 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ztpt02()

 subroutine ztpt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex*16, dimension( * ) AP, 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 )

ZTPT02

Purpose:
``` ZTPT02 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, when the triangular matrix A is stored in packed format.
Here A**T denotes the transpose of A, A**H denotes 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
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] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=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 ).```
Date
December 2016

Definition at line 151 of file ztpt02.f.

151 *
152 * -- LAPACK test routine (version 3.7.0) --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 * December 2016
156 *
157 * .. Scalar Arguments ..
158  CHARACTER diag, trans, uplo
159  INTEGER ldb, ldx, n, nrhs
160  DOUBLE PRECISION resid
161 * ..
162 * .. Array Arguments ..
163  DOUBLE PRECISION rwork( * )
164  COMPLEX*16 ap( * ), b( ldb, * ), work( * ), x( ldx, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  DOUBLE PRECISION zero, one
171  parameter( zero = 0.0d+0, one = 1.0d+0 )
172 * ..
173 * .. Local Scalars ..
174  INTEGER j
175  DOUBLE PRECISION anorm, bnorm, eps, xnorm
176 * ..
177 * .. External Functions ..
178  LOGICAL lsame
179  DOUBLE PRECISION dlamch, dzasum, zlantp
180  EXTERNAL lsame, dlamch, dzasum, zlantp
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL zaxpy, zcopy, ztpmv
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC dcmplx, max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Quick exit if N = 0 or NRHS = 0
191 *
192  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
193  resid = zero
194  RETURN
195  END IF
196 *
197 * Compute the 1-norm of A or A**H.
198 *
199  IF( lsame( trans, 'N' ) ) THEN
200  anorm = zlantp( '1', uplo, diag, n, ap, rwork )
201  ELSE
202  anorm = zlantp( 'I', uplo, diag, n, ap, rwork )
203  END IF
204 *
205 * Exit with RESID = 1/EPS if ANORM = 0.
206 *
207  eps = dlamch( 'Epsilon' )
208  IF( anorm.LE.zero ) THEN
209  resid = one / eps
210  RETURN
211  END IF
212 *
213 * Compute the maximum over the number of right hand sides of
214 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
215 *
216  resid = zero
217  DO 10 j = 1, nrhs
218  CALL zcopy( n, x( 1, j ), 1, work, 1 )
219  CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
220  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
221  bnorm = dzasum( n, work, 1 )
222  xnorm = dzasum( n, x( 1, j ), 1 )
223  IF( xnorm.LE.zero ) THEN
224  resid = one / eps
225  ELSE
226  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
227  END IF
228  10 CONTINUE
229 *
230  RETURN
231 *
232 * End of ZTPT02
233 *
double precision function zlantp(NORM, UPLO, DIAG, N, AP, WORK)
ZLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.
Definition: zlantp.f:127
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:74
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:144
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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