 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sgtt01()

 subroutine sgtt01 ( integer N, real, dimension( * ) DL, real, dimension( * ) D, real, dimension( * ) DU, real, dimension( * ) DLF, real, dimension( * ) DF, real, dimension( * ) DUF, real, dimension( * ) DU2, integer, dimension( * ) IPIV, real, dimension( ldwork, * ) WORK, integer LDWORK, real, dimension( * ) RWORK, real RESID )

SGTT01

Purpose:
``` SGTT01 reconstructs a tridiagonal matrix A from its LU factorization
and computes the residual
norm(L*U - A) / ( norm(A) * EPS ),
where EPS is the machine epsilon.```
Parameters
 [in] N ``` N is INTEGTER The order of the matrix A. N >= 0.``` [in] DL ``` DL is REAL array, dimension (N-1) The (n-1) sub-diagonal elements of A.``` [in] D ``` D is REAL array, dimension (N) The diagonal elements of A.``` [in] DU ``` DU is REAL array, dimension (N-1) The (n-1) super-diagonal elements of A.``` [in] DLF ``` DLF is REAL array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.``` [in] DF ``` DF is REAL array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DUF ``` DUF is REAL array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.``` [in] DU2 ``` DU2 is REAL array, dimension (N-2) The (n-2) elements of the second super-diagonal of U.``` [in] IPIV ``` IPIV is INTEGER array, dimension (N) The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.``` [out] WORK ` WORK is REAL array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL The scaled residual: norm(L*U - A) / (norm(A) * EPS)```

Definition at line 132 of file sgtt01.f.

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*
real function slangt(NORM, N, DL, D, DU)
SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slangt.f:106
real function slanhs(NORM, N, A, LDA, WORK)
SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: slanhs.f:108
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
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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