sorm22()

subroutine sorm22	(	character	side,
		character	trans,
		integer	m,
		integer	n,
		integer	n1,
		integer	n2,
		real, dimension( ldq, * )	q,
		integer	ldq,
		real, dimension( ldc, * )	c,
		integer	ldc,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SORM22 multiplies a general matrix by a banded orthogonal matrix.

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Purpose

!>
!>
!>  SORM22 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

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> = 'N': apply Q (No transpose); !> = 'C': apply Q**T (Conjugate transpose). !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix C. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
[in]	N1
[in]	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'. !>
[in]	Q	!> Q is REAL array, dimension !> (LDQ,M) if SIDE = 'L' !> (LDQ,N) if SIDE = 'R' !>
[in]	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'. !>
[in,out]	C	!> C is REAL 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. !>
[in]	LDC	!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !>
[in]	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. !>
[out]	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.