?orm22 / ?unm22

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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	`Q`^T * `C`	`C` * `Q`^T
`trans` = ‘C’ applies to `cunm22` and `zunm22` only	`Q`^H * `C`	`C` * `Q`^H

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 , Q^T , or Q^H from the left;

= ‘R’: apply Q , Q^T , or Q^H from the right.

trans

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

= ‘T’: apply Q^T (transpose) - sorm22 and dorm22 only; = ‘C’: apply Q^H (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 lwork ≥ m *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 , Q^T * C , Q^H * C , C * Q^T , C * Q^H , 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.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?orm22 / ?unm22

Syntax

Include Files

Description

Input Parameters

Output Parameters