SUBROUTINE DORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
$ LDC, WORK, LWORK, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER SIDE, TRANS, VECT
INTEGER INFO, K, LDA, LDC, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* If VECT = 'Q', DORMBR 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
*
* If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
* with
* SIDE = 'L' SIDE = 'R'
* TRANS = 'N': P * C C * P
* TRANS = 'T': P**T * C C * P**T
*
* Here Q and P**T are the orthogonal matrices determined by DGEBRD when
* reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
* P**T are defined as products of elementary reflectors H(i) and G(i)
* respectively.
*
* Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
* order of the orthogonal matrix Q or P**T that is applied.
*
* If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
* if nq >= k, Q = H(1) H(2) . . . H(k);
* if nq < k, Q = H(1) H(2) . . . H(nq-1).
*
* If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
* if k < nq, P = G(1) G(2) . . . G(k);
* if k >= nq, P = G(1) G(2) . . . G(nq-1).
*
* Arguments
* =========
*
* VECT (input) CHARACTER*1
* = 'Q': apply Q or Q**T;
* = 'P': apply P or P**T.
*
* SIDE (input) CHARACTER*1
* = 'L': apply Q, Q**T, P or P**T from the Left;
* = 'R': apply Q, Q**T, P or P**T from the Right.
*
* TRANS (input) CHARACTER*1
* = 'N': No transpose, apply Q or P;
* = 'T': Transpose, apply Q**T or P**T.
*
* M (input) INTEGER
* The number of rows of the matrix C. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix C. N >= 0.
*
* K (input) INTEGER
* If VECT = 'Q', the number of columns in the original
* matrix reduced by DGEBRD.
* If VECT = 'P', the number of rows in the original
* matrix reduced by DGEBRD.
* K >= 0.
*
* A (input) DOUBLE PRECISION array, dimension
* (LDA,min(nq,K)) if VECT = 'Q'
* (LDA,nq) if VECT = 'P'
* The vectors which define the elementary reflectors H(i) and
* G(i), whose products determine the matrices Q and P, as
* returned by DGEBRD.
*
* LDA (input) INTEGER
* The leading dimension of the array A.
* If VECT = 'Q', LDA >= max(1,nq);
* if VECT = 'P', LDA >= max(1,min(nq,K)).
*
* TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i) or G(i) which determines Q or P, as returned
* by DGEBRD in the array argument TAUQ or TAUP.
*
* C (input/output) 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
* or P*C or P**T*C or C*P or C*P**T.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) 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 >= N*NB if SIDE = 'L', and
* LWORK >= M*NB if SIDE = 'R', where NB is the optimal
* blocksize.
*
* 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 (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
CHARACTER TRANST
INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DORMLQ, DORMQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
APPLYQ = LSAME( VECT, 'Q' )
LEFT = LSAME( SIDE, 'L' )
NOTRAN = LSAME( TRANS, 'N' )
LQUERY = ( LWORK.EQ.-1 )
*
* NQ is the order of Q or P and NW is the minimum dimension of WORK
*
IF( LEFT ) THEN
NQ = M
NW = N
ELSE
NQ = N
NW = M
END IF
IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
INFO = -1
ELSE IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) ) THEN
INFO = -3
ELSE IF( M.LT.0 ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -5
ELSE IF( K.LT.0 ) THEN
INFO = -6
ELSE IF( ( APPLYQ .AND. LDA.LT.MAX( 1, NQ ) ) .OR.
$ ( .NOT.APPLYQ .AND. LDA.LT.MAX( 1, MIN( NQ, K ) ) ) )
$ THEN
INFO = -8
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
INFO = -11
ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
INFO = -13
END IF
*
IF( INFO.EQ.0 ) THEN
IF( APPLYQ ) THEN
IF( LEFT ) THEN
NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M-1, N, M-1,
$ -1 )
ELSE
NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, N-1, N-1,
$ -1 )
END IF
ELSE
IF( LEFT ) THEN
NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M-1, N, M-1,
$ -1 )
ELSE
NB = ILAENV( 1, 'DORMLQ', SIDE // TRANS, M, N-1, N-1,
$ -1 )
END IF
END IF
LWKOPT = MAX( 1, NW )*NB
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORMBR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
WORK( 1 ) = 1
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
IF( APPLYQ ) THEN
*
* Apply Q
*
IF( NQ.GE.K ) THEN
*
* Q was determined by a call to DGEBRD with nq >= k
*
CALL DORMQR( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
$ WORK, LWORK, IINFO )
ELSE IF( NQ.GT.1 ) THEN
*
* Q was determined by a call to DGEBRD with nq < k
*
IF( LEFT ) THEN
MI = M - 1
NI = N
I1 = 2
I2 = 1
ELSE
MI = M
NI = N - 1
I1 = 1
I2 = 2
END IF
CALL DORMQR( SIDE, TRANS, MI, NI, NQ-1, A( 2, 1 ), LDA, TAU,
$ C( I1, I2 ), LDC, WORK, LWORK, IINFO )
END IF
ELSE
*
* Apply P
*
IF( NOTRAN ) THEN
TRANST = 'T'
ELSE
TRANST = 'N'
END IF
IF( NQ.GT.K ) THEN
*
* P was determined by a call to DGEBRD with nq > k
*
CALL DORMLQ( SIDE, TRANST, M, N, K, A, LDA, TAU, C, LDC,
$ WORK, LWORK, IINFO )
ELSE IF( NQ.GT.1 ) THEN
*
* P was determined by a call to DGEBRD with nq <= k
*
IF( LEFT ) THEN
MI = M - 1
NI = N
I1 = 2
I2 = 1
ELSE
MI = M
NI = N - 1
I1 = 1
I2 = 2
END IF
CALL DORMLQ( SIDE, TRANST, MI, NI, NQ-1, A( 1, 2 ), LDA,
$ TAU, C( I1, I2 ), LDC, WORK, LWORK, IINFO )
END IF
END IF
WORK( 1 ) = LWKOPT
RETURN
*
* End of DORMBR
*
END