1DORMHR(1)                LAPACK routine (version 3.1)                DORMHR(1)
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NAME

6       DORMHR  - the general real M-by-N matrix C with   SIDE = 'L' SIDE = 'R'
7       TRANS = 'N'
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SYNOPSIS

10       SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA,  TAU,  C,  LDC,
11                          WORK, LWORK, INFO )
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13           CHARACTER      SIDE, TRANS
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15           INTEGER        IHI, ILO, INFO, LDA, LDC, LWORK, M, N
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17           DOUBLE         PRECISION  A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
18                          * )
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PURPOSE

21       DORMHR overwrites the general real M-by-N matrix C with  TRANS  =  'T':
22       Q**T * C       C * Q**T
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24       where  Q is a real orthogonal matrix of order nq, with nq = m if SIDE =
25       'L' and nq = n if SIDE = 'R'. Q is defined as the  product  of  IHI-ILO
26       elementary reflectors, as returned by DGEHRD:
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28       Q = H(ilo) H(ilo+1) . . . H(ihi-1).
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ARGUMENTS

32       SIDE    (input) CHARACTER*1
33               = 'L': apply Q or Q**T from the Left;
34               = 'R': apply Q or Q**T from the Right.
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36       TRANS   (input) CHARACTER*1
37               = 'N':  No transpose, apply Q;
38               = 'T':  Transpose, apply Q**T.
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40       M       (input) INTEGER
41               The number of rows of the matrix C. M >= 0.
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43       N       (input) INTEGER
44               The number of columns of the matrix C. N >= 0.
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46       ILO     (input) INTEGER
47               IHI      (input)  INTEGER ILO and IHI must have the same values
48               as in the previous call of DGEHRD.  Q  is  equal  to  the  unit
49               matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE
50               = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI
51               = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N >
52               0, and ILO = 1 and IHI = 0, if N = 0.
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54       A       (input) DOUBLE PRECISION array, dimension
55               (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The  vectors  which
56               define the elementary reflectors, as returned by DGEHRD.
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58       LDA     (input) INTEGER
59               The  leading dimension of the array A.  LDA >= max(1,M) if SIDE
60               = 'L'; LDA >= max(1,N) if SIDE = 'R'.
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62       TAU     (input) DOUBLE PRECISION array, dimension
63               (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
64               scalar  factor of the elementary reflector H(i), as returned by
65               DGEHRD.
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67       C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
68               On entry, the M-by-N matrix C.  On exit, C  is  overwritten  by
69               Q*C or Q**T*C or C*Q**T or C*Q.
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71       LDC     (input) INTEGER
72               The leading dimension of the array C. LDC >= max(1,M).
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74       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
75       (MAX(1,LWORK))
76               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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78       LWORK   (input) INTEGER
79               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
80               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
81               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
82               = 'R', where NB is the optimal blocksize.
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84               If  LWORK  = -1, then a workspace query is assumed; the routine
85               only calculates the optimal size of  the  WORK  array,  returns
86               this  value  as the first entry of the WORK array, and no error
87               message related to LWORK is issued by XERBLA.
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89       INFO    (output) INTEGER
90               = 0:  successful exit
91               < 0:  if INFO = -i, the i-th argument had an illegal value
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95 LAPACK routine (version 3.1)    November 2006                       DORMHR(1)
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