cunmbr.f −

**Functions/Subroutines**

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

CUNMBR

**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*

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 CGEBRD.

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

matrix reduced by CGEBRD.

K >= 0.

*A*

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*

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.

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