csytri.f

          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