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Annotation of rpl/lapack/lapack/dptts2.f, revision 1.12

1.12    ! bertrand    1: *> \brief \b DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
1.9       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
                      5: * Online html documentation available at 
                      6: *            http://www.netlib.org/lapack/explore-html/ 
                      7: *
                      8: *> \htmlonly
                      9: *> Download DPTTS2 + dependencies 
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptts2.f"> 
                     11: *> [TGZ]</a> 
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dptts2.f"> 
                     13: *> [ZIP]</a> 
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dptts2.f"> 
                     15: *> [TXT]</a>
                     16: *> \endhtmlonly 
                     17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
                     21: *       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
                     22: * 
                     23: *       .. Scalar Arguments ..
                     24: *       INTEGER            LDB, N, NRHS
                     25: *       ..
                     26: *       .. Array Arguments ..
                     27: *       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
                     28: *       ..
                     29: *  
                     30: *
                     31: *> \par Purpose:
                     32: *  =============
                     33: *>
                     34: *> \verbatim
                     35: *>
                     36: *> DPTTS2 solves a tridiagonal system of the form
                     37: *>    A * X = B
                     38: *> using the L*D*L**T factorization of A computed by DPTTRF.  D is a
                     39: *> diagonal matrix specified in the vector D, L is a unit bidiagonal
                     40: *> matrix whose subdiagonal is specified in the vector E, and X and B
                     41: *> are N by NRHS matrices.
                     42: *> \endverbatim
                     43: *
                     44: *  Arguments:
                     45: *  ==========
                     46: *
                     47: *> \param[in] N
                     48: *> \verbatim
                     49: *>          N is INTEGER
                     50: *>          The order of the tridiagonal matrix A.  N >= 0.
                     51: *> \endverbatim
                     52: *>
                     53: *> \param[in] NRHS
                     54: *> \verbatim
                     55: *>          NRHS is INTEGER
                     56: *>          The number of right hand sides, i.e., the number of columns
                     57: *>          of the matrix B.  NRHS >= 0.
                     58: *> \endverbatim
                     59: *>
                     60: *> \param[in] D
                     61: *> \verbatim
                     62: *>          D is DOUBLE PRECISION array, dimension (N)
                     63: *>          The n diagonal elements of the diagonal matrix D from the
                     64: *>          L*D*L**T factorization of A.
                     65: *> \endverbatim
                     66: *>
                     67: *> \param[in] E
                     68: *> \verbatim
                     69: *>          E is DOUBLE PRECISION array, dimension (N-1)
                     70: *>          The (n-1) subdiagonal elements of the unit bidiagonal factor
                     71: *>          L from the L*D*L**T factorization of A.  E can also be regarded
                     72: *>          as the superdiagonal of the unit bidiagonal factor U from the
                     73: *>          factorization A = U**T*D*U.
                     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 vectors B for the system of
                     80: *>          linear equations.
                     81: *>          On exit, the solution vectors, X.
                     82: *> \endverbatim
                     83: *>
                     84: *> \param[in] LDB
                     85: *> \verbatim
                     86: *>          LDB is INTEGER
                     87: *>          The leading dimension of the array B.  LDB >= max(1,N).
                     88: *> \endverbatim
                     89: *
                     90: *  Authors:
                     91: *  ========
                     92: *
                     93: *> \author Univ. of Tennessee 
                     94: *> \author Univ. of California Berkeley 
                     95: *> \author Univ. of Colorado Denver 
                     96: *> \author NAG Ltd. 
                     97: *
1.12    ! bertrand   98: *> \date September 2012
1.9       bertrand   99: *
1.12    ! bertrand  100: *> \ingroup doublePTcomputational
1.9       bertrand  101: *
                    102: *  =====================================================================
1.1       bertrand  103:       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
                    104: *
1.12    ! bertrand  105: *  -- LAPACK computational routine (version 3.4.2) --
1.1       bertrand  106: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    107: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.12    ! bertrand  108: *     September 2012
1.1       bertrand  109: *
                    110: *     .. Scalar Arguments ..
                    111:       INTEGER            LDB, N, NRHS
                    112: *     ..
                    113: *     .. Array Arguments ..
                    114:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
                    115: *     ..
                    116: *
                    117: *  =====================================================================
                    118: *
                    119: *     .. Local Scalars ..
                    120:       INTEGER            I, J
                    121: *     ..
                    122: *     .. External Subroutines ..
                    123:       EXTERNAL           DSCAL
                    124: *     ..
                    125: *     .. Executable Statements ..
                    126: *
                    127: *     Quick return if possible
                    128: *
                    129:       IF( N.LE.1 ) THEN
                    130:          IF( N.EQ.1 )
                    131:      $      CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
                    132:          RETURN
                    133:       END IF
                    134: *
1.8       bertrand  135: *     Solve A * X = B using the factorization A = L*D*L**T,
1.1       bertrand  136: *     overwriting each right hand side vector with its solution.
                    137: *
                    138:       DO 30 J = 1, NRHS
                    139: *
                    140: *           Solve L * x = b.
                    141: *
                    142:          DO 10 I = 2, N
                    143:             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
                    144:    10    CONTINUE
                    145: *
1.8       bertrand  146: *           Solve D * L**T * x = b.
1.1       bertrand  147: *
                    148:          B( N, J ) = B( N, J ) / D( N )
                    149:          DO 20 I = N - 1, 1, -1
                    150:             B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
                    151:    20    CONTINUE
                    152:    30 CONTINUE
                    153: *
                    154:       RETURN
                    155: *
                    156: *     End of DPTTS2
                    157: *
                    158:       END