LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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  A*x = b,  A**T *x = b,
or A**H *x = b.  Here A is a triangular matrix, A**T is the transpose
of A, A**H is the conjugate 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, A**T, or A**H, 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 155 of file ztrt02.f.

157 *
158 * -- LAPACK test routine --
159 * -- LAPACK is a software package provided by Univ. of Tennessee, --
160 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
161 *
162 * .. Scalar Arguments ..
163  CHARACTER DIAG, TRANS, UPLO
164  INTEGER LDA, LDB, LDX, N, NRHS
165  DOUBLE PRECISION RESID
166 * ..
167 * .. Array Arguments ..
168  DOUBLE PRECISION RWORK( * )
169  COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
170  \$ X( LDX, * )
171 * ..
172 *
173 * =====================================================================
174 *
175 * .. Parameters ..
176  DOUBLE PRECISION ZERO, ONE
177  parameter( zero = 0.0d+0, one = 1.0d+0 )
178 * ..
179 * .. Local Scalars ..
180  INTEGER J
181  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  DOUBLE PRECISION DLAMCH, DZASUM, ZLANTR
186  EXTERNAL lsame, dlamch, dzasum, zlantr
187 * ..
188 * .. External Subroutines ..
189  EXTERNAL zaxpy, zcopy, ztrmv
190 * ..
191 * .. Intrinsic Functions ..
192  INTRINSIC dcmplx, max
193 * ..
194 * .. Executable Statements ..
195 *
196 * Quick exit if N = 0 or NRHS = 0
197 *
198  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
199  resid = zero
200  RETURN
201  END IF
202 *
203 * Compute the 1-norm of A or A**H.
204 *
205  IF( lsame( trans, 'N' ) ) THEN
206  anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
207  ELSE
208  anorm = zlantr( 'I', uplo, diag, n, n, a, lda, rwork )
209  END IF
210 *
211 * Exit with RESID = 1/EPS if ANORM = 0.
212 *
213  eps = dlamch( 'Epsilon' )
214  IF( anorm.LE.zero ) THEN
215  resid = one / eps
216  RETURN
217  END IF
218 *
219 * Compute the maximum over the number of right hand sides of
220 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
221 *
222  resid = zero
223  DO 10 j = 1, nrhs
224  CALL zcopy( n, x( 1, j ), 1, work, 1 )
225  CALL ztrmv( uplo, trans, diag, n, a, lda, work, 1 )
226  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
227  bnorm = dzasum( n, work, 1 )
228  xnorm = dzasum( n, x( 1, j ), 1 )
229  IF( xnorm.LE.zero ) THEN
230  resid = one / eps
231  ELSE
232  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
233  END IF
234  10 CONTINUE
235 *
236  RETURN
237 *
238 * End of ZTRT02
239 *
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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