?geqr2

Syntax

call sgeqr2( m, n, a, lda, tau, work, info )

call dgeqr2( m, n, a, lda, tau, work, info )

call cgeqr2( m, n, a, lda, tau, work, info )

call zgeqr2( m, n, a, lda, tau, work, info )

Include Files

• mkl.fi

Description

The routine computes a QR factorization of a real/complex m-by-n matrix A as A = Q*R.

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^T for real flavors, or

H(i) = I - tau*v*v^H for complex flavors

where tau is a real/complex scalar stored in tau(i), and v is a real/complex vector with v_1:i-1 = 0 and v_i = 1.

On exit, v_i+1:m is stored in a(i+1:m, i).

Input Parameters

The data types are given for the Fortran interface.

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 sgeqr2

DOUBLE PRECISION for dgeqr2

COMPLEX for cgeqr2

DOUBLE COMPLEX for zgeqr2.

Arrays:

a(lda,*) contains the m-by-n matrix A.

The second dimension of a must be at least max(1, n).

work(n) is a workspace array.

lda

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

Output Parameters

a

Overwritten by the factorization data as follows:

on exit, the elements on and above the diagonal of the array a contain the min(n,m)-by-n upper trapezoidal matrix R (R is upper triangular if m≥n); the elements below the diagonal, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.

tau

REAL for sgeqr2

DOUBLE PRECISION for dgeqr2

COMPLEX for cgeqr2

DOUBLE COMPLEX for zgeqr2.

Array, size 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.

If info = -1011, memory allocation error occurred.