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Annotation of rpl/lapack/lapack/dptts2.f, revision 1.2

1.1       bertrand    1:       SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
                      2: *
                      3: *  -- LAPACK routine (version 3.2) --
                      4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                      5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
                      6: *     November 2006
                      7: *
                      8: *     .. Scalar Arguments ..
                      9:       INTEGER            LDB, N, NRHS
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       DOUBLE PRECISION   B( LDB, * ), D( * ), E( * )
                     13: *     ..
                     14: *
                     15: *  Purpose
                     16: *  =======
                     17: *
                     18: *  DPTTS2 solves a tridiagonal system of the form
                     19: *     A * X = B
                     20: *  using the L*D*L' factorization of A computed by DPTTRF.  D is a
                     21: *  diagonal matrix specified in the vector D, L is a unit bidiagonal
                     22: *  matrix whose subdiagonal is specified in the vector E, and X and B
                     23: *  are N by NRHS matrices.
                     24: *
                     25: *  Arguments
                     26: *  =========
                     27: *
                     28: *  N       (input) INTEGER
                     29: *          The order of the tridiagonal matrix A.  N >= 0.
                     30: *
                     31: *  NRHS    (input) INTEGER
                     32: *          The number of right hand sides, i.e., the number of columns
                     33: *          of the matrix B.  NRHS >= 0.
                     34: *
                     35: *  D       (input) DOUBLE PRECISION array, dimension (N)
                     36: *          The n diagonal elements of the diagonal matrix D from the
                     37: *          L*D*L' factorization of A.
                     38: *
                     39: *  E       (input) DOUBLE PRECISION array, dimension (N-1)
                     40: *          The (n-1) subdiagonal elements of the unit bidiagonal factor
                     41: *          L from the L*D*L' factorization of A.  E can also be regarded
                     42: *          as the superdiagonal of the unit bidiagonal factor U from the
                     43: *          factorization A = U'*D*U.
                     44: *
                     45: *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
                     46: *          On entry, the right hand side vectors B for the system of
                     47: *          linear equations.
                     48: *          On exit, the solution vectors, X.
                     49: *
                     50: *  LDB     (input) INTEGER
                     51: *          The leading dimension of the array B.  LDB >= max(1,N).
                     52: *
                     53: *  =====================================================================
                     54: *
                     55: *     .. Local Scalars ..
                     56:       INTEGER            I, J
                     57: *     ..
                     58: *     .. External Subroutines ..
                     59:       EXTERNAL           DSCAL
                     60: *     ..
                     61: *     .. Executable Statements ..
                     62: *
                     63: *     Quick return if possible
                     64: *
                     65:       IF( N.LE.1 ) THEN
                     66:          IF( N.EQ.1 )
                     67:      $      CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
                     68:          RETURN
                     69:       END IF
                     70: *
                     71: *     Solve A * X = B using the factorization A = L*D*L',
                     72: *     overwriting each right hand side vector with its solution.
                     73: *
                     74:       DO 30 J = 1, NRHS
                     75: *
                     76: *           Solve L * x = b.
                     77: *
                     78:          DO 10 I = 2, N
                     79:             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
                     80:    10    CONTINUE
                     81: *
                     82: *           Solve D * L' * x = b.
                     83: *
                     84:          B( N, J ) = B( N, J ) / D( N )
                     85:          DO 20 I = N - 1, 1, -1
                     86:             B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
                     87:    20    CONTINUE
                     88:    30 CONTINUE
                     89: *
                     90:       RETURN
                     91: *
                     92: *     End of DPTTS2
                     93: *
                     94:       END