LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dtrt02()

 subroutine dtrt02 ( character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, double precision resid )

DTRT02

Purpose:
``` DTRT02 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 or A**T, b is the column of B, x is the solution
vector, and EPS is the machine epsilon.
The norm used is the 1-norm.```
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 = 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 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 148 of file dtrt02.f.

150*
151* -- LAPACK test routine --
152* -- LAPACK is a software package provided by Univ. of Tennessee, --
153* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154*
155* .. Scalar Arguments ..
156 CHARACTER DIAG, TRANS, UPLO
157 INTEGER LDA, LDB, LDX, N, NRHS
158 DOUBLE PRECISION RESID
159* ..
160* .. Array Arguments ..
161 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ),
162 \$ X( LDX, * )
163* ..
164*
165* =====================================================================
166*
167* .. Parameters ..
168 DOUBLE PRECISION ZERO, ONE
169 parameter( zero = 0.0d+0, one = 1.0d+0 )
170* ..
171* .. Local Scalars ..
172 INTEGER J
173 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
174* ..
175* .. External Functions ..
176 LOGICAL LSAME
177 DOUBLE PRECISION DASUM, DLAMCH, DLANTR
178 EXTERNAL lsame, dasum, dlamch, dlantr
179* ..
180* .. External Subroutines ..
181 EXTERNAL daxpy, dcopy, dtrmv
182* ..
183* .. Intrinsic Functions ..
184 INTRINSIC max
185* ..
186* .. Executable Statements ..
187*
188* Quick exit if N = 0 or NRHS = 0
189*
190 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
191 resid = zero
192 RETURN
193 END IF
194*
195* Compute the 1-norm of op(A).
196*
197 IF( lsame( trans, 'N' ) ) THEN
198 anorm = dlantr( '1', uplo, diag, n, n, a, lda, work )
199 ELSE
200 anorm = dlantr( 'I', uplo, diag, n, n, a, lda, work )
201 END IF
202*
203* Exit with RESID = 1/EPS if ANORM = 0.
204*
205 eps = dlamch( 'Epsilon' )
206 IF( anorm.LE.zero ) THEN
207 resid = one / eps
208 RETURN
209 END IF
210*
211* Compute the maximum over the number of right hand sides of
212* norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS )
213*
214 resid = zero
215 DO 10 j = 1, nrhs
216 CALL dcopy( n, x( 1, j ), 1, work, 1 )
217 CALL dtrmv( uplo, trans, diag, n, a, lda, work, 1 )
218 CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
219 bnorm = dasum( n, work, 1 )
220 xnorm = dasum( n, x( 1, j ), 1 )
221 IF( xnorm.LE.zero ) THEN
222 resid = one / eps
223 ELSE
224 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
225 END IF
226 10 CONTINUE
227*
228 RETURN
229*
230* End of DTRT02
231*
double precision function dasum(n, dx, incx)
DASUM
Definition dasum.f:71
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function dlantr(norm, uplo, diag, m, n, a, lda, work)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlantr.f:141
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine dtrmv(uplo, trans, diag, n, a, lda, x, incx)
DTRMV
Definition dtrmv.f:147
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