Routine ZLANV2() Documented By Universal Report

Routine: ZLANV2()

# lines:	145
# code:	145
# comment:	0
# blank:	0
# Variables:	23
# Callers:	2
# Callings:	0
# Words:	68
# Keywords:	36

..
  Purpose
  =======
  ZLANV2 computes the Schur factorization of a complex 2-by-2
  nonhermitian matrix in standard form:
       [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
       [ C  D ]   [ SN  CS ] [  0  DD ] [-SN  CS ]
  Arguments
  =========
  A       (input/output) COMPLEX*16
  B       (input/output) COMPLEX*16
  C       (input/output) COMPLEX*16
  D       (input/output) COMPLEX*16
          On entry, the elements of the input matrix.
          On exit, they are overwritten by the elements of the
          standardised Schur form.
  RT1     (output) COMPLEX*16
  RT2     (output) COMPLEX*16
          The two eigenvalues.
  CS      (output) DOUBLE PRECISION
  SN      (output) COMPLEX*16
          Parameters of the rotation matrix.
  Further Details
  ===============
  Implemented by Mark R. Fahey, May 28, 1999
  =====================================================================
     .. Parameters ..

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001        SUBROUTINE ZLANV2( A , B , C , D , RT1 , RT2 , CS , SN )
002  
003  *     -- ScaLAPACK routine(version 1.7) --
004  *     Univ. of Tennessee , Univ. of California Berkeley , NAG Ltd. ,
005  *     Courant Institute , Argonne National Lab , and Rice University
006  *     May 28 , 1999
007  
008  *     .. Scalar Arguments ..
009        DOUBLE PRECISION CS
010        COMPLEX*16 A , B , C , D , RT1 , RT2 , SN
011        DOUBLE PRECISION RZERO , HALF , RONE
012        PARAMETER( RZERO = 0.0D + 0 , HALF = 0.5D + 0 ,
013       $RONE = 1.0D + 0 )
014        COMPLEX*16 ZERO , ONE
015        PARAMETER( ZERO =( 0.0D + 0 , 0.0D + 0 ) ,
016       $ONE =( 1.0D + 0 , 0.0D + 0 ) )
017  *     ..
018  *     .. Local Scalars ..
019        COMPLEX*16 AA , BB , DD , T , TEMP , TEMP2 , U , X , Y
020  *     ..
021  *     .. External Functions ..
022        COMPLEX*16 ZLADIV
023        EXTERNAL ZLADIV
024  *     ..
025  *     .. External Subroutines ..
026        EXTERNAL ZLARTG
027  *     ..
028  *     .. Intrinsic Functions ..
029        INTRINSIC DBLE , DCMPLX , DCONJG , DIMAG , SQRT
030  *     ..
031  *     .. Executable Statements ..
032  
033  *     Initialize CS and SN
034  
035        CS = RONE
036        SN = ZERO
037  
038        IF( C.EQ.ZERO ) THEN
038               
039            GO TO 10
040  
041        ELSE IF( B.EQ.ZERO ) THEN
042  
043  *         Swap rows and columns
044  
044               
045            CS = RZERO
046            SN = ONE
047            TEMP = D
048            D = A
049            A = TEMP
050            B = - C
051            C = ZERO
052            GO TO 10
053        ELSE IF(( A - D ).EQ.ZERO ) THEN
053               
054            TEMP = SQRT( B*C )
055            A = A + TEMP
056            D = D - TEMP
057            IF(( B + C ).EQ.ZERO ) THEN
057                   
058                CS = SQRT( HALF )
059                SN = DCMPLX( RZERO , RONE )*CS
060            ELSE
060                   
061                TEMP = SQRT( B + C )
062                TEMP2 = ZLADIV( SQRT( B ) , TEMP )
063                CS = DBLE( TEMP2 )
064                SN = ZLADIV( SQRT( C ) , TEMP )
065            END IF
066            B = B - C
067            C = ZERO
068            GO TO 10
069        ELSE
070  
071  *         Compute eigenvalue closest to D
072  
072               
073            T = D
074            U = B*C
075            X = HALF*( A - T )
076            Y = SQRT( X*X + U )
077            IF( DBLE( X )*DBLE( Y ) + DIMAG( X )*DIMAG( Y ).LT.RZERO )
077                   
078       $        Y = - Y
079                T = T - ZLADIV( U ,( X + Y ) )
080  
081  *             Do one QR step with exact shift T - resulting 2 x 2 in
082  *             triangular form.
083  
084                CALL ZLARTG( A - T , C , CS , SN , AA )
085  
086                D = D - T
087                BB = CS*B + SN*D
088                DD = - DCONJG( SN )*B + CS*D
089  
090                A = AA*CS + BB*DCONJG( SN ) + T
091                B = - AA*SN + BB*CS
092                C = ZERO
093                D = T
094  
095            END IF
096  
097     10 CONTINUE
098  
099  *     Store eigenvalues in RT1 and RT2.
100  
101        RT1 = A
102        RT2 = D
103        RETURN
104  
105  *     End of ZLANV2
106  
107        END2220

