SUBROUTINE SLAQTR( LTRAN, LREAL, N, T, LDT, B, W, SCALE, X, WORK,
$ INFO )
LOGICAL LREAL, LTRAN
INTEGER INFO, LDT, N
REAL SCALE, W
REAL B( * ), T( LDT, * ), WORK( * ), X( * )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
LOGICAL NOTRAN
INTEGER I, IERR, J, J1, J2, JNEXT, K, N1, N2
REAL BIGNUM, EPS, REC, SCALOC, SI, SMIN, SMINW,
$ SMLNUM, SR, TJJ, TMP, XJ, XMAX, XNORM, Z
REAL D( 2, 2 ), V( 2, 2 )
INTEGER ISAMAX
REAL SASUM, SDOT, SLAMCH, SLANGE
EXTERNAL ISAMAX, SASUM, SDOT, SLAMCH, SLANGE
EXTERNAL SAXPY, SLADIV, SLALN2, SSCAL
INTRINSIC ABS, MAX
NOTRAN = .NOT.LTRAN
INFO = 0
IF( N.EQ.0 )
$ RETURN
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
XNORM = SLANGE( 'M', N, N, T, LDT, D )
IF( .NOT.LREAL )
$ XNORM = MAX( XNORM, ABS( W ), SLANGE( 'M', N, 1, B, N, D ) )
SMIN = MAX( SMLNUM, EPS*XNORM )
WORK( 1 ) = ZERO
DO 10 J = 2, N
WORK( J ) = SASUM( J-1, T( 1, J ), 1 )
10 CONTINUE
IF( .NOT.LREAL ) THEN
DO 20 I = 2, N
WORK( I ) = WORK( I ) + ABS( B( I ) )
20 CONTINUE
END IF
N2 = 2*N
N1 = N
IF( .NOT.LREAL )
$ N1 = N2
K = ISAMAX( N1, X, 1 )
XMAX = ABS( X( K ) )
SCALE = ONE
IF( XMAX.GT.BIGNUM ) THEN
SCALE = BIGNUM / XMAX
CALL SSCAL( N1, SCALE, X, 1 )
XMAX = BIGNUM
END IF
IF( LREAL ) THEN
IF( NOTRAN ) THEN
JNEXT = N
DO 30 J = N, 1, -1
IF( J.GT.JNEXT )
$ GO TO 30
J1 = J
J2 = J
JNEXT = J - 1
IF( J.GT.1 ) THEN
IF( T( J, J-1 ).NE.ZERO ) THEN
J1 = J - 1
JNEXT = J - 2
END IF
END IF
IF( J1.EQ.J2 ) THEN
XJ = ABS( X( J1 ) )
TJJ = ABS( T( J1, J1 ) )
TMP = T( J1, J1 )
IF( TJJ.LT.SMIN ) THEN
TMP = SMIN
TJJ = SMIN
INFO = 1
END IF
IF( XJ.EQ.ZERO )
$ GO TO 30
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.BIGNUM*TJJ ) THEN
REC = ONE / XJ
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J1 ) = X( J1 ) / TMP
XJ = ABS( X( J1 ) )
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( WORK( J1 ).GT.( BIGNUM-XMAX )*REC ) THEN
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
END IF
END IF
IF( J1.GT.1 ) THEN
CALL SAXPY( J1-1, -X( J1 ), T( 1, J1 ), 1, X, 1 )
K = ISAMAX( J1-1, X, 1 )
XMAX = ABS( X( K ) )
END IF
ELSE
D( 1, 1 ) = X( J1 )
D( 2, 1 ) = X( J2 )
CALL SLALN2( .FALSE., 2, 1, SMIN, ONE, T( J1, J1 ),
$ LDT, ONE, ONE, D, 2, ZERO, ZERO, V, 2,
$ SCALOC, XNORM, IERR )
IF( IERR.NE.0 )
$ INFO = 2
IF( SCALOC.NE.ONE ) THEN
CALL SSCAL( N, SCALOC, X, 1 )
SCALE = SCALE*SCALOC
END IF
X( J1 ) = V( 1, 1 )
X( J2 ) = V( 2, 1 )
XJ = MAX( ABS( V( 1, 1 ) ), ABS( V( 2, 1 ) ) )
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( MAX( WORK( J1 ), WORK( J2 ) ).GT.
