LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dgtt01.f
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1*> \brief \b DGTT01
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 DGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
12* LDWORK, RWORK, RESID )
13*
14* .. Scalar Arguments ..
15* INTEGER LDWORK, N
16* DOUBLE PRECISION RESID
17* ..
18* .. Array Arguments ..
19* INTEGER IPIV( * )
20* DOUBLE PRECISION D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
21* \$ DU2( * ), DUF( * ), RWORK( * ),
22* \$ WORK( LDWORK, * )
23* ..
24*
25*
26*> \par Purpose:
27* =============
28*>
29*> \verbatim
30*>
31*> DGTT01 reconstructs a tridiagonal matrix A from its LU factorization
32*> and computes the residual
33*> norm(L*U - A) / ( norm(A) * EPS ),
34*> where EPS is the machine epsilon.
35*> \endverbatim
36*
37* Arguments:
38* ==========
39*
40*> \param[in] N
41*> \verbatim
42*> N is INTEGER
43*> The order of the matrix A. N >= 0.
44*> \endverbatim
45*>
46*> \param[in] DL
47*> \verbatim
48*> DL is DOUBLE PRECISION array, dimension (N-1)
49*> The (n-1) sub-diagonal elements of A.
50*> \endverbatim
51*>
52*> \param[in] D
53*> \verbatim
54*> D is DOUBLE PRECISION array, dimension (N)
55*> The diagonal elements of A.
56*> \endverbatim
57*>
58*> \param[in] DU
59*> \verbatim
60*> DU is DOUBLE PRECISION array, dimension (N-1)
61*> The (n-1) super-diagonal elements of A.
62*> \endverbatim
63*>
64*> \param[in] DLF
65*> \verbatim
66*> DLF is DOUBLE PRECISION array, dimension (N-1)
67*> The (n-1) multipliers that define the matrix L from the
68*> LU factorization of A.
69*> \endverbatim
70*>
71*> \param[in] DF
72*> \verbatim
73*> DF is DOUBLE PRECISION array, dimension (N)
74*> The n diagonal elements of the upper triangular matrix U from
75*> the LU factorization of A.
76*> \endverbatim
77*>
78*> \param[in] DUF
79*> \verbatim
80*> DUF is DOUBLE PRECISION array, dimension (N-1)
81*> The (n-1) elements of the first super-diagonal of U.
82*> \endverbatim
83*>
84*> \param[in] DU2
85*> \verbatim
86*> DU2 is DOUBLE PRECISION array, dimension (N-2)
87*> The (n-2) elements of the second super-diagonal of U.
88*> \endverbatim
89*>
90*> \param[in] IPIV
91*> \verbatim
92*> IPIV is INTEGER array, dimension (N)
93*> The pivot indices; for 1 <= i <= n, row i of the matrix was
94*> interchanged with row IPIV(i). IPIV(i) will always be either
95*> i or i+1; IPIV(i) = i indicates a row interchange was not
96*> required.
97*> \endverbatim
98*>
99*> \param[out] WORK
100*> \verbatim
101*> WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
102*> \endverbatim
103*>
104*> \param[in] LDWORK
105*> \verbatim
106*> LDWORK is INTEGER
107*> The leading dimension of the array WORK. LDWORK >= max(1,N).
108*> \endverbatim
109*>
110*> \param[out] RWORK
111*> \verbatim
112*> RWORK is DOUBLE PRECISION array, dimension (N)
113*> \endverbatim
114*>
115*> \param[out] RESID
116*> \verbatim
117*> RESID is DOUBLE PRECISION
118*> The scaled residual: norm(L*U - A) / (norm(A) * EPS)
119*> \endverbatim
120*
121* Authors:
122* ========
123*
124*> \author Univ. of Tennessee
125*> \author Univ. of California Berkeley
126*> \author Univ. of Colorado Denver
127*> \author NAG Ltd.
128*
129*> \ingroup double_lin
130*
131* =====================================================================
132 SUBROUTINE dgtt01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
133 \$ LDWORK, RWORK, RESID )
134*
135* -- LAPACK test routine --
136* -- LAPACK is a software package provided by Univ. of Tennessee, --
137* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*
139* .. Scalar Arguments ..
