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    1: *> \brief \b ZTPTRI
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZTPTRI + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztptri.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztptri.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztptri.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          DIAG, UPLO
   25: *       INTEGER            INFO, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       COMPLEX*16         AP( * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> ZTPTRI computes the inverse of a complex upper or lower triangular
   38: *> matrix A stored in packed format.
   39: *> \endverbatim
   40: *
   41: *  Arguments:
   42: *  ==========
   43: *
   44: *> \param[in] UPLO
   45: *> \verbatim
   46: *>          UPLO is CHARACTER*1
   47: *>          = 'U':  A is upper triangular;
   48: *>          = 'L':  A is lower triangular.
   49: *> \endverbatim
   50: *>
   51: *> \param[in] DIAG
   52: *> \verbatim
   53: *>          DIAG is CHARACTER*1
   54: *>          = 'N':  A is non-unit triangular;
   55: *>          = 'U':  A is unit triangular.
   56: *> \endverbatim
   57: *>
   58: *> \param[in] N
   59: *> \verbatim
   60: *>          N is INTEGER
   61: *>          The order of the matrix A.  N >= 0.
   62: *> \endverbatim
   63: *>
   64: *> \param[in,out] AP
   65: *> \verbatim
   66: *>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
   67: *>          On entry, the upper or lower triangular matrix A, stored
   68: *>          columnwise in a linear array.  The j-th column of A is stored
   69: *>          in the array AP as follows:
   70: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   71: *>          if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
   72: *>          See below for further details.
   73: *>          On exit, the (triangular) inverse of the original matrix, in
   74: *>          the same packed storage format.
   75: *> \endverbatim
   76: *>
   77: *> \param[out] INFO
   78: *> \verbatim
   79: *>          INFO is INTEGER
   80: *>          = 0:  successful exit
   81: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   82: *>          > 0:  if INFO = i, A(i,i) is exactly zero.  The triangular
   83: *>                matrix is singular and its inverse can not be computed.
   84: *> \endverbatim
   85: *
   86: *  Authors:
   87: *  ========
   88: *
   89: *> \author Univ. of Tennessee 
   90: *> \author Univ. of California Berkeley 
   91: *> \author Univ. of Colorado Denver 
   92: *> \author NAG Ltd. 
   93: *
   94: *> \date November 2011
   95: *
   96: *> \ingroup complex16OTHERcomputational
   97: *
   98: *> \par Further Details:
   99: *  =====================
  100: *>
  101: *> \verbatim
  102: *>
  103: *>  A triangular matrix A can be transferred to packed storage using one
  104: *>  of the following program segments:
  105: *>
  106: *>  UPLO = 'U':                      UPLO = 'L':
  107: *>
  108: *>        JC = 1                           JC = 1
  109: *>        DO 2 J = 1, N                    DO 2 J = 1, N
  110: *>           DO 1 I = 1, J                    DO 1 I = J, N
  111: *>              AP(JC+I-1) = A(I,J)              AP(JC+I-J) = A(I,J)
  112: *>      1    CONTINUE                    1    CONTINUE
  113: *>           JC = JC + J                      JC = JC + N - J + 1
  114: *>      2 CONTINUE                       2 CONTINUE
  115: *> \endverbatim
  116: *>
  117: *  =====================================================================
  118:       SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO )
  119: *
  120: *  -- LAPACK computational routine (version 3.4.0) --
  121: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  122: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  123: *     November 2011
  124: *
  125: *     .. Scalar Arguments ..
  126:       CHARACTER          DIAG, UPLO
  127:       INTEGER            INFO, N
  128: *     ..
  129: *     .. Array Arguments ..
  130:       COMPLEX*16         AP( * )
  131: *     ..
  132: *
  133: *  =====================================================================
  134: *
  135: *     .. Parameters ..
  136:       COMPLEX*16         ONE, ZERO
  137:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
  138:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
  139: *     ..
  140: *     .. Local Scalars ..
  141:       LOGICAL            NOUNIT, UPPER
  142:       INTEGER            J, JC, JCLAST, JJ
  143:       COMPLEX*16         AJJ
  144: *     ..
  145: *     .. External Functions ..
  146:       LOGICAL            LSAME
  147:       EXTERNAL           LSAME
  148: *     ..
  149: *     .. External Subroutines ..
  150:       EXTERNAL           XERBLA, ZSCAL, ZTPMV
  151: *     ..
  152: *     .. Executable Statements ..
  153: *
  154: *     Test the input parameters.
  155: *
  156:       INFO = 0
  157:       UPPER = LSAME( UPLO, 'U' )
  158:       NOUNIT = LSAME( DIAG, 'N' )
  159:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  160:          INFO = -1
  161:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
  162:          INFO = -2
  163:       ELSE IF( N.LT.0 ) THEN
  164:          INFO = -3
  165:       END IF
  166:       IF( INFO.NE.0 ) THEN
  167:          CALL XERBLA( 'ZTPTRI', -INFO )
  168:          RETURN
  169:       END IF
  170: *
  171: *     Check for singularity if non-unit.
  172: *
  173:       IF( NOUNIT ) THEN
  174:          IF( UPPER ) THEN
  175:             JJ = 0
  176:             DO 10 INFO = 1, N
  177:                JJ = JJ + INFO
  178:                IF( AP( JJ ).EQ.ZERO )
  179:      $            RETURN
  180:    10       CONTINUE
  181:          ELSE
  182:             JJ = 1
  183:             DO 20 INFO = 1, N
  184:                IF( AP( JJ ).EQ.ZERO )
  185:      $            RETURN
  186:                JJ = JJ + N - INFO + 1
  187:    20       CONTINUE
  188:          END IF
  189:          INFO = 0
  190:       END IF
  191: *
  192:       IF( UPPER ) THEN
  193: *
  194: *        Compute inverse of upper triangular matrix.
  195: *
  196:          JC = 1
  197:          DO 30 J = 1, N
  198:             IF( NOUNIT ) THEN
  199:                AP( JC+J-1 ) = ONE / AP( JC+J-1 )
  200:                AJJ = -AP( JC+J-1 )
  201:             ELSE
  202:                AJJ = -ONE
  203:             END IF
  204: *
  205: *           Compute elements 1:j-1 of j-th column.
  206: *
  207:             CALL ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
  208:      $                  AP( JC ), 1 )
  209:             CALL ZSCAL( J-1, AJJ, AP( JC ), 1 )
  210:             JC = JC + J
  211:    30    CONTINUE
  212: *
  213:       ELSE
  214: *
  215: *        Compute inverse of lower triangular matrix.
  216: *
  217:          JC = N*( N+1 ) / 2
  218:          DO 40 J = N, 1, -1
  219:             IF( NOUNIT ) THEN
  220:                AP( JC ) = ONE / AP( JC )
  221:                AJJ = -AP( JC )
  222:             ELSE
  223:                AJJ = -ONE
  224:             END IF
  225:             IF( J.LT.N ) THEN
  226: *
  227: *              Compute elements j+1:n of j-th column.
  228: *
  229:                CALL ZTPMV( 'Lower', 'No transpose', DIAG, N-J,
  230:      $                     AP( JCLAST ), AP( JC+1 ), 1 )
  231:                CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 )
  232:             END IF
  233:             JCLAST = JC
  234:             JC = JC - N + J - 2
  235:    40    CONTINUE
  236:       END IF
  237: *
  238:       RETURN
  239: *
  240: *     End of ZTPTRI
  241: *
  242:       END