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

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

10       SUBROUTINE SORMHR( 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           REAL           A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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PURPOSE

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

31       SIDE    (input) CHARACTER*1
32               = 'L': apply Q or Q**T from the Left;
33               = 'R': apply Q or Q**T from the Right.
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35       TRANS   (input) CHARACTER*1
36               = 'N':  No transpose, apply Q;
37               = 'T':  Transpose, apply Q**T.
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39       M       (input) INTEGER
40               The number of rows of the matrix C. M >= 0.
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42       N       (input) INTEGER
43               The number of columns of the matrix C. N >= 0.
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45       ILO     (input) INTEGER
46               IHI     (input) INTEGER ILO and IHI must have the  same  values
47               as  in  the  previous  call  of  SGEHRD. Q is equal to the unit
48               matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi).  If SIDE
49               = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and ILO = 1 and IHI
50               = 0, if M = 0; if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N >
51               0, and ILO = 1 and IHI = 0, if N = 0.
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53       A       (input) REAL array, dimension
54               (LDA,M)  if  SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which
55               define the elementary reflectors, as returned by SGEHRD.
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57       LDA     (input) INTEGER
58               The leading dimension of the array A.  LDA >= max(1,M) if  SIDE
59               = 'L'; LDA >= max(1,N) if SIDE = 'R'.
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61       TAU     (input) REAL array, dimension
62               (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
63               scalar factor of the elementary reflector H(i), as returned  by
64               SGEHRD.
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66       C       (input/output) REAL array, dimension (LDC,N)
67               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
68               Q*C or Q**T*C or C*Q**T or C*Q.
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70       LDC     (input) INTEGER
71               The leading dimension of the array C. LDC >= max(1,M).
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73       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
74               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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76       LWORK   (input) INTEGER
77               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
78               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
79               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
80               = 'R', where NB is the optimal blocksize.
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82               If  LWORK  = -1, then a workspace query is assumed; the routine
83               only calculates the optimal size of  the  WORK  array,  returns
84               this  value  as the first entry of the WORK array, and no error
85               message related to LWORK is issued by XERBLA.
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87       INFO    (output) INTEGER
88               = 0:  successful exit
89               < 0:  if INFO = -i, the i-th argument had an illegal value
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93 LAPACK routine (version 3.1)    November 2006                       SORMHR(1)
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