1: *> \brief \b DPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DPTTS2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptts2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dptts2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dptts2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER LDB, N, NRHS
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DPTTS2 solves a tridiagonal system of the form
37: *> A * X = B
38: *> using the L*D*L**T factorization of A computed by DPTTRF. D is a
39: *> diagonal matrix specified in the vector D, L is a unit bidiagonal
40: *> matrix whose subdiagonal is specified in the vector E, and X and B
41: *> are N by NRHS matrices.
42: *> \endverbatim
43: *
44: * Arguments:
45: * ==========
46: *
47: *> \param[in] N
48: *> \verbatim
49: *> N is INTEGER
50: *> The order of the tridiagonal matrix A. N >= 0.
51: *> \endverbatim
52: *>
53: *> \param[in] NRHS
54: *> \verbatim
55: *> NRHS is INTEGER
56: *> The number of right hand sides, i.e., the number of columns
57: *> of the matrix B. NRHS >= 0.
58: *> \endverbatim
59: *>
60: *> \param[in] D
61: *> \verbatim
62: *> D is DOUBLE PRECISION array, dimension (N)
63: *> The n diagonal elements of the diagonal matrix D from the
64: *> L*D*L**T factorization of A.
65: *> \endverbatim
66: *>
67: *> \param[in] E
68: *> \verbatim
69: *> E is DOUBLE PRECISION array, dimension (N-1)
70: *> The (n-1) subdiagonal elements of the unit bidiagonal factor
71: *> L from the L*D*L**T factorization of A. E can also be regarded
72: *> as the superdiagonal of the unit bidiagonal factor U from the
73: *> factorization A = U**T*D*U.
74: *> \endverbatim
75: *>
76: *> \param[in,out] B
77: *> \verbatim
78: *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
79: *> On entry, the right hand side vectors B for the system of
80: *> linear equations.
81: *> On exit, the solution vectors, X.
82: *> \endverbatim
83: *>
84: *> \param[in] LDB
85: *> \verbatim
86: *> LDB is INTEGER
87: *> The leading dimension of the array B. LDB >= max(1,N).
88: *> \endverbatim
89: *
90: * Authors:
91: * ========
92: *
93: *> \author Univ. of Tennessee
94: *> \author Univ. of California Berkeley
95: *> \author Univ. of Colorado Denver
96: *> \author NAG Ltd.
97: *
98: *> \ingroup doublePTcomputational
99: *
100: * =====================================================================
101: SUBROUTINE DPTTS2( N, NRHS, D, E, B, LDB )
102: *
103: * -- LAPACK computational routine --
104: * -- LAPACK is a software package provided by Univ. of Tennessee, --
105: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106: *
107: * .. Scalar Arguments ..
108: INTEGER LDB, N, NRHS
109: * ..
110: * .. Array Arguments ..
111: DOUBLE PRECISION B( LDB, * ), D( * ), E( * )
112: * ..
113: *
114: * =====================================================================
115: *
116: * .. Local Scalars ..
117: INTEGER I, J
118: * ..
119: * .. External Subroutines ..
120: EXTERNAL DSCAL
121: * ..
122: * .. Executable Statements ..
123: *
124: * Quick return if possible
125: *
126: IF( N.LE.1 ) THEN
127: IF( N.EQ.1 )
128: $ CALL DSCAL( NRHS, 1.D0 / D( 1 ), B, LDB )
129: RETURN
130: END IF
131: *
132: * Solve A * X = B using the factorization A = L*D*L**T,
133: * overwriting each right hand side vector with its solution.
134: *
135: DO 30 J = 1, NRHS
136: *
137: * Solve L * x = b.
138: *
139: DO 10 I = 2, N
140: B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
141: 10 CONTINUE
142: *
143: * Solve D * L**T * x = b.
144: *
145: B( N, J ) = B( N, J ) / D( N )
146: DO 20 I = N - 1, 1, -1
147: B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
148: 20 CONTINUE
149: 30 CONTINUE
150: *
151: RETURN
152: *
153: * End of DPTTS2
154: *
155: END
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