?(or,un)glq
生成具有正交行的实/复矩阵Q，且该矩阵定义为K个N阶基本反射器的乘积的前M行，即：Q=H(k)...H(2)H(1)，其中H为?gelqf返回的。
接口定义
C Interface：
void sorglq_(const int *m, const int *n, const int *k, float *a, const int *lda, const float *tau, float *work, const int *lwork, int *info);
void dorglq_(const int *m, const int *n, const int *k, double *a, const int *lda, const double *tau, double *work, const int *lwork, int *info);
void cunglq_(const int *m, const int *n, const int *k, float_Complex *a, const int *lda, const float_Complex *tau, float_Complex *work, const int *lwork, int *info);
void zunglq_(const int *m, const int *n, const int *k, double_Complex *a, const int *lda, const double_Complex *tau, double_Complex *work, const int *lwork, int *info);
Fortran Interface：
SORGLQ(M, N, K, A, LDA, TAU, WORK, LWORK, INFO);
DORGLQ(M, N, K, A, LDA, TAU, WORK, LWORK, INFO);
CUNGLQ(M, N, K, A, LDA, TAU, WORK, LWORK, INFO);
ZUNGLQ(M, N, K, 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Q的行数，m ≥ 0。 |
输入 |
n |
整数型 |
矩阵Q的列数，n ≥ m。 |
输入 |
k |
整数型 |
构成矩阵Q的基本反射器的数量，m ≥ k ≥0。 |
输入 |
a |
|
维度(lda, n)。
|
输入、输出 |
lda |
整数型 |
A的leading dimension，lda ≥ max(1, m)。 |
输入 |
tau |
|
tau(i)必须包含基本反射器H(i)的常量因子，其由?gelqf返回的。 |
输入 |
work |
|
维数(max(1,lwork))。若info=0，work(1)返回最优lwork值。 |
输出 |
lwork |
整数型 |
数组work的维数。lwork ≥ max(1, m)，对于最优性能：lwork ≥ m*nb，其中nb为最优块大小如果lwork=-1，则该例程只计算work数组的最优大小，并以work数组的第一个值返回。 |
输入 |
info |
整数型 |
|
输出 |
依赖
#include "klapack.h"
示例
C Interface：
int m = 4;
int n = 4;
int k = 4;
int lda = 4;
int info = 0;
double tau[4] = {1.003949, 1.125229, 1.978923, 0.000000};
double *work = NULL;
double qwork;
int lwork = -1;
/*
* tau:
* 1.003949 1.125229 1.978923 0.000000
* A (4x4, stored in column-major):
* -1.036040 -0.892502 -0.120115 -0.425611
* 0.654120 0.468127 0.644302 -0.601906
* -0.135860 0.502159 1.077637 -0.103204
* -0.480109 -1.207226 0.162668 0.227483
*/
double a[] = {-1.036040, 0.654120, 0.135860, -0.480109,
-0.892502, 0.468127, 0.502159, -1.207226,
-0.120115, 0.644302, 1.077637, 0.162668,
-0.425611, -0.601906, -0.103204, 0.227483};
/* Query optimal work size */
dorglq_(&m, &n, &k, a, &lda, tau, &qwork, &lwork, &info);
if (info != 0) {
return ERROR;
}
lwork = (int)qwork;
work = (double *)malloc(sizeof(double) * lwork);
/* Calculate Q */
dorglq_(&m, &n, &k, a, &lda, tau, work, &lwork, &info);
free(work);
/*
* Output:
* A output (stored in column-major)
* -0.003949 0.089763 0.576860 0.811886
* 0.896027 -0.205343 0.333180 -0.209669
* 0.427292 0.639078 -0.551720 0.323428
* 0.120589 -0.735769 -0.501826 0.438490
*/
Fortran Interface：
PARAMETER (m = 4)
PARAMETER (n = 4)
PARAMETER (k = 4)
PARAMETER (lda = 4)
INTEGER :: info = 0
REAL(8) :: tau(4)
REAL(8) :: qwork(1)
INTEGER :: lwork = -1
REAL(8), ALLOCATABLE :: work(:)
*
* tau:
* 1.003949 1.125229 1.978923 0.000000
* A (4x4, stored in column-major):
* -1.036040 -0.892502 -0.120115 -0.425611
* 0.654120 0.468127 0.644302 -0.601906
* -0.135860 0.502159 1.077637 -0.103204
* -0.480109 -1.207226 0.162668 0.227483
*
DATA tau /1.003949, 1.125229, 1.978923, 0.000000/
REAL(8) :: a(m, n)
DATA a / -1.036040, 0.654120, 0.135860, -0.480109,
$ -0.892502, 0.468127, 0.502159, -1.207226,
$ -0.120115, 0.644302, 1.077637, 0.162668,
$ -0.425611, -0.601906, -0.103204, 0.227483 /
EXTERNAL DORGLQ
* Query optimal work size
CALL DORGLQ(m, n, k, a, lda, tau, qwork, lwork, info)
IF (info.NE.0) THEN
CALL EXIT(1)
END IF
lwork = INT(qwork(1))
ALLOCATE(work(lwork))
* Calculate Q
CALL DORGLQ(m, n, k, a, lda, tau, work, lwork, info)
DEALLOCATE(work)
* Output:
* A output (stored in column-major)
* -0.003949 0.089763 0.576860 0.811886
* 0.896027 -0.205343 0.333180 -0.209669
* 0.427292 0.639078 -0.551720 0.323428
* 0.120589 -0.735769 -0.501826 0.438490