LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztptri.f
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00001 *> \brief \b ZTPTRI
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download ZTPTRI + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztptri.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       CHARACTER          DIAG, 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 *> ZTPTRI computes the inverse of a complex upper or lower triangular
00038 *> matrix A stored in packed format.
00039 *> \endverbatim
00040 *
00041 *  Arguments:
00042 *  ==========
00043 *
00044 *> \param[in] UPLO
00045 *> \verbatim
00046 *>          UPLO is CHARACTER*1
00047 *>          = 'U':  A is upper triangular;
00048 *>          = 'L':  A is lower triangular.
00049 *> \endverbatim
00050 *>
00051 *> \param[in] DIAG
00052 *> \verbatim
00053 *>          DIAG is CHARACTER*1
00054 *>          = 'N':  A is non-unit triangular;
00055 *>          = 'U':  A is unit triangular.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The order of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in,out] AP
00065 *> \verbatim
00066 *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
00067 *>          On entry, the upper or lower triangular matrix A, stored
00068 *>          columnwise in a linear array.  The j-th column of A is stored
00069 *>          in the array AP as follows:
00070 *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
00071 *>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
00072 *>          See below for further details.
00073 *>          On exit, the (triangular) inverse of the original matrix, in
00074 *>          the same packed storage format.
00075 *> \endverbatim
00076 *>
00077 *> \param[out] INFO
00078 *> \verbatim
00079 *>          INFO is INTEGER
00080 *>          = 0:  successful exit
00081 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00082 *>          > 0:  if INFO = i, A(i,i) is exactly zero.  The triangular
00083 *>                matrix is singular and its inverse can not be computed.
00084 *> \endverbatim
00085 *
00086 *  Authors:
00087 *  ========
00088 *
00089 *> \author Univ. of Tennessee 
00090 *> \author Univ. of California Berkeley 
00091 *> \author Univ. of Colorado Denver 
00092 *> \author NAG Ltd. 
00093 *
00094 *> \date November 2011
00095 *
00096 *> \ingroup complex16OTHERcomputational
00097 *
00098 *> \par Further Details:
00099 *  =====================
00100 *>
00101 *> \verbatim
00102 *>
00103 *>  A triangular matrix A can be transferred to packed storage using one
00104 *>  of the following program segments:
00105 *>
00106 *>  UPLO = 'U':                      UPLO = 'L':
00107 *>
00108 *>        JC = 1                           JC = 1
00109 *>        DO 2 J = 1, N                    DO 2 J = 1, N
00110 *>           DO 1 I = 1, J                    DO 1 I = J, N
00111 *>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
00112 *>      1    CONTINUE                    1    CONTINUE
00113 *>           JC = JC + J                      JC = JC + N - J + 1
00114 *>      2 CONTINUE                       2 CONTINUE
00115 *> \endverbatim
00116 *>
00117 *  =====================================================================
00118       SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
00119 *
00120 *  -- LAPACK computational routine (version 3.4.0) --
00121 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00122 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00123 *     November 2011
00124 *
00125 *     .. Scalar Arguments ..
00126       CHARACTER          DIAG, UPLO
00127       INTEGER            INFO, N
00128 *     ..
00129 *     .. Array Arguments ..
00130       COMPLEX*16         AP( * )
00131 *     ..
00132 *
00133 *  =====================================================================
00134 *
00135 *     .. Parameters ..
00136       COMPLEX*16         ONE, ZERO
00137       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
00138      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
00139 *     ..
00140 *     .. Local Scalars ..
00141       LOGICAL            NOUNIT, UPPER
00142       INTEGER            J, JC, JCLAST, JJ
00143       COMPLEX*16         AJJ
00144 *     ..
00145 *     .. External Functions ..
00146       LOGICAL            LSAME
00147       EXTERNAL           LSAME
00148 *     ..
00149 *     .. External Subroutines ..
00150       EXTERNAL           XERBLA, ZSCAL, ZTPMV
00151 *     ..
00152 *     .. Executable Statements ..
00153 *
00154 *     Test the input parameters.
00155 *
00156       INFO = 0
00157       UPPER = LSAME( UPLO, 'U' )
00158       NOUNIT = LSAME( DIAG, 'N' )
00159       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00160          INFO = -1
00161       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
00162          INFO = -2
00163       ELSE IF( N.LT.0 ) THEN
00164          INFO = -3
00165       END IF
00166       IF( INFO.NE.0 ) THEN
00167          CALL XERBLA( 'ZTPTRI', -INFO )
00168          RETURN
00169       END IF
00170 *
00171 *     Check for singularity if non-unit.
00172 *
00173       IF( NOUNIT ) THEN
00174          IF( UPPER ) THEN
00175             JJ = 0
00176             DO 10 INFO = 1, N
00177                JJ = JJ + INFO
00178                IF( AP( JJ ).EQ.ZERO )
00179      $            RETURN
00180    10       CONTINUE
00181          ELSE
00182             JJ = 1
00183             DO 20 INFO = 1, N
00184                IF( AP( JJ ).EQ.ZERO )
00185      $            RETURN
00186                JJ = JJ + N - INFO + 1
00187    20       CONTINUE
00188          END IF
00189          INFO = 0
00190       END IF
00191 *
00192       IF( UPPER ) THEN
00193 *
00194 *        Compute inverse of upper triangular matrix.
00195 *
00196          JC = 1
00197          DO 30 J = 1, N
00198             IF( NOUNIT ) THEN
00199                AP( JC+J-1 ) = ONE / AP( JC+J-1 )
00200                AJJ = -AP( JC+J-1 )
00201             ELSE
00202                AJJ = -ONE
00203             END IF
00204 *
00205 *           Compute elements 1:j-1 of j-th column.
00206 *
00207             CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
00208      $                  AP( JC ), 1 )
00209             CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
00210             JC = JC + J
00211    30    CONTINUE
00212 *
00213       ELSE
00214 *
00215 *        Compute inverse of lower triangular matrix.
00216 *
00217          JC = N*( N+1 ) / 2
00218          DO 40 J = N, 1, -1
00219             IF( NOUNIT ) THEN
00220                AP( JC ) = ONE / AP( JC )
00221                AJJ = -AP( JC )
00222             ELSE
00223                AJJ = -ONE
00224             END IF
00225             IF( J.LT.N ) THEN
00226 *
00227 *              Compute elements j+1:n of j-th column.
00228 *
00229                CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
00230      $                     AP( JCLAST ), AP( JC+1 ), 1 )
00231                CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
00232             END IF
00233             JCLAST = JC
00234             JC = JC - N + J - 2
00235    40    CONTINUE
00236       END IF
00237 *
00238       RETURN
00239 *
00240 *     End of ZTPTRI
00241 *
00242       END
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