Intel® oneAPI Math Kernel Library Developer Reference - Fortran
Computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
call sgerq2( m, n, a, lda, tau, work, info )
call dgerq2( m, n, a, lda, tau, work, info )
call cgerq2( m, n, a, lda, tau, work, info )
call zgerq2( m, n, a, lda, tau, work, info )
The routine computes a RQ factorization of a real/complex m-by-n matrix A as A = R*Q.
The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors :
Q = H(1)*H(2)* ... *H(k) for real flavors, or
Q = H(1)H*H(2)H* ... *H(k)H for complex flavors
where k = min(m, n).
Each H(i) has the form
H(i) = I - tau*v*vT for real flavors, or
H(i) = I - tau*v*vH for complex flavors
where tau is a real/complex scalar stored in tau(i), and v is a real/complex vector with v(n-k+i+1:n) = 0 and v(n-k+i) = 1.
On exit, v(1:n-k+i-1) is stored in a(m-k+i, 1:n-k+i-1).
INTEGER. The number of rows in the matrix A (m≥ 0).
INTEGER. The number of columns in A (n≥ 0).
REAL for sgerq2
DOUBLE PRECISION for dgerq2
COMPLEX for cgerq2
DOUBLE COMPLEX for zgerq2.
Arrays:
a(lda,*) contains the m-by-n matrix A.
The second dimension of a must be at least max(1, n).
work(m) is a workspace array.
INTEGER. The leading dimension of a; at least max(1, m).
Overwritten by the factorization data as follows:
on exit, if m ≤ n, the upper triangle of the subarray a(1:m, n-m+1:n ) contains the m-by-m upper triangular matrix R; if m > n, the elements on and above the (m-n)-th subdiagonal contain the m-by-n upper trapezoidal matrix R; the remaining elements, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
REAL for sgerq2
DOUBLE PRECISION for dgerq2
COMPLEX for cgerq2
DOUBLE COMPLEX for zgerq2.
Array, DIMENSION at least max(1, min(m, n)).
Contains scalar factors of the elementary reflectors.
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.