?geqlf

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

Syntax

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

Description

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.

Note

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

Input Parameters

matrix_layout

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

m

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

n

The number of columns in A (n 0).

a

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.

lda

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

Output Parameters

a

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.

tau

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:

orgql

to generate matrix Q (for real matrices);

ungql

to generate matrix Q (for complex matrices);

ormql

to apply matrix Q (for real matrices);

unmql

to apply matrix Q (for complex matrices).

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