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    1: *> \brief \b DTRTRS
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download DTRTRS + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrtrs.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrtrs.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrtrs.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
   22: *                          INFO )
   23: * 
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          DIAG, TRANS, UPLO
   26: *       INTEGER            INFO, LDA, LDB, N, NRHS
   27: *       ..
   28: *       .. Array Arguments ..
   29: *       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
   30: *       ..
   31: *  
   32: *
   33: *> \par Purpose:
   34: *  =============
   35: *>
   36: *> \verbatim
   37: *>
   38: *> DTRTRS solves a triangular system of the form
   39: *>
   40: *>    A * X = B  or  A**T * X = B,
   41: *>
   42: *> where A is a triangular matrix of order N, and B is an N-by-NRHS
   43: *> matrix.  A check is made to verify that A is nonsingular.
   44: *> \endverbatim
   45: *
   46: *  Arguments:
   47: *  ==========
   48: *
   49: *> \param[in] UPLO
   50: *> \verbatim
   51: *>          UPLO is CHARACTER*1
   52: *>          = 'U':  A is upper triangular;
   53: *>          = 'L':  A is lower triangular.
   54: *> \endverbatim
   55: *>
   56: *> \param[in] TRANS
   57: *> \verbatim
   58: *>          TRANS is CHARACTER*1
   59: *>          Specifies the form of the system of equations:
   60: *>          = 'N':  A * X = B  (No transpose)
   61: *>          = 'T':  A**T * X = B  (Transpose)
   62: *>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
   63: *> \endverbatim
   64: *>
   65: *> \param[in] DIAG
   66: *> \verbatim
   67: *>          DIAG is CHARACTER*1
   68: *>          = 'N':  A is non-unit triangular;
   69: *>          = 'U':  A is unit triangular.
   70: *> \endverbatim
   71: *>
   72: *> \param[in] N
   73: *> \verbatim
   74: *>          N is INTEGER
   75: *>          The order of the matrix A.  N >= 0.
   76: *> \endverbatim
   77: *>
   78: *> \param[in] NRHS
   79: *> \verbatim
   80: *>          NRHS is INTEGER
   81: *>          The number of right hand sides, i.e., the number of columns
   82: *>          of the matrix B.  NRHS >= 0.
   83: *> \endverbatim
   84: *>
   85: *> \param[in] A
   86: *> \verbatim
   87: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   88: *>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
   89: *>          upper triangular part of the array A contains the upper
   90: *>          triangular matrix, and the strictly lower triangular part of
   91: *>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
   92: *>          triangular part of the array A contains the lower triangular
   93: *>          matrix, and the strictly upper triangular part of A is not
   94: *>          referenced.  If DIAG = 'U', the diagonal elements of A are
   95: *>          also not referenced and are assumed to be 1.
   96: *> \endverbatim
   97: *>
   98: *> \param[in] LDA
   99: *> \verbatim
  100: *>          LDA is INTEGER
  101: *>          The leading dimension of the array A.  LDA >= max(1,N).
  102: *> \endverbatim
  103: *>
  104: *> \param[in,out] B
  105: *> \verbatim
  106: *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
  107: *>          On entry, the right hand side matrix B.
  108: *>          On exit, if INFO = 0, the solution matrix X.
  109: *> \endverbatim
  110: *>
  111: *> \param[in] LDB
  112: *> \verbatim
  113: *>          LDB is INTEGER
  114: *>          The leading dimension of the array B.  LDB >= max(1,N).
  115: *> \endverbatim
  116: *>
  117: *> \param[out] INFO
  118: *> \verbatim
  119: *>          INFO is INTEGER
  120: *>          = 0:  successful exit
  121: *>          < 0: if INFO = -i, the i-th argument had an illegal value
  122: *>          > 0: if INFO = i, the i-th diagonal element of A is zero,
  123: *>               indicating that the matrix is singular and the solutions
  124: *>               X have not been computed.
  125: *> \endverbatim
  126: *
  127: *  Authors:
  128: *  ========
  129: *
  130: *> \author Univ. of Tennessee 
  131: *> \author Univ. of California Berkeley 
  132: *> \author Univ. of Colorado Denver 
  133: *> \author NAG Ltd. 
  134: *
  135: *> \date November 2011
  136: *
  137: *> \ingroup doubleOTHERcomputational
  138: *
  139: *  =====================================================================
  140:       SUBROUTINE DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
  141:      $                   INFO )
  142: *
  143: *  -- LAPACK computational routine (version 3.4.0) --
  144: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  145: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  146: *     November 2011
  147: *
  148: *     .. Scalar Arguments ..
  149:       CHARACTER          DIAG, TRANS, UPLO
  150:       INTEGER            INFO, LDA, LDB, N, NRHS
  151: *     ..
  152: *     .. Array Arguments ..
  153:       DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
  154: *     ..
  155: *
  156: *  =====================================================================
  157: *
  158: *     .. Parameters ..
  159:       DOUBLE PRECISION   ZERO, ONE
  160:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
  161: *     ..
  162: *     .. Local Scalars ..
  163:       LOGICAL            NOUNIT
  164: *     ..
  165: *     .. External Functions ..
  166:       LOGICAL            LSAME
  167:       EXTERNAL           LSAME
  168: *     ..
  169: *     .. External Subroutines ..
  170:       EXTERNAL           DTRSM, XERBLA
  171: *     ..
  172: *     .. Intrinsic Functions ..
  173:       INTRINSIC          MAX
  174: *     ..
  175: *     .. Executable Statements ..
  176: *
  177: *     Test the input parameters.
  178: *
  179:       INFO = 0
  180:       NOUNIT = LSAME( DIAG, 'N' )
  181:       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  182:          INFO = -1
  183:       ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
  184:      $         LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
  185:          INFO = -2
  186:       ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
  187:          INFO = -3
  188:       ELSE IF( N.LT.0 ) THEN
  189:          INFO = -4
  190:       ELSE IF( NRHS.LT.0 ) THEN
  191:          INFO = -5
  192:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
  193:          INFO = -7
  194:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  195:          INFO = -9
  196:       END IF
  197:       IF( INFO.NE.0 ) THEN
  198:          CALL XERBLA( 'DTRTRS', -INFO )
  199:          RETURN
  200:       END IF
  201: *
  202: *     Quick return if possible
  203: *
  204:       IF( N.EQ.0 )
  205:      $   RETURN
  206: *
  207: *     Check for singularity.
  208: *
  209:       IF( NOUNIT ) THEN
  210:          DO 10 INFO = 1, N
  211:             IF( A( INFO, INFO ).EQ.ZERO )
  212:      $         RETURN
  213:    10    CONTINUE
  214:       END IF
  215:       INFO = 0
  216: *
  217: *     Solve A * x = b  or  A**T * x = b.
  218: *
  219:       CALL DTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
  220:      $            LDB )
  221: *
  222:       RETURN
  223: *
  224: *     End of DTRTRS
  225: *
  226:       END