Homepage > Man Pages > Category > Subroutines
Homepage > Man Pages > Name > L

# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: 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

```NAME
LAPACK-3  - 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 ),

SYNOPSIS
SUBROUTINE ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,  CSV,  SNV,
CSQ, SNQ )

LOGICAL        UPPER

DOUBLE         PRECISION A1, A3, B1, B3, CSQ, CSU, CSV

COMPLEX*16     A2, B2, SNQ, SNU, SNV

PURPOSE
ZLAGS2  computes  2-by-2  unitary  matrices  U, V and Q, such that if (
UPPER ) then
( -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) DOUBLE PRECISION
A2      (input) COMPLEX*16
A3      (input) DOUBLE PRECISION
On entry, A1, A2 and A3 are elements of the input 2-by-2
upper (lower) triangular matrix A.

B1      (input) DOUBLE PRECISION
B2      (input) COMPLEX*16
B3      (input) DOUBLE PRECISION
On entry, B1, B2 and B3 are elements of the input 2-by-2
upper (lower) triangular matrix B.

CSU     (output) DOUBLE PRECISION
SNU     (output) COMPLEX*16
The desired unitary matrix U.

CSV     (output) DOUBLE PRECISION
SNV     (output) COMPLEX*16
The desired unitary matrix V.

CSQ     (output) DOUBLE PRECISION
SNQ     (output) COMPLEX*16
The desired unitary matrix Q.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```