?gelqt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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 of the matrix A . m ≥ 0.

n

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

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