?ormlq

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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?ormlq

Multiplies a real matrix by the orthogonal matrix Q of the LQ factorization formed by ?gelqf.

Syntax

lapack_int LAPACKE_sormlq (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int k, const float* a, lapack_int lda, const float* tau, float* c, lapack_int ldc);

lapack_int LAPACKE_dormlq (int matrix_layout, char side, char trans, lapack_int m, lapack_int n, lapack_int k, const double* a, lapack_int lda, const double* tau, double* c, lapack_int ldc);

Include Files

mkl.h

Description

The routine multiplies a real m-by-n matrix C by Q or Q^T, where Q is the orthogonal matrix Q of the LQ factorization formed by the routine gelqf.

Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, Q^T*C, C*Q, or C*Q^T (overwriting the result on C).

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

side

Must be either 'L' or 'R'.

If side = 'L', Q or Q^T is applied to C from the left.

If side = 'R', Q or Q^T is applied to C from the right.

trans

Must be either 'N' or 'T'.

If trans = 'N', the routine multiplies C by Q.

If trans = 'T', the routine multiplies C by Q^T.

m

The number of rows in the matrix C (m≥ 0).

n

The number of columns in C (n≥ 0).

k

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

0 ≤k≤m if side = 'L';

0 ≤k≤n if side = 'R'.

a, c, tau

Arrays:

a and tau are arrays returned by ?gelqf.

The size of a must be:

For side = 'L' and column major layout, max(1, lda*m).

For side = 'R' and column major layout, max(1, lda*n).

For row major layout regardless of side, max(1, lda*k).

The dimension of tau must be at least max(1, k).

c(size max(1, ldc*n) for column major layout and max(1, ldc*m for row major layout) contains the m-by-n matrix C.

lda

The leading dimension of a. For column major layout, lda≥ max(1, k). For row major layout, if side = 'L', lda≥ max(1, m), or, if side = 'R', lda≥ max(1, n).

ldc

The leading dimension of c; ldc≥ max(1, m) for column major layout and max(1, n) for row major layout.

Output Parameters

c: Overwritten by the product Q*C, Q^T*C, C*Q, or C*Q^T (as specified by side and trans).

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

Application Notes

The complex counterpart of this routine is unmlq.

Parent topic: Orthogonal Factorizations: LAPACK Computational Routines

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?ormlq