 LAPACK  3.10.1 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 op(A)*X = B, when the
triangular matrix A is stored in packed format. 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] 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 ).```

Definition at line 145 of file ztpt02.f.

147 *
148 * -- LAPACK test routine --
149 * -- LAPACK is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  CHARACTER DIAG, TRANS, UPLO
154  INTEGER LDB, LDX, N, NRHS
155  DOUBLE PRECISION RESID
156 * ..
157 * .. Array Arguments ..
158  DOUBLE PRECISION RWORK( * )
159  COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  DOUBLE PRECISION ZERO, ONE
166  parameter( zero = 0.0d+0, one = 1.0d+0 )
167 * ..
168 * .. Local Scalars ..
169  INTEGER J
170  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
171 * ..
172 * .. External Functions ..
173  LOGICAL LSAME
174  DOUBLE PRECISION DLAMCH, DZASUM, ZLANTP
175  EXTERNAL lsame, dlamch, dzasum, zlantp
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL zaxpy, zcopy, ztpmv
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC dcmplx, max
182 * ..
183 * .. Executable Statements ..
184 *
185 * Quick exit if N = 0 or NRHS = 0
186 *
187  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
188  resid = zero
189  RETURN
190  END IF
191 *
192 * Compute the 1-norm of op(A).
193 *
194  IF( lsame( trans, 'N' ) ) THEN
195  anorm = zlantp( '1', uplo, diag, n, ap, rwork )
196  ELSE
197  anorm = zlantp( 'I', uplo, diag, n, ap, rwork )
198  END IF
199 *
200 * Exit with RESID = 1/EPS if ANORM = 0.
201 *
202  eps = dlamch( 'Epsilon' )
203  IF( anorm.LE.zero ) THEN
204  resid = one / eps
205  RETURN
206  END IF
207 *
208 * Compute the maximum over the number of right hand sides of
209 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
210 *
211  resid = zero
212  DO 10 j = 1, nrhs
213  CALL zcopy( n, x( 1, j ), 1, work, 1 )
214  CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
215  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
216  bnorm = dzasum( n, work, 1 )
217  xnorm = dzasum( n, x( 1, j ), 1 )
218  IF( xnorm.LE.zero ) THEN
219  resid = one / eps
220  ELSE
221  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
222  END IF
223  10 CONTINUE
224 *
225  RETURN
226 *
227 * End of ZTPT02
228 *
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 ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
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,...
Definition: zlantp.f:125
double precision function dzasum(N, ZX, INCX)
DZASUM
Definition: dzasum.f:72
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