sptts2.f

          SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          REAL               B( LDB, * ), D( * ), E( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SPTTS2 solves a tridiagonal system of the form
    *     A * X = B
    *  using the L*D*L' factorization of A computed by SPTTRF.  D is a
    *  diagonal matrix specified in the vector D, L is a unit bidiagonal
    *  matrix whose subdiagonal is specified in the vector E, and X and B
    *  are N by NRHS matrices.
    *
    *  Arguments
    *  =========
    *
    *  N       (input) INTEGER
    *          The order of the tridiagonal matrix A.  N >= 0.
    *
    *  NRHS    (input) INTEGER
    *          The number of right hand sides, i.e., the number of columns
    *          of the matrix B.  NRHS >= 0.
    *
    *  D       (input) REAL array, dimension (N)
    *          The n diagonal elements of the diagonal matrix D from the
    *          L*D*L' factorization of A.
    *
    *  E       (input) REAL array, dimension (N-1)
    *          The (n-1) subdiagonal elements of the unit bidiagonal factor
    *          L from the L*D*L' factorization of A.  E can also be regarded
    *          as the superdiagonal of the unit bidiagonal factor U from the
    *          factorization A = U'*D*U.
    *
    *  B       (input/output) REAL array, dimension (LDB,NRHS)
    *          On entry, the right hand side vectors B for the system of
    *          linear equations.
    *          On exit, the solution vectors, X.
    *
    *  LDB     (input) INTEGER
    *          The leading dimension of the array B.  LDB >= max(1,N).
    *
    *  =====================================================================
    *
    *     .. Local Scalars ..
          INTEGER            I, J
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SSCAL
    *     ..
    *     .. Executable Statements ..
    *
    *     Quick return if possible
    *
          IF( N.LE.1 ) THEN
             IF( N.EQ.1 )
         $      CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB )
             RETURN
          END IF
    *
    *     Solve A * X = B using the factorization A = L*D*L',
    *     overwriting each right hand side vector with its solution.
    *
          DO 30 J = 1, NRHS
    *
    *           Solve L * x = b.
    *
             DO 10 I = 2, N
                B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
       10    CONTINUE
    *
    *           Solve D * L' * x = b.
    *
             B( N, J ) = B( N, J ) / D( N )
             DO 20 I = N - 1, 1, -1
                B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
       20    CONTINUE
       30 CONTINUE
    *
          RETURN
    *
    *     End of SPTTS2
    *
          END