?gemlqt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?gemlqt

Multiplies a general matrix by the orthogonal/unitary matrix Q of the LQ factorization formed by ?gelqt .

Syntax

call sgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
call dgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
call cgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)
call zgemlqt(side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc, work, info)

Description

?gemlqt overwrites the general real m -by- n matrix C with

	`side = 'L'`	`side = 'R'`
`trans = 'N'`	`Q` * `C`	`C` * `Q`
`trans = 'T'`	`Q`^T * `C`	`C` * `Q`^T
`trans = 'C'`	`Q`^H * `C`	`C` * `Q`^H

where Q is a real or complex orthogonal matrix defined as the product of k elementary reflectors:

Q = H ( k ) H ( k - 1) … H (1) = I - VTV^T for real flavors

Q = H ( k ) ^HH ( k - 1) ^H … H (1) ^H = I - VTV^H for complex flavors

generated using the compact WY representation as returned by ?gelqt .

Q is of order m if side = ‘L’ and of order n if side = ‘R’.

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’: Transpose, op( Q ) = Q^H .

m

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

n

INTEGER . The number of columns of the matrix C . 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.

mb

INTEGER . The block size used for the storage of T . k ≥ mb ≥ 1. This must be the same value of mb used to generate T in ?gelqt .

v: REAL for sgemlqt DOUBLE PRECISION for dgemlqt COMPLEX for cgemlqt COMPLEX*16 for zgemlqt Array of size ( ldv , m ) if side = ‘L’ or ( ldv , n ) if side = ‘R’. The i -th row must contain the vector which defines the elementary reflector H ( i ), for i = 1,2,…, k , as returned by ?gelqt in the first k rows of its array argument a .

ldv

INTEGER . The leading dimension of the array v . ldv ≥ max(1, k ).

t: REAL for sgemlqt DOUBLE PRECISION for dgemlqt COMPLEX for cgemlqt COMPLEX*16 for zgemlqt Array of size ( ldt , k ). The upper triangular factors of the block reflectors as returned by ?gelqt , stored as a mb -by- k matrix.

ldt

INTEGER . The leading dimension of the array t . ldt ≥ mb .

c: REAL for sgemlqt DOUBLE PRECISION for dgemlqt COMPLEX for cgemlqt COMPLEX*16 for zgemlqt Array of size ( ldc , n ). On entry, the m -by- n matrix C .

ldc

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

Output Parameters

c: On exit, c is overwritten by op( Q )* C or C *op( Q ).
work: REAL for sgemlqt DOUBLE PRECISION for dgemlqt COMPLEX for cgemlqt COMPLEX*16 for zgemlqt Array. The size of work is n * mb if side = ‘L’, or m * mb if side = ‘R’.
info: info = 0: 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

?gemlqt

Syntax

Description

Input Parameters

Output Parameters