zsptri.f

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*> \brief \b ZSPTRI
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, N
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       COMPLEX*16         AP( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSPTRI computes the inverse of a complex symmetric indefinite matrix
*> A in packed storage using the factorization A = U*D*U**T or
*> A = L*D*L**T computed by ZSPTRF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
*>          On entry, the block diagonal matrix D and the multipliers
*>          used to obtain the factor U or L as computed by ZSPTRF,
*>          stored as a packed triangular matrix.
*>
*>          On exit, if INFO = 0, the (symmetric) inverse of the original
*>          matrix, stored as a packed triangular matrix. The j-th column
*>          of inv(A) is stored in the array AP as follows:
*>          if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
*>          if UPLO = 'L',
*>             AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          Details of the interchanges and the block structure of D
*>          as determined by ZSPTRF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is 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.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hptri
*
*  =====================================================================
      SUBROUTINE zsptri( UPLO, N, AP, IPIV, WORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX*16         AP( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      COMPLEX*16         ONE, ZERO
      parameter( one = ( 1.0d+0, 0.0d+0 ),
     $                   zero = ( 0.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
      COMPLEX*16         AK, AKKP1, AKP1, D, T, TEMP
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      COMPLEX*16         ZDOTU
      EXTERNAL           lsame, zdotu
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zcopy, zspmv, zswap
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs
*     ..
*     .. 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
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZSPTRI', -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
*
         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
*
*        Lower triangular storage: examine D from top to bottom.
*
         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
*
*        Compute inv(A) from the factorization A = U*D*U**T.
*
*        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
         kc = 1
   30    CONTINUE
*
*        If K > N, exit from loop.
*
         IF( k.GT.n )
     $      GO TO 50
*
         kcnext = kc + k
         IF( ipiv( k ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
            ap( kc+k-1 ) = one / ap( kc+k-1 )
*
*           Compute column K of the inverse.
*
            IF( k.GT.1 ) THEN
               CALL zcopy( k-1, ap( kc ), 1, work, 1 )
               CALL zspmv( uplo, k-1, -one, ap, work, 1, zero,
     $                     ap( kc ),
     $                     1 )
               ap( kc+k-1 ) = ap( kc+k-1 ) -
     $                        zdotu( k-1, work, 1, ap( kc ), 1 )
            END IF
            kstep = 1
         ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
            t = ap( kcnext+k-1 )
            ak = ap( kc+k-1 ) / t
            akp1 = 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
*
*           Compute columns K and K+1 of the inverse.
*
            IF( k.GT.1 ) THEN
               CALL zcopy( k-1, ap( kc ), 1, work, 1 )
               CALL zspmv( uplo, k-1, -one, ap, work, 1, zero,
     $                     ap( kc ),
     $                     1 )
               ap( kc+k-1 ) = ap( kc+k-1 ) -
     $                        zdotu( k-1, work, 1, ap( kc ), 1 )
               ap( kcnext+k-1 ) = ap( kcnext+k-1 ) -
     $                            zdotu( k-1, ap( kc ), 1,
     $                                   ap( kcnext ),
     $                            1 )
               CALL zcopy( k-1, ap( kcnext ), 1, work, 1 )
               CALL zspmv( uplo, k-1, -one, ap, work, 1, zero,
     $                     ap( kcnext ), 1 )
               ap( kcnext+k ) = ap( kcnext+k ) -
     $                          zdotu( 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
*
*           Interchange rows and columns K and KP in the leading
*           submatrix A(1:k+1,1:k+1)
*
            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 = ap( kc+j-1 )
               ap( kc+j-1 ) = ap( kx )
               ap( kx ) = temp
   40       CONTINUE
            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
*
*        Compute inv(A) from the factorization A = L*D*L**T.
*
*        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.
*
         npp = n*( n+1 ) / 2
         k = n
         kc = npp
   60    CONTINUE
*
*        If K < 1, exit from loop.
*
         IF( k.LT.1 )
     $      GO TO 80
*
         kcnext = kc - ( n-k+2 )
         IF( ipiv( k ).GT.0 ) THEN
*
*           1 x 1 diagonal block
*
*           Invert the diagonal block.
*
            ap( kc ) = one / ap( kc )
*
*           Compute column K of the inverse.
*
            IF( k.LT.n ) THEN
               CALL zcopy( n-k, ap( kc+1 ), 1, work, 1 )
               CALL zspmv( uplo, n-k, -one, ap( kc+n-k+1 ), work, 1,
     $                     zero, ap( kc+1 ), 1 )
               ap( kc ) = ap( kc ) - zdotu( n-k, work, 1, ap( kc+1 ),
     $                    1 )
            END IF
            kstep = 1
         ELSE
*
*           2 x 2 diagonal block
*
*           Invert the diagonal block.
*
            t = ap( kcnext+1 )
            ak = ap( kcnext ) / t
            akp1 = 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
*
*           Compute columns K-1 and K of the inverse.
*
            IF( k.LT.n ) THEN
               CALL zcopy( n-k, ap( kc+1 ), 1, work, 1 )
               CALL zspmv( uplo, n-k, -one, ap( kc+( n-k+1 ) ), work,
     $                     1,
     $                     zero, ap( kc+1 ), 1 )
               ap( kc ) = ap( kc ) - zdotu( n-k, work, 1, ap( kc+1 ),
     $                    1 )
               ap( kcnext+1 ) = ap( kcnext+1 ) -
     $                          zdotu( n-k, ap( kc+1 ), 1,
     $                          ap( kcnext+2 ), 1 )
               CALL zcopy( n-k, ap( kcnext+2 ), 1, work, 1 )
               CALL zspmv( uplo, n-k, -one, ap( kc+( n-k+1 ) ), work,
     $                     1,
     $                     zero, ap( kcnext+2 ), 1 )
               ap( kcnext ) = ap( kcnext ) -
     $                        zdotu( 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
*
*           Interchange rows and columns K and KP in the trailing
*           submatrix A(k-1:n,k-1:n)
*
            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 = ap( kc+j-k )
               ap( kc+j-k ) = ap( kx )
               ap( kx ) = temp
   70       CONTINUE
            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 of ZSPTRI
*
      SUBROUTINE zsptri( UPLO, N, AP, IPIV, WORK, INFO ) …
      END