cptts2.f

          SUBROUTINE CPTTS2( IUPLO, 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            IUPLO, LDB, N, NRHS
    *     ..
    *     .. Array Arguments ..
          REAL               D( * )
          COMPLEX            B( LDB, * ), E( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CPTTS2 solves a tridiagonal system of the form
    *     A * X = B
    *  using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF.
    *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
    *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
    *  the vector E, and X and B are N by NRHS matrices.
    *
    *  Arguments
    *  =========
    *
    *  IUPLO   (input) INTEGER
    *          Specifies the form of the factorization and whether the
    *          vector E is the superdiagonal of the upper bidiagonal factor
    *          U or the subdiagonal of the lower bidiagonal factor L.
    *          = 1:  A = U'*D*U, E is the superdiagonal of U
    *          = 0:  A = L*D*L', E is the subdiagonal of L
    *
    *  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
    *          factorization A = U'*D*U or A = L*D*L'.
    *
    *  E       (input) COMPLEX array, dimension (N-1)
    *          If IUPLO = 1, the (n-1) superdiagonal elements of the unit
    *          bidiagonal factor U from the factorization A = U'*D*U.
    *          If IUPLO = 0, the (n-1) subdiagonal elements of the unit
    *          bidiagonal factor L from the factorization A = L*D*L'.
    *
    *  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           CSSCAL
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          CONJG
    *     ..
    *     .. Executable Statements ..
    *
    *     Quick return if possible
    *
          IF( N.LE.1 ) THEN
             IF( N.EQ.1 )
         $      CALL CSSCAL( NRHS, 1. / D( 1 ), B, LDB )
             RETURN
          END IF
    *
          IF( IUPLO.EQ.1 ) THEN
    *
    *        Solve A * X = B using the factorization A = U'*D*U,
    *        overwriting each right hand side vector with its solution.
    *
             IF( NRHS.LE.2 ) THEN
                J = 1
        5       CONTINUE
    *
    *           Solve U' * x = b.
    *
                DO 10 I = 2, N
                   B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
       10       CONTINUE
    *
    *           Solve D * U * x = b.
    *
                DO 20 I = 1, N
                   B( I, J ) = B( I, J ) / D( I )
       20       CONTINUE
                DO 30 I = N - 1, 1, -1
                   B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
       30       CONTINUE
                IF( J.LT.NRHS ) THEN
                   J = J + 1
                   GO TO 5
                END IF
             ELSE
                DO 60 J = 1, NRHS
    *
    *              Solve U' * x = b.
    *
                   DO 40 I = 2, N
                      B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
       40          CONTINUE
    *
    *              Solve D * U * x = b.
    *
                   B( N, J ) = B( N, J ) / D( N )
                   DO 50 I = N - 1, 1, -1
                      B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
       50          CONTINUE
       60       CONTINUE
             END IF
          ELSE
    *
    *        Solve A * X = B using the factorization A = L*D*L',
    *        overwriting each right hand side vector with its solution.
    *
             IF( NRHS.LE.2 ) THEN
                J = 1
       65       CONTINUE
    *
    *           Solve L * x = b.
    *
                DO 70 I = 2, N
                   B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
       70       CONTINUE
    *
    *           Solve D * L' * x = b.
    *
                DO 80 I = 1, N
                   B( I, J ) = B( I, J ) / D( I )
       80       CONTINUE
                DO 90 I = N - 1, 1, -1
                   B( I, J ) = B( I, J ) - B( I+1, J )*CONJG( E( I ) )
       90       CONTINUE
                IF( J.LT.NRHS ) THEN
                   J = J + 1
                   GO TO 65
                END IF
             ELSE
                DO 120 J = 1, NRHS
    *
    *              Solve L * x = b.
    *
                   DO 100 I = 2, N
                      B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
      100          CONTINUE
    *
    *              Solve D * L' * x = b.
    *
                   B( N, J ) = B( N, J ) / D( N )
                   DO 110 I = N - 1, 1, -1
                      B( I, J ) = B( I, J ) / D( I ) -
         $                        B( I+1, J )*CONJG( E( I ) )
      110          CONTINUE
      120       CONTINUE
             END IF
          END IF
    *
          RETURN
    *
    *     End of CPTTS2
    *
          END