
C Interface：
char vect = 'N';
char uplo = 'L';
int n = 4;
int lda = n;
int info = 0;
double tau = (double*)malloc(n * sizeof(double));
double *work = NULL;
double *hous2 = NULL;
double qwork;
double qhous2;
int lwork = -1;
int lhous2 = -1;
double *d = (double*)malloc(n * sizeof(double));
double *e = (double*)malloc((n - 1) * sizeof(double));
double a[] = {0.521739, 0.043478, 0.304348, 0.130435,
0.043478, 0.304348, 0.043478, 0.652174,
0.304348, 0.043478, 0.086957, 0.521739,
0.130435, 0.652174, 0.521739, 0.086957};
/* Query optimal work size and hous2 size */
dsytrd_2stage_(&vect, &uplo, &n, a, &lda, d, e, tau, &qhous2, &lhous2, &qwork, &lwork, &info)
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
lhous2 = (int)qhous2;
hous2 = (double*)malloc(lhous2 * sizeof(double));
/* Calculate */
dsytrd_2stage_(&vect, &uplo, &n, a, &lda, d, e, tau, hous2, &lhous2, work, &lwork, &info);
if (info != 0) {
return ERROR;
}
free(work);
free(hous2);
free(tau);
/*
* Output:
* A output (stored in column-major)
* 0.521739 0.043478 0.304348 0.130435
* 0.043478 0.304348 0.043478 0.652174
* 0.304348 0.043478 0.086957 0.521739
* 0.130435 0.652174 0.521739 0.086957
*
* D output (stored in column-major)
* 0.521739 0.538688 0.325765 -0.386192
*
* E output (stored in column-major)
* -0.333963 -0.507861 -0.471868
*/
Fortran Interface：
CHARACTER :: vect = "N"
CHARACTER :: uplo = "L"
PARAMETER (n = 4)
PARAMETER (lda = 4)
INTEGER :: info = 0
REAL(8) :: tau(4)
REAL(8) :: qwork(1)
REAL(8) :: qhous2(1)
INTEGER :: lwork = -1
INTEGER :: lhous2 = -1
REAL(8), ALLOCATABLE :: work(:)
REAL(8), ALLOCATABLE :: hous2(:)
REAL(8), ALLOCATABLE :: d(:)
REAL(8), ALLOCATABLE :: e(:)
*
* tau:
* 1.003949 1.125229 1.978923 0.000000
* A (4x4, stored in column-major):
* 0.521739, 0.043478, 0.304348, 0.130435,
* 0.043478, 0.304348, 0.043478, 0.652174,
* 0.304348, 0.043478, 0.086957, 0.521739,
* 0.130435, 0.652174, 0.521739, 0.086957
*
REAL(8) :: a(m, n)
DATA a / 0.521739, 0.043478, 0.304348, 0.130435,
$ 0.043478, 0.304348, 0.043478, 0.652174,
$ 0.304348, 0.043478, 0.086957, 0.521739,
$ 0.130435, 0.652174, 0.521739, 0.086957 /
EXTERNAL DORGLQ
* Query optimal work size and hous2 size.
CALL DSYTRD_2STAGE(vect, uplo, n, a, lda, d, e, tau, qhous2, lhous2, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
lhous2 = INT(qhous2(1))
ALLOCATE(hous2(lhous2))
* Calculate
CALL DSYTRD_2STAGE(vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
DEALLOCATE(work)
DEALLOCATE(hous2)
* Output:
* A output (stored in column-major)
* 0.521739 0.043478 0.304348 0.130435
* 0.043478 0.304348 0.043478 0.652174
* 0.304348 0.043478 0.086957 0.521739
* 0.130435 0.652174 0.521739 0.086957
*
* D output (stored in column-major)
* 0.521739 0.538688 0.325765 -0.386192
*
* E output (stored in column-major)
* -0.333963 -0.507861 -0.471868
