Return to zgtsv.f CVS log

Up to [local] / rpl / lapack / lapack

Mise à jour de Lapack vers la version 3.4.2 et des scripts de compilation
pour rplcas. En particulier, le Makefile.am de giac a été modifié pour ne
compiler que le répertoire src.

    1: *> \brief <b> ZGTSV computes the solution to system of linear equations A * X = B for GT matrices <b>
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at 
    6: *            http://www.netlib.org/lapack/explore-html/ 
    7: *
    8: *> \htmlonly
    9: *> Download ZGTSV + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgtsv.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgtsv.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgtsv.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
   22: * 
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            INFO, LDB, N, NRHS
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * )
   28: *       ..
   29: *  
   30: *
   31: *> \par Purpose:
   32: *  =============
   33: *>
   34: *> \verbatim
   35: *>
   36: *> ZGTSV  solves the equation
   37: *>
   38: *>    A*X = B,
   39: *>
   40: *> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
   41: *> partial pivoting.
   42: *>
   43: *> Note that the equation  A**T *X = B  may be solved by interchanging the
   44: *> order of the arguments DU and DL.
   45: *> \endverbatim
   46: *
   47: *  Arguments:
   48: *  ==========
   49: *
   50: *> \param[in] N
   51: *> \verbatim
   52: *>          N is INTEGER
   53: *>          The order of the matrix A.  N >= 0.
   54: *> \endverbatim
   55: *>
   56: *> \param[in] NRHS
   57: *> \verbatim
   58: *>          NRHS is INTEGER
   59: *>          The number of right hand sides, i.e., the number of columns
   60: *>          of the matrix B.  NRHS >= 0.
   61: *> \endverbatim
   62: *>
   63: *> \param[in,out] DL
   64: *> \verbatim
   65: *>          DL is COMPLEX*16 array, dimension (N-1)
   66: *>          On entry, DL must contain the (n-1) subdiagonal elements of
   67: *>          A.
   68: *>          On exit, DL is overwritten by the (n-2) elements of the
   69: *>          second superdiagonal of the upper triangular matrix U from
   70: *>          the LU factorization of A, in DL(1), ..., DL(n-2).
   71: *> \endverbatim
   72: *>
   73: *> \param[in,out] D
   74: *> \verbatim
   75: *>          D is COMPLEX*16 array, dimension (N)
   76: *>          On entry, D must contain the diagonal elements of A.
   77: *>          On exit, D is overwritten by the n diagonal elements of U.
   78: *> \endverbatim
   79: *>
   80: *> \param[in,out] DU
   81: *> \verbatim
   82: *>          DU is COMPLEX*16 array, dimension (N-1)
   83: *>          On entry, DU must contain the (n-1) superdiagonal elements
   84: *>          of A.
   85: *>          On exit, DU is overwritten by the (n-1) elements of the first
   86: *>          superdiagonal of U.
   87: *> \endverbatim
   88: *>
   89: *> \param[in,out] B
   90: *> \verbatim
   91: *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
   92: *>          On entry, the N-by-NRHS right hand side matrix B.
   93: *>          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
   94: *> \endverbatim
   95: *>
   96: *> \param[in] LDB
   97: *> \verbatim
   98: *>          LDB is INTEGER
   99: *>          The leading dimension of the array B.  LDB >= max(1,N).
  100: *> \endverbatim
  101: *>
  102: *> \param[out] INFO
  103: *> \verbatim
  104: *>          INFO is INTEGER
  105: *>          = 0:  successful exit
  106: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
  107: *>          > 0:  if INFO = i, U(i,i) is exactly zero, and the solution
  108: *>                has not been computed.  The factorization has not been
  109: *>                completed unless i = N.
  110: *> \endverbatim
  111: *
  112: *  Authors:
  113: *  ========
  114: *
  115: *> \author Univ. of Tennessee 
  116: *> \author Univ. of California Berkeley 
  117: *> \author Univ. of Colorado Denver 
  118: *> \author NAG Ltd. 
  119: *
  120: *> \date September 2012
  121: *
  122: *> \ingroup complex16GTsolve
  123: *
