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

NAME

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

SYNOPSIS

10       SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO
11                          )
12
13           CHARACTER      SIDE, TRANS, UPLO
14
15           INTEGER        INFO, LDC, M, N
16
17           DOUBLE         PRECISION AP( * ), C( LDC, * ), TAU( * ), WORK( * )
18

PURPOSE

20       DOPMTR  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 DSPTRD using packed storage:
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 triangular packed storage used in previous call to
39               DSPTRD; = 'L': Lower triangular packed storage used in previous
40               call to DSPTRD.
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       AP      (input) DOUBLE PRECISION array, dimension
53               (M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors
54               which  define the elementary reflectors, as returned by DSPTRD.
55               AP is modified by the routine but restored on exit.
56
57       TAU     (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
58               or (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of
59               the elementary reflector H(i), as returned by DSPTRD.
60
61       C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
62               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
63               Q*C or Q**T*C or C*Q**T or C*Q.
64
65       LDC     (input) INTEGER
66               The leading dimension of the array C. LDC >= max(1,M).
67
68       WORK    (workspace) DOUBLE PRECISION array, dimension
69               (N) if SIDE = 'L' (M) if SIDE = 'R'
70
71       INFO    (output) INTEGER
72               = 0:  successful exit
73               < 0:  if INFO = -i, the i-th argument had an illegal value
74
75
76
77 LAPACK routine (version 3.1)    November 2006                       DOPMTR(1)
Impressum