?gelq2

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?gelq2

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

Syntax

lapack_int LAPACKE_sgelq2 (int matrix_layout, lapack_int m, lapack_int n, float* a, lapack_int lda, float* tau);

lapack_int LAPACKE_dgelq2 (int matrix_layout, lapack_int m, lapack_int n, double* a, lapack_int lda, double * tau);

lapack_int LAPACKE_cgelq2 (int matrix_layout, lapack_int m, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_complex_float* tau);

lapack_int LAPACKE_zgelq2 (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 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)^HH(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, 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

A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

m: The number of rows in the matrix A (m≥ 0).
n: The number of columns in A (n≥ 0).
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: 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 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

Array, size at least max(1, min(m, n)).

Contains scalar factors of the elementary reflectors.

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.

If info = -1011, memory allocation error occurred.

Parent topic: LAPACK Auxiliary Routines

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