1DORMRQ(1)                LAPACK routine (version 3.2)                DORMRQ(1)
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NAME

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

10       SUBROUTINE DORMRQ( SIDE, TRANS, M, N, K, A, LDA,  TAU,  C,  LDC,  WORK,
11                          LWORK, INFO )
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13           CHARACTER      SIDE, TRANS
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15           INTEGER        INFO, K, 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       DORMRQ overwrites the general real M-by-N matrix C with  TRANS  =  'T':
22       Q**T * C       C * Q**T
23       where Q is a real orthogonal matrix defined as the product of k elemen‐
24       tary reflectors
25             Q = H(1) H(2) . . . H(k)
26       as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N  if
27       SIDE = 'R'.
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ARGUMENTS

30       SIDE    (input) CHARACTER*1
31               = 'L': apply Q or Q**T from the Left;
32               = 'R': apply Q or Q**T from the Right.
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34       TRANS   (input) CHARACTER*1
35               = 'N':  No transpose, apply Q;
36               = 'T':  Transpose, apply Q**T.
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38       M       (input) INTEGER
39               The number of rows of the matrix C. M >= 0.
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41       N       (input) INTEGER
42               The number of columns of the matrix C. N >= 0.
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44       K       (input) INTEGER
45               The  number  of elementary reflectors whose product defines the
46               matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
47               0.
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49       A       (input) DOUBLE PRECISION array, dimension
50               (LDA,M)  if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
51               contain the vector which defines the elementary reflector H(i),
52               for  i = 1,2,...,k, as returned by DGERQF in the last k rows of
53               its array argument  A.   A  is  modified  by  the  routine  but
54               restored on exit.
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56       LDA     (input) INTEGER
57               The leading dimension of the array A. LDA >= max(1,K).
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59       TAU     (input) DOUBLE PRECISION array, dimension (K)
60               TAU(i) must contain the scalar factor of the elementary reflec‐
61               tor H(i), as returned by DGERQF.
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63       C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
64               On entry, the M-by-N matrix C.  On exit, C  is  overwritten  by
65               Q*C or Q**T*C or C*Q**T or C*Q.
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67       LDC     (input) INTEGER
68               The leading dimension of the array C. LDC >= max(1,M).
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70       WORK       (workspace/output)   DOUBLE   PRECISION   array,   dimension
71       (MAX(1,LWORK))
72               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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74       LWORK   (input) INTEGER
75               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
76               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
77               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
78               =  'R', where NB is the optimal blocksize.  If LWORK = -1, then
79               a workspace query is assumed; the routine only  calculates  the
80               optimal size of the WORK array, returns this value as the first
81               entry of the WORK array, and no error message related to  LWORK
82               is issued by XERBLA.
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84       INFO    (output) INTEGER
85               = 0:  successful exit
86               < 0:  if INFO = -i, the i-th argument had an illegal value
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90 LAPACK routine (version 3.2)    November 2008                       DORMRQ(1)
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