dlagts.f

          SUBROUTINE DLAGTS( JOB, N, A, B, C, D, IN, Y, TOL, INFO )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, JOB, N
          DOUBLE PRECISION   TOL
    *     ..
    *     .. Array Arguments ..
          INTEGER            IN( * )
          DOUBLE PRECISION   A( * ), B( * ), C( * ), D( * ), Y( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DLAGTS may be used to solve one of the systems of equations
    *
    *     (T - lambda*I)*x = y   or   (T - lambda*I)'*x = y,
    *
    *  where T is an n by n tridiagonal matrix, for x, following the
    *  factorization of (T - lambda*I) as
    *
    *     (T - lambda*I) = P*L*U ,
    *
    *  by routine DLAGTF. The choice of equation to be solved is
    *  controlled by the argument JOB, and in each case there is an option
    *  to perturb zero or very small diagonal elements of U, this option
    *  being intended for use in applications such as inverse iteration.
    *
    *  Arguments
    *  =========
    *
    *  JOB     (input) INTEGER
    *          Specifies the job to be performed by DLAGTS as follows:
    *          =  1: The equations  (T - lambda*I)x = y  are to be solved,
    *                but diagonal elements of U are not to be perturbed.
    *          = -1: The equations  (T - lambda*I)x = y  are to be solved
    *                and, if overflow would otherwise occur, the diagonal
    *                elements of U are to be perturbed. See argument TOL
    *                below.
    *          =  2: The equations  (T - lambda*I)'x = y  are to be solved,
    *                but diagonal elements of U are not to be perturbed.
    *          = -2: The equations  (T - lambda*I)'x = y  are to be solved
    *                and, if overflow would otherwise occur, the diagonal
    *                elements of U are to be perturbed. See argument TOL
    *                below.
    *
    *  N       (input) INTEGER
    *          The order of the matrix T.
    *
    *  A       (input) DOUBLE PRECISION array, dimension (N)
    *          On entry, A must contain the diagonal elements of U as
    *          returned from DLAGTF.
    *
    *  B       (input) DOUBLE PRECISION array, dimension (N-1)
    *          On entry, B must contain the first super-diagonal elements of
    *          U as returned from DLAGTF.
    *
    *  C       (input) DOUBLE PRECISION array, dimension (N-1)
    *          On entry, C must contain the sub-diagonal elements of L as
    *          returned from DLAGTF.
    *
    *  D       (input) DOUBLE PRECISION array, dimension (N-2)
    *          On entry, D must contain the second super-diagonal elements
    *          of U as returned from DLAGTF.
    *
    *  IN      (input) INTEGER array, dimension (N)
    *          On entry, IN must contain details of the matrix P as returned
    *          from DLAGTF.
    *
    *  Y       (input/output) DOUBLE PRECISION array, dimension (N)
    *          On entry, the right hand side vector y.
    *          On exit, Y is overwritten by the solution vector x.
    *
    *  TOL     (input/output) DOUBLE PRECISION
    *          On entry, with  JOB .lt. 0, TOL should be the minimum
    *          perturbation to be made to very small diagonal elements of U.
    *          TOL should normally be chosen as about eps*norm(U), where eps
    *          is the relative machine precision, but if TOL is supplied as
    *          non-positive, then it is reset to eps*max( abs( u(i,j) ) ).
    *          If  JOB .gt. 0  then TOL is not referenced.
    *
    *          On exit, TOL is changed as described above, only if TOL is
    *          non-positive on entry. Otherwise TOL is unchanged.
    *
    *  INFO    (output) INTEGER
    *          = 0   : successful exit
    *          .lt. 0: if INFO = -i, the i-th argument had an illegal value
    *          .gt. 0: overflow would occur when computing the INFO(th)
    *                  element of the solution vector x. This can only occur
    *                  when JOB is supplied as positive and either means
    *                  that a diagonal element of U is very small, or that
    *                  the elements of the right-hand side vector y are very
    *                  large.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            K
          DOUBLE PRECISION   ABSAK, AK, BIGNUM, EPS, PERT, SFMIN, TEMP
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          ABS, MAX, SIGN
    *     ..
    *     .. External Functions ..
          DOUBLE PRECISION   DLAMCH
          EXTERNAL           DLAMCH
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA
    *     ..
    *     .. Executable Statements ..
