计算矩阵的QR分解，即
。
接口定义
C Interface:
void dgeqrf_(const int *m, const int *n, double *a, const int *lda, double *tau, double *work, const int *lwork, int *info);
void sgeqrf_(const int *m, const int *n, float *a, const int *lda, float *tau, float *work, const int *lwork, int *info);
void cgeqrf_(const int *m, const int *n, float _Complex *a, const int *lda, float _Complex *tau, float _Complex *work, const int *lwork, int *info);
void zgeqrf_(const int *m, const int *n, double _Complex *a, const int *lda, double _Complex *tau, double _Complex *work, const int *lwork, int *info);
Fortran Interface:
DGEQRF(m, n, a, lda, tau, work, lwork, info);
SGEQRF(m, n, a, lda, tau, work, lwork, info);
CGEQRF(m, n, a, lda, tau, work, lwork, info);
ZGEQRF(m, n, a, lda, tau, work, lwork, info);
参数
参数名 |
类型 |
描述 |
输入/输出 |
|---|---|---|---|
m |
整型数 |
矩阵A的行数。 |
输入 |
n |
整型数 |
矩阵A的列数。 |
输入 |
a |
|
|
输入/输出 |
lda |
整型数 |
A的leading dimension大小，要求lda>=max(1, m)。 |
输出 |
tau |
|
初等反射的系数，长度为min(m,n)（参见说明）。 |
输出 |
work |
|
临时存储空间，使用lwork=-1调用后work[0]为最优的lwork值。 |
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，否则要求lwork>=n。 |
输入 |
info |
整数型 |
执行结果：
|
输出 |
分解结果矩阵Q通过一系列初等反射乘积表示：Q=H(1)*H(2)*...*H(k), k=min(m,n)。H(i)=I-tau*v*v'。tau为标量，v为向量且前i-1个元素为0，第i个元素为1，剩余元素保存在a的第i列中（a的下三角部分）。
依赖
#include "klapack.h"
示例
C Interface:
int m = 6;
int n = 4;
int lda = 6;
int info = 0;
double tau[4];
double *work = NULL;
double qwork;
int lwork = -1;
/*
* A (6x4, stored in column-major):
* 2.229 1.273 0.087 0.035
* 8.667 4.317 4.091 3.609
* 0.205 7.810 2.553 6.507
* 2.758 2.911 8.791 5.051
* 8.103 1.396 1.317 4.738
* 8.859 3.161 0.808 5.972
*/
double a[] = {2.229, 8.667, 0.205, 2.758, 8.103, 8.859,
1.273, 4.317, 7.810, 2.911, 1.396, 3.161,
0.087, 4.091, 2.553, 8.791, 1.317, 0.808,
0.035, 3.609, 6.507, 5.051, 4.738, 5.972};
/* Query optimal work size */
dgeqrf_(&m, &n, a, &lda, tau, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate QR */
dgeqrf_(&m, &n, a, &lda, tau, work, &lwork, &info);
free(work);
/*
* Output:
* tau
* 1.1464 1.0946 1.3670 1.7415
* A output (stored in column-major)
* -15.2274 -5.8577 -5.1387 -9.0573
* 0.4965 -8.2070 -4.5806 -6.5291
* 0.0117 0.8600 7.4527 1.3953
* 0.1580 0.1986 -0.6634 -3.5188
* 0.4642 -0.2130 -0.0183 0.2805
* 0.5075 -0.0510 0.1506 0.2642
*/
Fortran Interface:
PARAMETER (m = 6)
PARAMETER (n = 4)
PARAMETER (lda = 6)
INTEGER :: info = 0
REAL(8) :: tau(4)
REAL(8) :: qwork(1)
INTEGER :: lwork = -1
REAL(8), ALLOCATABLE :: work(:)
*
* A (6x4, stored in column-major):
* 2.229 1.273 0.087 0.035
* 8.667 4.317 4.091 3.609
* 0.205 7.810 2.553 6.507
* 2.758 2.911 8.791 5.051
* 8.103 1.396 1.317 4.738
* 8.859 3.161 0.808 5.972
*
REAL(8) :: a(m, n)
DATA a / 2.229, 8.667, 0.205, 2.758, 8.103, 8.859,
$ 1.273, 4.317, 7.810, 2.911, 1.396, 3.161,
$ 0.087, 4.091, 2.553, 8.791, 1.317, 0.808,
$ 0.035, 3.609, 6.507, 5.051, 4.738, 5.972 /
EXTERNAL DGEQRF
* Query optimal work size
CALL DGEQRF(m, n, a, lda, tau, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
* Calculate QR
CALL DGEQRF(m, n, a, lda, tau, work, lwork, info)
DEALLOCATE(work)
* Output:
* tau
* 1.1464 1.0946 1.3670 1.7415
* A output (stored in column-major)
* -15.2274 -5.8577 -5.1387 -9.0573
* 0.4965 -8.2070 -4.5806 -6.5291
* 0.0117 0.8600 7.4527 1.3953
* 0.1580 0.1986 -0.6634 -3.5188
* 0.4642 -0.2130 -0.0183 0.2805
* 0.5075 -0.0510 0.1506 0.2642