DORMBR (3)  Linux Manuals
NAME
dormbr.f 
SYNOPSIS
Functions/Subroutines
subroutine dormbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMBR
Function/Subroutine Documentation
subroutine dormbr (characterVECT, characterSIDE, characterTRANS, integerM, integerN, integerK, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK, integerLWORK, integerINFO)
DORMBR
Purpose:

If VECT = 'Q', DORMBR overwrites the general real MbyN matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**T * C C * Q**T If VECT = 'P', DORMBR overwrites the general real MbyN 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 DGEBRD 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 NQbyK matrix: if nq >= k, Q = H(1) H(2) . . . H(k); if nq < k, Q = H(1) H(2) . . . H(nq1). If VECT = 'P', A is assumed to have been a KbyNQ matrix: if k < nq, P = G(1) G(2) . . . G(k); if k >= nq, P = G(1) G(2) . . . G(nq1).
Parameters:

VECT
VECT is CHARACTER*1 = 'Q': apply Q or Q**T; = 'P': apply P or P**T.
SIDESIDE 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.
TRANSTRANS is CHARACTER*1 = 'N': No transpose, apply Q or P; = 'T': Transpose, apply Q**T or P**T.
MM is INTEGER The number of rows of the matrix C. M >= 0.
NN is INTEGER The number of columns of the matrix C. N >= 0.
KK is INTEGER If VECT = 'Q', the number of columns in the original matrix reduced by DGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by DGEBRD. K >= 0.
AA is DOUBLE PRECISION 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 DGEBRD.
LDALDA 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)).
TAUTAU is DOUBLE PRECISION 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 DGEBRD in the array argument TAUQ or TAUP.
CC is DOUBLE PRECISION array, dimension (LDC,N) On entry, the MbyN 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.
LDCLDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).
WORKWORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORKLWORK 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.
INFOINFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith 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 195 of file dormbr.f.
Author
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