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

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

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

20       SORMQR  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 defined as the product of k elemen‐
24       tary reflectors
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26             Q = H(1) H(2) . . . H(k)
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28       as  returned by SGEQRF. Q is of order M if SIDE = 'L' and of order N if
29       SIDE = 'R'.
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ARGUMENTS

33       SIDE    (input) CHARACTER*1
34               = 'L': apply Q or Q**T from the Left;
35               = 'R': apply Q or Q**T from the Right.
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37       TRANS   (input) CHARACTER*1
38               = 'N':  No transpose, apply Q;
39               = 'T':  Transpose, apply Q**T.
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41       M       (input) INTEGER
42               The number of rows of the matrix C. M >= 0.
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44       N       (input) INTEGER
45               The number of columns of the matrix C. N >= 0.
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47       K       (input) INTEGER
48               The number of elementary reflectors whose product  defines  the
49               matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
50               0.
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52       A       (input) REAL array, dimension (LDA,K)
53               The i-th column must contain the vector which defines the  ele‐
54               mentary  reflector H(i), for i = 1,2,...,k, as returned by SGE‐
55               QRF in the first k columns of its array argument A.  A is modi‐
56               fied by the routine but restored on exit.
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58       LDA     (input) INTEGER
59               The  leading  dimension  of the array A.  If SIDE = 'L', LDA >=
60               max(1,M); if SIDE = 'R', LDA >= max(1,N).
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62       TAU     (input) REAL array, dimension (K)
63               TAU(i) must contain the scalar factor of the elementary reflec‐
64               tor H(i), as returned by SGEQRF.
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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                       SORMQR(1)
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