```      SUBROUTINE CSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
INTEGER            IPIV( * )
COMPLEX            A( LDA, * ), WORK( * )
*     ..
*
*  Purpose
*  =======
*
*  CSYTRI computes the inverse of a complex symmetric indefinite matrix
*  A using the factorization A = U*D*U**T or A = L*D*L**T computed by
*  CSYTRF.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          Specifies whether the details of the factorization are stored
*          as an upper or lower triangular matrix.
*          = 'U':  Upper triangular, form is A = U*D*U**T;
*          = 'L':  Lower triangular, form is A = L*D*L**T.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input/output) COMPLEX array, dimension (LDA,N)
*          On entry, the block diagonal matrix D and the multipliers
*          used to obtain the factor U or L as computed by CSYTRF.
*
*          On exit, if INFO = 0, the (symmetric) inverse of the original
*          matrix.  If UPLO = 'U', the upper triangular part of the
*          inverse is formed and the part of A below the diagonal is not
*          referenced; if UPLO = 'L' the lower triangular part of the
*          inverse is formed and the part of A above the diagonal is
*          not referenced.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  IPIV    (input) INTEGER array, dimension (N)
*          Details of the interchanges and the block structure of D
*          as determined by CSYTRF.
*
*  WORK    (workspace) COMPLEX array, dimension (2*N)
*
*  INFO    (output) INTEGER
*          = 0: successful exit
*          < 0: if INFO = -i, the i-th argument had an illegal value
*          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
*               inverse could not be computed.
*
*  =====================================================================
*
*     .. Parameters ..
COMPLEX            ONE, ZERO
PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
\$                   ZERO = ( 0.0E+0, 0.0E+0 ) )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            K, KP, KSTEP
COMPLEX            AK, AKKP1, AKP1, D, T, TEMP
*     ..
*     .. External Functions ..
LOGICAL            LSAME
COMPLEX            CDOTU
EXTERNAL           LSAME, CDOTU
*     ..
*     .. External Subroutines ..
EXTERNAL           CCOPY, CSWAP, CSYMV, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
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
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CSYTRI', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
*     Check that the diagonal matrix D is nonsingular.
*
IF( UPPER ) THEN
*
*        Upper triangular storage: examine D from bottom to top
*
DO 10 INFO = N, 1, -1
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
\$         RETURN
10    CONTINUE
ELSE
*
*        Lower triangular storage: examine D from top to bottom.
*
DO 20 INFO = 1, N
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
\$         RETURN
20    CONTINUE
END IF
INFO = 0
*
IF( UPPER ) THEN
*
*        Compute inv(A) from the factorization A = U*D*U'.
*
*        K is the main loop index, increasing from 1 to N in steps of
*        1 or 2, depending on the size of the diagonal blocks.
*
K = 1
30    CONTINUE
*
*        If K > N, exit from loop.
*
IF( K.GT.N )
\$      GO TO 40
*
IF( IPIV( K ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
A( K, K ) = ONE / A( K, K )
*
*           Compute column K of the inverse.
*
IF( K.GT.1 ) THEN
CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
\$                     A( 1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
\$                     1 )
END IF
KSTEP = 1
ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
T = A( K, K+1 )
AK = A( K, K ) / T
AKP1 = A( K+1, K+1 ) / T
AKKP1 = A( K, K+1 ) / T
D = T*( AK*AKP1-ONE )
A( K, K ) = AKP1 / D
A( K+1, K+1 ) = AK / D
A( K, K+1 ) = -AKKP1 / D
*
*           Compute columns K and K+1 of the inverse.
*
IF( K.GT.1 ) THEN
CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
\$                     A( 1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( K-1, WORK, 1, A( 1, K ),
\$                     1 )
A( K, K+1 ) = A( K, K+1 ) -
\$                       CDOTU( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
CALL CCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
CALL CSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
\$                     A( 1, K+1 ), 1 )
A( K+1, K+1 ) = A( K+1, K+1 ) -
\$                         CDOTU( K-1, WORK, 1, A( 1, K+1 ), 1 )
END IF
KSTEP = 2
END IF
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
*
*           Interchange rows and columns K and KP in the leading
*           submatrix A(1:k+1,1:k+1)
*
CALL CSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
CALL CSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = A( K, K+1 )
A( K, K+1 ) = A( KP, K+1 )
A( KP, K+1 ) = TEMP
END IF
END IF
*
K = K + KSTEP
GO TO 30
40    CONTINUE
*
ELSE
*
*        Compute inv(A) from the factorization A = L*D*L'.
*
*        K is the main loop index, increasing from 1 to N in steps of
*        1 or 2, depending on the size of the diagonal blocks.
*
K = N
50    CONTINUE
*
*        If K < 1, exit from loop.
*
IF( K.LT.1 )
\$      GO TO 60
*
IF( IPIV( K ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
A( K, K ) = ONE / A( K, K )
*
*           Compute column K of the inverse.
*
IF( K.LT.N ) THEN
CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
\$                     ZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
\$                     1 )
END IF
KSTEP = 1
ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
T = A( K, K-1 )
AK = A( K-1, K-1 ) / T
AKP1 = A( K, K ) / T
AKKP1 = A( K, K-1 ) / T
D = T*( AK*AKP1-ONE )
A( K-1, K-1 ) = AKP1 / D
A( K, K ) = AK / D
A( K, K-1 ) = -AKKP1 / D
*
*           Compute columns K-1 and K of the inverse.
*
IF( K.LT.N ) THEN
CALL CCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
\$                     ZERO, A( K+1, K ), 1 )
A( K, K ) = A( K, K ) - CDOTU( N-K, WORK, 1, A( K+1, K ),
\$                     1 )
A( K, K-1 ) = A( K, K-1 ) -
\$                       CDOTU( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
\$                       1 )
CALL CCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
CALL CSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
\$                     ZERO, A( K+1, K-1 ), 1 )
A( K-1, K-1 ) = A( K-1, K-1 ) -
\$                         CDOTU( N-K, WORK, 1, A( K+1, K-1 ), 1 )
END IF
KSTEP = 2
END IF
*
KP = ABS( IPIV( K ) )
IF( KP.NE.K ) THEN
*
*           Interchange rows and columns K and KP in the trailing
*           submatrix A(k-1:n,k-1:n)
*
IF( KP.LT.N )
\$         CALL CSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
CALL CSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
TEMP = A( K, K )
A( K, K ) = A( KP, KP )
A( KP, KP ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = A( K, K-1 )
A( K, K-1 ) = A( KP, K-1 )
A( KP, K-1 ) = TEMP
END IF
END IF
*
K = K - KSTEP
GO TO 50
60    CONTINUE
END IF
*
RETURN
*
*     End of CSYTRI
*
END

```