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

6       DORMRQ  - the general real M-by-N matrix C with   SIDE = 'L' SIDE = 'R'
7       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
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24       where Q is a real orthogonal matrix defined as the product of k elemen‐
25       tary reflectors
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27             Q = H(1) H(2) . . . H(k)
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29       as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N  if
30       SIDE = 'R'.
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ARGUMENTS

34       SIDE    (input) CHARACTER*1
35               = 'L': apply Q or Q**T from the Left;
36               = 'R': apply Q or Q**T from the Right.
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38       TRANS   (input) CHARACTER*1
39               = 'N':  No transpose, apply Q;
40               = 'T':  Transpose, apply Q**T.
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42       M       (input) INTEGER
43               The number of rows of the matrix C. M >= 0.
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45       N       (input) INTEGER
46               The number of columns of the matrix C. N >= 0.
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48       K       (input) INTEGER
49               The  number  of elementary reflectors whose product defines the
50               matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
51               0.
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53       A       (input) DOUBLE PRECISION array, dimension
54               (LDA,M)  if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
55               contain the vector which defines the elementary reflector H(i),
56               for  i = 1,2,...,k, as returned by DGERQF in the last k rows of
57               its array argument  A.   A  is  modified  by  the  routine  but
58               restored on exit.
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60       LDA     (input) INTEGER
61               The leading dimension of the array A. LDA >= max(1,K).
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63       TAU     (input) DOUBLE PRECISION array, dimension (K)
64               TAU(i) must contain the scalar factor of the elementary reflec‐
65               tor H(i), as returned by DGERQF.
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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                       DORMRQ(1)
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