dpptri.f

          SUBROUTINE DPPTRI( UPLO, N, AP, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   AP( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DPPTRI 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 DPPTRF.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangular factor is stored in AP;
    *          = 'L':  Lower triangular factor is stored in AP.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  AP      (input/output) DOUBLE PRECISION 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.
    *
    *  INFO    (output) 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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE
          PARAMETER          ( ONE = 1.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            J, JC, JJ, JJN
          DOUBLE PRECISION   AJJ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   DDOT
          EXTERNAL           LSAME, DDOT
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DSCAL, DSPR, DTPMV, DTPTRI, 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( 'DPPTRI', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
    *     Invert the triangular Cholesky factor U or L.
    *
          CALL DTPTRI( UPLO, 'Non-unit', N, AP, INFO )
          IF( INFO.GT.0 )
         $   RETURN
    *
          IF( UPPER ) THEN
    *
    *        Compute the product inv(U) * inv(U)'.
    *
             JJ = 0
             DO 10 J = 1, N
                JC = JJ + 1
                JJ = JJ + J
                IF( J.GT.1 )
         $         CALL DSPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
                AJJ = AP( JJ )
                CALL DSCAL( J, AJJ, AP( JC ), 1 )
       10    CONTINUE
    *
          ELSE
    *
    *        Compute the product inv(L)' * inv(L).
    *
             JJ = 1
             DO 20 J = 1, N
                JJN = JJ + N - J + 1
                AP( JJ ) = DDOT( N-J+1, AP( JJ ), 1, AP( JJ ), 1 )
                IF( J.LT.N )
         $         CALL DTPMV( 'Lower', 'Transpose', 'Non-unit', N-J,
         $                     AP( JJN ), AP( JJ+1 ), 1 )
                JJ = JJN
       20    CONTINUE
          END IF
    *
          RETURN
    *
    *     End of DPPTRI
    *
          END