# cunmbr.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
Page Index

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

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:

December 2016

Definition at line 199 of file cunmbr.f.

## Author

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