$ ( BIGNUM-XMAX )*REC ) THEN
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
END IF
END IF
IF( J1.GT.1 ) THEN
CALL SAXPY( J1-1, -X( J1 ), T( 1, J1 ), 1, X, 1 )
CALL SAXPY( J1-1, -X( J2 ), T( 1, J2 ), 1, X, 1 )
K = ISAMAX( J1-1, X, 1 )
XMAX = ABS( X( K ) )
END IF
END IF
30 CONTINUE
ELSE
JNEXT = 1
DO 40 J = 1, N
IF( J.LT.JNEXT )
$ GO TO 40
J1 = J
J2 = J
JNEXT = J + 1
IF( J.LT.N ) THEN
IF( T( J+1, J ).NE.ZERO ) THEN
J2 = J + 1
JNEXT = J + 2
END IF
END IF
IF( J1.EQ.J2 ) THEN
XJ = ABS( X( J1 ) )
IF( XMAX.GT.ONE ) THEN
REC = ONE / XMAX
IF( WORK( J1 ).GT.( BIGNUM-XJ )*REC ) THEN
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J1 ) = X( J1 ) - SDOT( J1-1, T( 1, J1 ), 1, X, 1 )
XJ = ABS( X( J1 ) )
TJJ = ABS( T( J1, J1 ) )
TMP = T( J1, J1 )
IF( TJJ.LT.SMIN ) THEN
TMP = SMIN
TJJ = SMIN
INFO = 1
END IF
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.BIGNUM*TJJ ) THEN
REC = ONE / XJ
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J1 ) = X( J1 ) / TMP
XMAX = MAX( XMAX, ABS( X( J1 ) ) )
ELSE
XJ = MAX( ABS( X( J1 ) ), ABS( X( J2 ) ) )
IF( XMAX.GT.ONE ) THEN
REC = ONE / XMAX
IF( MAX( WORK( J2 ), WORK( J1 ) ).GT.( BIGNUM-XJ )*
$ REC ) THEN
CALL SSCAL( N, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
D( 1, 1 ) = X( J1 ) - SDOT( J1-1, T( 1, J1 ), 1, X,
$ 1 )
D( 2, 1 ) = X( J2 ) - SDOT( J1-1, T( 1, J2 ), 1, X,
$ 1 )
CALL SLALN2( .TRUE., 2, 1, SMIN, ONE, T( J1, J1 ),
$ LDT, ONE, ONE, D, 2, ZERO, ZERO, V, 2,
$ SCALOC, XNORM, IERR )
IF( IERR.NE.0 )
$ INFO = 2
IF( SCALOC.NE.ONE ) THEN
CALL SSCAL( N, SCALOC, X, 1 )
SCALE = SCALE*SCALOC
END IF
X( J1 ) = V( 1, 1 )
X( J2 ) = V( 2, 1 )
XMAX = MAX( ABS( X( J1 ) ), ABS( X( J2 ) ), XMAX )
END IF
40 CONTINUE
END IF
ELSE
SMINW = MAX( EPS*ABS( W ), SMIN )
IF( NOTRAN ) THEN
JNEXT = N
DO 70 J = N, 1, -1
IF( J.GT.JNEXT )
$ GO TO 70
J1 = J
J2 = J
JNEXT = J - 1
IF( J.GT.1 ) THEN
IF( T( J, J-1 ).NE.ZERO ) THEN
J1 = J - 1
JNEXT = J - 2
END IF
END IF
IF( J1.EQ.J2 ) THEN
Z = W
IF( J1.EQ.1 )
$ Z = B( 1 )
XJ = ABS( X( J1 ) ) + ABS( X( N+J1 ) )
TJJ = ABS( T( J1, J1 ) ) + ABS( Z )
TMP = T( J1, J1 )
