?geqrt2

Developer Reference for Intel® oneAPI Math Kernel Library for C

Download PDF

ID 766684

Date 4/28/2026

Version

Public

?geqrt2

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

Syntax

lapack_intLAPACKE_sgeqrt2 ( intmatrix_layout , lapack_intm , lapack_intn , float*a , lapack_intlda , float*t , lapack_intldt );

lapack_intLAPACKE_dgeqrt2 ( intmatrix_layout , lapack_intm , lapack_intn , double*a , lapack_intlda , double*t , lapack_intldt );

lapack_intLAPACKE_cgeqrt2 ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_float*a , lapack_intlda , lapack_complex_float*t , lapack_intldt );

lapack_intLAPACKE_zgeqrt2 ( intmatrix_layout , lapack_intm , lapack_intn , lapack_complex_double*a , lapack_intlda , lapack_complex_double*t , lapack_intldt );

Include Files

mkl.h

Description

sgeqrt2 dgeqrt2 cgeqrt2 zgeqrt2 geqrt2

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

where v_i represents the vector that defines 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 .

The block reflector H is then given by

H = I - V*T*V^{T} for real flavors, and

H = I - V*T*V^{H} for complex flavors,

where V^T is the transpose and V^H is the conjugate transpose of V .

Input Parameters

m

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

n

The number of columns in A ( n ≥ 0).

a

REAL for sgeqrt2 DOUBLE PRECISION for dgeqrt2 COMPLEX for cgeqrt2 COMPLEX*16 for zgeqrt2 .

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 .

ldt

The leading dimension of t ; at least max(1, n ).

Output Parameters

a

Overwritten by the factorization data as follows: The elements on and above the diagonal of the array contain the n -by- n upper triangular matrix R . The elements below the diagonal are the columns of V .

t

REAL for sgeqrt2 DOUBLE PRECISION for dgeqrt2 COMPLEX for cgeqrt2 COMPLEX*16 for zgeqrt2 .

Array, size at least max(1, ldt*n) .

The n -by- n upper triangular factor of the block reflector. The elements on and above the diagonal contain the block reflector T . The elements below the diagonal are not used.

Return Values

This function returns a value info .

If info = 0, the execution is successful.
If info < 0 and info = -i , the i th argument had an illegal value.
If info = -1011 , memory allocation error occurred.

Select Your Language

Using Intel.com Search

Quick Links

Recent Searches

Advanced Search

Only search in

Developer Reference for Intel® oneAPI Math Kernel Library for C

?geqrt2

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values