spptri.f

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*> \brief \b SPPTRI
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
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*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SPPTRI( UPLO, N, AP, INFO )
* 
*       .. Scalar Arguments ..
*       CHARACTER          UPLO
*       INTEGER            INFO, N
*       ..
*       .. Array Arguments ..
*       REAL               AP( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SPPTRI computes the inverse of a real symmetric positive definite
*> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*> computed by SPPTRF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          = 'U':  Upper triangular factor is stored in AP;
*>          = 'L':  Lower triangular factor is stored in AP.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*>          AP is REAL array, dimension (N*(N+1)/2)
*>          On entry, the triangular factor U or L from the Cholesky
*>          factorization A = U**T*U or A = L*L**T, packed columnwise as
*>          a linear array.  The j-th column of U or L is stored in the
*>          array AP as follows:
*>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
*>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
*>
*>          On exit, the upper or lower triangle of the (symmetric)
*>          inverse of A, overwriting the input factor U or L.
*> \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, the (i,i) element of the factor U or L is
*>                zero, and the inverse could not be computed.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup realOTHERcomputational
*
*  =====================================================================
      SUBROUTINE spptri( UPLO, N, AP, INFO )
*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      REAL               AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE
      parameter                ( one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, JC, JJ, JJN
      REAL               AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SDOT
      EXTERNAL           lsame, sdot
*     ..
*     .. External Subroutines ..
      EXTERNAL           sscal, sspr, stpmv, stptri, xerbla
*     ..
*     .. 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( 'SPPTRI', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Invert the triangular Cholesky factor U or L.
*
      CALL stptri( uplo, 'Non-unit', n, ap, info )
      IF( info.GT.0 )
     $   RETURN
*
      IF( upper ) THEN
*
*        Compute the product inv(U) * inv(U)**T.
*
         jj = 0
         DO 10 j = 1, n
            jc = jj + 1
            jj = jj + j
            IF( j.GT.1 )
     $         CALL sspr( 'Upper', j-1, one, ap( jc ), 1, ap )
            ajj = ap( jj )
            CALL sscal( j, ajj, ap( jc ), 1 )
   10    CONTINUE
*
      ELSE
*
*        Compute the product inv(L)**T * inv(L).
*
         jj = 1
         DO 20 j = 1, n
            jjn = jj + n - j + 1
            ap( jj ) = sdot( n-j+1, ap( jj ), 1, ap( jj ), 1 )
            IF( j.LT.n )
     $         CALL stpmv( 'Lower', 'Transpose', 'Non-unit', n-j,
     $                     ap( jjn ), ap( jj+1 ), 1 )
            jj = jjn
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of SPPTRI
*
      END