IF( TJJ.LT.SMINW ) THEN
TMP = SMINW
TJJ = SMINW
INFO = 1
END IF
IF( XJ.EQ.ZERO )
$ GO TO 70
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.BIGNUM*TJJ ) THEN
REC = ONE / XJ
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
CALL SLADIV( X( J1 ), X( N+J1 ), TMP, Z, SR, SI )
X( J1 ) = SR
X( N+J1 ) = SI
XJ = ABS( X( J1 ) ) + ABS( X( N+J1 ) )
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( WORK( J1 ).GT.( BIGNUM-XMAX )*REC ) THEN
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
END IF
END IF
IF( J1.GT.1 ) THEN
CALL SAXPY( J1-1, -X( J1 ), T( 1, J1 ), 1, X, 1 )
CALL SAXPY( J1-1, -X( N+J1 ), T( 1, J1 ), 1,
$ X( N+1 ), 1 )
X( 1 ) = X( 1 ) + B( J1 )*X( N+J1 )
X( N+1 ) = X( N+1 ) - B( J1 )*X( J1 )
XMAX = ZERO
DO 50 K = 1, J1 - 1
XMAX = MAX( XMAX, ABS( X( K ) )+
$ ABS( X( K+N ) ) )
50 CONTINUE
END IF
ELSE
D( 1, 1 ) = X( J1 )
D( 2, 1 ) = X( J2 )
D( 1, 2 ) = X( N+J1 )
D( 2, 2 ) = X( N+J2 )
CALL SLALN2( .FALSE., 2, 2, SMINW, ONE, T( J1, J1 ),
$ LDT, ONE, ONE, D, 2, ZERO, -W, V, 2,
$ SCALOC, XNORM, IERR )
IF( IERR.NE.0 )
$ INFO = 2
IF( SCALOC.NE.ONE ) THEN
CALL SSCAL( 2*N, SCALOC, X, 1 )
SCALE = SCALOC*SCALE
END IF
X( J1 ) = V( 1, 1 )
X( J2 ) = V( 2, 1 )
X( N+J1 ) = V( 1, 2 )
X( N+J2 ) = V( 2, 2 )
XJ = MAX( ABS( V( 1, 1 ) )+ABS( V( 1, 2 ) ),
$ ABS( V( 2, 1 ) )+ABS( V( 2, 2 ) ) )
IF( XJ.GT.ONE ) THEN
REC = ONE / XJ
IF( MAX( WORK( J1 ), WORK( J2 ) ).GT.
$ ( BIGNUM-XMAX )*REC ) THEN
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
END IF
END IF
IF( J1.GT.1 ) THEN
CALL SAXPY( J1-1, -X( J1 ), T( 1, J1 ), 1, X, 1 )
CALL SAXPY( J1-1, -X( J2 ), T( 1, J2 ), 1, X, 1 )
CALL SAXPY( J1-1, -X( N+J1 ), T( 1, J1 ), 1,
$ X( N+1 ), 1 )
CALL SAXPY( J1-1, -X( N+J2 ), T( 1, J2 ), 1,
$ X( N+1 ), 1 )
X( 1 ) = X( 1 ) + B( J1 )*X( N+J1 ) +
$ B( J2 )*X( N+J2 )
X( N+1 ) = X( N+1 ) - B( J1 )*X( J1 ) -
$ B( J2 )*X( J2 )
XMAX = ZERO
DO 60 K = 1, J1 - 1
XMAX = MAX( ABS( X( K ) )+ABS( X( K+N ) ),
$ XMAX )
60 CONTINUE
END IF
END IF
70 CONTINUE
ELSE
JNEXT = 1
DO 80 J = 1, N
IF( J.LT.JNEXT )
$ GO TO 80
J1 = J
J2 = J
JNEXT = J + 1
