1SORMTR(1)                LAPACK routine (version 3.1)                SORMTR(1)
2
3
4

NAME

6       SORMTR  - the general real M-by-N matrix C with   SIDE = 'L' SIDE = 'R'
7       TRANS = 'N'
8

SYNOPSIS

10       SUBROUTINE SORMTR( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC,  WORK,
11                          LWORK, INFO )
12
13           CHARACTER      SIDE, TRANS, UPLO
14
15           INTEGER        INFO, LDA, LDC, LWORK, M, N
16
17           REAL           A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
18

PURPOSE

20       SORMTR  overwrites  the  general real M-by-N matrix C with TRANS = 'T':
21       Q**T * C       C * Q**T
22
23       where Q is a real orthogonal matrix of order nq, with nq = m if SIDE  =
24       'L'  and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 ele‐
25       mentary reflectors, as returned by SSYTRD:
26
27       if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
28
29       if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
30
31

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.
36
37       UPLO    (input) CHARACTER*1
38               = 'U': Upper triangle of A contains elementary reflectors  from
39               SSYTRD;  = 'L': Lower triangle of A contains elementary reflec‐
40               tors from SSYTRD.
41
42       TRANS   (input) CHARACTER*1
43               = 'N':  No transpose, apply Q;
44               = 'T':  Transpose, apply Q**T.
45
46       M       (input) INTEGER
47               The number of rows of the matrix C. M >= 0.
48
49       N       (input) INTEGER
50               The number of columns of the matrix C. N >= 0.
51
52       A       (input) REAL array, dimension
53               (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The  vectors  which
54               define the elementary reflectors, as returned by SSYTRD.
55
56       LDA     (input) INTEGER
57               The  leading dimension of the array A.  LDA >= max(1,M) if SIDE
58               = 'L'; LDA >= max(1,N) if SIDE = 'R'.
59
60       TAU     (input) REAL array, dimension
61               (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the
62               scalar  factor of the elementary reflector H(i), as returned by
63               SSYTRD.
64
65       C       (input/output) REAL array, dimension (LDC,N)
66               On entry, the M-by-N matrix C.  On exit, C  is  overwritten  by
67               Q*C or Q**T*C or C*Q**T or C*Q.
68
69       LDC     (input) INTEGER
70               The leading dimension of the array C. LDC >= max(1,M).
71
72       WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
73               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
74
75       LWORK   (input) INTEGER
76               The  dimension  of  the  array  WORK.   If SIDE = 'L', LWORK >=
77               max(1,N); if SIDE = 'R', LWORK >= max(1,M).  For  optimum  per‐
78               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
79               = 'R', where NB is the optimal blocksize.
80
81               If LWORK = -1, then a workspace query is assumed;  the  routine
82               only  calculates  the  optimal  size of the WORK array, returns
83               this value as the first entry of the WORK array, and  no  error
84               message related to LWORK is issued by XERBLA.
85
86       INFO    (output) INTEGER
87               = 0:  successful exit
88               < 0:  if INFO = -i, the i-th argument had an illegal value
89
90
91
92 LAPACK routine (version 3.1)    November 2006                       SORMTR(1)
Impressum