LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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dormbr.f File Reference

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Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dormbr ( character  VECT,
character  SIDE,
character  TRANS,
integer  M,
integer  N,
integer  K,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( * )  TAU,
double precision, dimension( ldc, * )  C,
integer  LDC,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DORMBR

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Purpose: 
 If VECT = 'Q', DORMBR 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', DORMBR 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 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 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:
[in]VECT
          VECT is CHARACTER*1
          = 'Q': apply Q or Q**T;
          = 'P': apply P or P**T.
[in]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.
[in]TRANS
          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q  or P;
          = 'T':  Transpose, apply Q**T or P**T.
[in]M
          M is INTEGER
          The number of rows of the matrix C. M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix C. N >= 0.
[in]K
          K 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.
[in]A
          A 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.
[in]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)).
[in]TAU
          TAU 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.
[in,out]C
          C is DOUBLE PRECISION 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.
[in]LDC
          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]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.
[out]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 195 of file dormbr.f.

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