 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zgtt01()

 subroutine zgtt01 ( integer N, complex*16, dimension( * ) DL, complex*16, dimension( * ) D, complex*16, dimension( * ) DU, complex*16, dimension( * ) DLF, complex*16, dimension( * ) DF, complex*16, dimension( * ) DUF, complex*16, dimension( * ) DU2, integer, dimension( * ) IPIV, complex*16, dimension( ldwork, * ) WORK, integer LDWORK, double precision, dimension( * ) RWORK, double precision RESID )

ZGTT01

Purpose:
``` ZGTT01 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 COMPLEX*16 array, dimension (N-1) The (n-1) sub-diagonal elements of A.``` [in] D ``` D is COMPLEX*16 array, dimension (N) The diagonal elements of A.``` [in] DU ``` DU is COMPLEX*16 array, dimension (N-1) The (n-1) super-diagonal elements of A.``` [in] DLF ``` DLF is COMPLEX*16 array, dimension (N-1) The (n-1) multipliers that define the matrix L from the LU factorization of A.``` [in] DF ``` DF is COMPLEX*16 array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A.``` [in] DUF ``` DUF is COMPLEX*16 array, dimension (N-1) The (n-1) elements of the first super-diagonal of U.``` [in] DU2 ``` DU2 is COMPLEX*16 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 COMPLEX*16 array, dimension (LDWORK,N)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. LDWORK >= max(1,N).``` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The scaled residual: norm(L*U - A) / (norm(A) * EPS)```

Definition at line 132 of file zgtt01.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  DOUBLE PRECISION RESID
142 * ..
143 * .. Array Arguments ..
144  INTEGER IPIV( * )
145  DOUBLE PRECISION RWORK( * )
146  COMPLEX*16 D( * ), DF( * ), DL( * ), DLF( * ), DU( * ),
147  \$ DU2( * ), DUF( * ), 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
159  COMPLEX*16 LI
160 * ..
161 * .. External Functions ..
162  DOUBLE PRECISION DLAMCH, ZLANGT, ZLANHS
163  EXTERNAL dlamch, zlangt, zlanhs
164 * ..
165 * .. Intrinsic Functions ..
166  INTRINSIC min
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL zaxpy, zswap
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick return if possible
174 *
175  IF( n.LE.0 ) THEN
176  resid = zero
177  RETURN
178  END IF
179 *
180  eps = dlamch( 'Epsilon' )
181 *
182 * Copy the matrix U to WORK.
183 *
184  DO 20 j = 1, n
185  DO 10 i = 1, n
186  work( i, j ) = zero
187  10 CONTINUE
188  20 CONTINUE
189  DO 30 i = 1, n
190  IF( i.EQ.1 ) THEN
191  work( i, i ) = df( i )
192  IF( n.GE.2 )
193  \$ work( i, i+1 ) = duf( i )
194  IF( n.GE.3 )
195  \$ work( i, i+2 ) = du2( i )
196  ELSE IF( i.EQ.n ) THEN
197  work( i, i ) = df( i )
198  ELSE
199  work( i, i ) = df( i )
200  work( i, i+1 ) = duf( i )
201  IF( i.LT.n-1 )
202  \$ work( i, i+2 ) = du2( i )
203  END IF
204  30 CONTINUE
205 *
206 * Multiply on the left by L.
207 *
208  lastj = n
209  DO 40 i = n - 1, 1, -1
210  li = dlf( i )
211  CALL zaxpy( lastj-i+1, li, work( i, i ), ldwork,
212  \$ work( i+1, i ), ldwork )
213  ip = ipiv( i )
214  IF( ip.EQ.i ) THEN
215  lastj = min( i+2, n )
216  ELSE
217  CALL zswap( lastj-i+1, work( i, i ), ldwork, work( i+1, i ),
218  \$ ldwork )
219  END IF
220  40 CONTINUE
221 *
222 * Subtract the matrix A.
223 *
224  work( 1, 1 ) = work( 1, 1 ) - d( 1 )
225  IF( n.GT.1 ) THEN
226  work( 1, 2 ) = work( 1, 2 ) - du( 1 )
227  work( n, n-1 ) = work( n, n-1 ) - dl( n-1 )
228  work( n, n ) = work( n, n ) - d( n )
229  DO 50 i = 2, n - 1
230  work( i, i-1 ) = work( i, i-1 ) - dl( i-1 )
231  work( i, i ) = work( i, i ) - d( i )
232  work( i, i+1 ) = work( i, i+1 ) - du( i )
233  50 CONTINUE
234  END IF
235 *
236 * Compute the 1-norm of the tridiagonal matrix A.
237 *
238  anorm = zlangt( '1', n, dl, d, du )
239 *
240 * Compute the 1-norm of WORK, which is only guaranteed to be
241 * upper Hessenberg.
242 *
243  resid = zlanhs( '1', n, work, ldwork, rwork )
244 *
245 * Compute norm(L*U - A) / (norm(A) * EPS)
246 *
247  IF( anorm.LE.zero ) THEN
248  IF( resid.NE.zero )
249  \$ resid = one / eps
250  ELSE
251  resid = ( resid / anorm ) / eps
252  END IF
253 *
254  RETURN
255 *
256 * End of ZGTT01
257 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:81
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
double precision function zlangt(NORM, N, DL, D, DU)
ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlangt.f:106
double precision function zlanhs(NORM, N, A, LDA, WORK)
ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition: zlanhs.f:109
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