zlaqr3 (l) - Linux Manuals

NAME

SYNOPSIS

SUBROUTINE ZLAQR3(

WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK )

    

INTEGER IHIZ, ILOZ, KBOT, KTOP, LDH, LDT, LDV, LDWV, LDZ, LWORK, N, ND, NH, NS, NV, NW

    

LOGICAL WANTT, WANTZ

    

COMPLEX*16 H( LDH, * ), SH( * ), T( LDT, * ), V( LDV, * ), WORK( * ), WV( LDWV, * ), Z( LDZ, * )

    

COMPLEX*16 ZERO, ONE

    

PARAMETER ( ZERO = ( 0.0d0, 0.0d0 ), ONE = ( 1.0d0, 0.0d0 ) )

    

DOUBLE PRECISION RZERO, RONE

    

PARAMETER ( RZERO = 0.0d0, RONE = 1.0d0 )

    

COMPLEX*16 BETA, CDUM, S, TAU

    

DOUBLE PRECISION FOO, SAFMAX, SAFMIN, SMLNUM, ULP

    

INTEGER I, IFST, ILST, INFO, INFQR, J, JW, KCOL, KLN, KNT, KROW, KWTOP, LTOP, LWK1, LWK2, LWK3, LWKOPT, NMIN

    

DOUBLE PRECISION DLAMCH

    

INTEGER ILAENV

    

EXTERNAL DLAMCH, ILAENV

    

EXTERNAL DLABAD, ZCOPY, ZGEHRD, ZGEMM, ZLACPY, ZLAHQR, ZLAQR4, ZLARF, ZLARFG, ZLASET, ZTREXC, ZUNMHR

    

INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, MAX, MIN

    

DOUBLE PRECISION CABS1

    

CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )

    

JW = MIN( NW, KBOT-KTOP+1 )

    

IF( JW.LE.2 ) THEN

    

LWKOPT = 1

    

ELSE

    

CALL ZGEHRD( JW, 1, JW-1, T, LDT, WORK, WORK, -1, INFO )

    

LWK1 = INT( WORK( 1 ) )

    

CALL ZUNMHR( aqRaq, aqNaq, JW, JW, 1, JW-1, T, LDT, WORK, V, LDV, WORK, -1, INFO )

    

LWK2 = INT( WORK( 1 ) )

    

CALL ZLAQR4( .true., .true., JW, 1, JW, T, LDT, SH, 1, JW, V, LDV, WORK, -1, INFQR )

    

LWK3 = INT( WORK( 1 ) )

    

LWKOPT = MAX( JW+MAX( LWK1, LWK2 ), LWK3 )

    

END IF

    

IF( LWORK.EQ.-1 ) THEN

    

WORK( 1 ) = DCMPLX( LWKOPT, 0 )

    

RETURN

    

END IF

    

NS = 0

    

ND = 0

    

WORK( 1 ) = ONE

    

IF( KTOP.GT.KBOT ) RETURN

    

IF( NW.LT.1 ) RETURN

    

SAFMIN = DLAMCH( aqSAFE MINIMUMaq )

    

SAFMAX = RONE / SAFMIN

    

CALL DLABAD( SAFMIN, SAFMAX )

    

ULP = DLAMCH( aqPRECISIONaq )

    

SMLNUM = SAFMIN*( DBLE( N ) / ULP )

    

JW = MIN( NW, KBOT-KTOP+1 )

    

KWTOP = KBOT - JW + 1

    

IF( KWTOP.EQ.KTOP ) THEN

    

S = ZERO

    

ELSE

    

S = H( KWTOP, KWTOP-1 )

    

END IF

    

IF( KBOT.EQ.KWTOP ) THEN

    

SH( KWTOP ) = H( KWTOP, KWTOP )

    

NS = 1

    

ND = 0

    

IF( CABS1( S ).LE.MAX( SMLNUM, ULP*CABS1( H( KWTOP, KWTOP ) ) ) ) THEN

    

NS = 0

    

ND = 1

    

IF( KWTOP.GT.KTOP ) H( KWTOP, KWTOP-1 ) = ZERO

    

END IF

    

WORK( 1 ) = ONE

    

RETURN

    

END IF

    

CALL ZLACPY( aqUaq, JW, JW, H( KWTOP, KWTOP ), LDH, T, LDT )

    

CALL ZCOPY( JW-1, H( KWTOP+1, KWTOP ), LDH+1, T( 2, 1 ), LDT+1 )

    

CALL ZLASET( aqAaq, JW, JW, ZERO, ONE, V, LDV )

    

NMIN = ILAENV( 12, aqZLAQR3aq, aqSVaq, JW, 1, JW, LWORK )

    

IF( JW.GT.NMIN ) THEN

    

CALL ZLAQR4( .true., .true., JW, 1, JW, T, LDT, SH( KWTOP ), 1, JW, V, LDV, WORK, LWORK, INFQR )

    

ELSE

    

CALL ZLAHQR( .true., .true., JW, 1, JW, T, LDT, SH( KWTOP ), 1, JW, V, LDV, INFQR )

    

END IF

    

NS = JW

    

