 LAPACK  3.8.0 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  A*x = b  or  A'*x = b.
Here A is a triangular matrix, A' is the transpose of A, and x and b
are N by NRHS matrices.  The test ratio is the maximum over the
number of right hand sides of
norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
where op(A) denotes A or A' 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'*x = b (Transpose) = 'C': A'*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 ).```
Date
December 2016

Definition at line 152 of file dtrt02.f.

152 *
153 * -- LAPACK test routine (version 3.7.0) --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 * December 2016
157 *
158 * .. Scalar Arguments ..
159  CHARACTER diag, trans, uplo
160  INTEGER lda, ldb, ldx, n, nrhs
161  DOUBLE PRECISION resid
162 * ..
163 * .. Array Arguments ..
164  DOUBLE PRECISION a( lda, * ), b( ldb, * ), work( * ),
165  \$ x( ldx, * )
166 * ..
167 *
168 * =====================================================================
169 *
170 * .. Parameters ..
171  DOUBLE PRECISION zero, one
172  parameter( zero = 0.0d+0, one = 1.0d+0 )
173 * ..
174 * .. Local Scalars ..
175  INTEGER j
176  DOUBLE PRECISION anorm, bnorm, eps, xnorm
177 * ..
178 * .. External Functions ..
179  LOGICAL lsame
180  DOUBLE PRECISION dasum, dlamch, dlantr
181  EXTERNAL lsame, dasum, dlamch, dlantr
182 * ..
183 * .. External Subroutines ..
184  EXTERNAL daxpy, dcopy, dtrmv
185 * ..
186 * .. Intrinsic Functions ..
187  INTRINSIC max
188 * ..
189 * .. Executable Statements ..
190 *
191 * Quick exit if N = 0 or NRHS = 0
192 *
193  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
194  resid = zero
195  RETURN
196  END IF
197 *
198 * Compute the 1-norm of A or A'.
199 *
200  IF( lsame( trans, 'N' ) ) THEN
201  anorm = dlantr( '1', uplo, diag, n, n, a, lda, work )
202  ELSE
203  anorm = dlantr( 'I', uplo, diag, n, n, a, lda, work )
204  END IF
205 *
206 * Exit with RESID = 1/EPS if ANORM = 0.
207 *
208  eps = dlamch( 'Epsilon' )
209  IF( anorm.LE.zero ) THEN
210  resid = one / eps
211  RETURN
212  END IF
213 *
214 * Compute the maximum over the number of right hand sides of
215 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
216 *
217  resid = zero
218  DO 10 j = 1, nrhs
219  CALL dcopy( n, x( 1, j ), 1, work, 1 )
220  CALL dtrmv( uplo, trans, diag, n, a, lda, work, 1 )
221  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
222  bnorm = dasum( n, work, 1 )
223  xnorm = dasum( n, x( 1, j ), 1 )
224  IF( xnorm.LE.zero ) THEN
225  resid = one / eps
226  ELSE
227  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
228  END IF
229  10 CONTINUE
230 *
231  RETURN
232 *
233 * End of DTRT02
234 *
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:91
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:149
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: dlantr.f:143
Here is the call graph for this function:
Here is the caller graph for this function: