sormhr()

subroutine sormhr	(	character	SIDE,
		character	TRANS,
		integer	M,
		integer	N,
		integer	ILO,
		integer	IHI,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( * )	TAU,
		real, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	WORK,
		integer	LWORK,
		integer	INFO
	)

SORMHR

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Purpose:

 SORMHR 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 SGEHRD:

 Q = H(ilo) H(ilo+1) . . . H(ihi-1).

Parameters

[in]	SIDE	SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
[in]	TRANS	TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
[in]	M	M is INTEGER The number of rows of the matrix C. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix C. N >= 0.
[in]	ILO	ILO is INTEGER
[in]	IHI	IHI is INTEGER ILO and IHI must have the same values as in the previous call of SGEHRD. 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.
[in]	A	A is REAL array, dimension (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SGEHRD.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
[in]	TAU	TAU is REAL 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 SGEHRD.
[in,out]	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.
[in]	LDC	LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
[out]	WORK	WORK is REAL array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]	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 >= 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.
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Definition at line 181 of file sormhr.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE, TRANS
      INTEGER            IHI, ILO, INFO, LDA, LDC, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), C( LDC, * ), TAU( * ),
     $                   WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            LEFT, LQUERY
      INTEGER            I1, I2, IINFO, LWKOPT, MI, NB, NH, NI, NQ, NW
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            ILAENV
      EXTERNAL           ilaenv, lsame
*     ..
*     .. External Subroutines ..
      EXTERNAL           sormqr, 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, 'SORMQR', side // trans, nh, n, nh, -1 )
         ELSE
            nb = ilaenv( 1, 'SORMQR', 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( 'SORMHR', -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 sormqr( 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 SORMHR
*

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