ILST = INFQR + 1

    

DO 10 KNT = INFQR + 1, JW

    

FOO = CABS1( T( NS, NS ) )

    

IF( FOO.EQ.RZERO ) FOO = CABS1( S )

    

IF( CABS1( S )*CABS1( V( 1, NS ) ).LE.MAX( SMLNUM, ULP*FOO ) ) THEN

    

NS = NS - 1

    

ELSE

    

IFST = NS

    

CALL ZTREXC( aqVaq, JW, T, LDT, V, LDV, IFST, ILST, INFO )

    

ILST = ILST + 1

    

END IF

    

10 CONTINUE

    

IF( NS.EQ.0 ) S = ZERO

    

IF( NS.LT.JW ) THEN

    

DO 30 I = INFQR + 1, NS

    

IFST = I

    

DO 20 J = I + 1, NS

    

IF( CABS1( T( J, J ) ).GT.CABS1( T( IFST, IFST ) ) ) IFST = J

    

20 CONTINUE

    

ILST = I

    

IF( IFST.NE.ILST ) CALL ZTREXC( aqVaq, JW, T, LDT, V, LDV, IFST, ILST, INFO )

    

30 CONTINUE

    

END IF

    

DO 40 I = INFQR + 1, JW

    

SH( KWTOP+I-1 ) = T( I, I )

    

40 CONTINUE

    

IF( NS.LT.JW .OR. S.EQ.ZERO ) THEN

    

IF( NS.GT.1 .AND. S.NE.ZERO ) THEN

    

CALL ZCOPY( NS, V, LDV, WORK, 1 )

    

DO 50 I = 1, NS

    

WORK( I ) = DCONJG( WORK( I ) )

    

50 CONTINUE

    

BETA = WORK( 1 )

    

CALL ZLARFG( NS, BETA, WORK( 2 ), 1, TAU )

    

WORK( 1 ) = ONE

    

CALL ZLASET( aqLaq, JW-2, JW-2, ZERO, ZERO, T( 3, 1 ), LDT )

    

CALL ZLARF( aqLaq, NS, JW, WORK, 1, DCONJG( TAU ), T, LDT, WORK( JW+1 ) )

    

CALL ZLARF( aqRaq, NS, NS, WORK, 1, TAU, T, LDT, WORK( JW+1 ) )

    

CALL ZLARF( aqRaq, JW, NS, WORK, 1, TAU, V, LDV, WORK( JW+1 ) )

    

CALL ZGEHRD( JW, 1, NS, T, LDT, WORK, WORK( JW+1 ), LWORK-JW, INFO )

    

END IF

    

IF( KWTOP.GT.1 ) H( KWTOP, KWTOP-1 ) = S*DCONJG( V( 1, 1 ) )

    

CALL ZLACPY( aqUaq, JW, JW, T, LDT, H( KWTOP, KWTOP ), LDH )

    

CALL ZCOPY( JW-1, T( 2, 1 ), LDT+1, H( KWTOP+1, KWTOP ), LDH+1 )

    

IF( NS.GT.1 .AND. S.NE.ZERO ) CALL ZUNMHR( aqRaq, aqNaq, JW, NS, 1, NS, T, LDT, WORK, V, LDV, WORK( JW+1 ), LWORK-JW, INFO )

    

IF( WANTT ) THEN

    

LTOP = 1

    

ELSE

    

LTOP = KTOP

    

END IF

    

DO 60 KROW = LTOP, KWTOP - 1, NV

    

KLN = MIN( NV, KWTOP-KROW )

    

CALL ZGEMM( aqNaq, aqNaq, KLN, JW, JW, ONE, H( KROW, KWTOP ), LDH, V, LDV, ZERO, WV, LDWV )

    

CALL ZLACPY( aqAaq, KLN, JW, WV, LDWV, H( KROW, KWTOP ), LDH )

    

60 CONTINUE

    

IF( WANTT ) THEN

    

DO 70 KCOL = KBOT + 1, N, NH

    

KLN = MIN( NH, N-KCOL+1 )

    

CALL ZGEMM( aqCaq, aqNaq, JW, KLN, JW, ONE, V, LDV, H( KWTOP, KCOL ), LDH, ZERO, T, LDT )

    

CALL ZLACPY( aqAaq, JW, KLN, T, LDT, H( KWTOP, KCOL ), LDH )

    

70 CONTINUE

    

END IF

    

IF( WANTZ ) THEN

    

DO 80 KROW = ILOZ, IHIZ, NV

    

KLN = MIN( NV, IHIZ-KROW+1 )

    

CALL ZGEMM( aqNaq, aqNaq, KLN, JW, JW, ONE, Z( KROW, KWTOP ), LDZ, V, LDV, ZERO, WV, LDWV )

    

CALL ZLACPY( aqAaq, KLN, JW, WV, LDWV, Z( KROW, KWTOP ), LDZ )

    

80 CONTINUE

    

END IF

    

END IF

    

ND = JW - NS

    

NS = NS - INFQR

    

WORK( 1 ) = DCMPLX( LWKOPT, 0 )

    

END

PURPOSE