 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrt02()

 subroutine ztrt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, double precision RESID )

ZTRT02

Purpose:
``` ZTRT02 computes the residual for the computed solution to a
triangular system of linear equations op(A)*X = B, where A is a
triangular matrix. The test ratio is the maximum over
norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
where op(A) = A, A**T, or A**H, b is the column of B, x is the
solution vector, and EPS is the machine epsilon.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] TRANS ``` TRANS is CHARACTER*1 Specifies the operation applied to A. = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose)``` [in] DIAG ``` DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular = 'U': Unit triangular``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in] NRHS ``` NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.``` [in] A ``` A is COMPLEX*16 array, dimension (LDA,N) The triangular matrix A. If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [in] X ``` X is COMPLEX*16 array, dimension (LDX,NRHS) The computed solution vectors for the system of linear equations.``` [in] LDX ``` LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).``` [in] B ``` B is COMPLEX*16 array, dimension (LDB,NRHS) The right hand side vectors for the system of linear equations.``` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).``` [out] WORK ` WORK is COMPLEX*16 array, dimension (N)` [out] RWORK ` RWORK is DOUBLE PRECISION array, dimension (N)` [out] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).```

Definition at line 153 of file ztrt02.f.

155*
156* -- LAPACK test routine --
157* -- LAPACK is a software package provided by Univ. of Tennessee, --
158* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159*
160* .. Scalar Arguments ..
161 CHARACTER DIAG, TRANS, UPLO
162 INTEGER LDA, LDB, LDX, N, NRHS
163 DOUBLE PRECISION RESID
164* ..
165* .. Array Arguments ..
166 DOUBLE PRECISION RWORK( * )
167 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
168 \$ X( LDX, * )
169* ..
170*
171* =====================================================================
172*
173* .. Parameters ..
174 DOUBLE PRECISION ZERO, ONE
175 parameter( zero = 0.0d+0, one = 1.0d+0 )
176* ..
177* .. Local Scalars ..
178 INTEGER J
179 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
180* ..
181* .. External Functions ..
182 LOGICAL LSAME
183 DOUBLE PRECISION DLAMCH, DZASUM, ZLANTR
184 EXTERNAL lsame, dlamch, dzasum, zlantr
185* ..
186* .. External Subroutines ..
187 EXTERNAL zaxpy, zcopy, ztrmv
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC dcmplx, max
191* ..
192* .. Executable Statements ..
193*
194* Quick exit if N = 0 or NRHS = 0
195*
196 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
197 resid = zero
198 RETURN
199 END IF
200*
201* Compute the 1-norm of op(A).
202*
203 IF( lsame( trans, 'N' ) ) THEN
204 anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
205 ELSE
206 anorm = zlantr( 'I', uplo, diag, n, n, a, lda, rwork )
207 END IF
208*
209* Exit with RESID = 1/EPS if ANORM = 0.
210*
211 eps = dlamch( 'Epsilon' )
212 IF( anorm.LE.zero ) THEN
213 resid = one / eps
214 RETURN
215 END IF
216*
217* Compute the maximum over the number of right hand sides of
218* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS )
219*
220 resid = zero
221 DO 10 j = 1, nrhs
222 CALL zcopy( n, x( 1, j ), 1, work, 1 )
223 CALL ztrmv( uplo, trans, diag, n, a, lda, work, 1 )
224 CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
225 bnorm = dzasum( n, work, 1 )
226 xnorm = dzasum( n, x( 1, j ), 1 )
227 IF( xnorm.LE.zero ) THEN
228 resid = one / eps
229 ELSE
230 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
231 END IF
232 10 CONTINUE
233*
234 RETURN
235*
236* End of ZTRT02
237*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
double precision function zlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlantr.f:142
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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