1SORMR3(1)                LAPACK routine (version 3.2)                SORMR3(1)
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NAME

6       SORMR3  -  overwrites  the general real m by n matrix C with   Q * C if
7       SIDE = 'L' and TRANS = 'N', or   Q'* C if SIDE = 'L' and TRANS  =  'T',
8       or   C * Q if SIDE = 'R' and TRANS = 'N', or   C * Q' if SIDE = 'R' and
9       TRANS = '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 where Q is a
23       real orthogonal matrix defined as the product of k  elementary  reflec‐
24       tors
25             Q = H(1) H(2) . . . H(k)
26       as  returned by STZRZF. 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' from the Left
32               = 'R': apply Q or Q' from the Right
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34       TRANS   (input) CHARACTER*1
35               = 'N': apply Q  (No transpose)
36               = 'T': apply Q' (Transpose)
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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       L       (input) INTEGER
50               The number of columns of the matrix A containing the meaningful
51               part  of  the Householder reflectors.  If SIDE = 'L', M >= L >=
52               0, if SIDE = 'R', N >= L >= 0.
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54       A       (input) REAL array, dimension
55               (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row  must
56               contain the vector which defines the elementary reflector H(i),
57               for i = 1,2,...,k, as returned by STZRZF in the last k rows  of
58               its  array  argument  A.   A  is  modified  by  the routine but
59               restored on exit.
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61       LDA     (input) INTEGER
62               The leading dimension of the array A. LDA >= max(1,K).
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64       TAU     (input) REAL array, dimension (K)
65               TAU(i) must contain the scalar factor of the elementary reflec‐
66               tor H(i), as returned by STZRZF.
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68       C       (input/output) REAL array, dimension (LDC,N)
69               On  entry,  the  m-by-n matrix C.  On exit, C is overwritten by
70               Q*C or Q'*C or C*Q' or C*Q.
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72       LDC     (input) INTEGER
73               The leading dimension of the array C. LDC >= max(1,M).
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75       WORK    (workspace) REAL array, dimension
76               (N) if SIDE = 'L', (M) if SIDE = 'R'
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78       INFO    (output) INTEGER
79               = 0: successful exit
80               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

83       Based on contributions by
84         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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88 LAPACK routine (version 3.2)    November 2008                       SORMR3(1)
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