?geqrt

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?geqrt

Computes a blocked QR factorization of a general real or complex matrix using the compact WY representation of Q.

Syntax

lapack_int LAPACKE_sgeqrt (int matrix_layout, lapack_int m, lapack_int n, lapack_int nb, float* a, lapack_int lda, float* t, lapack_int ldt);

lapack_int LAPACKE_dgeqrt (int matrix_layout, lapack_int m, lapack_int n, lapack_int nb, double* a, lapack_int lda, double* t, lapack_int ldt);

lapack_int LAPACKE_cgeqrt (int matrix_layout, lapack_int m, lapack_int n, lapack_int nb, lapack_complex_float* a, lapack_int lda, lapack_complex_float* t, lapack_int ldt);

lapack_int LAPACKE_zgeqrt (int matrix_layout, lapack_int m, lapack_int n, lapack_int nb, lapack_complex_double* a, lapack_int lda, lapack_complex_double* t, lapack_int ldt);

Include Files

mkl.h

Description

The strictly lower triangular matrix V contains the elementary reflectors H(i) in the ith column below the diagonal. For example, if m=5 and n=3, the matrix V is

where v_i represents one of the vectors that define H(i). The vectors are returned in the lower triangular part of array a.

NOTE:

The 1s along the diagonal of V are not stored in a.

Let k = min(m,n). The number of blocks is b = ceiling(k/nb), where each block is of order nb except for the last block, which is of order ib = k - (b-1)*nb. For each of the b blocks, a upper triangular block reflector factor is computed:t1, t2, ..., tb. The nb-by-nb (and ib-by-ib for the last block) ts are stored in the nb-by-n array t as

t = (t1t2 ... tb).

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).
nb: The block size to be used in the blocked QR (min(m, n) ≥ nb ≥ 1).
a: Array a of size max(1, lda*n) for column major layout and max(1, lda*m) for row major layout 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.
ldt: The leading dimension of t; at least nb for column major layout and max(1, min(m, n)) for row major layout.

Output Parameters

a

Overwritten by the factorization data as follows:

The elements on and above the diagonal of the array contain the min(m,n)-by-n upper trapezoidal matrix R (R is upper triangular if m≥n); the elements below the diagonal, with the array t, present the orthogonal matrix Q as a product of min(m,n) elementary reflectors (see Orthogonal Factorizations).

t

Array, size max(1, ldt*min(m, n)) for column major layout and max(1, ldt*nb) for row major layout.

The upper triangular block reflector's factors stored as a sequence of upper triangular blocks.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info < 0 and info = -i, the i-th parameter had an illegal value.

Parent topic: Orthogonal Factorizations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?geqrt

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values