?ormrz

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 7/13/2023

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?ormrz

Multiplies a real matrix by the orthogonal matrix defined from the factorization formed by ?tzrzf.

Syntax

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

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

Include Files

mkl.h

Description

The ?ormrz routine multiplies a real m-by-n matrix C by Q or Q^T, where Q is the real orthogonal matrix defined as a product of k elementary reflectors H(i) of order n: Q = H(1)* H(2)*...*H(k) as returned by the factorization routine tzrzf .

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 over C).

The matrix Q is of order m if side = 'L' and of order n if side = 'R'.

The ?ormrz routine replaces the deprecated ?latzm routine.

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'.

l

The number of columns of the matrix A containing the meaningful part of the Householder reflectors. Constraints:

0 ≤l≤m, if side = 'L';

0 ≤l≤n, if side = 'R'.

a, tau, c

Arrays: a(size for side = 'L': max(1, lda*m) for column major layout and max(1, lda*k) for row major layout; for side = 'R': max(1, lda*b) for column major layout and max(1, lda*k) for row major layout), tau, c (size max(1, ldc*n) for column major layout and max(1, ldc*m) for row major layout).

On entry, the ith row of a must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by stzrzf/dtzrzf in the last k rows of its array argument a.

tau[i - 1] must contain the scalar factor of the elementary reflector H(i), as returned by stzrzf/dtzrzf.

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

c contains the m-by-n matrix C.

lda

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

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 unmrz.

Parent topic: Orthogonal Factorizations: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?ormrz

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes