?geqrt3

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 10/15/2026

Version

Public

?geqrt3

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

Syntax

lapack_int LAPACKE_sgeqrt3(int matrix_layout, lapack_int m, lapack_int n, float *a,
                           lapack_int lda, float *t, lapack_int ldt);

lapack_int LAPACKE_dgeqrt3(int matrix_layout, lapack_int m, lapack_int n, double *a,
                           lapack_int lda, double *t, lapack_int ldt);

lapack_int LAPACKE_cgeqrt3(int matrix_layout, lapack_int m, lapack_int n,
                           lapack_complex_float *a, lapack_int lda,
                           lapack_complex_float *t, lapack_int ldt);

lapack_int LAPACKE_zgeqrt3(int matrix_layout, lapack_int m, lapack_int n,
                           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 i th 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 part of triangular 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. The value of m must be greater than or equal to n.

n

The number of columns in A ( n ≥ 0).

a

REAL for sgeqrt3 DOUBLE PRECISION for dgeqrt3 COMPLEX for cgeqrt3 COMPLEX*16 for zgeqrt3 .

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: 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 sgeqrt3 DOUBLE PRECISION for dgeqrt3 COMPLEX for cgeqrt3 COMPLEX*16 for zgeqrt3 . Array, size ldt by 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.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?geqrt3

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values