LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dpptri.f
Go to the documentation of this file.
00001 *> \brief \b DPPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DPPTRI + dependencies 
00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptri.f"> 
00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DPPTRI( UPLO, N, AP, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       DOUBLE PRECISION   AP( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DPPTRI computes the inverse of a real symmetric positive definite
00038 *> matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
00039 *> computed by DPPTRF.
00040 *> \endverbatim
00041 *
00042 *  Arguments:
00043 *  ==========
00044 *
00045 *> \param[in] UPLO
00046 *> \verbatim
00047 *>          UPLO is CHARACTER*1
00048 *>          = 'U':  Upper triangular factor is stored in AP;
00049 *>          = 'L':  Lower triangular factor is stored in AP.
00050 *> \endverbatim
00051 *>
00052 *> \param[in] N
00053 *> \verbatim
00054 *>          N is INTEGER
00055 *>          The order of the matrix A.  N >= 0.
00056 *> \endverbatim
00057 *>
00058 *> \param[in,out] AP
00059 *> \verbatim
00060 *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
00061 *>          On entry, the triangular factor U or L from the Cholesky
00062 *>          factorization A = U**T*U or A = L*L**T, packed columnwise as
00063 *>          a linear array.  The j-th column of U or L is stored in the
00064 *>          array AP as follows:
00065 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
00066 *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
00067 *>
00068 *>          On exit, the upper or lower triangle of the (symmetric)
00069 *>          inverse of A, overwriting the input factor U or L.
00070 *> \endverbatim
00071 *>
00072 *> \param[out] INFO
00073 *> \verbatim
00074 *>          INFO is INTEGER
00075 *>          = 0:  successful exit
00076 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00077 *>          > 0:  if INFO = i, the (i,i) element of the factor U or L is
00078 *>                zero, and the inverse could not be computed.
00079 *> \endverbatim
00080 *
00081 *  Authors:
00082 *  ========
00083 *
00084 *> \author Univ. of Tennessee 
00085 *> \author Univ. of California Berkeley 
00086 *> \author Univ. of Colorado Denver 
00087 *> \author NAG Ltd. 
00088 *
00089 *> \date November 2011
00090 *
00091 *> \ingroup doubleOTHERcomputational
00092 *
00093 *  =====================================================================
00094       SUBROUTINE DPPTRI( UPLO, N, AP, INFO )
00095 *
00096 *  -- LAPACK computational routine (version 3.4.0) --
00097 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00098 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00099 *     November 2011
00100 *
00101 *     .. Scalar Arguments ..
00102       CHARACTER          UPLO
00103       INTEGER            INFO, N
00104 *     ..
00105 *     .. Array Arguments ..
00106       DOUBLE PRECISION   AP( * )
00107 *     ..
00108 *
00109 *  =====================================================================
00110 *
00111 *     .. Parameters ..
00112       DOUBLE PRECISION   ONE
00113       PARAMETER          ( ONE = 1.0D+0 )
00114 *     ..
00115 *     .. Local Scalars ..
00116       LOGICAL            UPPER
00117       INTEGER            J, JC, JJ, JJN
00118       DOUBLE PRECISION   AJJ
00119 *     ..
00120 *     .. External Functions ..
00121       LOGICAL            LSAME
00122       DOUBLE PRECISION   DDOT
00123       EXTERNAL           LSAME, DDOT
00124 *     ..
00125 *     .. External Subroutines ..
00126       EXTERNAL           DSCAL, DSPR, DTPMV, DTPTRI, XERBLA
00127 *     ..
00128 *     .. Executable Statements ..
00129 *
00130 *     Test the input parameters.
00131 *
00132       INFO = 0
00133       UPPER = LSAME( UPLO, 'U' )
00134       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00135          INFO = -1
00136       ELSE IF( N.LT.0 ) THEN
00137          INFO = -2
00138       END IF
00139       IF( INFO.NE.0 ) THEN
00140          CALL XERBLA( 'DPPTRI', -INFO )
00141          RETURN
00142       END IF
00143 *
00144 *     Quick return if possible
00145 *
00146       IF( N.EQ.0 )
00147      $   RETURN
00148 *
00149 *     Invert the triangular Cholesky factor U or L.
00150 *
00151       CALL DTPTRI( UPLO, 'Non-unit', N, AP, INFO )
00152       IF( INFO.GT.0 )
00153      $   RETURN
00154 *
00155       IF( UPPER ) THEN
00156 *
00157 *        Compute the product inv(U) * inv(U)**T.
00158 *
00159          JJ = 0
00160          DO 10 J = 1, N
00161             JC = JJ + 1
00162             JJ = JJ + J
00163             IF( J.GT.1 )
00164      $         CALL DSPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
00165             AJJ = AP( JJ )
00166             CALL DSCAL( J, AJJ, AP( JC ), 1 )
00167    10    CONTINUE
00168 *
00169       ELSE
00170 *
00171 *        Compute the product inv(L)**T * inv(L).
00172 *
00173          JJ = 1
00174          DO 20 J = 1, N
00175             JJN = JJ + N - J + 1
00176             AP( JJ ) = DDOT( N-J+1, AP( JJ ), 1, AP( JJ ), 1 )
00177             IF( J.LT.N )
00178      $         CALL DTPMV( 'Lower', 'Transpose', 'Non-unit', N-J,
00179      $                     AP( JJN ), AP( JJ+1 ), 1 )
00180             JJ = JJN
00181    20    CONTINUE
00182       END IF
00183 *
00184       RETURN
00185 *
00186 *     End of DPPTRI
00187 *
00188       END
 All Files Functions