?gerqf
计算矩阵的RQ分解，即A = R * Q。
接口定义
C Interface：
void sgerqf_(const int *M, const int *N, float *A, const int *LDA, float *TAU, float *WORK, const int *LWORK, int *INFO);
void dgerqf_(const int *M, const int *N, double *A, const int *LDA, double *TAU, double *WORK, const int *LWORK, int *INFO);
void cgerqf_(const int *M, const int *N, float _Complex *A, const int *LDA, float _Complex *TAU, float _Complex *WORK, const int *LWORK, int *INFO);
void zgerqf_(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：
DGERQF(m, n, a, lda, tau, work, lwork, info);
SGERQF(m, n, a, lda, tau, work, lwork, info);
CGERQF(m, n, a, lda, tau, work, lwork, info);
ZGERQF(m, n, a, lda, tau, work, lwork, info);
参数
参数名 |
类型 |
描述 |
输入/输出 |
|---|---|---|---|
m |
整数型 |
矩阵A的行数。 |
输入 |
n |
整数型 |
矩阵A的列数。 |
输入 |
a |
|
|
输入/输出 |
lda |
整数型 |
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 */
dgerqf_(&m, &n, a, &lda, tau, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate RQ */
dgerqf_(&m, &n, a, &lda, tau, work, &lwork, &info);
free(work);
/*
* Output:
* tau
* 0.000000 1.683018 1.409717 1.534598
* A output (stored in column-major)
* 1.359608 2.967627 -1.011896 -0.433983
* 0.345857 0.516770 0.307017 -2.757397
* -5.500889 -8.779283 -0.546907 0.184390
* 0.141517 -0.775170 6.494784 -1.230625
* -1.582355 0.047133 -2.152892 -10.320058
* -6.035814 -6.347009 -9.449164 -11.171009
*/
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 DGERQF
* Query optimal work size
CALL DGERQF(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 RQ
CALL DGERQF(m, n, a, lda, tau, work, lwork, info)
DEALLOCATE(work)
* Output:
* tau
* 0.000000 1.683018 1.409717 1.534598
* A output (stored in column-major)
* 1.359608 2.967627 -1.011896 -0.433983
* 0.345857 0.516770 0.307017 -2.757397
* -5.500889 -8.779283 -0.546907 0.184390
* 0.141517 -0.775170 6.494784 -1.230625
* -1.582355 0.047133 -2.152892 -10.320058
* -6.035814 -6.347009 -9.449164 -11.171009