subroutine spptri	(	character	UPLO,
		integer	N,
		real, dimension( * )	AP,
		integer	INFO
	)

SPPTRI

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Purpose:

 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.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangular factor is stored in AP; = 'L': Lower triangular factor is stored in AP.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	AP	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.
[out]	INFO	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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Definition at line 95 of file spptri.f.

*
*  -- 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
*

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