LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
cgtt02.f
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1 *> \brief \b CGTT02
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 CGTT02( 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 * COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CGTT02 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 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] TRANS
40 *> \verbatim
41 *> TRANS is CHARACTER
42 *> Specifies the form of the residual.
43 *> = 'N': B - A * X (No transpose)
44 *> = 'T': B - A**T * X (Transpose)
45 *> = 'C': B - A**H * X (Conjugate transpose)
46 *> \endverbatim
47 *>
48 *> \param[in] N
49 *> \verbatim
50 *> N is INTEGTER
51 *> The order of the matrix A. N >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] NRHS
55 *> \verbatim
56 *> NRHS is INTEGER
57 *> The number of right hand sides, i.e., the number of columns
58 *> of the matrices B and X. NRHS >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] DL
62 *> \verbatim
63 *> DL is COMPLEX array, dimension (N-1)
64 *> The (n-1) sub-diagonal elements of A.
65 *> \endverbatim
66 *>
67 *> \param[in] D
68 *> \verbatim
69 *> D is COMPLEX array, dimension (N)
70 *> The diagonal elements of A.
71 *> \endverbatim
72 *>
73 *> \param[in] DU
74 *> \verbatim
75 *> DU is COMPLEX array, dimension (N-1)
76 *> The (n-1) super-diagonal elements of A.
77 *> \endverbatim
78 *>
79 *> \param[in] X
80 *> \verbatim
81 *> X is COMPLEX array, dimension (LDX,NRHS)
82 *> The computed solution vectors X.
83 *> \endverbatim
84 *>
85 *> \param[in] LDX
86 *> \verbatim
87 *> LDX is INTEGER
88 *> The leading dimension of the array X. LDX >= max(1,N).
89 *> \endverbatim
90 *>
91 *> \param[in,out] B
92 *> \verbatim
93 *> B is COMPLEX array, dimension (LDB,NRHS)
94 *> On entry, the right hand side vectors for the system of
95 *> linear equations.
96 *> On exit, B is overwritten with the difference B - op(A)*X.
97 *> \endverbatim
98 *>
99 *> \param[in] LDB
100 *> \verbatim
101 *> LDB is INTEGER
102 *> The leading dimension of the array B. LDB >= max(1,N).
103 *> \endverbatim
104 *>
105 *> \param[out] RESID
106 *> \verbatim
107 *> RESID is REAL
108 *> norm(B - op(A)*X) / (norm(op(A)) * norm(X) * EPS)
109 *> \endverbatim
110 *
111 * Authors:
112 * ========
113 *
114 *> \author Univ. of Tennessee
115 *> \author Univ. of California Berkeley
116 *> \author Univ. of Colorado Denver
117 *> \author NAG Ltd.
118 *
119 *> \ingroup complex_lin
120 *
121 * =====================================================================
122  SUBROUTINE cgtt02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
123  $ RESID )
124 *
125 * -- LAPACK test routine --
126 * -- LAPACK is a software package provided by Univ. of Tennessee, --
127 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128 *
129 * .. Scalar Arguments ..
130  CHARACTER TRANS
131  INTEGER LDB, LDX, N, NRHS
132  REAL RESID
133 * ..
134 * .. Array Arguments ..
135  COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * ),
136  $ x( ldx, * )
137 * ..
138 *
139 * =====================================================================
140 *
141 * .. Parameters ..
142  REAL ONE, ZERO
143  parameter( one = 1.0e+0, zero = 0.0e+0 )
144 * ..
145 * .. Local Scalars ..
146  INTEGER J
147  REAL ANORM, BNORM, EPS, XNORM
148 * ..
149 * .. External Functions ..
150  LOGICAL LSAME
151  REAL CLANGT, SCASUM, SLAMCH
152  EXTERNAL lsame, clangt, scasum, slamch
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL clagtm
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC max
159 * ..
160 * .. Executable Statements ..
161 *
162 * Quick exit if N = 0 or NRHS = 0
163 *
164  resid = zero
165  IF( n.LE.0 .OR. nrhs.EQ.0 )
166  $ RETURN
167 *
168 * Compute the maximum over the number of right hand sides of
169 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
170 *
171  IF( lsame( trans, 'N' ) ) THEN
172  anorm = clangt( '1', n, dl, d, du )
173  ELSE
174  anorm = clangt( 'I', n, dl, d, du )
175  END IF
176 *
177 * Exit with RESID = 1/EPS if ANORM = 0.
178 *
179  eps = slamch( 'Epsilon' )
180  IF( anorm.LE.zero ) THEN
181  resid = one / eps
182  RETURN
183  END IF
184 *
185 * Compute B - op(A)*X and store in B.
186 *
187  CALL clagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
188  $ ldb )
189 *
190  DO 10 j = 1, nrhs
191  bnorm = scasum( n, b( 1, j ), 1 )
192  xnorm = scasum( n, x( 1, j ), 1 )
193  IF( xnorm.LE.zero ) THEN
194  resid = one / eps
195  ELSE
196  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
197  END IF
198  10 CONTINUE
199 *
200  RETURN
201 *
202 * End of CGTT02
203 *
204  END
subroutine cgtt02(TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
CGTT02
Definition: cgtt02.f:124
subroutine clagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: clagtm.f:145