 LAPACK  3.10.1 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 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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