?gelq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?gelq

Computes an LQ factorization of a general matrix.

Syntax

call sgelq ( m , n , a , lda , t , tsize , work , lwork , info )

call dgelq ( m , n , a , lda , t , tsize , work , lwork , info )

call cgelq ( m , n , a , lda , t , tsize , work , lwork , info )

call zgelq ( m , n , a , lda , t , tsize , work , lwork , info )

Description

The ?gelq routines computes an LQ factorization of an m -by- n matrix A . If the matrix is short and wide ( n is substantially larger than m ), a highly scalable algorithm is used to avoid communication overhead.

NOTE:

The internal format of the elementary reflectors generated by ?gelq is only compatible with the ?gemlq routine and not any other LQ routines.

NOTE:

An optimized version of ?gelq is not available.

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.

a: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq Array, size (lda, n) . Contains the m -by- n matrix A .

lda

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

tsize

INTEGER .

If tsize ≥ 5, the size of the array t . If tsize = -1 or tsize = -2, then the routine performs a workspace query. The routine calculates the sizes required for the t and work arrays and returns these values as the first entries of the t and work arrays, without issuing any error message related to t or work by xerbla .

If tsize = -1, the routine calculates the optimal size of t for optimum performance and returns this value in t(1) . If tsize = -2, the routine calculates then minimum size required for t and returns this value in t(1) .

lwork

INTEGER . The size of the array work . If lwork = -1 or lwork = -2, then the routine performs a workspace query. The routine only calculates the sizes of the t and work arrays and returns these values as the first entries of the t and work arrays, without issuing any error message related to t or work by xerbla .

If lwork = -1, the routine calculates the optimal size of work for optimum performance and returns this value in work(1) . If lwork = -2, the routine calculates the minimum size required for work and returns this value in work(1) .

Output Parameters

a: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq The elements on and below the diagonal of the array contain the lower trapezoidal matrix L ( L is lower triangular if m ≤ n ). The elements above the diagonal are used to store part of the internal data structure representing Q .
t: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq Array, size (max(5,tsize)). If info = 0, t(1) returns the optimal value for tsize . You can specify that it return the minimum required value for tsize instead - see the tsize description for details. The remaining entries of t contains part of the data structure used to represent Q . To apply or construct Q, you need to retain a and t and pass them to other routines.
work: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq Array, size (max(1,lwork)) . If info = 0, work(1) contains the optimal value for lwork . You can specify that it return the minimum required value for lwork instead - see the lwork description for details.

info

INTEGER .

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

NOTE:

?gemlq

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gelq

Syntax

Description

Input Parameters

Output Parameters