Purpose
Overwrites general real m-by-n/n-by-m matrices C and D with
[ op(C) ]
U * [ ] if TRANU = 'N', or
[ op(D) ]
T [ op(C) ]
U * [ ] if TRANU = 'T',
[ op(D) ]
where U is defined as the product of symplectic reflectors and
Givens rotations,
U = diag( H(1),H(1) ) G(1) diag( F(1),F(1) )
diag( H(2),H(2) ) G(2) diag( F(2),F(2) )
....
diag( H(k),H(k) ) G(k) diag( F(k),F(k) ),
with k = m-1, as returned by the SLICOT Library routines MB04PU
or MB04RU.
Specification
SUBROUTINE MB04QS( TRANC, TRAND, TRANU, M, N, ILO, V, LDV, W, LDW,
$ C, LDC, D, LDD, CS, TAU, DWORK, LDWORK, INFO )
C .. Scalar Arguments ..
CHARACTER TRANC, TRAND, TRANU
INTEGER ILO, INFO, LDC, LDD, LDV, LDW, LDWORK, M, N
C .. Array Arguments ..
DOUBLE PRECISION C(LDC,*), CS(*), D(LDD,*), DWORK(*), TAU(*),
$ V(LDV,*), W(LDW,*)
Arguments
Mode Parameters
TRANC CHARACTER*1
Specifies the form of op( C ) as follows:
= 'N': op( C ) = C;
= 'T': op( C ) = C';
= 'C': op( C ) = C'.
TRAND CHARACTER*1
Specifies the form of op( D ) as follows:
= 'N': op( D ) = D;
= 'T': op( D ) = D';
= 'C': op( D ) = D'.
TRANU CHARACTER*1
Specifies whether U or U' is applied as follows:
= 'N': apply U;
= 'T': apply U'.
Input/Output Parameters
M (input) INTEGER
The number of rows of the matrices op(C) and op(D).
M >= 0.
N (input) INTEGER
The number of columns of the matrices op(C) and op(D).
N >= 0.
ILO (input) INTEGER
ILO must have the same value as in the previous call of
MB04PU or MB04RU. U is equal to the unit matrix except in
the submatrix
U([ilo+1:m m+ilo+1:2*m], [ilo+1:m m+ilo+1:2*m]).
1 <= ILO <= M+1.
V (input) DOUBLE PRECISION array, dimension (LDV,M)
On entry, the leading M-by-M part of this array must
contain in its columns the vectors which define the
elementary reflectors H(i).
LDV INTEGER
The leading dimension of the array V. LDV >= MAX(1,M).
W (input) DOUBLE PRECISION array, dimension (LDW,M)
On entry, the leading M-by-M part of this array must
contain in its columns the vectors which define the
elementary reflectors F(i).
LDW INTEGER
The leading dimension of the array W. LDW >= MAX(1,M).
C (input/output) DOUBLE PRECISION array, dimension
(LDC,N) if TRANC = 'N',
(LDC,M) if TRANC = 'T' or TRANC = 'C'.
On entry with TRANC = 'N', the leading M-by-N part of this
array must contain the matrix C.
On entry with TRANC = 'T' or TRANC = 'C', the leading
N-by-M part of this array must contain the transpose of
the matrix C.
On exit with TRANC = 'N', the leading M-by-N part of this
array contains the updated matrix C.
On exit with TRANC = 'T' or TRANC = 'C', the leading
N-by-M part of this array contains the transpose of the
updated matrix C.
LDC INTEGER
The leading dimension of the array C.
LDC >= MAX(1,M), if TRANC = 'N';
LDC >= MAX(1,N), if TRANC = 'T' or TRANC = 'C'.
D (input/output) DOUBLE PRECISION array, dimension
(LDD,N) if TRAND = 'N',
(LDD,M) if TRAND = 'T' or TRAND = 'C'.
On entry with TRAND = 'N', the leading M-by-N part of this
array must contain the matrix D.
On entry with TRAND = 'T' or TRAND = 'C', the leading
N-by-M part of this array must contain the transpose of
the matrix D.
On exit with TRAND = 'N', the leading M-by-N part of this
array contains the updated matrix D.
On exit with TRAND = 'T' or TRAND = 'C', the leading
N-by-M part of this array contains the transpose of the
updated matrix D.
LDD INTEGER
The leading dimension of the array D.
LDD >= MAX(1,M), if TRAND = 'N';
LDD >= MAX(1,N), if TRAND = 'T' or TRAND = 'C'.
CS (input) DOUBLE PRECISION array, dimension (2*N-2)
On entry, the first 2*N-2 elements of this array must
contain the cosines and sines of the symplectic Givens
rotations G(i), as returned by MB04PU or MB04RU.
TAU (input) DOUBLE PRECISION array, dimension (N-1)
On entry, the first N-1 elements of this array must
contain the scalar factors of the elementary reflectors
F(i), as returned by MB04PU or MB04RU.
Workspace
DWORK DOUBLE PRECISION array, dimension (LDWORK)
On exit, if INFO = 0, DWORK(1) returns the optimal value
of LDWORK.
On exit, if INFO = -18, DWORK(1) returns the minimum
value of LDWORK.
LDWORK INTEGER
The length of the array DWORK. LDWORK >= MAX(1,N).
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of the
DWORK array, returns this value as the first entry of
the DWORK array, and no error message related to LDWORK
is issued by XERBLA.
Error Indicator
INFO INTEGER
= 0: successful exit;
< 0: if INFO = -i, the i-th argument had an illegal
value.
Further Comments
NoneExample
Program Text
NoneProgram Data
NoneProgram Results
None