sormbr(3)

NAME

SORMBR - VECT = 'Q', SORMBR overwrites the general real M

by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

SUBROUTINE  SORMBR(  VECT,  SIDE,  TRANS, M, N, K, A, LDA,
TAU, C, LDC, WORK, LWORK, INFO )
    CHARACTER      SIDE, TRANS, VECT
    INTEGER        INFO, K, LDA, LDC, LWORK, M, N
    REAL           A( LDA, * ), C( LDC, *  ),  TAU(  *  ),
WORK( * )

PURPOSE

If VECT = 'Q', SORMBR overwrites the general real M-by-N

matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q

TRANS = 'T': Q**T * C C * Q**T

If VECT = 'P', SORMBR overwrites the general real M-by-N

matrix C with

SIDE = 'L' SIDE = 'R'

TRANS = 'N': P * C C * P
TRANS = 'T': P**T * C C * P**T

Here Q and P**T are the orthogonal matrices determined by

SGEBRD when reducing a real matrix A to bidiagonal form: A = Q *

B * P**T. Q and P**T are defined as products of elementary re

flectors H(i) and G(i) respectively.

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq

is the order of the orthogonal matrix Q or P**T that is applied.

If VECT = 'Q', A is assumed to have been an NQ-by-K ma

trix: if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:

if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).

ARGUMENTS

VECT (input) CHARACTER*1

= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.

SIDE (input) CHARACTER*1

= 'L': apply Q, Q**T, P or P**T from the Left;
= 'R': apply Q, Q**T, P or P**T from the Right.

TRANS (input) CHARACTER*1

= 'N': No transpose, apply Q or P;
= 'T': Transpose, apply Q**T or P**T.

M (input) INTEGER

The number of rows of the matrix C. M >= 0.

N (input) INTEGER

The number of columns of the matrix C. N >= 0.

K (input) INTEGER

If VECT = 'Q', the number of columns in the origi

nal matrix reduced by SGEBRD. If VECT = 'P', the number of rows

in the original matrix reduced by SGEBRD. K >= 0.

A (input) REAL array, dimension

(LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if

VECT = 'P' The vectors which define the elementary reflectors

H(i) and G(i), whose products determine the matrices Q and P, as

returned by SGEBRD.

LDA (input) INTEGER

The leading dimension of the array A. If VECT =

'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU (input) REAL array, dimension (min(nq,K))

TAU(i) must contain the scalar factor of the ele

mentary reflector H(i) or G(i) which determines Q or P, as re

turned by SGEBRD in the array argument TAUQ or TAUP.

C (input/output) REAL array, dimension (LDC,N)

On entry, the M-by-N matrix C. On exit, C is

overwritten by Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or

C*P or C*P**T.

LDC (input) INTEGER

The leading dimension of the array C. LDC >=

max(1,M).

WORK (workspace/output) REAL array, dimension (LWORK)

On exit, if INFO = 0, WORK(1) returns the optimal

LWORK.

LWORK (input) INTEGER

The dimension of the array WORK. If SIDE = 'L',

LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum

performance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if

SIDE = 'R', where NB is the optimal blocksize.

If LWORK = -1, then a workspace query is assumed;

the routine only calculates the optimal size of the WORK array,

returns this value as the first entry of the WORK array, and no

error message related to LWORK is issued by XERBLA.

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

SORMBR(3)