?gemlqt

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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