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template<typename T>
void gelq2(integer *m, integer *n, T *a, integer *lda, T *tau, T *work, integer *info)# LQ factorization of a real m-by-n matrix a.
Purpose:
LQ factorization of a real m-by-n matrix a The factorization has the form A = Q * R
Further Details
The matrix Q is represented as a product of elementary reflectors Q = H(k) . . . H(2) H(1), where k = min(m,n). Each H(i) has the form H(i) = I - tau * V * V**T where tau is a real scalar, and V is a real vector with V(1:i-1) = 0 and V(i) = 1; V(i+1:N) is stored on exit in A(i,i+1:N), and tau in tau(i).
- Parameters:
m – [in]
m is integer*
The number of rows of the matrix a. m >= 0.
n – [in]
n is integer*
The number of columns of the matrix a. n >= 0.
a – [inout]
a is float/double/COMPLEX/COMPLEX*16 array, dimension (lda,n)
On entry, the m-by-n matrix.
On exit, the elements on and below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array tau, represent the orthogonal matrix Q as a product of elementary reflectors (see Further Details).lda – [in]
lda is integer*
The leading dimension of the matrix a, lda >= fla_max(1,m)
tau – [out]
tau is float/double/COMPLEX/COMPLEX*16 array, dimension (min(m,n))
The scalar factors of the elementary reflectors (see Further Details).
WORK – [out] WORK is COMPLEX array, dimension (M)
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value