sormbr.f man page

sormbr.f —

Synopsis

Functions/Subroutines

subroutine sormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
SORMBR

Function/Subroutine Documentation

subroutine sormbr (characterVECT, characterSIDE, characterTRANS, integerM, integerN, integerK, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( ldc, * )C, integerLDC, real, dimension( * )WORK, integerLWORK, integerINFO)

SORMBR

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 reflectors 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 matrix:
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).

Parameters:

VECT

VECT is CHARACTER*1
= 'Q': apply Q or Q**T;
= 'P': apply P or P**T.

SIDE

SIDE is 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

TRANS is CHARACTER*1
= 'N':  No transpose, apply Q  or P;
= 'T':  Transpose, apply Q**T or P**T.

M

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

N

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

K

K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by SGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by SGEBRD.
K >= 0.

A

A is 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

LDA is 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

TAU is REAL array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by SGEBRD in the array argument TAUQ or TAUP.

C

C is 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

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is 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

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 196 of file sormbr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

sormbr(3) is an alias of sormbr.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK