LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ ctpt02()

 subroutine ctpt02 ( character UPLO, character TRANS, character DIAG, integer N, integer NRHS, complex, dimension( * ) AP, complex, dimension( ldx, * ) X, integer LDX, complex, dimension( ldb, * ) B, integer LDB, complex, dimension( * ) WORK, real, dimension( * ) RWORK, real RESID )

CTPT02

Purpose:
``` CTPT02 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 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 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 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 array, dimension (N)` [out] RWORK ` RWORK is REAL array, dimension (N)` [out] RESID ``` RESID is REAL 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 ctpt02.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  REAL resid
161 * ..
162 * .. Array Arguments ..
163  REAL rwork( * )
164  COMPLEX ap( * ), b( ldb, * ), work( * ), x( ldx, * )
165 * ..
166 *
167 * =====================================================================
168 *
169 * .. Parameters ..
170  REAL zero, one
171  parameter( zero = 0.0e+0, one = 1.0e+0 )
172 * ..
173 * .. Local Scalars ..
174  INTEGER j
175  REAL anorm, bnorm, eps, xnorm
176 * ..
177 * .. External Functions ..
178  LOGICAL lsame
179  REAL clantp, scasum, slamch
180  EXTERNAL lsame, clantp, scasum, slamch
181 * ..
182 * .. External Subroutines ..
183  EXTERNAL caxpy, ccopy, ctpmv
184 * ..
185 * .. Intrinsic Functions ..
186  INTRINSIC cmplx, 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 = clantp( '1', uplo, diag, n, ap, rwork )
201  ELSE
202  anorm = clantp( 'I', uplo, diag, n, ap, rwork )
203  END IF
204 *
205 * Exit with RESID = 1/EPS if ANORM = 0.
206 *
207  eps = slamch( '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 ccopy( n, x( 1, j ), 1, work, 1 )
219  CALL ctpmv( uplo, trans, diag, n, ap, work, 1 )
220  CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
221  bnorm = scasum( n, work, 1 )
222  xnorm = scasum( 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 CTPT02
233 *
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:144
real function scasum(N, CX, INCX)
SCASUM
Definition: scasum.f:74
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
real function clantp(NORM, UPLO, DIAG, N, AP, WORK)
CLANTP 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: clantp.f:127
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