dormhr3

!>
!> 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).
!> 

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!> 

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T.
!> 

M

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!> 

ILO

!>          ILO is INTEGER
!> 

IHI

!>          IHI is 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

!>          A is 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

!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
!> 

TAU

!>          TAU is 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

!>          C is 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

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

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.
!> 

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 

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