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    1: *> \brief \b DTRTI2 computes the inverse of a triangular matrix (unblocked algorithm).
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DTRTI2 + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrti2.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrti2.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrti2.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          DIAG, UPLO
   25: *       INTEGER            INFO, LDA, N
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   A( LDA, * )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DTRTI2 computes the inverse of a real upper or lower triangular
   38: *> matrix.
   39: *>
   40: *> This is the Level 2 BLAS version of the algorithm.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] UPLO
   47: *> \verbatim
   48: *>          UPLO is CHARACTER*1
   49: *>          Specifies whether the matrix A is upper or lower triangular.
   50: *>          = 'U':  Upper triangular
   51: *>          = 'L':  Lower triangular
   52: *> \endverbatim
   53: *>
   54: *> \param[in] DIAG
   55: *> \verbatim
   56: *>          DIAG is CHARACTER*1
   57: *>          Specifies whether or not the matrix A is unit triangular.
   58: *>          = 'N':  Non-unit triangular
   59: *>          = 'U':  Unit triangular
   60: *> \endverbatim
   61: *>
   62: *> \param[in] N
   63: *> \verbatim
   64: *>          N is INTEGER
   65: *>          The order of the matrix A.  N >= 0.
   66: *> \endverbatim
   67: *>
   68: *> \param[in,out] A
   69: *> \verbatim
   70: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   71: *>          On entry, the triangular matrix A.  If UPLO = 'U', the
   72: *>          leading n by n upper triangular part of the array A contains
   73: *>          the upper triangular matrix, and the strictly lower
   74: *>          triangular part of A is not referenced.  If UPLO = 'L', the
   75: *>          leading n by n lower triangular part of the array A contains
   76: *>          the lower triangular matrix, and the strictly upper
   77: *>          triangular part of A is not referenced.  If DIAG = 'U', the
   78: *>          diagonal elements of A are also not referenced and are
   79: *>          assumed to be 1.
   80: *>
   81: *>          On exit, the (triangular) inverse of the original matrix, in
   82: *>          the same storage format.
   83: *> \endverbatim
   84: *>
   85: *> \param[in] LDA
   86: *> \verbatim
   87: *>          LDA is INTEGER
   88: *>          The leading dimension of the array A.  LDA >= max(1,N).
   89: *> \endverbatim
   90: *>
   91: *> \param[out] INFO
   92: *> \verbatim
   93: *>          INFO is INTEGER
   94: *>          = 0: successful exit
   95: *>          < 0: if INFO = -k, the k-th argument had an illegal value
   96: *> \endverbatim
   97: *
   98: *  Authors:
   99: *  ========
  100: *
  101: *> \author Univ. of Tennessee 
  102: *> \author Univ. of California Berkeley 
  103: *> \author Univ. of Colorado Denver 
  104: *> \author NAG Ltd. 
  105: *
  106: *> \date September 2012
  107: *
  108: *> \ingroup doubleOTHERcomputational
  109: *
  110: *  =====================================================================
  111:       SUBROUTINE DTRTI2( UPLO, DIAG, N, A, LDA, INFO )
  112: *
  113: *  -- LAPACK computational routine (version 3.4.2) --
  114: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  115: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  116: *     September 2012
  117: *
  118: *     .. Scalar Arguments ..
  119:       CHARACTER          DIAG, UPLO
  120:       INTEGER            INFO, LDA, N
  121: *     ..
  122: *     .. Array Arguments ..
  123:       DOUBLE PRECISION   A( LDA, * )
  124: *     ..
  125: *
  126: *  =====================================================================
  127: *
  128: *     .. Parameters ..
  129:       DOUBLE PRECISION   ONE
  130:       PARAMETER          ( ONE = 1.0D+0 )
  131: *     ..
  132: *     .. Local Scalars ..
  133:       LOGICAL            NOUNIT, UPPER
  134:       INTEGER            J
  135:       DOUBLE PRECISION   AJJ
  136: *     ..
  137: *     .. External Functions ..
  138:       LOGICAL            LSAME
  139:       EXTERNAL           LSAME
  140: *     ..
  141: *     .. External Subroutines ..
  142:       EXTERNAL           DSCAL, DTRMV, XERBLA
  143: *     ..
  144: *     .. Intrinsic Functions ..
  145:       INTRINSIC          MAX
  146: *     ..
  147: *     .. Executable Statements ..
  148: *
  149: *     Test the input parameters.
  150: *
  151:       INFO = 0
  152:       UPPER = LSAME( UPLO, 'U' )
  153:       NOUNIT = LSAME( DIAG, 'N' )
  154:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  155:          INFO = -1
  156:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
  157:          INFO = -2
  158:       ELSE IF( N.LT.0 ) THEN
  159:          INFO = -3
  160:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  161:          INFO = -5
  162:       END IF
  163:       IF( INFO.NE.0 ) THEN
  164:          CALL XERBLA( 'DTRTI2', -INFO )
  165:          RETURN
  166:       END IF
  167: *
  168:       IF( UPPER ) THEN
  169: *
  170: *        Compute inverse of upper triangular matrix.
  171: *
  172:          DO 10 J = 1, N
  173:             IF( NOUNIT ) THEN
  174:                A( J, J ) = ONE / A( J, J )
  175:                AJJ = -A( J, J )
  176:             ELSE
  177:                AJJ = -ONE
  178:             END IF
  179: *
  180: *           Compute elements 1:j-1 of j-th column.
  181: *
  182:             CALL DTRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA,
  183:      $                  A( 1, J ), 1 )
  184:             CALL DSCAL( J-1, AJJ, A( 1, J ), 1 )
  185:    10    CONTINUE
  186:       ELSE
  187: *
  188: *        Compute inverse of lower triangular matrix.
  189: *
  190:          DO 20 J = N, 1, -1
  191:             IF( NOUNIT ) THEN
  192:                A( J, J ) = ONE / A( J, J )
  193:                AJJ = -A( J, J )
  194:             ELSE
  195:                AJJ = -ONE
  196:             END IF
  197:             IF( J.LT.N ) THEN
  198: *
  199: *              Compute elements j+1:n of j-th column.
  200: *
  201:                CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J,
  202:      $                     A( J+1, J+1 ), LDA, A( J+1, J ), 1 )
  203:                CALL DSCAL( N-J, AJJ, A( J+1, J ), 1 )
  204:             END IF
  205:    20    CONTINUE
  206:       END IF
  207: *
  208:       RETURN
  209: *
  210: *     End of DTRTI2
  211: *
  212:       END