  124: *  =====================================================================
  125:       SUBROUTINE ZGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
  126: *
  127: *  -- LAPACK driver routine (version 3.4.2) --
  128: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  129: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  130: *     September 2012
  131: *
  132: *     .. Scalar Arguments ..
  133:       INTEGER            INFO, LDB, N, NRHS
  134: *     ..
  135: *     .. Array Arguments ..
  136:       COMPLEX*16         B( LDB, * ), D( * ), DL( * ), DU( * )
  137: *     ..
  138: *
  139: *  =====================================================================
  140: *
  141: *     .. Parameters ..
  142:       COMPLEX*16         ZERO
  143:       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
  144: *     ..
  145: *     .. Local Scalars ..
  146:       INTEGER            J, K
  147:       COMPLEX*16         MULT, TEMP, ZDUM
  148: *     ..
  149: *     .. Intrinsic Functions ..
  150:       INTRINSIC          ABS, DBLE, DIMAG, MAX
  151: *     ..
  152: *     .. External Subroutines ..
  153:       EXTERNAL           XERBLA
  154: *     ..
  155: *     .. Statement Functions ..
  156:       DOUBLE PRECISION   CABS1
  157: *     ..
  158: *     .. Statement Function definitions ..
  159:       CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
  160: *     ..
  161: *     .. Executable Statements ..
  162: *
  163:       INFO = 0
  164:       IF( N.LT.0 ) THEN
  165:          INFO = -1
  166:       ELSE IF( NRHS.LT.0 ) THEN
  167:          INFO = -2
  168:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  169:          INFO = -7
  170:       END IF
  171:       IF( INFO.NE.0 ) THEN
  172:          CALL XERBLA( 'ZGTSV ', -INFO )
  173:          RETURN
  174:       END IF
  175: *
  176:       IF( N.EQ.0 )
  177:      $   RETURN
  178: *
  179:       DO 30 K = 1, N - 1
  180:          IF( DL( K ).EQ.ZERO ) THEN
  181: *
  182: *           Subdiagonal is zero, no elimination is required.
  183: *
  184:             IF( D( K ).EQ.ZERO ) THEN
  185: *
  186: *              Diagonal is zero: set INFO = K and return; a unique
  187: *              solution can not be found.
  188: *
  189:                INFO = K
  190:                RETURN
  191:             END IF
  192:          ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
  193: *
  194: *           No row interchange required
  195: *
  196:             MULT = DL( K ) / D( K )
  197:             D( K+1 ) = D( K+1 ) - MULT*DU( K )
  198:             DO 10 J = 1, NRHS
  199:                B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
  200:    10       CONTINUE
  201:             IF( K.LT.( N-1 ) )
  202:      $         DL( K ) = ZERO
  203:          ELSE
  204: *
  205: *           Interchange rows K and K+1
  206: *
  207:             MULT = D( K ) / DL( K )
  208:             D( K ) = DL( K )
  209:             TEMP = D( K+1 )
  210:             D( K+1 ) = DU( K ) - MULT*TEMP
  211:             IF( K.LT.( N-1 ) ) THEN
  212:                DL( K ) = DU( K+1 )
  213:                DU( K+1 ) = -MULT*DL( K )
  214:             END IF
  215:             DU( K ) = TEMP
  216:             DO 20 J = 1, NRHS
  217:                TEMP = B( K, J )
  218:                B( K, J ) = B( K+1, J )
  219:                B( K+1, J ) = TEMP - MULT*B( K+1, J )
  220:    20       CONTINUE
  221:          END IF
  222:    30 CONTINUE
  223:       IF( D( N ).EQ.ZERO ) THEN
  224:          INFO = N
  225:          RETURN
  226:       END IF
  227: *
  228: *     Back solve with the matrix U from the factorization.
  229: *
  230:       DO 50 J = 1, NRHS
  231:          B( N, J ) = B( N, J ) / D( N )
  232:          IF( N.GT.1 )
  233:      $      B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
  234:          DO 40 K = N - 2, 1, -1
  235:             B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
  236:      $                  B( K+2, J ) ) / D( K )
  237:    40    CONTINUE
  238:    50 CONTINUE
  239: *
  240:       RETURN
  241: *
  242: *     End of ZGTSV
  243: *
  244:       END