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Shell Programming and Scripting
sed replace values of column with ordered numbering
Post 302529913 by ygemici on Saturday 11th of June 2011 06:59:03 AM
06-11-2011
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LEARN ABOUT REDHAT
zlags2
ZLAGS2(l) ) ZLAGS2(l) 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 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) 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 version 3.0 15 June 2000 ZLAGS2(l)