# clags2.f(3) [centos man page]

```clags2.f(3)							      LAPACK							       clags2.f(3)

NAME
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 (logicalUPPER, realA1, complexA2, realA3, realB1, complexB2, realB3, realCSU, complexSNU, realCSV, complexSNV, realCSQ,
complexSNQ)
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.

Date:
November 2011

Definition at line 158 of file clags2.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       clags2.f(3)```

## Check Out this Related Man Page

```CLAGS2(l)								 )								 CLAGS2(l)

NAME
CLAGS2  -  compute  2-by-2 unitary matrices U, V and Q, such that if ( UPPER ) then  U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and
V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then  U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3	)  (  0  x  )  and
V'*B*Q = V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where  U = ( CSU SNU ), V = ( CSV SNV ),

SYNOPSIS
SUBROUTINE CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU, CSV, SNV, CSQ, SNQ )

LOGICAL	  UPPER

REAL 	  A1, A3, B1, B3, CSQ, CSU, CSV

COMPLEX	  A2, B2, SNQ, SNU, SNV

PURPOSE
CLAGS2  computes  2-by-2  unitary  matrices  U, V and Q, such that if ( UPPER ) then U'*A*Q = U'*( A1 A2 )*Q = ( x 0 ) ( 0 A3 ) ( x x ) and
V'*B*Q = V'*( B1 B2 )*Q = ( x 0 ) ( 0 B3 ) ( x x ) or if ( .NOT.UPPER ) then U'*A*Q = U'*( A1 0 )*Q = ( x x ) ( A2 A3 ) ( 0 x ) and  V'*B*Q
= V'*( B1 0 )*Q = ( x x ) ( B2 B3 ) ( 0 x ) where U = ( CSU SNU ), V = ( CSV SNV ),	 ( -CONJG(SNU)	CSU )	   ( -CONJG(SNV) CSV )

Q = (	   CSQ	    SNQ )
( -CONJG(SNQ)  CSQ )

Z' denotes the conjugate transpose of Z.

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.

ARGUMENTS
UPPER   (input) LOGICAL
= .TRUE.: the input matrices A and B are upper triangular.
= .FALSE.: the input matrices A and B are lower triangular.

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

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

CSU     (output) REAL
SNU     (output) COMPLEX The desired unitary matrix U.

CSV     (output) REAL
SNV     (output) COMPLEX The desired unitary matrix V.

CSQ     (output) REAL
SNQ     (output) COMPLEX The desired unitary matrix Q.

LAPACK version 3.0						   15 June 2000 							 CLAGS2(l)```
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