203 lines
6.0 KiB
FortranFixed
203 lines
6.0 KiB
FortranFixed
SUBROUTINE SORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
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$ LDC, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE, TRANS
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INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), C( LDC, * ), TAU( * ),
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$ WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* SORMHR overwrites the general real M-by-N matrix C with
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*
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* SIDE = 'L' SIDE = 'R'
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* TRANS = 'N': Q * C C * Q
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* TRANS = 'T': Q**T * C C * Q**T
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*
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* where Q is a real orthogonal matrix of order nq, with nq = m if
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* SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
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* IHI-ILO elementary reflectors, as returned by SGEHRD:
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*
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* Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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*
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* Arguments
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* =========
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*
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* SIDE (input) CHARACTER*1
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* = 'L': apply Q or Q**T from the Left;
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* = 'R': apply Q or Q**T from the Right.
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*
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* TRANS (input) CHARACTER*1
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* = 'N': No transpose, apply Q;
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* = 'T': Transpose, apply Q**T.
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*
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* M (input) INTEGER
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* The number of rows of the matrix C. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix C. N >= 0.
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*
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* ILO (input) INTEGER
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* IHI (input) INTEGER
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* ILO and IHI must have the same values as in the previous call
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* of SGEHRD. Q is equal to the unit matrix except in the
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* submatrix Q(ilo+1:ihi,ilo+1:ihi).
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* If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
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* ILO = 1 and IHI = 0, if M = 0;
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* if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
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* ILO = 1 and IHI = 0, if N = 0.
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*
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* A (input) REAL array, dimension
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* (LDA,M) if SIDE = 'L'
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* (LDA,N) if SIDE = 'R'
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* The vectors which define the elementary reflectors, as
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* returned by SGEHRD.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A.
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* LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
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*
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* TAU (input) REAL array, dimension
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* (M-1) if SIDE = 'L'
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* (N-1) if SIDE = 'R'
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i), as returned by SGEHRD.
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*
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* C (input/output) REAL array, dimension (LDC,N)
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* On entry, the M-by-N matrix C.
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* On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
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*
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* LDC (input) INTEGER
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* The leading dimension of the array C. LDC >= max(1,M).
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*
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* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK.
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* If SIDE = 'L', LWORK >= max(1,N);
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* if SIDE = 'R', LWORK >= max(1,M).
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* For optimum performance LWORK >= N*NB if SIDE = 'L', and
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* LWORK >= M*NB if SIDE = 'R', where NB is the optimal
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* blocksize.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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LOGICAL LEFT, LQUERY
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INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL ILAENV, LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SORMQR, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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NH = IHI - ILO
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LEFT = LSAME( SIDE, 'L' )
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LQUERY = ( LWORK.EQ.-1 )
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*
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* NQ is the order of Q and NW is the minimum dimension of WORK
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*
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IF( LEFT ) THEN
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NQ = M
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NW = N
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ELSE
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NQ = N
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NW = M
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END IF
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IF( .NOT.LEFT .AND. .NOT.LSAME( SIDE, 'R' ) ) THEN
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INFO = -1
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ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.LSAME( TRANS, 'T' ) )
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$ THEN
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INFO = -2
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ELSE IF( M.LT.0 ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, NQ ) ) THEN
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INFO = -5
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ELSE IF( IHI.LT.MIN( ILO, NQ ) .OR. IHI.GT.NQ ) THEN
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INFO = -6
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ELSE IF( LDA.LT.MAX( 1, NQ ) ) THEN
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INFO = -8
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -11
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ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN
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INFO = -13
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( LEFT ) THEN
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NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, NH, N, NH, -1 )
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ELSE
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NB = ILAENV( 1, 'SORMQR', SIDE // TRANS, M, NH, NH, -1 )
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END IF
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LWKOPT = MAX( 1, NW )*NB
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SORMHR', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 .OR. NH.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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IF( LEFT ) THEN
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MI = NH
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NI = N
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I1 = ILO + 1
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I2 = 1
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ELSE
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MI = M
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NI = NH
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I1 = 1
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I2 = ILO + 1
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END IF
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*
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CALL SORMQR( SIDE, TRANS, MI, NI, NH, A( ILO+1, ILO ), LDA,
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$ TAU( ILO ), C( I1, I2 ), LDC, WORK, LWORK, IINFO )
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*
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WORK( 1 ) = LWKOPT
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RETURN
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*
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* End of SORMHR
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*
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END
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