    *
          INFO = 0
          IF( ( ABS( JOB ).GT.2 ) .OR. ( JOB.EQ.0 ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DLAGTS', -INFO )
             RETURN
          END IF
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          EPS = DLAMCH( 'Epsilon' )
          SFMIN = DLAMCH( 'Safe minimum' )
          BIGNUM = ONE / SFMIN
    *
          IF( JOB.LT.0 ) THEN
             IF( TOL.LE.ZERO ) THEN
                TOL = ABS( A( 1 ) )
                IF( N.GT.1 )
         $         TOL = MAX( TOL, ABS( A( 2 ) ), ABS( B( 1 ) ) )
                DO 10 K = 3, N
                   TOL = MAX( TOL, ABS( A( K ) ), ABS( B( K-1 ) ),
         $               ABS( D( K-2 ) ) )
       10       CONTINUE
                TOL = TOL*EPS
                IF( TOL.EQ.ZERO )
         $         TOL = EPS
             END IF
          END IF
    *
          IF( ABS( JOB ).EQ.1 ) THEN
             DO 20 K = 2, N
                IF( IN( K-1 ).EQ.0 ) THEN
                   Y( K ) = Y( K ) - C( K-1 )*Y( K-1 )
                ELSE
                   TEMP = Y( K-1 )
                   Y( K-1 ) = Y( K )
                   Y( K ) = TEMP - C( K-1 )*Y( K )
                END IF
       20    CONTINUE
             IF( JOB.EQ.1 ) THEN
                DO 30 K = N, 1, -1
                   IF( K.LE.N-2 ) THEN
                      TEMP = Y( K ) - B( K )*Y( K+1 ) - D( K )*Y( K+2 )
                   ELSE IF( K.EQ.N-1 ) THEN
                      TEMP = Y( K ) - B( K )*Y( K+1 )
                   ELSE
                      TEMP = Y( K )
                   END IF
                   AK = A( K )
                   ABSAK = ABS( AK )
                   IF( ABSAK.LT.ONE ) THEN
                      IF( ABSAK.LT.SFMIN ) THEN
                         IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK )
         $                    THEN
                            INFO = K
                            RETURN
                         ELSE
                            TEMP = TEMP*BIGNUM
                            AK = AK*BIGNUM
                         END IF
                      ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN
                         INFO = K
                         RETURN
                      END IF
                   END IF
                   Y( K ) = TEMP / AK
       30       CONTINUE
             ELSE
                DO 50 K = N, 1, -1
                   IF( K.LE.N-2 ) THEN
                      TEMP = Y( K ) - B( K )*Y( K+1 ) - D( K )*Y( K+2 )
                   ELSE IF( K.EQ.N-1 ) THEN
                      TEMP = Y( K ) - B( K )*Y( K+1 )
                   ELSE
                      TEMP = Y( K )
                   END IF
                   AK = A( K )
                   PERT = SIGN( TOL, AK )
       40          CONTINUE
                   ABSAK = ABS( AK )
                   IF( ABSAK.LT.ONE ) THEN
                      IF( ABSAK.LT.SFMIN ) THEN
                         IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK )
         $                    THEN
                            AK = AK + PERT
                            PERT = 2*PERT
                            GO TO 40
                         ELSE
                            TEMP = TEMP*BIGNUM
                            AK = AK*BIGNUM
                         END IF
                      ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN
                         AK = AK + PERT
                         PERT = 2*PERT
                         GO TO 40
                      END IF
                   END IF
                   Y( K ) = TEMP / AK
       50       CONTINUE
             END IF
          ELSE
    *
    *        Come to here if  JOB = 2 or -2
    *
             IF( JOB.EQ.2 ) THEN
                DO 60 K = 1, N
                   IF( K.GE.3 ) THEN
                      TEMP = Y( K ) - B( K-1 )*Y( K-1 ) - D( K-2 )*Y( K-2 )
                   ELSE IF( K.EQ.2 ) THEN
                      TEMP = Y( K ) - B( K-1 )*Y( K-1 )
                   ELSE
                      TEMP = Y( K )
                   END IF
                   AK = A( K )
                   ABSAK = ABS( AK )
                   IF( ABSAK.LT.ONE ) THEN
                      IF( ABSAK.LT.SFMIN ) THEN
                         IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK )
         $                    THEN
                            INFO = K
                            RETURN
                         ELSE
                            TEMP = TEMP*BIGNUM
                            AK = AK*BIGNUM
                         END IF
                      ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN
                         INFO = K
                         RETURN
                      END IF
                   END IF
                   Y( K ) = TEMP / AK
       60       CONTINUE
             ELSE
                DO 80 K = 1, N
                   IF( K.GE.3 ) THEN
                      TEMP = Y( K ) - B( K-1 )*Y( K-1 ) - D( K-2 )*Y( K-2 )
                   ELSE IF( K.EQ.2 ) THEN
                      TEMP = Y( K ) - B( K-1 )*Y( K-1 )
                   ELSE
                      TEMP = Y( K )
                   END IF
                   AK = A( K )
                   PERT = SIGN( TOL, AK )
       70          CONTINUE
                   ABSAK = ABS( AK )
                   IF( ABSAK.LT.ONE ) THEN
                      IF( ABSAK.LT.SFMIN ) THEN
                         IF( ABSAK.EQ.ZERO .OR. ABS( TEMP )*SFMIN.GT.ABSAK )
         $                    THEN
                            AK = AK + PERT
                            PERT = 2*PERT
                            GO TO 70
                         ELSE
                            TEMP = TEMP*BIGNUM
                            AK = AK*BIGNUM
                         END IF
                      ELSE IF( ABS( TEMP ).GT.ABSAK*BIGNUM ) THEN
                         AK = AK + PERT
                         PERT = 2*PERT
                         GO TO 70
                      END IF
                   END IF
                   Y( K ) = TEMP / AK
       80       CONTINUE
             END IF
    *
             DO 90 K = N, 2, -1
                IF( IN( K-1 ).EQ.0 ) THEN
                   Y( K-1 ) = Y( K-1 ) - C( K-1 )*Y( K )
                ELSE
                   TEMP = Y( K-1 )
                   Y( K-1 ) = Y( K )
                   Y( K ) = TEMP - C( K-1 )*Y( K )
                END IF
       90    CONTINUE
          END IF
    *
    *     End of DLAGTS
    *
          END