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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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7788:45f5faba05a2 7789:82be108cc558
1 SUBROUTINE SPTTS2( N, NRHS, D, E, B, LDB )
2 *
3 * -- LAPACK routine (version 3.1) --
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER LDB, N, NRHS
9 * ..
10 * .. Array Arguments ..
11 REAL B( LDB, * ), D( * ), E( * )
12 * ..
13 *
14 * Purpose
15 * =======
16 *
17 * SPTTS2 solves a tridiagonal system of the form
18 * A * X = B
19 * using the L*D*L' factorization of A computed by SPTTRF. D is a
20 * diagonal matrix specified in the vector D, L is a unit bidiagonal
21 * matrix whose subdiagonal is specified in the vector E, and X and B
22 * are N by NRHS matrices.
23 *
24 * Arguments
25 * =========
26 *
27 * N (input) INTEGER
28 * The order of the tridiagonal matrix A. N >= 0.
29 *
30 * NRHS (input) INTEGER
31 * The number of right hand sides, i.e., the number of columns
32 * of the matrix B. NRHS >= 0.
33 *
34 * D (input) REAL array, dimension (N)
35 * The n diagonal elements of the diagonal matrix D from the
36 * L*D*L' factorization of A.
37 *
38 * E (input) REAL array, dimension (N-1)
39 * The (n-1) subdiagonal elements of the unit bidiagonal factor
40 * L from the L*D*L' factorization of A. E can also be regarded
41 * as the superdiagonal of the unit bidiagonal factor U from the
42 * factorization A = U'*D*U.
43 *
44 * B (input/output) REAL array, dimension (LDB,NRHS)
45 * On entry, the right hand side vectors B for the system of
46 * linear equations.
47 * On exit, the solution vectors, X.
48 *
49 * LDB (input) INTEGER
50 * The leading dimension of the array B. LDB >= max(1,N).
51 *
52 * =====================================================================
53 *
54 * .. Local Scalars ..
55 INTEGER I, J
56 * ..
57 * .. External Subroutines ..
58 EXTERNAL SSCAL
59 * ..
60 * .. Executable Statements ..
61 *
62 * Quick return if possible
63 *
64 IF( N.LE.1 ) THEN
65 IF( N.EQ.1 )
66 $ CALL SSCAL( NRHS, 1. / D( 1 ), B, LDB )
67 RETURN
68 END IF
69 *
70 * Solve A * X = B using the factorization A = L*D*L',
71 * overwriting each right hand side vector with its solution.
72 *
73 DO 30 J = 1, NRHS
74 *
75 * Solve L * x = b.
76 *
77 DO 10 I = 2, N
78 B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
79 10 CONTINUE
80 *
81 * Solve D * L' * x = b.
82 *
83 B( N, J ) = B( N, J ) / D( N )
84 DO 20 I = N - 1, 1, -1
85 B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
86 20 CONTINUE
87 30 CONTINUE
88 *
89 RETURN
90 *
91 * End of SPTTS2
92 *
93 END