# dorm22.f - Man Page

SRC/dorm22.f

## Synopsis

### Functions/Subroutines

subroutine **dorm22** (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)**DORM22** multiplies a general matrix by a banded orthogonal matrix.

## Function/Subroutine Documentation

### subroutine dorm22 (character side, character trans, integer m, integer n, integer n1, integer n2, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

**DORM22** multiplies a general matrix by a banded orthogonal matrix.

**Purpose**

DORM22 overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T where Q is a real orthogonal matrix of order NQ, with NQ = M if SIDE = 'L' and NQ = N if SIDE = 'R'. The orthogonal matrix Q processes a 2-by-2 block structure [ Q11 Q12 ] Q = [ ] [ Q21 Q22 ], where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix.

**Parameters***SIDE*SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.

*TRANS*TRANS is CHARACTER*1 = 'N': apply Q (No transpose); = 'C': apply Q**T (Conjugate transpose).

*M*M is INTEGER The number of rows of the matrix C. M >= 0.

*N*N is INTEGER The number of columns of the matrix C. N >= 0.

*N1**N2*N1 is INTEGER N2 is INTEGER The dimension of Q12 and Q21, respectively. N1, N2 >= 0. The following requirement must be satisfied: N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

*Q*Q is DOUBLE PRECISION array, dimension (LDQ,M) if SIDE = 'L' (LDQ,N) if SIDE = 'R'

*LDQ*LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

*C*C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

*LDC*LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).

*WORK*WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

*LWORK*LWORK is 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.

*INFO*INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **161** of file **dorm22.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dorm22(3) is an alias of dorm22.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK