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    1: *> \brief \b DPPTRS
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DPPTRS + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpptrs.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpptrs.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpptrs.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       CHARACTER          UPLO
   25: *       INTEGER            INFO, LDB, N, NRHS
   26: *       ..
   27: *       .. Array Arguments ..
   28: *       DOUBLE PRECISION   AP( * ), B( LDB, * )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *> DPPTRS solves a system of linear equations A*X = B with a symmetric
   38: *> positive definite matrix A in packed storage using the Cholesky
   39: *> factorization A = U**T*U or A = L*L**T computed by DPPTRF.
   40: *> \endverbatim
   41: *
   42: *  Arguments:
   43: *  ==========
   44: *
   45: *> \param[in] UPLO
   46: *> \verbatim
   47: *>          UPLO is CHARACTER*1
   48: *>          = 'U':  Upper triangle of A is stored;
   49: *>          = 'L':  Lower triangle of A is stored.
   50: *> \endverbatim
   51: *>
   52: *> \param[in] N
   53: *> \verbatim
   54: *>          N is INTEGER
   55: *>          The order of the matrix A.  N >= 0.
   56: *> \endverbatim
   57: *>
   58: *> \param[in] NRHS
   59: *> \verbatim
   60: *>          NRHS is INTEGER
   61: *>          The number of right hand sides, i.e., the number of columns
   62: *>          of the matrix B.  NRHS >= 0.
   63: *> \endverbatim
   64: *>
   65: *> \param[in] AP
   66: *> \verbatim
   67: *>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
   68: *>          The triangular factor U or L from the Cholesky factorization
   69: *>          A = U**T*U or A = L*L**T, packed columnwise in a linear
   70: *>          array.  The j-th column of U or L is stored in the array AP
   71: *>          as follows:
   72: *>          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
   73: *>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
   74: *> \endverbatim
   75: *>
   76: *> \param[in,out] B
   77: *> \verbatim
   78: *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
   79: *>          On entry, the right hand side matrix B.
   80: *>          On exit, the solution matrix X.
   81: *> \endverbatim
   82: *>
   83: *> \param[in] LDB
   84: *> \verbatim
   85: *>          LDB is INTEGER
   86: *>          The leading dimension of the array B.  LDB >= max(1,N).
   87: *> \endverbatim
   88: *>
   89: *> \param[out] INFO
   90: *> \verbatim
   91: *>          INFO is INTEGER
   92: *>          = 0:  successful exit
   93: *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   94: *> \endverbatim
   95: *
   96: *  Authors:
   97: *  ========
   98: *
   99: *> \author Univ. of Tennessee
  100: *> \author Univ. of California Berkeley
  101: *> \author Univ. of Colorado Denver
  102: *> \author NAG Ltd.
  103: *
  104: *> \ingroup doubleOTHERcomputational
  105: *
  106: *  =====================================================================
  107:       SUBROUTINE DPPTRS( UPLO, N, NRHS, AP, B, LDB, INFO )
  108: *
  109: *  -- LAPACK computational routine --
  110: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  111: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  112: *
  113: *     .. Scalar Arguments ..
  114:       CHARACTER          UPLO
  115:       INTEGER            INFO, LDB, N, NRHS
  116: *     ..
  117: *     .. Array Arguments ..
  118:       DOUBLE PRECISION   AP( * ), B( LDB, * )
  119: *     ..
  120: *
  121: *  =====================================================================
  122: *
  123: *     .. Local Scalars ..
  124:       LOGICAL            UPPER
  125:       INTEGER            I
  126: *     ..
  127: *     .. External Functions ..
  128:       LOGICAL            LSAME
  129:       EXTERNAL           LSAME
  130: *     ..
  131: *     .. External Subroutines ..
  132:       EXTERNAL           DTPSV, XERBLA
  133: *     ..
  134: *     .. Intrinsic Functions ..
  135:       INTRINSIC          MAX
  136: *     ..
  137: *     .. Executable Statements ..
  138: *
  139: *     Test the input parameters.
  140: *
  141:       INFO = 0
  142:       UPPER = LSAME( UPLO, 'U' )
  143:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
  144:          INFO = -1
  145:       ELSE IF( N.LT.0 ) THEN
  146:          INFO = -2
  147:       ELSE IF( NRHS.LT.0 ) THEN
  148:          INFO = -3
  149:       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
  150:          INFO = -6
  151:       END IF
  152:       IF( INFO.NE.0 ) THEN
  153:          CALL XERBLA( 'DPPTRS', -INFO )
  154:          RETURN
  155:       END IF
  156: *
  157: *     Quick return if possible
  158: *
  159:       IF( N.EQ.0 .OR. NRHS.EQ.0 )
  160:      $   RETURN
  161: *
  162:       IF( UPPER ) THEN
  163: *
  164: *        Solve A*X = B where A = U**T * U.
  165: *
  166:          DO 10 I = 1, NRHS
  167: *
  168: *           Solve U**T *X = B, overwriting B with X.
  169: *
  170:             CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', N, AP,
  171:      $                  B( 1, I ), 1 )
  172: *
  173: *           Solve U*X = B, overwriting B with X.
  174: *
  175:             CALL DTPSV( 'Upper', 'No transpose', 'Non-unit', N, AP,
  176:      $                  B( 1, I ), 1 )
  177:    10    CONTINUE
  178:       ELSE
  179: *
  180: *        Solve A*X = B where A = L * L**T.
  181: *
  182:          DO 20 I = 1, NRHS
  183: *
  184: *           Solve L*Y = B, overwriting B with X.
  185: *
  186:             CALL DTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
  187:      $                  B( 1, I ), 1 )
  188: *
  189: *           Solve L**T *X = Y, overwriting B with X.
  190: *
  191:             CALL DTPSV( 'Lower', 'Transpose', 'Non-unit', N, AP,
  192:      $                  B( 1, I ), 1 )
  193:    20    CONTINUE
  194:       END IF
  195: *
  196:       RETURN
  197: *
  198: *     End of DPPTRS
  199: *
  200:       END