# clags2.f - Man Page

SRC/clags2.f

## Synopsis

### Functions/Subroutines

subroutine clags2 (upper, a1, a2, a3, b1, b2, b3, csu, snu, csv, snv, csq, snq)
CLAGS2

## Function/Subroutine Documentation

### subroutine clags2 (logical upper, real a1, complex a2, real a3, real b1, complex b2, real b3, real csu, complex snu, real csv, complex snv, real csq, complex snq)

CLAGS2

Purpose:

``` CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
that if ( UPPER ) then

U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
( 0  A3 )     ( x  x  )
and
V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
( 0  B3 )     ( x  x  )

or if ( .NOT.UPPER ) then

U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
( A2 A3 )     ( 0  x  )
and
V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
( B2 B3 )     ( 0  x  )
where

U = (   CSU    SNU ), V = (  CSV    SNV ),
( -SNU**H  CSU )      ( -SNV**H CSV )

Q = (   CSQ    SNQ )
( -SNQ**H  CSQ )

The rows of the transformed A and B are parallel. Moreover, if the
input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
of A is not zero. If the input matrices A and B are both not zero,
then the transformed (2,2) element of B is not zero, except when the
first rows of input A and B are parallel and the second rows are
zero.```
Parameters

UPPER

```          UPPER is LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.```

A1

`          A1 is REAL`

A2

`          A2 is COMPLEX`

A3

```          A3 is REAL
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.```

B1

`          B1 is REAL`

B2

`          B2 is COMPLEX`

B3

```          B3 is REAL
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.```

CSU

`          CSU is REAL`

SNU

```          SNU is COMPLEX
The desired unitary matrix U.```

CSV

`          CSV is REAL`

SNV

```          SNV is COMPLEX
The desired unitary matrix V.```

CSQ

`          CSQ is REAL`

SNQ

```          SNQ is COMPLEX
The desired unitary matrix Q.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 156 of file clags2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clags2(3) is an alias of clags2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK