?gelqf
计算矩阵的LQ分解，即A = L * Q。
接口定义
C Interface：
void sgelqf_(const int *M, const int *N, float *A, const int *LDA, float *TAU, float *WORK, const int *LWORK, int *INFO);
void dgelqf_(const int *M, const int *N, double *A, const int *LDA, double *TAU, double *WORK, const int *LWORK, int *INFO);
void cgelqf_(const int *M, const int *N, float _Complex *A, const int *LDA, float _Complex *TAU, float _Complex *WORK, const int *LWORK, int *INFO);
void zgelqf_(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：
DGELQF(m, n, a, lda, tau, work, lwork, info);
SGELQF(m, n, a, lda, tau, work, lwork, info);
CGELQF(m, n, a, lda, tau, work, lwork, info);
ZGELQF(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 */
dgelqf_(&m, &n, a, &lda, tau, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate LQ */
dgelqf_(&m, &n, a, &lda, tau, work, &lwork, &info);
free(work);
/*
* Output:
* tau
* 1.867784 1.115696 1.413422 0.000000
* A output (stored in column-major)
* -2.568611 -9.848324 -4.223656 -4.202616
* -7.832678 -9.363028 0.265340 5.150248
* 5.402586 9.567440 4.194706 4.480431
* 0.018134 -0.653528 -7.929047 -1.156667
* 1.133611 -0.463361 0.007295 -0.604570
* 0.644209 -2.887734 3.399866 4.103192
*/
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 DGELQF
* Query optimal work size
CALL DGELQF(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 LQ
CALL DGELQF(m, n, a, lda, tau, work, lwork, info)
DEALLOCATE(work)
* Output:
* tau
* 1.867784 1.115696 1.413422 0.000000
* A output (stored in column-major)
* -2.568611 -9.848324 -4.223656 -4.202616
* -7.832678 -9.363028 0.265340 5.150248
* 5.402586 9.567440 4.194706 4.480431
* 0.018134 -0.653528 -7.929047 -1.156667
* 1.133611 -0.463361 0.007295 -0.604570
* 0.644209 -2.887734 3.399866 4.103192