?geqrt2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?geqrt2

Computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Syntax

call sgeqrt2(m, n, a, lda, t, ldt, info)

call dgeqrt2(m, n, a, lda, t, ldt, info)

call cgeqrt2(m, n, a, lda, t, ldt, info)

call zgeqrt2(m, n, a, lda, t, ldt, info)

call geqrt2(a, t, [info])

Include Files

mkl.fi, lapack.f90

Description

The strictly lower triangular matrix V contains the elementary reflectors H(i) in the ith column below the diagonal. For example, if m=5 and n=3, the matrix V is

where v_i represents the vector that defines H(i). The vectors are returned in the lower triangular part of array a.

NOTE:

The 1s along the diagonal of V are not stored in a.

The block reflector H is then given by

H = I - V*T*V^T for real flavors, and

H = I - V*T*V^H for complex flavors,

where V^T is the transpose and V^H is the conjugate transpose of V.

Input Parameters

m

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

n

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

a

REAL for sgeqrt2

DOUBLE PRECISION for dgeqrt2

COMPLEX for cgeqrt2

COMPLEX*16 for zgeqrt2.

Array, size lda by n. Array a contains the m-by-n matrix A.

lda

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

ldt

INTEGER. The leading dimension of t; at least max(1, n).

Output Parameters

a

Overwritten by the factorization data as follows:

The elements on and above the diagonal of the array contain the n-by-n upper triangular matrix R. The elements below the diagonal are the columns of V.

t

REAL for sgeqrt2

DOUBLE PRECISION for dgeqrt2

COMPLEX for cgeqrt2

COMPLEX*16 for zgeqrt2.

Array, size (ldt, min(m, n)).

The n-by-n upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T. The elements below the diagonal are not used.

info

INTEGER.

If info = 0, the execution is successful.

If info < 0 and info = -i, the ith argument had an illegal value.

If info = -1011, memory allocation error occurred.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?geqrt2