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sptts2.f
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1 *> \brief \b SPTTS2 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 SPTTS2 + dependencies
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER LDB, N, NRHS
25 * ..
26 * .. Array Arguments ..
27 * REAL B( LDB, * ), D( * ), E( * )
28 * ..
29 *
30 *
31 *> \par Purpose:
32 * =============
33 *>
34 *> \verbatim
35 *>
36 *> SPTTS2 solves a tridiagonal system of the form
37 *> A * X = B
38 *> using the L*D*L**T factorization of A computed by SPTTRF. 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 REAL 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 REAL 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 REAL 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 *> \date September 2012
99 *
100 *> \ingroup realPTcomputational
101 *
102 * =====================================================================
103  SUBROUTINE sptts2( N, NRHS, D, E, B, LDB )
104 *
105 * -- LAPACK computational routine (version 3.4.2) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * September 2012
109 *
110 * .. Scalar Arguments ..
111  INTEGER ldb, n, nrhs
112 * ..
113 * .. Array Arguments ..
114  REAL b( ldb, * ), d( * ), e( * )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Local Scalars ..
120  INTEGER i, j
121 * ..
122 * .. External Subroutines ..
123  EXTERNAL sscal
124 * ..
125 * .. Executable Statements ..
126 *
127 * Quick return if possible
128 *
129  IF( n.LE.1 ) THEN
130  IF( n.EQ.1 )
131  $ CALL sscal( nrhs, 1. / d( 1 ), b, ldb )
132  RETURN
133  END IF
134 *
135 * Solve A * X = B using the factorization A = L*D*L**T,
136 * overwriting each right hand side vector with its solution.
137 *
138  DO 30 j = 1, nrhs
139 *
140 * Solve L * x = b.
141 *
142  DO 10 i = 2, n
143  b( i, j ) = b( i, j ) - b( i-1, j )*e( i-1 )
144  10 CONTINUE
145 *
146 * Solve D * L**T * x = b.
147 *
148  b( n, j ) = b( n, j ) / d( n )
149  DO 20 i = n - 1, 1, -1
150  b( i, j ) = b( i, j ) / d( i ) - b( i+1, j )*e( i )
151  20 CONTINUE
152  30 CONTINUE
153 *
154  RETURN
155 *
156 * End of SPTTS2
157 *
158  END