LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sgtt02.f
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1 *> \brief \b SGTT02
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 SGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
12 * RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER TRANS
16 * INTEGER LDB, LDX, N, NRHS
17 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> SGTT02 computes the residual for the solution to a tridiagonal
31 *> system of equations:
32 *> RESID = norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS),
33 *> where EPS is the machine epsilon.
34 *> The norm used is the 1-norm.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] TRANS
41 *> \verbatim
42 *> TRANS is CHARACTER
43 *> Specifies the form of the residual.
44 *> = 'N': B - A * X (No transpose)
45 *> = 'T': B - A**T * X (Transpose)
46 *> = 'C': B - A**H * X (Conjugate transpose = Transpose)
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGTER
52 *> The order of the matrix A. N >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] NRHS
56 *> \verbatim
57 *> NRHS is INTEGER
58 *> The number of right hand sides, i.e., the number of columns
59 *> of the matrices B and X. NRHS >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] DL
63 *> \verbatim
64 *> DL is REAL array, dimension (N-1)
65 *> The (n-1) sub-diagonal elements of A.
66 *> \endverbatim
67 *>
68 *> \param[in] D
69 *> \verbatim
70 *> D is REAL array, dimension (N)
71 *> The diagonal elements of A.
72 *> \endverbatim
73 *>
74 *> \param[in] DU
75 *> \verbatim
76 *> DU is REAL array, dimension (N-1)
77 *> The (n-1) super-diagonal elements of A.
78 *> \endverbatim
79 *>
80 *> \param[in] X
81 *> \verbatim
82 *> X is REAL array, dimension (LDX,NRHS)
83 *> The computed solution vectors X.
84 *> \endverbatim
85 *>
86 *> \param[in] LDX
87 *> \verbatim
88 *> LDX is INTEGER
89 *> The leading dimension of the array X. LDX >= max(1,N).
90 *> \endverbatim
91 *>
92 *> \param[in,out] B
93 *> \verbatim
94 *> B is REAL array, dimension (LDB,NRHS)
95 *> On entry, the right hand side vectors for the system of
96 *> linear equations.
97 *> On exit, B is overwritten with the difference B - op(A)*X.
98 *> \endverbatim
99 *>
100 *> \param[in] LDB
101 *> \verbatim
102 *> LDB is INTEGER
103 *> The leading dimension of the array B. LDB >= max(1,N).
104 *> \endverbatim
105 *>
106 *> \param[out] RESID
107 *> \verbatim
108 *> RESID is REAL
109 *> norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS)
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \ingroup single_lin
121 *
122 * =====================================================================
123  SUBROUTINE sgtt02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
124  $ RESID )
125 *
126 * -- LAPACK test routine --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 *
130 * .. Scalar Arguments ..
131  CHARACTER TRANS
132  INTEGER LDB, LDX, N, NRHS
133  REAL RESID
134 * ..
135 * .. Array Arguments ..
136  REAL B( LDB, * ), D( * ), DL( * ), DU( * ),
137  $ x( ldx, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL ONE, ZERO
144  parameter( one = 1.0e+0, zero = 0.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER J
148  REAL ANORM, BNORM, EPS, XNORM
149 * ..
150 * .. External Functions ..
151  LOGICAL LSAME
152  REAL SASUM, SLAMCH, SLANGT
153  EXTERNAL lsame, sasum, slamch, slangt
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL slagtm
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC max
160 * ..
161 * .. Executable Statements ..
162 *
163 * Quick exit if N = 0 or NRHS = 0
164 *
165  resid = zero
166  IF( n.LE.0 .OR. nrhs.EQ.0 )
167  $ RETURN
168 *
169 * Compute the maximum over the number of right hand sides of
170 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
171 *
172  IF( lsame( trans, 'N' ) ) THEN
173  anorm = slangt( '1', n, dl, d, du )
174  ELSE
175  anorm = slangt( 'I', n, dl, d, du )
176  END IF
177 *
178 * Exit with RESID = 1/EPS if ANORM = 0.
179 *
180  eps = slamch( 'Epsilon' )
181  IF( anorm.LE.zero ) THEN
182  resid = one / eps
183  RETURN
184  END IF
185 *
186 * Compute B - op(A)*X and store in B.
187 *
188  CALL slagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
189  $ ldb )
190 *
191  DO 10 j = 1, nrhs
192  bnorm = sasum( n, b( 1, j ), 1 )
193  xnorm = sasum( n, x( 1, j ), 1 )
194  IF( xnorm.LE.zero ) THEN
195  resid = one / eps
196  ELSE
197  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
198  END IF
199  10 CONTINUE
200 *
201  RETURN
202 *
203 * End of SGTT02
204 *
205  END
subroutine slagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: slagtm.f:145
subroutine sgtt02(TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
SGTT02
Definition: sgtt02.f:125