1SOPMTR(1)                LAPACK routine (version 3.2)                SOPMTR(1)
2
3
4

NAME

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

SYNOPSIS

10       SUBROUTINE SOPMTR( 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           REAL           AP( * ), C( LDC, * ), TAU( * ), WORK( * )
18

PURPOSE

20       SOPMTR  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 of order nq, with nq = m if SIDE  =
23       'L'  and nq = n if SIDE = 'R'. Q is defined as the product of nq-1 ele‐
24       mentary reflectors, as returned by SSPTRD using packed storage:
25       if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
26       if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
27

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.
32
33       UPLO    (input) CHARACTER*1
34               = 'U': Upper triangular packed storage used in previous call to
35               SSPTRD; = 'L': Lower triangular packed storage used in previous
36               call to SSPTRD.
37
38       TRANS   (input) CHARACTER*1
39               = 'N':  No transpose, apply Q;
40               = 'T':  Transpose, apply Q**T.
41
42       M       (input) INTEGER
43               The number of rows of the matrix C. M >= 0.
44
45       N       (input) INTEGER
46               The number of columns of the matrix C. N >= 0.
47
48       AP      (input) REAL array, dimension
49               (M*(M+1)/2) if SIDE = 'L' (N*(N+1)/2) if SIDE = 'R' The vectors
50               which  define the elementary reflectors, as returned by SSPTRD.
51               AP is modified by the routine but restored on exit.
52
53       TAU     (input) REAL array, dimension (M-1) if SIDE = 'L'
54               or (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of
55               the elementary reflector H(i), as returned by SSPTRD.
56
57       C       (input/output) REAL array, dimension (LDC,N)
58               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
59               Q*C or Q**T*C or C*Q**T or C*Q.
60
61       LDC     (input) INTEGER
62               The leading dimension of the array C. LDC >= max(1,M).
63
64       WORK    (workspace) REAL array, dimension
65               (N) if SIDE = 'L' (M) if SIDE = 'R'
66
67       INFO    (output) INTEGER
68               = 0:  successful exit
69               < 0:  if INFO = -i, the i-th argument had an illegal value
70
71
72
73 LAPACK routine (version 3.2)    November 2008                       SOPMTR(1)
Impressum