# 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) CLAGS2Function/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 Univ. of Colorado Denver NAG Ltd. Date: November 2011 Definition at line 158 of file clags2.f.AuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 clags2.f(3)

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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, SNVPURPOSE

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 3.015 June 2000 CLAGS2(l)