140 INTEGER LDWORK, N
141 DOUBLE PRECISION RESID
142* ..
143* .. Array Arguments ..
144 INTEGER IPIV( * )
145 DOUBLE PRECISION D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
146 \$ du2( * ), duf( * ), rwork( * ),
147 \$ work( ldwork, * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 DOUBLE PRECISION ONE, ZERO
154 parameter( one = 1.0d+0, zero = 0.0d+0 )
155* ..
156* .. Local Scalars ..
157 INTEGER I, IP, J, LASTJ
158 DOUBLE PRECISION ANORM, EPS, LI
159* ..
160* .. External Functions ..
161 DOUBLE PRECISION DLAMCH, DLANGT, DLANHS
162 EXTERNAL dlamch, dlangt, dlanhs
163* ..
164* .. Intrinsic Functions ..
165 INTRINSIC min
166* ..
167* .. External Subroutines ..
168 EXTERNAL daxpy, dswap
169* ..
170* .. Executable Statements ..
171*
172* Quick return if possible
173*
174 IF( n.LE.0 ) THEN
175 resid = zero
176 RETURN
177 END IF
178*
179 eps = dlamch( 'Epsilon' )
180*
181* Copy the matrix U to WORK.
182*
183 DO 20 j = 1, n
184 DO 10 i = 1, n
185 work( i, j ) = zero
186 10 CONTINUE
187 20 CONTINUE
188 DO 30 i = 1, n
189 IF( i.EQ.1 ) THEN
190 work( i, i ) = df( i )
191 IF( n.GE.2 )
192 \$ work( i, i+1 ) = duf( i )
193 IF( n.GE.3 )
194 \$ work( i, i+2 ) = du2( i )
195 ELSE IF( i.EQ.n ) THEN
196 work( i, i ) = df( i )
197 ELSE
198 work( i, i ) = df( i )
199 work( i, i+1 ) = duf( i )
200 IF( i.LT.n-1 )
201 \$ work( i, i+2 ) = du2( i )
202 END IF
203 30 CONTINUE
204*
205* Multiply on the left by L.
206*
207 lastj = n
208 DO 40 i = n - 1, 1, -1
209 li = dlf( i )
210 CALL daxpy( lastj-i+1, li, work( i, i ), ldwork,
211 \$ work( i+1, i ), ldwork )
212 ip = ipiv( i )
213 IF( ip.EQ.i ) THEN
214 lastj = min( i+2, n )
215 ELSE
216 CALL dswap( lastj-i+1, work( i, i ), ldwork, work( i+1, i ),
217 \$ ldwork )
218 END IF
219 40 CONTINUE
220*
221* Subtract the matrix A.
222*
223 work( 1, 1 ) = work( 1, 1 ) - d( 1 )
224 IF( n.GT.1 ) THEN
225 work( 1, 2 ) = work( 1, 2 ) - du( 1 )
226 work( n, n-1 ) = work( n, n-1 ) - dl( n-1 )
227 work( n, n ) = work( n, n ) - d( n )
228 DO 50 i = 2, n - 1
229 work( i, i-1 ) = work( i, i-1 ) - dl( i-1 )
230 work( i, i ) = work( i, i ) - d( i )
231 work( i, i+1 ) = work( i, i+1 ) - du( i )
232 50 CONTINUE
233 END IF
234*
235* Compute the 1-norm of the tridiagonal matrix A.
236*
237 anorm = dlangt( '1', n, dl, d, du )
238*
239* Compute the 1-norm of WORK, which is only guaranteed to be
240* upper Hessenberg.
241*
242 resid = dlanhs( '1', n, work, ldwork, rwork )
243*
244* Compute norm(L*U - A) / (norm(A) * EPS)
245*
246 IF( anorm.LE.zero ) THEN
247 IF( resid.NE.zero )
248 \$ resid = one / eps
249 ELSE
250 resid = ( resid / anorm ) / eps
251 END IF
252*
253 RETURN
254*
255* End of DGTT01
256*
257 END
subroutine dgtt01(n, dl, d, du, dlf, df, duf, du2, ipiv, work, ldwork, rwork, resid)
DGTT01
Definition dgtt01.f:134
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
subroutine dswap(n, dx, incx, dy, incy)
DSWAP
Definition dswap.f:82