?gelqt3

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?gelqt3

?gelqt3 recursively computes a LQ factorization of a general real or complex M-by-N matrix A , using the compact WY representation of Q .

Syntax

call sgelqt3 ( m , n , a , lda , t , ldt , info )

call dgelqt3 ( m , n , a , lda , t , ldt , info )

call cgelqt3 ( m , n , a , lda , t , ldt , info )

call zgelqt3 ( m , n , a , lda , t , ldt , info )

Description

?gelqt3 recursively computes a LQ factorization of a real or complex m -by- n matrix A , using the compact WY representation of Q . Based on the algorithm of Elmroth and Gustavson [ELMROTH00].

The matrix V stores the elementary reflectors H(i) in the i -th row above the diagonal. For example, if m =5 and n =3, the matrix V is

V = ( 1 v ₁ v ₁ v ₁ v ₁ ) ( 1 v ₂ v ₂ v ₂ ) ( 1 v ₃ v ₃ )

where the v_i s represent the vectors which define H(i), which are returned in the array a . The 1 elements 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 matrices, or

H = I - V * T * V^H for complex matrices.

Input Parameters

m

INTEGER . The number of rows of the matrix A . m ≤ n .

n

INTEGER . The number of columns of the matrix A . n ≥ 0.

a: REAL for sgelqt3 DOUBLE PRECISION for dgelqt3 COMPLEX for cgelqt3 COMPLEX*16 for zgelqt3 Array of size ( lda , n ). On entry, the real or complex m -by- n matrix A .

lda

INTEGER . The leading dimension of the array a . lda ≥ max(1, m ).

ldt

INTEGER . The leading dimension of the array t . ldt ≥ max(1, n ).

Output Parameters

a: On exit, the elements on and below the diagonal contain the n -by- n lower triangular matrix L ; the elements above the diagonal are the rows of V . See Description for further details.
t: REAL for sgelqt3 DOUBLE PRECISION for dgelqt3 COMPLEX for cgelqt3 COMPLEX*16 for zgelqt3 Array of size ( ldt , 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. See Description for further details.

info

INTEGER .

info = 0: successful exit.
info < 0: if info = - i , the i -th argument had an illegal value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gelqt3

Syntax

Description

Input Parameters

Output Parameters