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SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, 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
INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DORMHR 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'. Q is defined as the product of
* IHI-ILO elementary reflectors, as returned by DGEHRD:
*
* Q = H(ilo) H(ilo+1) . . . H(ihi-1).
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': apply Q or Q**T from the Left;
* = 'R': apply Q or Q**T from the Right.
*
* TRANS (input) CHARACTER*1
* = 'N': No transpose, apply Q;
* = 'T': Transpose, apply Q**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.
*
* ILO (input) INTEGER
* IHI (input) INTEGER
* ILO and IHI must have the same values as in the previous call
* of DGEHRD. Q is equal to the unit matrix except in the
* submatrix Q(ilo+1:ihi,ilo+1:ihi).
* If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
* ILO = 1 and IHI = 0, if M = 0;
* if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
* ILO = 1 and IHI = 0, if N = 0.
*
* A (input) DOUBLE PRECISION array, dimension
* (LDA,M) if SIDE = 'L'
* (LDA,N) if SIDE = 'R'
* The vectors which define the elementary reflectors, as
* returned by DGEHRD.
*
* LDA (input) INTEGER
* The leading dimension of the array A.
* LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
*
* TAU (input) DOUBLE PRECISION array, dimension
* (M-1) if SIDE = 'L'
* (N-1) if SIDE = 'R'
* TAU(i) must contain the scalar factor of the elementary
* reflector H(i), as returned by DGEHRD.
*
* 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.
*
* 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 LEFT, LQUERY
INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL LSAME, ILAENV
* ..
* .. External Subroutines ..
EXTERNAL DORMQR, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input arguments
*
INFO = 0
NH = IHI - ILO
LEFT = LSAME( SIDE, 'L' )
LQUERY = ( LWORK.EQ.-1 )
*
* NQ is the order of Q and NW is the minimum dimension of WORK
*
IF( LEFT ) THEN
NQ = M
NW = N
ELSE
NQ = N
NW = M
END IF
IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
$ THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN
INFO = -5
ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN
INFO = -6
ELSE IF( LDA.LT.MAX( 1, NQ ) ) 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( LEFT ) THEN
NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, NH, N, NH, -1 )
ELSE
NB = ILAENV( 1, 'DORMQR', SIDE // TRANS, M, NH, NH, -1 )
END IF
LWKOPT = MAX( 1, NW )*NB
WORK( 1 ) = LWKOPT
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORMHR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
IF( LEFT ) THEN
MI = NH
NI = N
I1 = ILO + 1
I2 = 1
ELSE
MI = M
NI = NH
I1 = 1
I2 = ILO + 1
END IF
*
CALL DORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA,
$ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO )
*
WORK( 1 ) = LWKOPT
RETURN
*
* End of DORMHR
*
END
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