subroutine sorm22 (SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC, WORK, LWORK, INFO)
SORM22 multiplies a general matrix by a banded orthogonal matrix.
SORM22 multiplies a general matrix by a banded orthogonal matrix.
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:
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 REAL 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 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.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
WORK is REAL 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
Definition at line 165 of file sorm22.f.
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