LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
zpptri.f
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00001 *> \brief \b ZPPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZPPTRI + dependencies 
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00011 *> [TGZ]</a> 
00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zpptri.f"> 
00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zpptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZPPTRI( UPLO, N, AP, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          UPLO
00025 *       INTEGER            INFO, N
00026 *       ..
00027 *       .. Array Arguments ..
00028 *       COMPLEX*16         AP( * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> ZPPTRI computes the inverse of a complex Hermitian positive definite
00038 *> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
00039 *> computed by ZPPTRF.
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 COMPLEX*16 array, dimension (N*(N+1)/2)
00061 *>          On entry, the triangular factor U or L from the Cholesky
00062 *>          factorization A = U**H*U or A = L*L**H, 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 (Hermitian)
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 complex16OTHERcomputational
00092 *
00093 *  =====================================================================
00094       SUBROUTINE ZPPTRI( 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       COMPLEX*16         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       COMPLEX*16         ZDOTC
00123       EXTERNAL           LSAME, ZDOTC
00124 *     ..
00125 *     .. External Subroutines ..
00126       EXTERNAL           XERBLA, ZDSCAL, ZHPR, ZTPMV, ZTPTRI
00127 *     ..
00128 *     .. Intrinsic Functions ..
00129       INTRINSIC          DBLE
00130 *     ..
00131 *     .. Executable Statements ..
00132 *
00133 *     Test the input parameters.
00134 *
00135       INFO = 0
00136       UPPER = LSAME( UPLO, 'U' )
00137       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00138          INFO = -1
00139       ELSE IF( N.LT.0 ) THEN
00140          INFO = -2
00141       END IF
00142       IF( INFO.NE.0 ) THEN
00143          CALL XERBLA( 'ZPPTRI', -INFO )
00144          RETURN
00145       END IF
00146 *
00147 *     Quick return if possible
00148 *
00149       IF( N.EQ.0 )
00150      $   RETURN
00151 *
00152 *     Invert the triangular Cholesky factor U or L.
00153 *
00154       CALL ZTPTRI( UPLO, 'Non-unit', N, AP, INFO )
00155       IF( INFO.GT.0 )
00156      $   RETURN
00157       IF( UPPER ) THEN
00158 *
00159 *        Compute the product inv(U) * inv(U)**H.
00160 *
00161          JJ = 0
00162          DO 10 J = 1, N
00163             JC = JJ + 1
00164             JJ = JJ + J
00165             IF( J.GT.1 )
00166      $         CALL ZHPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
00167             AJJ = AP( JJ )
00168             CALL ZDSCAL( J, AJJ, AP( JC ), 1 )
00169    10    CONTINUE
00170 *
00171       ELSE
00172 *
00173 *        Compute the product inv(L)**H * inv(L).
00174 *
00175          JJ = 1
00176          DO 20 J = 1, N
00177             JJN = JJ + N - J + 1
00178             AP( JJ ) = DBLE( ZDOTC( N-J+1, AP( JJ ), 1, AP( JJ ), 1 ) )
00179             IF( J.LT.N )
00180      $         CALL ZTPMV( 'Lower', 'Conjugate transpose', 'Non-unit',
00181      $                     N-J, AP( JJN ), AP( JJ+1 ), 1 )
00182             JJ = JJN
00183    20    CONTINUE
00184       END IF
00185 *
00186       RETURN
00187 *
00188 *     End of ZPPTRI
00189 *
00190       END
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