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

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

10       SUBROUTINE SORMLQ( 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       SORMLQ  overwrites  the  general real M-by-N matrix C with TRANS = 'T':
21       Q**T * C       C * Q**T
22       where Q is a real orthogonal matrix defined as the product of k elemen‐
23       tary reflectors
24             Q = H(k) . . . H(2) H(1)
25       as  returned by SGELQF. Q is of order M if SIDE = 'L' and of order N if
26       SIDE = 'R'.
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ARGUMENTS

29       SIDE    (input) CHARACTER*1
30               = 'L': apply Q or Q**T from the Left;
31               = 'R': apply Q or Q**T from the Right.
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33       TRANS   (input) CHARACTER*1
34               = 'N':  No transpose, apply Q;
35               = 'T':  Transpose, apply Q**T.
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37       M       (input) INTEGER
38               The number of rows of the matrix C. M >= 0.
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40       N       (input) INTEGER
41               The number of columns of the matrix C. N >= 0.
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43       K       (input) INTEGER
44               The number of elementary reflectors whose product  defines  the
45               matrix Q.  If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
46               0.
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48       A       (input) REAL array, dimension
49               (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row  must
50               contain the vector which defines the elementary reflector H(i),
51               for i = 1,2,...,k, as returned by SGELQF in the first k rows of
52               its  array  argument  A.   A  is  modified  by  the routine but
53               restored on exit.
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55       LDA     (input) INTEGER
56               The leading dimension of the array A. LDA >= max(1,K).
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58       TAU     (input) REAL array, dimension (K)
59               TAU(i) must contain the scalar factor of the elementary reflec‐
60               tor H(i), as returned by SGELQF.
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62       C       (input/output) REAL array, dimension (LDC,N)
63               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
64               Q*C or Q**T*C or C*Q**T or C*Q.
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66       LDC     (input) INTEGER
67               The leading dimension of the array C. LDC >= max(1,M).
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69       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
70               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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72       LWORK   (input) INTEGER
73               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
74               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
75               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
76               =  'R', where NB is the optimal blocksize.  If LWORK = -1, then
77               a workspace query is assumed; the routine only  calculates  the
78               optimal size of the WORK array, returns this value as the first
79               entry of the WORK array, and no error message related to  LWORK
80               is issued by XERBLA.
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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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88 LAPACK routine (version 3.2)    November 2008                       SORMLQ(1)
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