?gerq2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?gerq2

Computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Syntax

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 )

Include Files

mkl.fi

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) 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*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(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

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.

lda

INTEGER. The leading 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

DOUBLE COMPLEX 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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gerq2