?gelq2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?gelq2

Computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Syntax

call sgelq2(m, n, a, lda, tau, work, info)
call dgelq2(m, n, a, lda, tau, work, info)
call cgelq2(m, n, a, lda, tau, work, info)
call zgelq2(m, n, a, lda, tau, work, info)

Include Files

mkl.fi

Description

The routine computes an LQ factorization of a real/complex m -by- n matrix A as A = L*Q .

The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min( m , n ) elementary reflectors :

Q = H(k) ... H(2) H(1) (or Q = H(k)^{H} ... H(2)^{H}H(1)^{H} for complex flavors), where k = min(m, n)

Each H (i) has the form

H(i) = I - tau*v*v^{T} for real flavors, or

H(i) = I - tau*v*v^{H} for complex flavors,

where tau is a real/complex scalar stored in tau (i), and v is a real/complex vector with v_{1:i-1} = 0 and v_{i} = 1 .

On exit, v_{i+1:n} (for real functions) and conjg(v_{i+1:n}) (for complex functions) are stored in a(i, i+1:n) .

On exit, the j -th ( i +1 ≤ j ≤ n ) component of vector v (for real functions) or its conjugate (for complex functions) is stored in a[i - 1 + lda*(j - 1)] for column major layout or in a[j - 1 + lda*(i - 1)] for row major layout.

Input Parameters

The data types are given for the Fortran interface.

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 A ( n≥ 0 ).

a , work: REAL for sgelq2 DOUBLE PRECISION for dgelq2 COMPLEX for cgelq2 DOUBLE COMPLEX for zgelq2 . Arrays: a ( lda ,*) contains the m -by- n matrix A . The second dimension of a must be at least max(1, n) . work(m) is a workspace array.
a: Array, size at least max(1, lda*n) for column major and max(1, lda*m) for row major layout. Array a contains the m -by- n matrix A .

lda

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

Output Parameters

a: Overwritten by the factorization data as follows: on exit, the elements on and below the diagonal of the array a contain the m -by-min( n , m ) lower trapezoidal matrix L ( L is lower triangular if n≥m ); the elements above the diagonal, with the array tau , represent the orthogonal/unitary matrix Q as a product of min( n , m ) elementary reflectors.
tau: REAL for sgelq2 DOUBLE PRECISION for dgelq2 COMPLEX for cgelq2 DOUBLE COMPLEX for zgelq2 . Array, size at least max(1, min(m, n)) . Contains scalar factors of the elementary reflectors.

info

INTEGER .

If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.
If info = -1011 , memory allocation error occurred.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gelq2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values