NAME

zlags2 - 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 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.

SunSoft, Inc.  —  Last change: 27 Jun 1995