?ormr3/?unmr3

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?ormr3/?unmr3

Multiplies a general matrix by the orthogonal/unitary matrix from a RZ factorization determined by ?tzrzf (unblocked algorithm).

Syntax

call sormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )

call dormr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )

call cunmr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )

call zunmr3( side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info )

Include Files

mkl.fi

Description

The routine ?ormr3/?unmr3 overwrites the general real/complex m-by-n matrix C with

Q*C if side = 'L' and trans = 'N', or

Q^T*C / Q^H*C if side = 'L' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors), or

C*Q if side = 'R' and trans = 'N', or

C*Q^T / C*Q^H if side = 'R' and trans = 'T' (for real flavors) or trans = 'C' (for complex flavors).

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

Q = H(1)*H(2)*...*H(k) as returned by ?tzrzf.

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

Input Parameters

side

CHARACTER*1.

= 'L': apply Q or Q^T / Q^H from the left

= 'R': apply Q or Q^T / Q^H from the right

trans

CHARACTER*1.

= 'N': apply Q (no transpose)

= 'T': apply Q^T (transpose, for real flavors)

= 'C': apply Q^H (conjugate transpose, for complex flavors)

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.

l

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

If side = 'L', m≥l≥ 0,

if side = 'R', n≥l≥ 0.

a

REAL for sormr3

DOUBLE PRECISION for dormr3

COMPLEX for cunmr3

DOUBLE COMPLEX for zunmr3.

Array, DIMENSION

(lda, m) if side = 'L',

(lda, 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 ?tzrzf in the last k rows of its array argument a. The array a is modified by the routine but restored on exit.

lda

INTEGER.

The leading dimension of the array a. lda≥ max(1,k).

tau

REAL for sormr3

DOUBLE PRECISION for dormr3

COMPLEX for cunmr3

DOUBLE COMPLEX for zunmr3.

Array, DIMENSION (k).

tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by ?tzrzf.

c

REAL for sormr3

DOUBLE PRECISION for dormr3

COMPLEX for cunmr3

DOUBLE COMPLEX for zunmr3.

Array, DIMENSION (ldc, n).

On entry, the m-by-n matrix C.

ldc

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

work

REAL for sormr3

DOUBLE PRECISION for dormr3

COMPLEX for cunmr3

DOUBLE COMPLEX for zunmr3.

Workspace array, DIMENSION

(n) if side = 'L',

(m) if side = 'R'.

Output Parameters

c

On exit, c is overwritten by Q*C or Q^T*C / Q^H*C, or C*Q, or C*Q^T / C*Q^H.

info

INTEGER.

= 0: successful exit

< 0: if info = -i, the i-th argument had an illegal value

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?ormr3/?unmr3