?gelq2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

sgelq2 dgelq2 cgelq2 zgelq2

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 ( m≥ 0 ).

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