LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sptt02.f
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1 *> \brief \b SPTT02
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SPTT02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LDB, LDX, N, NRHS
15 * REAL RESID
16 * ..
17 * .. Array Arguments ..
18 * REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> SPTT02 computes the residual for the solution to a symmetric
28 *> tridiagonal system of equations:
29 *> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
30 *> where EPS is the machine epsilon.
31 *> \endverbatim
32 *
33 * Arguments:
34 * ==========
35 *
36 *> \param[in] N
37 *> \verbatim
38 *> N is INTEGTER
39 *> The order of the matrix A.
40 *> \endverbatim
41 *>
42 *> \param[in] NRHS
43 *> \verbatim
44 *> NRHS is INTEGER
45 *> The number of right hand sides, i.e., the number of columns
46 *> of the matrices B and X. NRHS >= 0.
47 *> \endverbatim
48 *>
49 *> \param[in] D
50 *> \verbatim
51 *> D is REAL array, dimension (N)
52 *> The n diagonal elements of the tridiagonal matrix A.
53 *> \endverbatim
54 *>
55 *> \param[in] E
56 *> \verbatim
57 *> E is REAL array, dimension (N-1)
58 *> The (n-1) subdiagonal elements of the tridiagonal matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] X
62 *> \verbatim
63 *> X is REAL array, dimension (LDX,NRHS)
64 *> The n by nrhs matrix of solution vectors X.
65 *> \endverbatim
66 *>
67 *> \param[in] LDX
68 *> \verbatim
69 *> LDX is INTEGER
70 *> The leading dimension of the array X. LDX >= max(1,N).
71 *> \endverbatim
72 *>
73 *> \param[in,out] B
74 *> \verbatim
75 *> B is REAL array, dimension (LDB,NRHS)
76 *> On entry, the n by nrhs matrix of right hand side vectors B.
77 *> On exit, B is overwritten with the difference B - A*X.
78 *> \endverbatim
79 *>
80 *> \param[in] LDB
81 *> \verbatim
82 *> LDB is INTEGER
83 *> The leading dimension of the array B. LDB >= max(1,N).
84 *> \endverbatim
85 *>
86 *> \param[out] RESID
87 *> \verbatim
88 *> RESID is REAL
89 *> norm(B - A*X) / (norm(A) * norm(X) * EPS)
90 *> \endverbatim
91 *
92 * Authors:
93 * ========
94 *
95 *> \author Univ. of Tennessee
96 *> \author Univ. of California Berkeley
97 *> \author Univ. of Colorado Denver
98 *> \author NAG Ltd.
99 *
100 *> \ingroup single_lin
101 *
102 * =====================================================================
103  SUBROUTINE sptt02( N, NRHS, D, E, X, LDX, B, LDB, RESID )
104 *
105 * -- LAPACK test routine --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 *
109 * .. Scalar Arguments ..
110  INTEGER LDB, LDX, N, NRHS
111  REAL RESID
112 * ..
113 * .. Array Arguments ..
114  REAL B( LDB, * ), D( * ), E( * ), X( LDX, * )
115 * ..
116 *
117 * =====================================================================
118 *
119 * .. Parameters ..
120  REAL ONE, ZERO
121  parameter( one = 1.0e+0, zero = 0.0e+0 )
122 * ..
123 * .. Local Scalars ..
124  INTEGER J
125  REAL ANORM, BNORM, EPS, XNORM
126 * ..
127 * .. External Functions ..
128  REAL SASUM, SLAMCH, SLANST
129  EXTERNAL sasum, slamch, slanst
130 * ..
131 * .. Intrinsic Functions ..
132  INTRINSIC max
133 * ..
134 * .. External Subroutines ..
135  EXTERNAL slaptm
136 * ..
137 * .. Executable Statements ..
138 *
139 * Quick return if possible
140 *
141  IF( n.LE.0 ) THEN
142  resid = zero
143  RETURN
144  END IF
145 *
146 * Compute the 1-norm of the tridiagonal matrix A.
147 *
148  anorm = slanst( '1', n, d, e )
149 *
150 * Exit with RESID = 1/EPS if ANORM = 0.
151 *
152  eps = slamch( 'Epsilon' )
153  IF( anorm.LE.zero ) THEN
154  resid = one / eps
155  RETURN
156  END IF
157 *
158 * Compute B - A*X.
159 *
160  CALL slaptm( n, nrhs, -one, d, e, x, ldx, one, b, ldb )
161 *
162 * Compute the maximum over the number of right hand sides of
163 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
164 *
165  resid = zero
166  DO 10 j = 1, nrhs
167  bnorm = sasum( n, b( 1, j ), 1 )
168  xnorm = sasum( n, x( 1, j ), 1 )
169  IF( xnorm.LE.zero ) THEN
170  resid = one / eps
171  ELSE
172  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
173  END IF
174  10 CONTINUE
175 *
176  RETURN
177 *
178 * End of SPTT02
179 *
180  END
subroutine sptt02(N, NRHS, D, E, X, LDX, B, LDB, RESID)
SPTT02
Definition: sptt02.f:104
subroutine slaptm(N, NRHS, ALPHA, D, E, X, LDX, BETA, B, LDB)
SLAPTM
Definition: slaptm.f:116