Variables in Routine ZLANV2()

Summary Report
Data Type	Quantity	Size(byte)
*COMPLEX16**	19	?
DOUBLE PRECISION	4	16
TOTAL	23	16

List of Variables

COMPLEX*16

A AA B BB C
D DD ONE RT1 RT2
SN T TEMP TEMP2 U
X Y ZERO ZLADIV

DOUBLE PRECISION

CS HALF RONE RZERO

Variables Dependence Graph
Put the mouse over a right hand side variable to display the corresponding line of the dependence
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A <--- AA = A + TEMP, SNA = AA*CS + BB*DCONJG( SN ) + T, TA = AA*CS + BB*DCONJG( SN ) + T, TEMPA = TEMP{2A = A + TEMP}, AAA = AA*CS + BB*DCONJG( SN ) + T, BBA = AA*CS + BB*DCONJG( SN ) + T, CSA = AA*CS + BB*DCONJG( SN ) + T

B <--- SNB = -AA*SN + BB*CS, AAB = -AA*SN + BB*CS, BB = B - C, BBB = -AA*SN + BB*CS, CB = -C{2B = B - C}, CSB = -AA*SN + BB*CS

BB <--- SNBB = CS*B + SN*D, BBB = CS*B + SN*D, CSBB = CS*B + SN*D, DBB = CS*B + SN*D

C <--- ZEROC = ZERO{2C = ZERO, 3C = ZERO}

CS <--- RONECS = RONE, RZEROCS = RZERO, TEMP2CS = DBLE( TEMP2 ), HALFCS = SQRT( HALF )

D <--- AD = A, TD = D - T{2D = T}, TEMPD = D - TEMP, DD = D - TEMP{2D = D - T}

DD <--- SNDD = -DCONJG( SN )*B + CS*D, BDD = -DCONJG( SN )*B + CS*D, CSDD = -DCONJG( SN )*B + CS*D, DDD = -DCONJG( SN )*B + CS*D

RT1 <--- ART1 = A

RT2 <--- DRT2 = D

SN <--- ONESN = ONE, RONESN = DCMPLX( RZERO, RONE )*CS, RZEROSN = DCMPLX( RZERO, RONE )*CS, TEMPSN = ZLADIV( SQRT( C ), TEMP ), ZEROSN = ZERO, ZLADIVSN = ZLADIV( SQRT( C ), TEMP ), CSN = ZLADIV( SQRT( C ), TEMP ), CSSN = DCMPLX( RZERO, RONE )*CS

T <--- TT = T - ZLADIV( U, ( X+Y ) ), UT = T - ZLADIV( U, ( X+Y ) ), XT = T - ZLADIV( U, ( X+Y ) ), YT = T - ZLADIV( U, ( X+Y ) ), ZLADIVT = T - ZLADIV( U, ( X+Y ) ), DT = D

TEMP <--- BTEMP = SQRT( B*C ){2TEMP = SQRT( B+C )}, CTEMP = SQRT( B*C ){2TEMP = SQRT( B+C )}, DTEMP = D

TEMP2 <--- TEMPTEMP2 = ZLADIV( SQRT( B ), TEMP ), ZLADIVTEMP2 = ZLADIV( SQRT( B ), TEMP ), BTEMP2 = ZLADIV( SQRT( B ), TEMP )

U <--- BU = B*C, CU = B*C

X <--- AX = HALF*( A-T ), TX = HALF*( A-T ), HALFX = HALF*( A-T )

Y <--- UY = SQRT( X*X+U ), XY = SQRT( X*X+U )