1SORMRZ(1)               LAPACK routine (version 3.1.1)               SORMRZ(1)
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NAME

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

10       SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, 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, L, LDA, LDC, LWORK, M, N
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17           REAL           A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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PURPOSE

20       SORMRZ  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 STZRZF. 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       L       (input) INTEGER
53               The number of columns of the matrix A containing the meaningful
54               part  of  the Householder reflectors.  If SIDE = 'L', M >= L >=
55               0, if SIDE = 'R', N >= L >= 0.
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57       A       (input) REAL array, dimension
58               (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row  must
59               contain the vector which defines the elementary reflector H(i),
60               for i = 1,2,...,k, as returned by STZRZF in the last k rows  of
61               its  array  argument  A.   A  is  modified  by  the routine but
62               restored on exit.
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64       LDA     (input) INTEGER
65               The leading dimension of the array A. LDA >= max(1,K).
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67       TAU     (input) REAL array, dimension (K)
68               TAU(i) must contain the scalar factor of the elementary reflec‐
69               tor H(i), as returned by STZRZF.
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71       C       (input/output) REAL array, dimension (LDC,N)
72               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
73               Q*C or Q**H*C or C*Q**H or C*Q.
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75       LDC     (input) INTEGER
76               The leading dimension of the array C. LDC >= max(1,M).
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78       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
79               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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81       LWORK   (input) INTEGER
82               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
83               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
84               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
85               = 'R', where NB is the optimal blocksize.
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87               If  LWORK  = -1, then a workspace query is assumed; the routine
88               only calculates the optimal size of  the  WORK  array,  returns
89               this  value  as the first entry of the WORK array, and no error
90               message related to LWORK is issued by XERBLA.
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92       INFO    (output) INTEGER
93               = 0:  successful exit
94               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

97       Based on contributions by
98         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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103 LAPACK routine (version 3.1.1)  February 2007                       SORMRZ(1)