Computes the QL factorization of a general m-by-n matrix.


lapack_int LAPACKE_sgelqf (int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, float* tau);

lapack_int LAPACKE_dgelqf (int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, double* tau);

lapack_int LAPACKE_cgelqf (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_complex_float* tau);

lapack_int LAPACKE_zgelqf (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_complex_double* tau);

Include Files

  • mkl.h


The routine forms the QL factorization of a general m-by-n matrix A (see Orthogonal Factorizations). No pivoting is performed.

The routine does not form the matrix Q explicitly. Instead, Q is represented as a product of min(m, n) elementary reflectors. Routines are provided to work with Q in this representation.


This routine supports the Progress Routine feature. See Progress Function for details.

Input Parameters


Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).


The number of rows in the matrix A (m 0).


The number of columns in A (n 0).


Array a of size max(1, lda*n) for column major layout and max(1, lda*m) for row major layout contains the matrix A.


The leading dimension of a; at least max(1, m)for column major layout and max(1, n) for row major layout.

Output Parameters


Overwritten on exit by the factorization data as follows:

if mn, the lower triangle of the subarray a(m-n+1:m, 1:n) contains the n-by-n lower triangular matrix L; if mn, the elements on and below the (n-m)-th superdiagonal contain the m-by-n lower trapezoidal matrix L; in both cases, the remaining elements, with the array tau, represent the orthogonal/unitary matrix Q as a product of elementary reflectors.


Array, size at least max(1, min(m, n)). Contains scalar factors of the elementary reflectors for the matrix Q (see Orthogonal Factorizations).

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

Application Notes

Related routines include:


to generate matrix Q (for real matrices);


to generate matrix Q (for complex matrices);


to apply matrix Q (for real matrices);


to apply matrix Q (for complex matrices).

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