# cunm22.f - Man Page

## Synopsis

### Functions/Subroutines

subroutine cunm22 (SIDE, TRANS, M, N, N1, N2, Q, LDQ, C, LDC, WORK, LWORK, INFO)
CUNM22 multiplies a general matrix by a banded unitary matrix.

## Function/Subroutine Documentation

### subroutine cunm22 (character SIDE, character TRANS, integer M, integer N, integer N1, integer N2, complex, dimension( ldq, * ) Q, integer LDQ, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( * ) WORK, integer LWORK, integer INFO)

CUNM22 multiplies a general matrix by a banded unitary matrix.

Purpose

```  CUNM22 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

where Q is a complex unitary matrix of order NQ, with NQ = M if
SIDE = 'L' and NQ = N if SIDE = 'R'.
The unitary matrix Q processes a 2-by-2 block structure

[  Q11  Q12  ]
Q = [            ]
[  Q21  Q22  ],

where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
N2-by-N2 upper triangular matrix.```
Parameters:

SIDE

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

TRANS

```          TRANS is CHARACTER*1
= 'N':  apply Q (No transpose);
= 'C':  apply Q**H (Conjugate transpose).```

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.```

N1
N2

```          N1 is INTEGER
N2 is INTEGER
The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
The following requirement must be satisfied:
N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.```

Q

```          Q is COMPLEX array, dimension
(LDQ,M) if SIDE = 'L'
(LDQ,N) if SIDE = 'R'```

LDQ

```          LDQ is INTEGER
The leading dimension of the array Q.
LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.```

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.```

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).
For optimum performance LWORK >= M*N.

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

NAG Ltd.

Date:

January 2015

Definition at line 164 of file cunm22.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cunm22(3) is an alias of cunm22.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK