LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
sgtt01.f
Go to the documentation of this file.
1 *> \brief \b SGTT01
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 SGTT01( N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK,
12 * LDWORK, RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * INTEGER LDWORK, N
16 * REAL RESID
17 * ..
18 * .. Array Arguments ..
19 * INTEGER IPIV( * )
20 * REAL D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
21 * \$ DU2( * ), DUF( * ), RWORK( * ),
22 * \$ WORK( LDWORK, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> SGTT01 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 INTEGTER
43 *> The order of the matrix A. N >= 0.
44 *> \endverbatim
45 *>
46 *> \param[in] DL
47 *> \verbatim
48 *> DL is REAL 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 REAL array, dimension (N)
55 *> The diagonal elements of A.
56 *> \endverbatim
57 *>
58 *> \param[in] DU
59 *> \verbatim
60 *> DU is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (N)
113 *> \endverbatim
114 *>
115 *> \param[out] RESID
116 *> \verbatim
117 *> RESID is REAL
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 single_lin
130 *
131 * =====================================================================
132  SUBROUTINE sgtt01( 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  REAL RESID
142 * ..
143 * .. Array Arguments ..
144  INTEGER IPIV( * )
145  REAL D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
146  \$ du2( * ), duf( * ), rwork( * ),
147  \$ work( ldwork, * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  REAL ONE, ZERO
154  parameter( one = 1.0e+0, zero = 0.0e+0 )
155 * ..
156 * .. Local Scalars ..
157  INTEGER I, IP, J, LASTJ
158  REAL ANORM, EPS, LI
159 * ..
160 * .. External Functions ..
161  REAL SLAMCH, SLANGT, SLANHS
162  EXTERNAL slamch, slangt, slanhs
163 * ..
164 * .. Intrinsic Functions ..
165  INTRINSIC min
166 * ..
167 * .. External Subroutines ..
168  EXTERNAL saxpy, sswap
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 = slamch( '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 saxpy( 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 sswap( 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 = slangt( '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 = slanhs( '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 SGTT01
256 *
257  END
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine sgtt01(N, DL, D, DU, DLF, DF, DUF, DU2, IPIV, WORK, LDWORK, RWORK, RESID)
SGTT01
Definition: sgtt01.f:134