IF( J.LT.N ) THEN
IF( T( J+1, J ).NE.ZERO ) THEN
J2 = J + 1
JNEXT = J + 2
END IF
END IF
IF( J1.EQ.J2 ) THEN
XJ = ABS( X( J1 ) ) + ABS( X( J1+N ) )
IF( XMAX.GT.ONE ) THEN
REC = ONE / XMAX
IF( WORK( J1 ).GT.( BIGNUM-XJ )*REC ) THEN
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
X( J1 ) = X( J1 ) - SDOT( J1-1, T( 1, J1 ), 1, X, 1 )
X( N+J1 ) = X( N+J1 ) - SDOT( J1-1, T( 1, J1 ), 1,
$ X( N+1 ), 1 )
IF( J1.GT.1 ) THEN
X( J1 ) = X( J1 ) - B( J1 )*X( N+1 )
X( N+J1 ) = X( N+J1 ) + B( J1 )*X( 1 )
END IF
XJ = ABS( X( J1 ) ) + ABS( X( J1+N ) )
Z = W
IF( J1.EQ.1 )
$ Z = B( 1 )
TJJ = ABS( T( J1, J1 ) ) + ABS( Z )
TMP = T( J1, J1 )
IF( TJJ.LT.SMINW ) THEN
TMP = SMINW
TJJ = SMINW
INFO = 1
END IF
IF( TJJ.LT.ONE ) THEN
IF( XJ.GT.BIGNUM*TJJ ) THEN
REC = ONE / XJ
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
CALL SLADIV( X( J1 ), X( N+J1 ), TMP, -Z, SR, SI )
X( J1 ) = SR
X( J1+N ) = SI
XMAX = MAX( ABS( X( J1 ) )+ABS( X( J1+N ) ), XMAX )
ELSE
XJ = MAX( ABS( X( J1 ) )+ABS( X( N+J1 ) ),
$ ABS( X( J2 ) )+ABS( X( N+J2 ) ) )
IF( XMAX.GT.ONE ) THEN
REC = ONE / XMAX
IF( MAX( WORK( J1 ), WORK( J2 ) ).GT.
$ ( BIGNUM-XJ ) / XMAX ) THEN
CALL SSCAL( N2, REC, X, 1 )
SCALE = SCALE*REC
XMAX = XMAX*REC
END IF
END IF
D( 1, 1 ) = X( J1 ) - SDOT( J1-1, T( 1, J1 ), 1, X,
$ 1 )
D( 2, 1 ) = X( J2 ) - SDOT( J1-1, T( 1, J2 ), 1, X,
$ 1 )
D( 1, 2 ) = X( N+J1 ) - SDOT( J1-1, T( 1, J1 ), 1,
$ X( N+1 ), 1 )
D( 2, 2 ) = X( N+J2 ) - SDOT( J1-1, T( 1, J2 ), 1,
$ X( N+1 ), 1 )
D( 1, 1 ) = D( 1, 1 ) - B( J1 )*X( N+1 )
D( 2, 1 ) = D( 2, 1 ) - B( J2 )*X( N+1 )
D( 1, 2 ) = D( 1, 2 ) + B( J1 )*X( 1 )
D( 2, 2 ) = D( 2, 2 ) + B( J2 )*X( 1 )
CALL SLALN2( .TRUE., 2, 2, SMINW, ONE, T( J1, J1 ),
$ LDT, ONE, ONE, D, 2, ZERO, W, V, 2,
$ SCALOC, XNORM, IERR )
IF( IERR.NE.0 )
$ INFO = 2
IF( SCALOC.NE.ONE ) THEN
CALL SSCAL( N2, SCALOC, X, 1 )
SCALE = SCALOC*SCALE
END IF
X( J1 ) = V( 1, 1 )
X( J2 ) = V( 2, 1 )
X( N+J1 ) = V( 1, 2 )
X( N+J2 ) = V( 2, 2 )
XMAX = MAX( ABS( X( J1 ) )+ABS( X( N+J1 ) ),
$ ABS( X( J2 ) )+ABS( X( N+J2 ) ), XMAX )
END IF
80 CONTINUE
END IF
END IF
RETURN
END