1SORMR3(1)                LAPACK routine (version 3.1)                SORMR3(1)
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NAME

6       SORMR3  -  the  general real m by n matrix C with   Q * C if SIDE = 'L'
7       and TRANS = 'N', or   Q'* C if SIDE = 'L' and TRANS = 'T', or   C  *  Q
8       if  SIDE  =  'R' and TRANS = 'N', or   C * Q' if SIDE = 'R' and TRANS =
9       'T',
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SYNOPSIS

12       SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,  WORK,
13                          INFO )
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15           CHARACTER      SIDE, TRANS
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17           INTEGER        INFO, K, L, LDA, LDC, M, N
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19           REAL           A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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PURPOSE

22       SORMR3 overwrites the general real m by n matrix C with
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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 STZRZF. 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' from the Left
36               = 'R': apply Q or Q' from the Right
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38       TRANS   (input) CHARACTER*1
39               = 'N': apply Q  (No transpose)
40               = 'T': apply Q' (Transpose)
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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       L       (input) INTEGER
54               The number of columns of the matrix A containing the meaningful
55               part of the Householder reflectors.  If SIDE = 'L', M >=  L  >=
56               0, if SIDE = 'R', N >= L >= 0.
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58       A       (input) REAL array, dimension
59               (LDA,M)  if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
60               contain the vector which defines the elementary reflector H(i),
61               for  i = 1,2,...,k, as returned by STZRZF in the last k rows of
62               its array argument  A.   A  is  modified  by  the  routine  but
63               restored on exit.
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65       LDA     (input) INTEGER
66               The leading dimension of the array A. LDA >= max(1,K).
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68       TAU     (input) REAL array, dimension (K)
69               TAU(i) must contain the scalar factor of the elementary reflec‐
70               tor H(i), as returned by STZRZF.
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72       C       (input/output) REAL array, dimension (LDC,N)
73               On entry, the m-by-n matrix C.  On exit, C  is  overwritten  by
74               Q*C or Q'*C or C*Q' or C*Q.
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76       LDC     (input) INTEGER
77               The leading dimension of the array C. LDC >= max(1,M).
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79       WORK    (workspace) REAL array, dimension
80               (N) if SIDE = 'L', (M) if SIDE = 'R'
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82       INFO    (output) INTEGER
83               = 0: successful exit
84               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

87       Based on contributions by
88         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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93 LAPACK routine (version 3.1)    November 2006                       SORMR3(1)
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