?gerq2

Syntax

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

Description

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), where k = min(m, n)

Each H(i) has the form

H(i) = I - tau*v*v'

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).

Input Parameters

m

INTEGER. The number of rows in the matrix A (m ≥ 0).

n

INTEGER. The number of columns in A (n ≥ 0).

a, work

REAL for sgerq2

DOUBLE PRECISION for dgerq2

COMPLEX for cgerq2

COMPLEX*16 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.

lda

INTEGER. The first dimension of a; at least max(1, m).

Output Parameters

a

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.

tau

REAL for sgerq2

DOUBLE PRECISION for dgerq2

COMPLEX for cgerq2

COMPLEX*16 for zgerq2.

Array, DIMENSION at least max(1, min(m, n)).

Contains scalar factors of the elementary reflectors.

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.