LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dgtt02.f
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1*> \brief \b DGTT02
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 DGTT02( 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* DOUBLE PRECISION RESID
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
21* \$ X( LDX, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> DGTT02 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
71*> The diagonal elements of A.
72*> \endverbatim
73*>
74*> \param[in] DU
75*> \verbatim
76*> DU is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
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 double_lin
121*
122* =====================================================================
123 SUBROUTINE dgtt02( 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 DOUBLE PRECISION RESID
134* ..
135* .. Array Arguments ..
136 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
137 \$ x( ldx, * )
138* ..
139*
140* =====================================================================
141*
142* .. Parameters ..
143 DOUBLE PRECISION ONE, ZERO
144 parameter( one = 1.0d+0, zero = 0.0d+0 )
145* ..
146* .. Local Scalars ..
147 INTEGER J
148 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
149* ..
150* .. External Functions ..
151 LOGICAL LSAME
152 DOUBLE PRECISION DASUM, DLAMCH, DLANGT
153 EXTERNAL lsame, dasum, dlamch, dlangt
154* ..
155* .. External Subroutines ..
156 EXTERNAL dlagtm
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 = dlangt( '1', n, dl, d, du )
174 ELSE
175 anorm = dlangt( 'I', n, dl, d, du )
176 END IF
177*
178* Exit with RESID = 1/EPS if ANORM = 0.
179*
180 eps = dlamch( '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 dlagtm( trans, n, nrhs, -one, dl, d, du, x, ldx, one, b,
189 \$ ldb )
190*
191 DO 10 j = 1, nrhs
192 bnorm = dasum( n, b( 1, j ), 1 )
193 xnorm = dasum( 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 DGTT02
204*
205 END
subroutine dgtt02(TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, RESID)
DGTT02
Definition: dgtt02.f:125
subroutine dlagtm(TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA, B, LDB)
DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix,...
Definition: dlagtm.f:145