dormbr.f (3) Linux Manual Page

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 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:

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 DGEBRD.

 If VECT = ‘P’, the number of rows in the original

 matrix reduced by DGEBRD.

 K >= 0.

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.

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 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.

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.

LDC

 LDC is INTEGER

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

WORK

 WORK is DOUBLE PRECISION 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 195 of file dormbr.f.

Author

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