01:       SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
02: *
03: *  -- LAPACK routine (version 3.2) --
04: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
05: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
06: *     November 2006
07: *
08: *     .. Scalar Arguments ..
09:       INTEGER            LDB, N, NRHS
10: *     ..
11: *     .. Array Arguments ..
12:       REAL               B( LDB, * ), D( * ), E( * )
13: *     ..
14: *
15: *  Purpose
16: *  =======
17: *
18: *  SPTTS2 solves a tridiagonal system of the form
19: *     A * X = B
20: *  using the L*D*L' factorization of A computed by SPTTRF.  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) REAL 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) REAL 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) REAL 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           SSCAL
60: *     ..
61: *     .. Executable Statements ..
62: *
63: *     Quick return if possible
64: *
65:       IF( N.LE.1 ) THEN
66:          IF( N.EQ.1 )
67:      $      CALL SSCAL( NRHS, 1. / 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 SPTTS2
93: *
94:       END
95: