?geqrt3

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

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

call sgeqrt3(m, n, a, lda, t, ldt, info)
call dgeqrt3(m, n, a, lda, t, ldt, info)
call cgeqrt3(m, n, a, lda, t, ldt, info)
call zgeqrt3(m, n, a, lda, t, ldt, info)

call geqrt3(a, t [, info])

Include Files

mkl.fi , mkl_lapack.f90

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

INTEGER. The number of rows in the matrix A. The value of m must be greater than or equal to n.

n

INTEGER . 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 ( lda , n ) . Array a contains the m -by- n matrix A .

lda

INTEGER . The leading dimension of a ; at least max(1, m ) .

ldt

INTEGER . 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.

info

INTEGER .

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.

Return Values

No return value, info is an Output Parameter.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?geqrt3

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values