Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?orm22/?unm22

Multiplies a general matrix by an orthogonal/unitary matrix with a 2x2 structure.

Syntax

call sorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info )

call dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info )

call cunm22(side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)

call zunm22(side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)

Include Files
  • mkl.fi
Description

?orm22/?unm22 overwrites the general real/complex m-by-n matrix C with

 

side = 'L'

side = 'R'

trans = 'N'

Q * C

C * Q

trans = 'T'

applies to sorm22 and dorm22 only

QT * C

C * QT

trans = 'C'

applies to cunm22 and zunm22 only

QH * C

C * QH

where Q is a real orthogonal/complex unitary matrix of order nq, with nq = m if side = 'L' and nq = n if side = 'R'.

The orthogonal/unitary matrix Q processes a 2-by-2 block structure:

where Q12 is an n1-by-n1 lower triangular matrix and Q21 is an n2-by-n2 upper triangular matrix.

Input Parameters
side

CHARACTER*1. = 'L': apply Q, QT, or QH from the left;

= 'R': apply Q, QT, or QH from the right.

trans

CHARACTER*1. = 'N': apply Q (no transpose);

= 'T': apply QT (transpose) - sorm22 and dorm22 only;

= 'C': apply QH (conjugate transpose) - cunm22 and zunm22 only.

m

INTEGER. The number of rows of the matrix C.

m 0.

n

INTEGER. The number of columns of the matrix C.

n 0.

n1

INTEGER. The dimension of Q12.

n1 0.

The following requirement must be satisfied: n1 + n2 = m if side = 'L' and n1 + n2 = n if side = 'R'.

n2

INTEGER. The dimension of Q21.

n2 0.

The following requirement must be satisfied: n1 + n2 = m if side = 'L' and n1 + n2 = n if side = 'R'.

q

REAL for sorm22

DOUBLE PRECISION for dorm22

COMPLEX for cunm22

DOUBLE COMPLEX for zunm22

Array, size (ldq,m) if side = 'L' and (ldq,n) if side = 'R'.

ldq

INTEGER. The leading dimension of the array q.

ldq max(1,m) if side = 'L';

ldq max(1,n) if side = 'R'.

c

REAL for sorm22

DOUBLE PRECISION for dorm22

COMPLEX for cunm22

DOUBLE COMPLEX for zunm22

Array, size (ldc,n)

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

ldc

INTEGER. The leading dimension of the array c.

ldc max(1,m).

lwork

INTEGER. The dimension of the array work.

If side = 'L', lwork max(1,n);

if side = 'R', lwork max(1,m).

For optimum performance lworkm*n.

If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla.

Output Parameters

c

On exit, c is overwritten by the product:

Q*C,

QT*C,

QH * C,

C*QT,

C * QH, or

C*Q.

work

REAL for sorm22

DOUBLE PRECISION for dorm22

COMPLEX for cunm22

DOUBLE COMPLEX for zunm22

Array, size (max(1,lwork))

On exit, if info = 0, work(1) returns the optimal lwork.

info

INTEGER. = 0: successful exit.

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