 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ ztrt03()

 subroutine ztrt03 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex*16, dimension( lda, * ) A, integer LDA, double precision SCALE, double precision, dimension( * ) CNORM, double precision TSCAL, complex*16, dimension( ldx, * ) X, integer LDX, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( * ) WORK, double precision RESID )

ZTRT03

Purpose:
``` ZTRT03 computes the residual for the solution to a scaled triangular
system of equations A*x = s*b,  A**T *x = s*b,  or  A**H *x = s*b.
Here A is a triangular matrix, A**T denotes the transpose of A, A**H
denotes the conjugate transpose of A, s is a scalar, and x and b are
N by NRHS matrices.  The test ratio is the maximum over the number of
right hand sides of
norm(s*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 = s*b (No transpose) = 'T': A**T *x = s*b (Transpose) = 'C': A**H *x = s*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] SCALE ``` SCALE is DOUBLE PRECISION The scaling factor s used in solving the triangular system.``` [in] CNORM ``` CNORM is DOUBLE PRECISION array, dimension (N) The 1-norms of the columns of A, not counting the diagonal.``` [in] TSCAL ``` TSCAL is DOUBLE PRECISION The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.``` [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] RESID ``` RESID is DOUBLE PRECISION The maximum over the number of right hand sides of norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).```

Definition at line 169 of file ztrt03.f.

171*
172* -- LAPACK test routine --
173* -- LAPACK is a software package provided by Univ. of Tennessee, --
174* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
175*
176* .. Scalar Arguments ..
177 CHARACTER DIAG, TRANS, UPLO
178 INTEGER LDA, LDB, LDX, N, NRHS
179 DOUBLE PRECISION RESID, SCALE, TSCAL
180* ..
181* .. Array Arguments ..
182 DOUBLE PRECISION CNORM( * )
183 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
184 \$ X( LDX, * )
185* ..
186*
187* =====================================================================
188*
189* .. Parameters ..
190 DOUBLE PRECISION ONE, ZERO
191 parameter( one = 1.0d+0, zero = 0.0d+0 )
192* ..
193* .. Local Scalars ..
194 INTEGER IX, J
195 DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
196* ..
197* .. External Functions ..
198 LOGICAL LSAME
199 INTEGER IZAMAX
200 DOUBLE PRECISION DLAMCH
201 EXTERNAL lsame, izamax, dlamch
202* ..
203* .. External Subroutines ..
204 EXTERNAL zaxpy, zcopy, zdscal, ztrmv
205* ..
206* .. Intrinsic Functions ..
207 INTRINSIC abs, dble, dcmplx, max
208* ..
209* .. Executable Statements ..
210*
211* Quick exit if N = 0
212*
213 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
214 resid = zero
215 RETURN
216 END IF
217 eps = dlamch( 'Epsilon' )
218 smlnum = dlamch( 'Safe minimum' )
219*
220* Compute the norm of the triangular matrix A using the column
221* norms already computed by ZLATRS.
222*
223 tnorm = zero
224 IF( lsame( diag, 'N' ) ) THEN
225 DO 10 j = 1, n
226 tnorm = max( tnorm, tscal*abs( a( j, j ) )+cnorm( j ) )
227 10 CONTINUE
228 ELSE
229 DO 20 j = 1, n
230 tnorm = max( tnorm, tscal+cnorm( j ) )
231 20 CONTINUE
232 END IF
233*
234* Compute the maximum over the number of right hand sides of
235* norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
236*
237 resid = zero
238 DO 30 j = 1, nrhs
239 CALL zcopy( n, x( 1, j ), 1, work, 1 )
240 ix = izamax( n, work, 1 )
241 xnorm = max( one, abs( x( ix, j ) ) )
242 xscal = ( one / xnorm ) / dble( n )
243 CALL zdscal( n, xscal, work, 1 )
244 CALL ztrmv( uplo, trans, diag, n, a, lda, work, 1 )
245 CALL zaxpy( n, dcmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
246 ix = izamax( n, work, 1 )
247 err = tscal*abs( work( ix ) )
248 ix = izamax( n, x( 1, j ), 1 )
249 xnorm = abs( x( ix, j ) )
250 IF( err*smlnum.LE.xnorm ) THEN
251 IF( xnorm.GT.zero )
252 \$ err = err / xnorm
253 ELSE
254 IF( err.GT.zero )
255 \$ err = one / eps
256 END IF
257 IF( err*smlnum.LE.tnorm ) THEN
258 IF( tnorm.GT.zero )
259 \$ err = err / tnorm
260 ELSE
261 IF( err.GT.zero )
262 \$ err = one / eps
263 END IF
264 resid = max( resid, err )
265 30 CONTINUE
266*
267 RETURN
268*
269* End of ZTRT03
270*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
integer function izamax(N, ZX, INCX)
IZAMAX
Definition: izamax.f:71
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
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
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