 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
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 dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:147
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
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