SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
CHARACTER UPLO
INTEGER INFO, N
INTEGER IPIV( * )
COMPLEX*16 AP( * ), WORK( * )
DOUBLE PRECISION ONE
COMPLEX*16 CONE, ZERO
PARAMETER ( ONE = 1.0D+0, CONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
LOGICAL UPPER
INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
DOUBLE PRECISION AK, AKP1, D, T
COMPLEX*16 AKKP1, TEMP
LOGICAL LSAME
COMPLEX*16 ZDOTC
EXTERNAL LSAME, ZDOTC
EXTERNAL XERBLA, ZCOPY, ZHPMV, ZSWAP
INTRINSIC ABS, DBLE, DCONJG
INFO = 0
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHPTRI', -INFO )
RETURN
END IF
IF( N.EQ.0 )
$ RETURN
IF( UPPER ) THEN
KP = N*( N+1 ) / 2
DO 10 INFO = N, 1, -1
IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
$ RETURN
KP = KP - INFO
10 CONTINUE
ELSE
KP = 1
DO 20 INFO = 1, N
IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
$ RETURN
KP = KP + N - INFO + 1
20 CONTINUE
END IF
INFO = 0
IF( UPPER ) THEN
K = 1
KC = 1
30 CONTINUE
IF( K.GT.N )
$ GO TO 50
KCNEXT = KC + K
IF( IPIV( K ).GT.0 ) THEN
AP( KC+K-1 ) = ONE / DBLE( AP( KC+K-1 ) )
IF( K.GT.1 ) THEN
CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
$ AP( KC ), 1 )
AP( KC+K-1 ) = AP( KC+K-1 ) -
$ DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
END IF
KSTEP = 1
ELSE
T = ABS( AP( KCNEXT+K-1 ) )
AK = DBLE( AP( KC+K-1 ) ) / T
AKP1 = DBLE( AP( KCNEXT+K ) ) / T
AKKP1 = AP( KCNEXT+K-1 ) / T
D = T*( AK*AKP1-ONE )
AP( KC+K-1 ) = AKP1 / D
AP( KCNEXT+K ) = AK / D
AP( KCNEXT+K-1 ) = -AKKP1 / D
IF( K.GT.1 ) THEN
CALL ZCOPY( K-1, AP( KC ), 1, WORK, 1 )
CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
$ AP( KC ), 1 )
AP( KC+K-1 ) = AP( KC+K-1 ) -
$ DBLE( ZDOTC( K-1, WORK, 1, AP( KC ), 1 ) )
AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
$ ZDOTC( K-1, AP( KC ), 1, AP( KCNEXT ),
$ 1 )
CALL ZCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
CALL ZHPMV( UPLO, K-1, -CONE, AP, WORK, 1, ZERO,
$ AP( KCNEXT ), 1 )
AP( KCNEXT+K ) = AP( KCNEXT+K ) -
$ DBLE( ZDOTC( K-1, WORK, 1, AP( KCNEXT ),
$ 1 ) )
END IF
KSTEP = 2
KCNEXT = KCNEXT + K + 1
END IF
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
KPC = ( KP-1 )*KP / 2 + 1
CALL ZSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
KX = KPC + KP - 1
DO 40 J = KP + 1, K - 1
KX = KX + J - 1
TEMP = DCONJG( AP( KC+J-1 ) )
AP( KC+J-1 ) = DCONJG( AP( KX ) )
AP( KX ) = TEMP
40 CONTINUE
AP( KC+KP-1 ) = DCONJG( AP( KC+KP-1 ) )
TEMP = AP( KC+K-1 )
AP( KC+K-1 ) = AP( KPC+KP-1 )
AP( KPC+KP-1 ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = AP( KC+K+K-1 )
AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
AP( KC+K+KP-1 ) = TEMP
END IF
END IF
K = K + KSTEP
KC = KCNEXT
GO TO 30
50 CONTINUE
ELSE
NPP = N*( N+1 ) / 2
K = N
KC = NPP
60 CONTINUE
IF( K.LT.1 )
$ GO TO 80
KCNEXT = KC - ( N-K+2 )
IF( IPIV( K ).GT.0 ) THEN
AP( KC ) = ONE / DBLE( AP( KC ) )
IF( K.LT.N ) THEN
CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+N-K+1 ), WORK, 1,
$ ZERO, AP( KC+1 ), 1 )
AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
$ AP( KC+1 ), 1 ) )
END IF
KSTEP = 1
ELSE
T = ABS( AP( KCNEXT+1 ) )
AK = DBLE( AP( KCNEXT ) ) / T
AKP1 = DBLE( AP( KC ) ) / T
AKKP1 = AP( KCNEXT+1 ) / T
D = T*( AK*AKP1-ONE )
AP( KCNEXT ) = AKP1 / D
AP( KC ) = AK / D
AP( KCNEXT+1 ) = -AKKP1 / D
IF( K.LT.N ) THEN
CALL ZCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
$ 1, ZERO, AP( KC+1 ), 1 )
AP( KC ) = AP( KC ) - DBLE( ZDOTC( N-K, WORK, 1,
$ AP( KC+1 ), 1 ) )
AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
$ ZDOTC( N-K, AP( KC+1 ), 1,
$ AP( KCNEXT+2 ), 1 )
CALL ZCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
CALL ZHPMV( UPLO, N-K, -CONE, AP( KC+( N-K+1 ) ), WORK,
$ 1, ZERO, AP( KCNEXT+2 ), 1 )
AP( KCNEXT ) = AP( KCNEXT ) -
$ DBLE( ZDOTC( N-K, WORK, 1, AP( KCNEXT+2 ),
$ 1 ) )
END IF
KSTEP = 2
KCNEXT = KCNEXT - ( N-K+3 )
END IF
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
IF( KP.LT.N )
$ CALL ZSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
KX = KC + KP - K
DO 70 J = K + 1, KP - 1
KX = KX + N - J + 1
TEMP = DCONJG( AP( KC+J-K ) )
AP( KC+J-K ) = DCONJG( AP( KX ) )
AP( KX ) = TEMP
70 CONTINUE
AP( KC+KP-K ) = DCONJG( AP( KC+KP-K ) )
TEMP = AP( KC )
AP( KC ) = AP( KPC )
AP( KPC ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = AP( KC-N+K-1 )
AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
AP( KC-N+KP-1 ) = TEMP
END IF
END IF
K = K - KSTEP
KC = KCNEXT
GO TO 60
80 CONTINUE
END IF
RETURN
END