cunmbr-f(3)

cunmbr.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

CUNMBR

Purpose:

 If VECT = 'Q', CUNMBR overwrites the general complex M-by-N matrix C
 with
 SIDE = 'L' SIDE = 'R'
 TRANS = 'N': Q * C C * Q
 TRANS = 'C': Q**H * C C * Q**H
 If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
 with
 SIDE = 'L' SIDE = 'R'
 TRANS = 'N': P * C C * P
 TRANS = 'C': P**H * C C * P**H
 Here Q and P**H are the unitary matrices determined by CGEBRD when
 reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
 and P**H 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 unitary matrix Q or P**H 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**H;
 = 'P': apply P or P**H.

SIDE

 SIDE is CHARACTER*1
 = 'L': apply Q, Q**H, P or P**H from the Left;
 = 'R': apply Q, Q**H, P or P**H from the Right.

TRANS

 TRANS is CHARACTER*1
 = 'N': No transpose, apply Q or P;
 = 'C': Conjugate transpose, apply Q**H or P**H.

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

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

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

 A is COMPLEX 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 CGEBRD.

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 COMPLEX 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 CGEBRD in the array argument TAUQ or TAUP.

 C is COMPLEX array, dimension (LDC,N)
 On entry, the M-by-N matrix C.
 On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
 or P*C or P**H*C or C*P or C*P**H.

LDC

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

WORK

 WORK is COMPLEX 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);
 if N = 0 or M = 0, LWORK >= 1.
 For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
 and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
 optimal blocksize. (NB = 0 if M = 0 or N = 0.)
 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 197 of file cunmbr.f.

Author

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