?gelqt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?gelqt

?gelqt computes a blocked LQ factorization of a real or complex m -by- n matrix A using the compact WY representation of Q .

Syntax

call sgelqt(m, n, mb, a, lda, t, ldt, work, info)
call dgelqt(m, n, mb, a, lda, t, ldt, work, info)
call cgelqt(m, n, mb, a, lda, t, ldt, work, info)
call zgelqt(m, n, mb, a, lda, t, ldt, work, info)

Description

?gelqt computes a blocked LQ factorization of a real or complex m -by- n matrix A using the compact WY representation of Q .

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 . Let k = min( m , n ). The number of blocks is b = ceiling( k / mb ), where each block is of order mb except for the last block, which is of order ib = k - ( b -1)* mb . For each of the b blocks, a upper triangular block reflector factor is computed: T1 , T2 , …, TB . The mb -by- mb (and ib -by- ib for the last block) T ‘s are stored in the mb -by- k matrix T as

T = ( T1T2 … TB ).

Input Parameters

m: INTEGER. The number of rows in the matrix A. The value of m must be at least zero.

n: INTEGER. The number of columns in the matrix A. The value of n must be at least zero.

mb

INTEGER . The block size to be used in the blocked QR. min( m , n ) ≥ mb ≥ 1.

a: REAL for sgelqt DOUBLE PRECISION for dgelqt COMPLEX for cgelqt COMPLEX*16 for zgelqt Array of size ( lda , n ). On entry, the 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 ≥ mb .

Output Parameters

a: On exit, the elements on and below the diagonal of the array contain the m -by-min( m , n ) lower trapezoidal matrix L ( L is lower triangular if m ≤ n ); the elements above the diagonal are the rows of V .
t: REAL for sgelqt DOUBLE PRECISION for dgelqt COMPLEX for cgelqt COMPLEX*16 for zgelqt Array of size ( ldt , min( m , n )). The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. See Description for further details.
work: REAL for sgelqt DOUBLE PRECISION for dgelqt COMPLEX for cgelqt COMPLEX*16 for zgelqt Array of size ( mb * n ).

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

?gelqt

Syntax

Description

Input Parameters

Output Parameters