?gemqr

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?gemqr

Multiples a matrix C by a real orthogonal or complex unitary matrix Q , as computed by ?geqr , with best performance for tall and skinny matrices.

Syntax

call sgemqr ( side , trans , m , n , k , a , lda , t , tsize , c , ldc , work , lwork , info )

call dgemqr ( side , trans , m , n , k , a , lda , t , tsize , c , ldc , work , lwork , info )

call cgemqr ( side , trans , m , n , k , a , lda , t , tsize , c , ldc , work , lwork , info )

call zgemqr ( side , trans , m , n , k , a , lda , t , tsize , c , ldc , work , lwork , info )

Description

The ?gemqr routine multiplies an m -by- n matrix C by Op( Q ), where matrix Q is the factor from the LQ factorization of matrix A formed by ?geqr , and

Op( Q ) = Q , or

Op( Q ) = Q^T , or

Op( Q ) = Q^H .

You must use ?geqr for LQ factorization before calling ?gemqr . ?gemqr is not compatible with QR factorization routines other than ?geqr .

For real flavors, C is real and Q is real orthogonal.

For complex flavors, C is complex and Q is complex unitary.

If matrix A is tall and skinny, a highly scalable algorithm is used to avoid communication overhead. Otherwise, ?ormqr or ?unmqr is used.

Input Parameters

side: CHARACTER*1 . If side = 'L' : apply Op( Q ) from the left. If side = 'R' ‘: apply Op( Q ) from the right.
trans: CHARACTER*1 . If trans = 'N' : No transpose, Op( Q ) = Q . If trans = 'T' : Transpose, Op( Q ) = Q^T . If trans = 'C' : Conjugate transpose, Op( Q ) = Q^H .

m

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

n

INTEGER . The number of columns of the matrix C . m ≥ n ≥ 0.

k

INTEGER . The number of elementary reflectors whose product defines the matrix Q.

If side = ‘L’, m ≥ k ≥ 0. if side = ‘R’, n ≥ k ≥ 0.

a: REAL for sgemqr DOUBLE PRECISION for dgemqr COMPLEX for cgemqr COMPLEX*16 for zgemqr Array, size (lda,k) . Part of the data structure to represent Q as returned by ?geqr .

lda

INTEGER . The leading dimension of the array a .

If side = 'L' , lda ≥ max(1,m) . If side = 'R' , lda ≥ max(1,n) .

t: REAL for sgemlq DOUBLE PRECISION for dgemlq COMPLEX for cgemlq COMPLEX*16 for zgemlq Array, size (max(5,tsize)) . Part of the data structure to represent Q as returned by ?geqr .

tsize

INTEGER . The size of the array t . tsize ≥ 5.

c: REAL for sgemqr DOUBLE PRECISION for dgemqr COMPLEX for cgemqr COMPLEX*16 for zgemqr Array of size (ldc,n) . On entry, contains the m -by- n matrix C .

ldc

INTEGER . The leading dimension of the array c . ldc ≥ max(1,m) .

lwork

INTEGER . The size of the array work .

If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array and returns this value as work(1) ; no error message related to lwork is issued by xerbla .

Output Parameters

c: On exit, c is overwritten by Op( Q )* C or C *Op( Q ).
work: REAL for sgemlq DOUBLE PRECISION for dgemlq COMPLEX for cgemlq COMPLEX*16 for zgemlq Workspace array of size (max(1,lwork)) .

info

INTEGER .

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

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gemqr

Syntax

Description

Input Parameters

Output Parameters