?geqr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?geqr

Computes a QR factorization of a general matrix, with best performance for tall and skinny matrices.

Syntax

call sgeqr ( m , n , a , lda , t , tsize , work , lwork , info )

call dgeqr ( m , n , a , lda , t , tsize , work , lwork , info )

call cgeqr ( m , n , a , lda , t , tsize , work , lwork , info )

call zgeqr ( m , n , a , lda , t , tsize , work , lwork , info )

Description

The ?geqr routine computes a QR factorization of an m -by- n matrix A . If the matrix is tall and skinny ( m is substantially larger than m ), a highly scalable algorithm is used to avoid communication overhead.

NOTE:

The internal format of the elementary reflectors generated by ?geqr is only compatible with the ?gemqr routine and not any other QR routines.

Input Parameters

m

INTEGER . The number of rows of the matrix A . m ≥ 0.

n

REAL for sgeqr

INTEGER . The number of columns of the matrix A . n ≥ 0.

a

DOUBLE PRECISION for dgeqr COMPLEX for cgeqr COMPLEX*16 for zgeqr Array of size (lda,n). On entry, the m -by- n matrix A .

lda

INTEGER . The leading dimension of the array a . lda≥ max(1,m) .

tsize

INTEGER .

If tsize ≥ 5, the size of the array t . If tsize = -1 or tsize = -2, then the routine performs a workspace query. The routine calculates the sizes required for the t and work arrays and returns these values as the first entries of the t and work arrays, without issuing any error message related to t or work by xerbla .

If tsize = -1, the routine calculates the optimal size of t for optimum performance and returns this value in t(1) . If tsize = -2, the routine calculates then minimum size required for t and returns this value in t(1) .

lwork

INTEGER . The size of the array work . If lwork = -1 or lwork = -2, then the routine performs a workspace query. The routine only calculates the sizes of the t and work arrays and returns these values as the first entries of the t and work arrays, without issuing any error message related to t or work by xerbla .

If lwork = -1, the routine calculates the optimal size of work for optimum performance and returns this value in work(1) . If lwork = -2, the routine calculates the minimum size required for work and returns this value in work(1) .

Output Parameters

a: REAL for sgeqr DOUBLE PRECISION for dgeqr COMPLEX for cgeqr COMPLEX*16 for zgeqr On exit, 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 represent Q .
t: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq Array, size (max(5,tsize)). If info = 0, t(1) returns the optimal value for tsize . You can specify that it return the minimum required value for tsize instead - see the tsize description for details. The remaining entries of t contains part of the data structure used to represent Q . To apply or construct Q, you need to retain a and t and pass them to other routines.
work: REAL for sgelq DOUBLE PRECISION for dgelq COMPLEX for cgelq COMPLEX*16 for zgelq Array, size (max(1,lwork)) . If info = 0, work(1) contains the optimal value for lwork . You can specify that it return the minimum required value for lwork instead - see the lwork description for details.

info

INTEGER .

info = 0 indicates a successful exit.
info < 0: if info = - i , the i -th argument had an illegal value.

NOTE:

?gemqr

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?geqr

Syntax

Description

Input Parameters

Output Parameters