?geqrt3

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

sgeqrt3 dgeqrt3 cgeqrt3 zgeqrt3 geqrt3

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 ( m ≥ 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