1 SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**T 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**T 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**T factorization of A. E can also be regarded
42 * as the superdiagonal of the unit bidiagonal factor U from the
43 * factorization A = U**T*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**T,
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**T * 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
2 *
3 * -- LAPACK routine (version 3.3.1) --
4 * -- LAPACK is a software package provided by Univ. of Tennessee, --
5 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6 * -- April 2011 --
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**T 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**T 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**T factorization of A. E can also be regarded
42 * as the superdiagonal of the unit bidiagonal factor U from the
43 * factorization A = U**T*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**T,
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**T * 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