?geql2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

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

call sgeql2 ( m , n , a , lda , tau , work , info )

call dgeql2 ( m , n , a , lda , tau , work , info )

call cgeql2 ( m , n , a , lda , tau , work , info )

call zgeql2 ( m , n , a , lda , tau , work , info )

sgeql2 dgeql2 cgeql2 zgeql2

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

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) , 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(m-k+i+1:m) = 0 and v(m-k+i) = 1 .

On exit, v(1:m-k+i-1) is stored in a(1:m-k+i-1, n-k+i) .

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 sgeql2 DOUBLE PRECISION for dgeql2 COMPLEX for cgeql2 DOUBLE COMPLEX for zgeql2 . 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.
lda: INTEGER . The leading dimension of a ; at least max(1, m) .

a: Overwritten by the factorization data as follows: on exit, if m≥n , the lower triangle of the subarray a(m-n+1:m, 1:n) contains the n -by- n lower triangular matrix L ; if m < n , the elements on and below the ( n - m )th superdiagonal contain the m -by- n lower trapezoidal matrix L ; the remaining elements, with the array tau , represent the orthogonal/unitary matrix Q as a product of elementary reflectors.
tau: REAL for sgeql2 DOUBLE PRECISION for dgeql2 COMPLEX for cgeql2 DOUBLE COMPLEX for zgeql2 . Array, DIMENSION at least max(1, min(m, n)) . Contains scalar factors of the elementary reflectors.

info

INTEGER .